But what is 274207380?
never mind. Someone already responded. Btw, you have the -1 superscripted which means the equation isn't the largest prime number.
His comment karma is about 250 less than the two comments currently posted. This is his troll account. He just deletes the posts after. (I purge mine from time to time, so sometimes I have 30k comment karma and no comments)
And in Go, which has a 19-by-19 board and over 10150 possible positions, even an amateur human can still rout the worldโs top-ranked computer programs.
Well, yes. I think it will never be known which is a larger number. Heck BB(1001) could be larger.
I guess they were writing about making the "largest number" as a thought exercise to talk about the BB concept. But I'd still put the ! at the end to one up them.
Well, yes. I think it will never be known which is a larger number. Heck BB(1001) could be larger.
I'm sorry, but yes it is absolutely known which is bigger. BB(1001) is vastly, vastly, vastly larger than BB(1000)!. This is exactly what I meant when I said that factorials are child's play compared to things that are discussed in the article.
I mean, to try to give an idea of how fast it grows: it is not possible to compute BB(8000). It grows so damn fast that using our standard mathematical axioms, it is simply not possible to know what the value of BB(8000) is. It's just too big. Not in the sense that "we can't write it down in the universe" or something like that, but in the sense that we could never write down a well-defined mathematical expression and know for sure that it represents BB(8000), even in principle if we had as much space or time as we wanted.
Compare this to something like the factorial. It has a formula. Given enough time, we could, in principle, compute 8000! or 8000! or 99!99!99! or any other combination of any number of those symbols that you like. Even absurdly fast-growing things like Knuth's up-arrow notation, which most people already have a hard time getting their head around, is trivial compared to the Busy beaver function.
That may be, but in a contest I would write down BB(8000!)!. My point was that as enormous as these numbers are, they all can be increased immensely with just an exclamation point.
And I would write down BB(BB(6)) and absolutely blow your number out of the water. In fact, you could write down 5 million extra factorials, and my BB(BB(6)) would still blow your number out of the water. You could write a factorial on every atom in the universe, and you would have wasted your time, since just writing one more BB() would have made more of an effect than all of those factorials combined.
In other words: my point is that factorials don't increasing things "immensely" from the point of view of the busy beaver function. Saying "BB(8000)! is immensely bigger than BB(8000)" is like saying "8000! + 1 is immensely bigger than 8000!".
To try to give a bit of a comparison here to explain why factorials are child's play:
You mentioned that BB(4)! is 1.23 x 10172 .
OK, but what is BB(BB(4)) (i.e., instead of doing an extra factorial, do an extra busy beaver)? Well, it's bigger than Graham's number, which is a number so large that you have to read a moderately lengthy Wikipedia article just to try to get a grasp on how big it is. It's a number that, even if you used power towers like 99999999... , there would not be enough space in the universe for you to write down a representation of it. You could write a 9 followed by a factorial sign on every atom in the observable universe, and you wouldn't have gotten close to Graham's number, which isn't even close to BB(BB(4)) (in fact, it's even less than BB(23)).
I've used a range of values for x to find the largest primes in decimal, hexadecimal, base64, ASCII and extended ASCII (but those last two might be hard to post in a comment).
I've also used y=20 to match the maximum reddit username length, but you can obviously change that if you want a larger number of characters.
Sticking with reddit usernames:
Base 10 gives 99999999999999997_10.
Base 16 gives fffffffffffffffe9_16 (295147905179352825833_10).
Base 64 gives ________________f_64 (5070602400912917605986812821471_10), but you have to remember that the final underscore is separating the number and the base and isn't part of the number itself.
Excellent. I just took this one too. (99999999999999999989 here)
Thanks a lot! :)
b4b ยท -5 points ยท Posted at 22:06:47 on May 25, 2016 ยท (Permalink)
Why do you "collect" reddit user names? This is not cool. It just makes you a jerk. Someone one day might come out with such a clever name only to learn that it was used by you.
And technically you can be hit by a bus tomorrow + reddit does not really delete old accounts.
Well I only have like...four maybe. So there's that. And to be honest, this one is the most clever. And last time I checked, usernames were not some sort of commodity or anything.
EDIT: Mentally I just made my first million. A username parking scheme to sell especially clever ones to desperate people.
Halyon ยท 2 points ยท Posted at 22:40:42 on May 25, 2016 ยท (Permalink)
That's a clever use of NextPrime, never thought to use it like that! Very nice :) of course these are increasing in size for (relatively) small bases b but there must come a point if we include the base in the username where the base takes too much of the available space (if the base is 20 digits long, for instance) so I'd reason that a maximum over b exists - in the morning I may look into finding it, which should be reasonably straightforward (wolfram seems to be handling it well for x=1015 in your example).
If you're ok with using arbitrary bases and unconventional conventions, I came up with an answer over here, and in a followup comment.
And yes, as you suspected the length of the base matters. For finding the largest number (non-prime), I basically just compared all the values of {highest digit x times}_{9 (19-x) times} for x in 1..18 . So if 9 was the highest digit I would have calculated 999999999999999999_9 to 9_999999999999999999. From the few experiments I've done it looks like the base can take up about half the string before the value starts going down, although that's obviously not a proof.
R3D1AL ยท 0 points ยท Posted at 21:11:26 on May 25, 2016 ยท (Permalink)
He writes the prime in hexadecimal and then writes the base in decimal.
If we could use different bases to write what base we're using then we could go back to /u/Halyon 's suggestion and just say 10_10. Which makes me realize how ridiculous writing base-10 is.
ableman ยท 6 points ยท Posted at 19:00:25 on May 25, 2016 ยท (Permalink)
But then why limit yourself to base 16, how many different characters does reddit accept for usernames? That's the base you should go to (although, I guess it'll get ambigious if you start using things other than letters and numbers, so you have to limit yourself to base 36, maybe 37 if you want to be weasily).
26 lowercase + 26 uppercase + 10 numeric + - + _ are the valid username characters, which together make the standard base64url format defined in RFC-4648.
But if you adhere to the rule saying you need the _ to express the base at the end, that means you can only express it in Base63. There's no standard out there so while you could assume - to be high, you wouldn't intuitively know whether lowercase came before uppercase, etc. Then again, you can go down to Base62 and there's no standard for that, either...
In the end either you can have Base64URL without expressing the base at the end or a nonstandard Base63/Base62 implementation, which could just be a Base64URL encoding without the _ (or - either, maybe, depending on which you choose) since _ comes at the end of Base64URL.
I was thinking the way you were thinking, but then I realized that you aren't actually limited to base 63 or 64. You're just limited to the first 63 (or 64 if you treat the last underscore as special) digits of whatever base you want! With that in mind, this is the largest number that can be expressed in that format that could also be a reddit username:
----------_999999999
Convention: the digits go the following order 0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ-, the base is expressed in base 10, and we are disallowing _ to be used in the number itself.
Which is pretty large. Note that it's not a prime. I'm planning to try to find the largest prime than can be expressed using the same convention, but it's a bit trickier. I just found the largest integer because I think it'll come in handy as an upper bound.
I figured it was obvious that the username needs to be readable without guessing, given that I dedicated most of my post to that idea. ----------_999999999 is purely meaningless because there is no standard for Base 999999999 and therefore no meaningful way to determine what - corresponds to in that base. Your "convention" is arbitrary and therefore useless.
The problem with primes is that the higher you get, the rarer they get. As a limit, we can see that as we approach infinity, there are infinite whole numbers between one prime to the next. The "biggest prime" is undefined.
Halyon ยท 2 points ยท Posted at 22:34:43 on May 25, 2016 ยท (Permalink)
Oh I know that "biggest prime" is undefined. That was my point. With an infinitude of primes, you have to stop somewhere.
gnorty ยท -2 points ยท Posted at 23:26:36 on May 25, 2016 ยท (Permalink)
you have to stop somewhere.
and his chosen stopping point was that the number could be fitted into a reddit username. I'm not seeing the point you are trying so hard to make...
No. A prime number is a number with no divisors other than itself and 1. This is independent of any specific choice of representation. A numerical base is just a way of writing things down.
[deleted] ยท 1 points ยท Posted at 22:04:15 on May 25, 2016 ยท (Permalink)
OK, I was more wondering if the fractions end up different when using bin, Oct, hex etc...
You can almost perfectly convert miles and kilometers using the Fibonnaci sequence.
1 1 2 3 5 8 13 21 34....
Each number, after a few, is miles and the number after it is very nearly the corresponding number of kilometers and vice versa.
vidarino ยท 1801 points ยท Posted at 15:06:59 on May 25, 2016 ยท (Permalink)
Neat, never thought of that.
Makes perfect sense, though, since phi (the factor the sequence increases with) is 1.618, and there is 1.609 km in a mile.
[deleted] ยท 33 points ยท Posted at 17:22:27 on May 25, 2016 ยท (Permalink)
As an engineer I just use a factor of 0.5 when backpacking and need to translate for my American friends. I keep my gps in kilometers and they always want miles. It is close enough and super easy.
[deleted] ยท 1 points ยท Posted at 20:17:29 on May 25, 2016 ยท (Permalink)
If you're 3 clicks from the car it doesn't matter much. 1.5 miles is close enough to 1.8 miles, especially if you consider significant figures and round to the nearest whole mile, i.e., "about 2 miles."
[deleted] ยท 7 points ยท Posted at 19:08:59 on May 25, 2016 ยท (Permalink)
I use .5 and if the number's big I add another 10%.
[deleted] ยท 5 points ยท Posted at 20:38:59 on May 25, 2016 ยท (Permalink)
I always doubled the miles and then took off 20% since getting 20% is easy.
Never knew exactly how many km to a mile, but if those numbers are right, then you can get a ridiculously accurate estimate by averaging the Fibonacci answer and the minus 20% answer. Neat.
What do you mean by "the factor the sequence increases with"? I'm tired and just tried multiplying each value in the sequence by 1.618, which produced a result that was close. Granted, I've not covered this stuff yet in school.
pemboo ยท 8 points ยท Posted at 19:39:47 on May 25, 2016 ยท (Permalink)
As with a lot of maths, the journey is as interesting, if not better, than the destination itself so I'll leave you with a video showing how you get there.
The most interesting things to me was that it actually has the golden ratio, phi, in there (it's (1+sqrt(5))/2 which is irrational, so you also need to divide my square root 5 to be able to get integers out of the formula.
Other than that, it reminded me of differential equations, and I thought I had moved past that stage in my life.
pemboo ยท 1 points ยท Posted at 20:11:57 on May 25, 2016 ยท (Permalink)
It is differential equations.
What's more interest is that it's a linear combination of 2 irrationals that leads to integer results.
[deleted] ยท 20 points ยท Posted at 17:52:28 on May 25, 2016 ยท (Permalink)
The ratio between two sequential numbers in the series approaches 1.618 as the numbers get larger. 3/2 = 1.5, 5/3 = 1.66, 8/5 = 1.6, 13/8 = 1.625 ... 144/89 = 1.6179.
If you're interested, this is called a "limit". A proof is here.
eltoro ยท 1 points ยท Posted at 00:42:55 on May 26, 2016 ยท (Permalink)
Phi is the most irrational number because it is the hardest to approximate accurately with fractions.
Related to the fact that the continued fraction is 1,1,1,1,1,...
lerjj ยท 8 points ยท Posted at 17:51:34 on May 25, 2016 ยท (Permalink)*
So first, we're going to do this by inspection - the first couple of Fibonacci numbers are 1,1,2,3,5,8,13,... The ratio between successive terms are 1,2,1.5,1.67,1.6,1.625... It would appear that the ratio is settling down to be something like 1.6 Checking successively higher values we find that it is very close to 1.618 which is approximately the golden ratio phi (which in turn is the positive solution to x2 =x+1). Now for the proof:
Assume that for sufficiently far in terms, they are in a fixed ratio of r. We'll now consider three terms: F1, F2 and F3. By the construction of the Fibonacci sequence, F3=F2+F1, and since they are in constant ratio, F2=rF1 and F3=r2F1. Plugging that in gives r2 =r+1, i.e. r=phi (where phi~1.618...)
Uh, I guess I should have clarified that I'm still in high school (England), so some of the vocabulary you're using is alien to me.
lerjj ยท 1 points ยท Posted at 18:23:02 on May 25, 2016 ยท (Permalink)
I tidied it up a little (some of what I wrote had tried to format itself which I didn't expect, and it didn't do a great job of it). I'm also (kinda) at school in England. (I'm on exam leave for A2s, so I've already had my official last day).
F1, F2, and F3 here are just any random trio of sequential numbers in the sequence, called F, with what would be a subscript to let you tell the difference, if reddit allowed subscripts. It looks like r is the constant ratio mentioned above, 1.618.
Fixing his notation a bit, where reddit's markdown got weird, what he wrote is:
1. F3 = F2 + F1
2. F2 = r * F1
3. F3 = r2 * F1
4. Substituting Equations 2 and 3 into Equation 1 yields r2 * F1 = r * F1 + F1, which simplifies into r2 = r + 1
Where F1 is any number you care to choose in the sequence, F2 is the next number in the sequence after F1, and F3 is the next number in the sequence after F2. If it helps, we can define them as F1=3, F2=5, and F3=8. They could also be defined as F1=1, F2=2, and F3=3. Or F1=34, F2=55, and F3=89. It doesn't really matter, all that matters is that F1 is the number immediately before F2 in the sequence, and F2 is the number immediately before F3 in the sequence.
Equations 1 through 3 are the basic definitions of our pattern, the Fibbonaci Sequence. Equation 1 says that any position in the sequence is equal to the sum of the two numbers that came before it. Equation 2 says that any number in the sequence is also equal to some constant value multiplied by the number that came before it. Equation 3 extends this to say that any number in the sequence is equal to that constant value from before, squared, multiplied by the number that came two places before it. Finally, in Equation 4, we substitute the values in Equations 2 and 3 into Equation 1, which puts Equation 1 into terms of our variable F1. Since all the terms in our new substitution are multiplied by our variable F1, we can divide both sides of the equation by F1 to yield the simplified form.
What this does is allow us to isolate this constant multiple. If you were to take another look at Equation 2, you'd see that any number in the sequence divided by the number that came before it in the sequence is equal to r (or, to rewrite the equation: F2/F1 = r). A ratio is just the result of dividing any two numbers. However, the ratio in this sequence is special: No matter which two F2 and F1 you pick, so long as they share the defined relationship above, they will be within .5 of the same value as any other two. So yes, 2/1 = 2, but let's choose numbers farther along in the sequence. If F2 = 89 and F1 = 55, 89/55 = 1.618182. Take it to the next step beyond that, set F1 = 89 and F2 = 144, and you get 144/89 = 1.617978. And the numbers will keep getting closer to each other the farther along you get. We would normally call what's happening here a limit, but that's either pre-Calculus or Calculus material, and I'm not sure if you're that far yet.
He finished by saying r = phi, because phi is (from what I just looked up, so I didn't know this until just now) the symbol used when referring to the Golden Ratio, which is defined by simplifying the simplified form of Equation 4 up there to get r = 1 + 1/r. Phi, for what it's worth, is just a Greek letter. Mathematics, and just about every discipline that uses it, will use Greek letters as extra variables, or sometimes as specific variables, in order to note that whatever it is representing is different from a regular number.
I, uh. I tried my best to explain this simply, realized half way through that I was writing a wall of text, got to the end and now I'm fairly sure I've done nothing useful. But I put too much time into this to not post it. So I hope it helps.
Also works with any sequence of that format. Only really worth doing Fibonacci and Lucas numbers (1 3 4 7 11 18 29 47 76...), and then you only need to do the Lucas numbers up to 29 because after that they start approximating earlier numbers. 29 -> 47 is basically 3 -> 5 from Fibonacci.
ktkps ยท 1 points ยท Posted at 04:55:16 on May 26, 2016 ยท (Permalink)
The universe and our world is ruled by Pi Man.....
Interestingly, you can start a pseudo-Fibonacci series with any two numbers and the ratio between consecutive numbers will still rapidly converge on phi: lets do 8 and 100 for the hell of it:
[deleted] ยท 1 points ยท Posted at 21:06:45 on May 25, 2016 ยท (Permalink)
He said "almost perfectly"... but he actually meant "close approximation".
It's neat and all, but I can't calculate fibonnaci sequences off the top of my head. It's easier and more accurate to memorize the ratio and do the math than to memorize the Fibonacci ratio and do the math.
No, it's just a coincidence that the ratio of miles to kilometers (1 mi = 1.6 km) is close to the ratio between consecutive numbers in the fibonacci sequence (phi, or 1.618ish)
phi (the factor the sequence increases with) is 1.618, and there is 1.609 km in a mile.
So as the numbers get larger, the difference would keep increasing. However, you wouldn't need to go to those distances for any practical purpose where you wouldn't anyway use a calculator.
Edit: had to come back to edit because I forgot something obvious - the ratio between consecutive numbers in the Fibonacci sequence itself converges to 1.618 as the numbers become greater (you can see how the ratio for the first few numbers are all over the place - 2/1 = 2, 3/2 = 1.5, 5/3 = 1.67, 8/5 = 1.60, etc.). It would be interesting to find out at what point the miles to km conversion using the Fibonacci sequence is the closest.
It looks like the percent difference between the numbers stays roughly the same.
233 miles is about 374.977 km and the next fib # is 377 (0.54% difference)
11984 miles is about 19286.38 km and the next fib # is 19392 (0.55% difference)
Makes sense! Seems to agree with the other reply to my comment, as fib's increase with ratio 1.618, and the km to miles ratio is ~1.609
If you divide the difference .009 by 1.618, you get the ~.55% difference.
I tried the second starting at 2,2 and 4,4 and 12,86 and for all of these the difference comes to less then a percent after 5 or 6 steps. so yes it does work for random starting numbers.
TGODie ยท 1 points ยท Posted at 19:26:20 on May 25, 2016 ยท (Permalink)
This is fucking dope. Cheers
[deleted] ยท 1 points ยท Posted at 20:14:35 on May 25, 2016 ยท (Permalink)*
Because the ratio in successive terms of the Fibonacci sequence tends towards the golden ratio which is ~ 1.618. And the conversion rate from miles to km is ~ 1.609. So the next term in the Fibonacci sequence is a very good approximation of the conversion of that number of miles to km.
[deleted] ยท 1 points ยท Posted at 20:32:45 on May 25, 2016 ยท (Permalink)*
They don't, and neither do the kilometres. The sequence has nothing directly to do with them. The relationship between adjacent numbers in the sequence is about the same as the relationship between kilometres and miles.
That's the extent of the 'math fact'. There's nothing else to it, the kilometres and miles don't line up to the sequence, the relationship between each adjacent number is just the same ratio. Pick any number and the adjacent number 'up' is that number converted to kilometres, and the adjacent number down is that number converted to miles.
More exact - or at least, it becomes wrong by a more consistent amount. The difference between the exact km conversion and the expected km amount using the next Fibonacci term tends towards 0.54%.
This is because the difference between two terms in the Fibonacci sequence tends towards a specific value - the golden ratio, ~ 1.618. This is pretty close to the mile/km conversion ratio of ~ 1.609 which is why this works, and why as the sequence tends towards a known ratio the error tends towards a fixed amount.
50mph = 10x5 mph <--- taking 5 from the fibonnaci sequence. The next number in the sequence is 8 (1,1,2,3,5,8...)
10x8=80km/h
(real value is 80.46km/h)
The value of the ratio is pretty much identical amongst the entire fibonacci sequence from 5,8 onwards. So any number in the sequence above that is going to be exact to within 1or2%
The ratio of the n+1th term of the sequence to the nth converges on the conversion factor between miles and kilometers. Any sequence that converges on such a ratio would be similarly accurate as an approximation.
Yup. Ratio of F_n+1/Fn goes to phi as n increases. I'm not positive about this but that might imply that there's a range of values where the conversion is better than it is for arbitrarily high values.
Edit: For essentially all purposes this isn't the case as it converges very rapidly and the series of ratios is Cauchy based off of a very quick mental check. 2nd Edit: The series converges, there was no need to say it is Cauchy, that was a dumb thing of me to say.
Just use factors, or numbers which are at least close. For example, 520 = 40 * 13. 13 is a Fibonacci number, so if there are 520 km, there are roughly 40 * 8 miles.
There's another easy way. The actual conversion factor is 1.609 km per mile, but 1.6 is accurate to within 1%. (Note that 8 and 5 appear in the Fibonacci sequence, so that method contains this same approximation.)
1.6 is the same thing as 16/10. So you can do miles to km by doubling 4 times and then shifting the decimal point left by one position. And you can do km to miles by shifting the decimal point to the right once and then halving 4 times.
In your example, 520 becomes 5200, then you halve it to get 2600, halve again to 1300, and halve two more times to get 650 and then 325. The actual answer is 323.1 km, so it's pretty close. You made it easy by picking something that was a multiple of 8.
There are about 323 miles in 520 km. The closest consecutive Fibonacci numbers to those are 377 and 610.
Kered13 ยท 1 points ยท Posted at 22:21:39 on May 25, 2016 ยท (Permalink)*
500 km is 300 miles (Fibonacci terms multiplied by 100), 20 km is 12 miles (Using 1 to 0.6 conversion, multiplied by 20). 312 miles.
This is how I do it. Break it down into parts and use Fibonacci terms, 1 to 0.6,an 1.6 to 1 (these are actually equivalent to the Fibonacci terms 5:3 and 8:5, but I have memorized then this way), and easy multiples of those. It's accurate enough for everyday purposes.
This makes sense, as a kms = 1.6* miles and as the Fibonacci sequence goes on, the relationship between a number and the next gets closer and closer to ~1.6(the golden number)
This would be true for any sequence where you add the prior values together. 1,3,4,7,11,18 so 11miles is 18ish km. This is because the golden ratio applies to any sequence where the next value is the sum of the two previous ones.
It works for the obvious reason expressed by vidarino, but it isn't all that helpful since if it were a very large number you would have to generate the Fib sequence to generate the next term which would be harder (or the same) as multiplying by 1.6. Just sayin'
I picked my license plate directly because of this sequence. I've used cardboard to illustrate the sequence before and after my numbers, and am waiting to nerd out on the first officer to pull me over.
You can also extend this to non-Fibonacci numbers by finding Fibonacci numbers that sum to it -- for example, to go from 28 miles to kilometers, 28 = 13 + 13 + 2, so it's about 21 + 21 + 3 = 45 kilometers.
[deleted] ยท 1 points ยท Posted at 20:20:01 on May 25, 2016 ยท (Permalink)
And the cool thing is you can convert any given number of miles into kilometers by using Zackendorf's theorem, which states that every positive integer can be interpreted as a sum of one or more distinct Fibonacci Numbers.
For example : 7 (2+5) miles is nearly 11 (3+8) kilometers.
I never realized this, but have always been able to fairly accurately estimate the conversion in my head. Pretty much useless, living in the US, but still fun sometimes.
Solgir ยท 1 points ยท Posted at 21:00:40 on May 25, 2016 ยท (Permalink)
Holy shit! That is some amazing trick!
nahamed ยท 1 points ยท Posted at 21:53:50 on May 25, 2016 ยท (Permalink)
wow awesome
[deleted] ยท 1 points ยท Posted at 21:54:35 on May 25, 2016 ยท (Permalink)
Interesting but almost useless. After the first half dozen or so numbers, I'm not likely to know what precedes or follows the number I am looking at in the Fibonacci series.
I got a tattoo of the golden spiral and I have been inadvertently learning more about it ever since from so many different people. It's a wonderful experience. Honestly, it's the most I have ever enjoyed math, and all I had to do was put it permanently on my body.
this is more of a statistics fact, but if there is a 1 in x chance of something happening, in x attempts, for large numbers over 50 or so, the likelihood of it happening is about 63%
1-(1-1/x)^x
For example, if there's a 1 in 10,000 chance of getting hit by a meteor if you go outside, if you go outside 10,000 times, you have a 63% chance of getting hit with a meteor at some point. If there's a 1 in a million chance of winning the lottery and you buy a million (random) lottery tickets, you have a 63% chance of winning.
Edit: for the lottery example, the key word is random - yeah if you consciously buy every possible combination then it's 100%. If you buy one ticket in a million different lotteries, or a million randomly generated tickets for any one in a million lottery, then it's 63%
What he is calculating is 1 minus the odds of not winning on any of the attempts.
There are probable scenarios where you win 1 time, 2 times, 3 times, and so on. So to calculate the odds of winning at least once, the easier way than summing all of those possible winning scenarios is to find the odds of not winning, then reducing one by that value.
Say x = 100, so the odds of not winning 100 times in a row are (99/100)100
The compliment of that is simply 1 - (99/100)100 = 0.63397
The odds of not winning are 99/100 for one try. For two attempts it's (99/100)2. What is special about this problem is that the 1 in 100 event is repeated, 100 times.
This reminds me of when Kevin Spacey in 21 gives Jim Sturgess the Monty Hall problem.
Edit: I'm awful at math and have no idea if it actually applies, this whole thread just reminded me of that scene.
GGme ยท -3 points ยท Posted at 23:40:25 on May 25, 2016 ยท (Permalink)*
That is ridiculous. Once the 3rd door is open, there is a 50% chance for each of the unopened doors, regardless of when a final decision is made. The host knows where both goats are, so regardless of the contestant's initial pick, there is at least one door with a goat behind; or two. Either way, one door is opened revealing a goat, and the two closed doors now have 1 car and 1 goat. 50/50
Edit: I see it now. 2/3 of the time, the host is forced to help your odds by eliminating a goat. 1/3 of the time he has no impact.
You're missing one key part of the problem. The host knows where the car is and always chooses the door it isn't behind. You have a 1/3 chance that you're correct on your first guess and therefore 2/3 it's one of the other doors. You can rule out one of the two when he opens the door and so the odds of it being the door you didn't choose are 2/3.
The problem is easier to understand if you increase the number of doors. Let's say you have 100 doors and after you pick one, the host eliminates 98 out of the 99 doors remaining. He can't eliminate the right door so either you picked the right one from the beginning or he got rid of 98 wrong answers for you leaving only the right door behind. The odds of you picking the right door from the beginning is only 1%. There is a 99% chance that you didn't and the host removed all the wrong doors for you.
Nope. You always want to switch. The only way to lose is to pick the winning door initially. Since the host will always get rid of a losing door, you'll win anytime you initially pick a losing door.
So since you only have a 1/3 chance to lose, you have a 2/3 chance to win.
If you don't switch, you have 2/3 chance to lose. You can only win if you pick the winning door.
This blew my mind. Are you a wizard dude? Holy shit.
Dude if I had gold I would give it to you. '60% of the time it works every time' And you relate it to the probability answer of roughly 63%? I'm done. I'm just done. This is peak reddit, the singularity where memes become reality.
I like to make big sandwiches and squeeze them to make them thinner so I can take a bite. 63% of the time, the mustard doesn't come out from the sides.
00Deege ยท 0 points ยท Posted at 18:10:39 on May 25, 2016 ยท (Permalink)
I like turtles.
Carotti ยท 29 points ยท Posted at 16:02:32 on May 25, 2016 ยท (Permalink)
Sandwich/Squeeze theorem is the same thing. I've also heard it called "the theorem of the wandering drunk and two policemen" which is a nice description
My teacher referred to the squeeze theorem as "The Two Policemen Theorem" once and declined to tell us where the name came from. For the longest time I had some... interesting notions about the reason for that name.
My professor taught this as the policemen theorem. He was a strange Russian named Boris who would make a joke, but since the class couldnt distinguish between sarcasm and normal tone, he would promptly yell 'JOKE!' at the end.
I wouldn't call it a method though that may be lost in translation from whatever language to english, french, or whatever it might have been translated to.
wumpa ยท 2 points ยท Posted at 17:07:10 on May 25, 2016 ยท (Permalink)
My undergrad lecturer called it the "sandwich theorem" and it's called that in some textbooks too, interchangeable nomenclature with the squeeze theorem.
IAmMosh ยท 2 points ยท Posted at 17:36:40 on May 25, 2016 ยท (Permalink)
(Some schools up here in Canada actually teach it as the 'sandwich method')
I had a lecturer from Italy saying that over there, it's usually called the Policeman Theorem. The idea being that if you're stuck between two policeman, you're only going to one place - jail.
My Russian (Soviet educated) calculus professor told us that when she was in school in Ukraine, it was taught to her as the "proof of the three policemen," wherein one is very, very drunk, and the other two are holding him up to walk him home.
You know what the best part of having just graduated high school ; seeing your maths class pay off by understanding a reddit maths fact.
Kered13 ยท 3 points ยท Posted at 21:48:34 on May 25, 2016 ยท (Permalink)*
In high school I proved this to myself using the binomial expansion of (1 - 1/x)x and the Taylor series for ex.
EDIT: Here's the full proof:
We wish to find Lim(x -> infinity, 1 - (1 - 1/x)x ). This is 1 - Lim(x -> infinity, (1 - 1/x)x ). Using the binomial theorem, (1 - 1/x)x expands to:
sum(k=0 to x, (-1)^k * (x choose k)/x^k)
= sum(k=0 to x, (-1)^k * x!/(k!(x-k)! * x^k)) [1]
Let's focus on the x!/(k!(x-k)! * xk ) term:
x!/(k!(x-k)! * x^k)
Canceling terms in the binomial coefficient:
= product(i=0 to k, (x - i))/(k! * x^k)
Expanding this product of binomials:
= sum(i=0 to k, C_i * x^i)/(k! * x^k)
Where C_i is a constant. We don't care about the value of this constant, except that C_k=1, which is easy to see from the product of monomials. The rest of the C_i's will disappear when we take the limit. The above is a rational function, a ratio of two polynomials P(x) and Q(x), and a fact of rational functions, which is fairly easy to prove, is that if P(x) and Q(x) have the same degree (the degree of a polynomial is the highest power it contains) then the limit of P(x)/Q(x) as x goes to infinity is equal to the ratio of the coefficients of the largest degree. In our case both polynomials have degree k. The coefficient on top is C_k=1, and the coefficient on the bottom is k!. Therefore we have,
No, easier way definitely than squeeze theorem. Lim [1 - ((x-1)/x)x] as x goes to infinity can be simplified to lim [1-(1-1/x)x]. set y=limit. take ln of both sides. Do l'hopitals and lastly take e to the power of both sides getting 1-(1/e)
Call the limit = y and take the ln of both sides. Rewrite the fun side as ln((x-1)/x)/(1/x) and apply L'Hopital's rule. You get -1 so you know that ln(y) = -1 so y (the variable i chose to represent the answer) is 1/e
Mmm, let's see. 1 - 1 + 2. Yep. Put a little x in there and an e and some parentheticals because math. Mmm hmm. Checks out.
smaug13 ยท 8 points ยท Posted at 15:27:05 on May 25, 2016 ยท (Permalink)
that is because eb is defined as the number that (1+b/x)x approaches when x goes to infinity. Let b=-1 and you get:
(1-1/x)x = e-1 = 1/e
So 1-(1-1/x)x = 1-1/e
If x approaches infinity. That doesn't happen in our case, but if you let x be a very very big number (like a thousand or so) it will get close enough to call it day.
[deleted] ยท 1 points ยท Posted at 19:40:17 on May 25, 2016 ยท (Permalink)
Thank you for this! I noticed the trend toward 63% or so a few years years back (I was way too into obtaining shiny/perfect Pokemon in late middle school, so I wanted to know my odds in x hatches), but I didn't find the exact value.
If you rolled a 6 sided die 6 times you would not get a 6 about a third of the time. It turns out that as you add more faces the odds of not getting a certain number after n rolls approaches 1/e. So since you either get at least one success or no success at all, the odds of no success at all approaches 1 - 1/e.
Complements counting. The probability of something happening at least once is 1 minus the probability of it not happening. If something has a 1/1000 chance of happening, then the probability of it not happening in 1000 tries is (1 - 1/1000)1000. Additionally, as x approaches infinity, (1 - 1/x)x approaches 1/e. Thus, for x large, the probability of something with a 1/x chance of happening over x tries is approximately (1 - 1/e)
I experimentally saw this distribution as a kid (wrote a program to map out random picks out of 100 or more options, mapped which ones got picked, always got about 2/3 coverage and 1/3 distributed in some variant of duplicates), but mistook it most likely limiting to 66.6..%. :/
Imagine he gives you the option to change your choice before he opens one with a goat, and this time if you agree to change, you get two doors. You obviously swap because why have one door when you could have two? Having agreed to swap, he then opens one of your own two doors, showing you that it's a goat - which one of your two will always be. Your remaining door therefore has a 2 in 3 chance of having the cash.
If there are 100 doors, and you pick one, and Monty opens 98 and asks if you want to switch, intuitively there is a much higher chance the money is not behind your door but in fact the one remaining - why else would he leave it closed, other than your 1 in 100 guess being correct?
Everyone skips over the most important part, and you kind of tacked it on at the end. The door he opens is always a goat, you know this BEFORE you switch doors. It's the most important part, because if he just eliminated a random door your odds don't change, but he always eliminates a goat door.
[deleted] ยท 7 points ยท Posted at 21:00:13 on May 25, 2016 ยท (Permalink)*
Apparently people are really bad at statistics, thus you're being downvoted :. Statistics don't care about intent, prior events or anything like that. The collective odds of the initial pick being right is always 1/3 regardless of what happens after it is picked. Switching is always the right choice.
[deleted] ยท 3 points ยท Posted at 23:30:40 on May 25, 2016 ยท (Permalink)
Edit: To clarify, this post is referring to the alternate form where the host can reveal the car. In the standard form the host cannot reveal the car, and the usual "2/3 win when switching" answer is correct.
I went into more detail in response to looksfamiliar, but you're right that you'll pick the door with the car in 1/3 of all cases, and what happens afterward doesn't change whether you picked the car or not in any given case.
The complication is that the formulation of the problem specifies that the host reveals a goat, which effectively says "We're only looking at a subset of all possible games that could have occured." Because we're not looking at all games the odds can be (and indeed are) skewed by the criteria we choose to determine which games we include and exclude. By analogy, imagine if the problem specified that the host revealed the car. In that case your chance of having picked the car in the specified situation would be 0, even though your chance of picking the car in general would still be 1/3.
Because the host could have revealed the car, before the host opened any doors the possible outcomes would have been:
1/3 you pick the car * 0/2 the host reveals the car = 0
1/3 you pick the car * 2/2 the host doesn't reveal the car = 1/3 win by staying
2/3 you pick a goat * 1/2 the host reveals the car = 1/3 lose regardless
2/3 you pick a goat * 1/2 the host doesn't reveal the car = 1/3 win by switching
Since the host didn't reveal the car we can eliminate that possibility from consideration, and we divide the staying/switching win probabilities for these criteria (1/3) by the probability of the host not revealing the car (2/3) to get the 1/2 conditional probability of winning by either strategy, given that the host didn't reveal the car and we're limiting ourselves to games matching the criteria.
Statistics don't care about intent or prior events, but in this case it still does matter. If the host accidentally reveals a goat you are not better of by switching, because he is more likely to reveal a goat (100% of the time in 1/3 of the cases) to reveal a goat when you picked the car than when you didn't (reveals a goat only 50% of the time, in 2/3 of the cases).
So now if you only know that he revealed a goat, but not that he did it deliberately, then you can't eliminate the possibility that he would have revealed a car. This means that you have a 1/3 possibility that the host reveals a car that you can remove, but the two other possibilities (host reveals goat, you picked the car; host reveals goat, you picked a goat) are equally likely.
If he did the picking of the goat deliberately this 1/3 possibility of the host revealing a car never exists, and so it can't be eliminated either.
The Monty Hall problem boils down to the question "Given that the host has revealed a goat, what is the probability that the car is behind the door you initially selected?" In the standard form of the problem the host always reveals a goat, so the condition "Given that the host has revealed a goat" doesn't change the probabilities or reveal any new information and can be ignored.
In the alternate form of the question where he can reveal the car the condition is relevant and actually changes the probabilities. To show why, let's arbitrarily label the door hiding the car as door 1, the leftmost goat as door 2, and the rightmost goat as door 3. If we pick a door randomly and then the host randomly opens one of the remaining two doors without worrying about whether the car's behind it there are 6 possible outcomes:
#1: We pick door 1 (probability 1/3), host opens door 2 (probability 1/2), total: 1/3*1/2 = 1/6
#2: We pick door 1 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#3: We pick door 2 (1/3), host opens door 1 (1/2), total: 1/3*1/2 = 1/6 <--- car
#4: We pick door 2 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#5: We pick door 3 (1/3), host opens door 1 (1/2), total: 1/3*1/2 = 1/6 <--- car
#6: we pick door 3 (1/3), host opens door 2 (1/2), total: 1/3*1/2 = 1/6
If case #3 or #5 occurs the host reveals the car and our chances of winning by either staying or switching to the third door drop to 0. What if he doesn't reveal the car? Then we're in one of cases #1, #2, #4, or #6. In #1 and #2 we win by staying and in #4 and #6 we win by switching. Since the chances of each case occurring are equal, we have even odds for either strategy, and thus win 1/2 of the time given that the host didn't reveal the goat.
Your overall chances of winning by staying are still 1/3, as you still win if and only if you pick the door with the goat initially (2 of the 6 cases). What changes is that by imposing the condition "Given that the host has revealed a goat" we're limiting ourselves to considering 4 cases, and in 2/4 of those cases we win by switching.
So why doesn't that happen in the standard form? The difference is that the rules prevent the host from opening the door with the car. In case #3 we pick door 2 with a goat, and the host would open door 1 with the car, but he's not allowed to, so he's forced to open door 3 instead. That effectively morphs #3 into #4, which increases the overall chances of winning when switching by 1/6. Likewise #5 morphs into #6, increasing the switching odds by another 1/6 for a total of 4/6=2/3.
Creating another list like before we get:
#1: We pick door 1 (probability 1/3), host opens door 2 (probability 1/2), total: 1/3*1/2 = 1/6
#2: We pick door 1 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#3: We pick door 2 (1/3), host opens door 3 (1), total: 1/3*1 = 1/3
#4: We pick door 3 (1/3), host opens door 2 (1), total: 1/3*1 = 1/3
We still have a 1/3 chance to pick each door, but this time if we pick a door with a goat there's only one possible case per door since there's only one available door with a goat behind it for the host to reveal. It's only the 1/3 chance where we pick the car door that we have two subcases, and these two equally likely subcases split the 1/3 probability into two halves of 1/6 probability. Thus we have 1/6+1/6 = 1/3 chance to win by staying (or lose by switching), and 1/3+1/3=2/3 chance to win by switching.
[deleted] ยท 2 points ยท Posted at 01:40:21 on May 26, 2016 ยท (Permalink)
Damn. You are right. I didn't think you were and sought out to prove you wrong, but the intention does matter. I keep making tables of possibilities and if the intention of the host was to pick a door at random, and they just so happen to pick a goat, switching to the other door only yields a success rate of 1/2. If the intention of the host was to always reveal a door that contains a goat, switching success rate is 2/3 and the one I initially choose is 1/3.
[deleted] ยท 1 points ยท Posted at 11:01:25 on May 26, 2016 ยท (Permalink)
Whilst you are right, you make the decision to switch after the host opens his door. Therefore it doesn't matter the total probability. As I said, if he reveals the car, you have lost. If he reveals a goat then we are back to 1/3 to 2/3. It's that simple.
Your analysis shows that it reduces your chance as you stand before he opens the door because there is always a chance he will reveal the car with his random choice (in this modified ruleset for others confused by us) and force you into losing.
If he reveals a goat then we are back to 1/3 to 2/3. It's that simple.
Imagine a third variation of the game where everything is the same as the standard and alternate variations, except that the host always reveals the car if you didn't pick it initially. In that case switching will always lose, because either the host already revealed the car or the car was behind the door you picked initially. In that case the conditional probability of (the car being behind the third door, given that the host revealed the goat) is 0, since that never happens even though he sometimes reveals a goat.
That shows that changing the algorithm the host uses to choose which door to open can change the distribution of possible outcomes, which in turn changes the conditional probability of (the car being behind the third door, given that the host revealed a goat).
Your analysis shows that it reduces your chance as you stand before he opens the door because there is always a chance he will reveal the car with his random choice (in this modified ruleset for others confused by us) and force you into losing.
Suppose you have two possibilities A and B with probabilities > 0 where exactly one of them must occur, so there's no overlap or third alternative. If the overall probability of an event happening across A and B combined is 1/3, then either the probability is 1/3 in both of them, or it's greater than 1/3 in one of them and less than 1/3 in the other. The exact ratios will depend on the probability of A happening vs. B happening, but that generalization holds for any combination of probabilities having an overall 1/3 probability; the math just wouldn't work otherwise.
We agree that the probability of the car being behind the door you picked, given that the host hasn't opened a door yet, is 1/3. There are two possible outcomes of the host opening the door: either he reveals the car, or he doesn't. If he does reveal the car then the probability that the car is behind your door drops to 0. Using the general reasoning above, if he doesn't reveal the car that must mean that the probability that the car is behind your door rises. If that wasn't the case the probability of the goat being behind your door would be less than 1/3 in situation A (host reveals the car) and less than or equal to 1/3 in situation B (host doesn't reveal the car), which would only work if the overall chance of you picking the car was less than 1/3.
Conversely, in the standard problem where situation A (the host reveals the car) never happens all of the probability comes from situation B, and so the chance of the car being behind your door in situation B (he reveals a goat) must equal the overall probability of that happening, 1/3.
[deleted] ยท 1 points ยท Posted at 18:47:41 on May 26, 2016 ยท (Permalink)
OK, so I agree with this:
If he does reveal the car then the probability that the car is behind your door drops to 0.
But I dont agree with this:
Using the general reasoning above, if he doesn't reveal the car that must mean that the probability that the car is behind your door rises.
and I'm not sure why. However if he reveals the car, you have new information. But if he reveals a goat (by chance with these rules) then you dont have any new information. It should still be 1/3 to 2/3.
But if he reveals a goat (by chance with these rules) then you dont have any new information.
In the variation of the game where the host can reveal the car, before the host opens the door it's possible he will indeed reveal the car. If he then reveals a goat the new information is that he didn't reveal the car.
Looking at it another way:
Before the host reveals the goat, the player knows there is a non-zero chance the host will reveal the car.
After the host reveals the goat, the player knows that there is zero chance the host revealed the car, because the player knows that didn't happen.
Because the probability of (the host reveals the car) is different before and after the host opens the door, there must have been new information that led to that probability changing.
Conversely, in the standard problem where the host can't reveal the car, the fact that the host reveals a goat doesn't provide any new information. This is because the player knew there was a 100% chance the host would reveal a goat, so no probabilities change.
Bonus fact about the Monty Hall problem: when the correct interpretation was advanced in a column by a female mathematician in 1990, despite the solution being provable with some very simple computer modelling in a way that wasn't possible when it was first explained, she was accused of using "female logic" and her "incompetence" derided by a number of people who somehow had attained PhDs despite not being able to do some quite basic maths.
(You are now subscribed to Stats Facts)
bloouup ยท 17 points ยท Posted at 18:02:18 on May 25, 2016 ยท (Permalink)
Marilyn vos Savant was also recognized by the Guinness Book of World Records as having the highest IQ of all time.
Savant comes from Latin sapere ("to be wise") by way of Middle French, where "savant" is the present participle of savoir, meaning "to know." "Savant" shares roots with the English words "sapient" ("possessing great wisdom") and "sage" ("having or showing wisdom through reflection and experience"). The term is sometimes used in common parlance to refer to a person who demonstrates extraordinary knowledge in a particular subject, or an extraordinary ability to perform a particular task (such as complex arithmetic), but who has much more limited capacities in other areas.
"In her book The Power of Logical Thinking, Vos Savant (1996, p. 15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer". Pigeons repeatedly exposed to the problem show that they rapidly learn always to switch, unlike humans (Herbranson and Schroeder, 2010)." from the wiki article.
That just cracks me up. The brightest of humanity consistently being outdone by pigeons.
Whoa your second point blew my mind. I'm trying to figure it out still, though. I believe it works based on the data, but don't understand. Switching from door 1 to door 2 gives a 2/3 chance of success, but couldn't the same be said for switching from door 2 to door 1? It makes sense for the 100 doors thing, but I don't get the three door problem.
It doesn't matter which for you picked first, the act of switching gives you a two thirds chance of winning.
The key is that the host is always going to reveal a goat, he'll never reveal a car. The revealing is really just a formality, you're making a choice between the door you pick and all the doors you didn't pick.
Finally! This did it for me. I've read dozens of explanations for this, but this one is the only one to help me get it. I knew it would finally happen. Thanks!
It still leaves me reeling a bit but here's the best explanation I remember:
There are 3 doors. One of them has the prize behind it. You have no further information, so whichever door you pick has a 1/3 chance of being correct, and a 2/3 chance of being incorrect.
Now Monty reveals one of the wrong doors, and asks you if you want to switch. On its face, you are making a new choice between two doors, 50/50 either way right? However in reality, he's asking you "Do you think your original choice was correct?"
Your original choice still has a 1/3 chance of being correct, because that's what it was when you picked it and that hasn't actually changed. So if you stick with that door, you'll have won 1/3 of the time and lost 2/3 of the time, same as if he revealed the winning door right away. Since the only other option is to switch, then switching provides a 2/3 chance of being the winning door, since the one you originally picked is only correct 1/3 of the time.
The nice thing about the Monty Hall problem is that its so small you can actually just work out the possibilities to show that it works.
Lets say you pick door 1 and stick with it. There are thee options for what will happen:
The car is behind door 1 and you win
the car is behind door 2 and you lose
the car is behind door 3 and you lose
very simple 1 in 3 chance of winning.
Lets say you pick door 1 and switch. Your outcomes become
The car was behind door number one, he showed you either door 2 or 3 (it doesn't matter which) you switched to the other and now you lose.
The car was behind door number two, he showed you door 3, you switched and won.
The car was behind door number three, he showed you door 2, you switched and won.
2 in 3 chance of winning by switching.
The other way to think about it is that if initially pick a goat and switch, you will win. You will pick the goat 2 out of 3 times. The only way switching makes you lose if you happened to get the 1 out of 3 chance that you correctly picked the car the first time.
The nice thing about the Monty Hall problem is that its so small you can actually just work out the possibilities to show that it works.
Lets say you pick door 1 and stick with it. There are thee options for what will happen:
The car is behind door 1 and you win
the car is behind door 2 and you lose
the car is behind door 3 and you lose
very simple 1 in 3 chance of winning.
Lets say you pick door 1 and switch. Your outcomes become
The car was behind door number one, he showed you either door 2 or 3 (it doesn't matter which) you switched to the other and now you lose.
The car was behind door number two, he showed you door 3, you switched and won.
The car was behind door number two, he showed you door 2 and the game was over
The car was behind door number three, he showed you door 2, you switched and won.
The car was behind door number three, he showed you door 3 and the game was over
2 in 3 chance of winning by switching.
The other way to think about it is that if initially pick a goat and switch, you will win. You will pick the goat 2 out of 3 times. The only way switching makes you lose if you happened to get the 1 out of 3 chance that you correctly picked the car the first time.
The problem with the Monty Hall problem is that way too many people don't pose the question in a manner that makes it clear that the bold parts can not happen.
[deleted] ยท 2 points ยท Posted at 16:39:30 on May 25, 2016 ยท (Permalink)
The simple way to understand this is that due to always opening the remainong empty doors, you're actually trying to pick an empty door as the "correct" door so you can then simply change your choice to the other non opened door. Your chances of winning then after opening the remaining empty doors simply reflect your chances of choosing an empty door.
So A% equals your chance of choosing the empty door while B% is the chance of choosing the door with a prize. While choosing a door you have B% chance of choosing the correct door but after opening the remaining empty doors you have the A% chance that you chose an empty door and swapping doors is the right move to get the prize.
After the host reveals that 98 of those 99 other doors don't have the money, that last door is still in the second bucket: 99/100 chance of having the money.
The same applies to 3 doors: 1/3 correct, 2/3 incorrect. Host removes on of those two doors, but the second bucket is still "2/3".
I tried REALLY FUCKING HARD to make sense of it using only the Wikipedia article and failed, and then reading this makes me feel like a complete idiot. It's so obvious.
[deleted] ยท 1 points ยท Posted at 21:54:19 on May 25, 2016 ยท (Permalink)
You once looked at three doors the same, even if you were unsure of the odds to begin with after the host reveals the contents of one of the other two doors you now see only two doors the same way. One, is your choice you previously without any knowledge about any one of the three doors. The other, is the one and only choice left you did not make based on the same information you had when you made your first choice. Now, you have new information not only about the goat door but about your odds of winning between the other two doors. You will have to ask yourself questions that frankly seem to have nothing to do with statistics but rather logistics.
If you had picked the WINNING door(assuming a goat isn't all you ever dream of) would the host announce you the winner (assuming they, or an informant of theirs knows the contents of each door) right away without any further play?
Should this not be a sudden happy ending, what are the chances they're trying to pawn another goat off on you?
If your chances were 1/3 at the start and 50/50 now, even though making a different choice will actually result in a different outcome rather you knew it or not, does it make a statistical difference?
Looking at two doors with hidden contents hoping for one to be the winner(when the other is not) is always a 50/50 without any prior knowledge. Looking at one opened door and two closed doors hoping for the same is still a 50/50 whether or not you had previously made a choice or not. They are separate events because your initial choice was never revealed. The fact the contestants would win in this situation 63% of the time is a separate statistic because it doesn't reflect anything about either of the two scenarios. Just before you make your choice to change or stay with door X it is still a 50/50, you've only had one door eliminated from the choosing. You still have no way of certainly telling if you would have won the game had you made the right choice the first time.
Honestly, This was really hard to explain whether I'm right or wrong but ultimately I would change my choice.
[deleted] ยท 17 points ยท Posted at 15:46:55 on May 25, 2016 ยท (Permalink)
That Monty Hall one really messes with me.
I'm going to have to read it more intently when I'm not at work.
[deleted] ยท 11 points ยท Posted at 16:14:41 on May 25, 2016 ยท (Permalink)
I don't see these as the same situation.
My answer is yes, definitely.
N546RV ยท 22 points ยท Posted at 16:18:14 on May 25, 2016 ยท (Permalink)
I don't see these as the same situation.
Why not?
[deleted] ยท 14 points ยท Posted at 16:20:59 on May 25, 2016 ยท (Permalink)
I'm having a hard time articulating it.
Which is obviously because my feeling is wrong and they're identical situations...
I guess it's because I chose 14 and the game chose 83. So no matter which one I picked, it would be that number or 83, in the end.
To me, it's less likely that I picked x out of 100 correct, therefore, the other option must be more likely. (as it is not truly out of 100)
N546RV ยท 22 points ยท Posted at 16:27:40 on May 25, 2016 ยท (Permalink)
But the same logic applies regardless of the number of doors; it's simply made more obvious by examining the extreme case of 100 doors. In all cases, you're likely to have picked the wrong door initially. The host then eliminates all but two doors, one of which is the one you picked. Since your first guess was most likely wrong, this means that the other remaining door is most likely right.
Practically speaking, the 100-door example would be much more useful. In that case, you could be pretty frickin sure that the other door was the right choice. I'm not a statistics guy, but I'd suspect that the chances of the other door containing the prize would be the opposite of the chances of your first guess being right, eg you had a 1/100 chance of your first guess being right, ergo there's a 99/100 chance that switching is the right decision.
With the three-door problem, the margin is much smaller. It's still a win statistically - you go from 1/3 to 2/3 chance of winning - but it's not the same open-and-shut case as the 100-door problem.
Important to note that this ONLY works if the host knows which door is correct.
[deleted] ยท 1 points ยท Posted at 17:55:04 on May 25, 2016 ยท (Permalink)
Correct. If the host can open a prize door then you learn nothing useful about the remaining doors.
[deleted] ยท 1 points ยท Posted at 19:54:06 on May 25, 2016 ยท (Permalink)*
[deleted]
[deleted] ยท 1 points ยท Posted at 20:13:12 on May 25, 2016 ยท (Permalink)*
No, because there isn't a transfer of information going on, because the host does not have information to transfer. If you pick the wrong door he only has a 2/3*(1/2) chance of opening a door with a goat.
The original problem only works because the host knows which door is the correct answer. If he does not there is no information gained when he opens a door, because he could have chosen the prize.
Doesn't it still work as long as the host doesn't actually open the prize door? In the 100 door case, if the host opens 98 doors and they all have goats, it would still make sense to switch.
[deleted] ยท 0 points ยท Posted at 05:46:12 on May 29, 2016 ยท (Permalink)
Nope, because either you or the host just got lucky.
Why does the host doing it by luck matter vs doing it by intention? Sure, it's very unlikely they avoid the prize by chance, but when they do, you're in the exact same situation.
[deleted] ยท 1 points ยท Posted at 06:33:21 on May 29, 2016 ยท (Permalink)
It means that there is a 50/50 chance that they guessed right or you did.
The difference is if they know which door it isn't they can't accidentally open it, so all of those possibilities are lost, so the remaining door grabs the probability. On the other hand if both of you are just randomly guessing the probability distributes evenly.
Basically when you say "given they don't select the prize" you need to divide by the probability they don't select the prize door. This completely kills off the additional probability that would be added if they are randomly guessing. If they aren't this prob is 1, so the remaining door absorbs the prob from the other doors.
[deleted] ยท 3 points ยท Posted at 16:31:51 on May 25, 2016 ยท (Permalink)
But, if switching is a 50% chance...how is not switching not a 50% chance as well?
That's the part I can't reconcile.
After it's revealed that door 3 is a goat, we learn that it was a 50% choice the entire time....how does switching a 50% chance choice make a difference?
When you switch you don't have a 50% chance of winning, you have a two thirds chance if winning.
The key is that there host is always going to show a goat.
If you start by picking a goat (2/3 chance), the host will reveal the other good, leaving behind the prize, so if you switch you'll always win in this scenario.
If you pick the prize first (1/3 chance) the host will reveal one of the goats, leading behind the other goat, so if you switch you'll always lose.
There's a 2/3 chance of being in a winning position when you always switch, and a 1/3 chance of being in a losing position when you always switch, so you have 2/3 odds.
It still hurts my simple brain a little, but I think I get it. Any situation in which you picked a goat is one where you want to switch, and two thirds of the time you have a goat, so switching is usually the better answer. Am I getting it right?
I think originally I wasn't seeing the big picture. I was super focused on only the final "2 doors" choice, that I never looked at it from the "examine all outcomes" point of view.
The best way to "get" it is to actually play the game, as Monty. This is what I did a long time ago.
You take 3 playing cards (Ace, Jack, Jack, let's say), and ask a friend to choose one. Now show your friend one of the remaining Jacks and give them a chance to stay or switch. Do this a couple dozen times and you'll realize that when it's time for you to reveal a Jack, you more often than not have only one card you can reveal. So more often than not, you're revealing where the Ace really is.
Think about it this way, there are three possible scenarios according to which box you chose:
Door You picked: Goat A.
Door He opened: Goat B.
Swap door: Car.
Door He opened: Goat A.
Door you picked: Goat B.
Swap Door: Car.
Door He opened: Goat A.
Swap Door: Goat B.
Door you picked: Car.
In two of these scenarios swapping gets you the car, in only one of them sticking gets you the car. So you should always swap because your odds are better.
[deleted] ยท 1 points ยท Posted at 17:53:37 on May 25, 2016 ยท (Permalink)
Because the host is revealing information he knows that you do not know. If the host does not know which door is correct and opens randomly then there is a 50/50 chance of the door you started with being the winner, assuming he did not reveal the prize. But if the host knows and won't reveal the winning door then there was a 2/3 chance it was one of the other doors initially, and once he reveals a goat the remaining door gains that entire probability, because if you were right, which happens 1/3 of the time he could have picked either door. If you were wrong which happens 2/3 of the time, though, he had no choice of which door to pick. So overall you end up with a 2/3 chance of winning if you switch, since you picked the wrong door 2/3 of the time, and if you picked the wrong door the remaining door MUST be correct.
okuRaku ยท -3 points ยท Posted at 16:35:03 on May 25, 2016 ยท (Permalink)
It's only 50% if you switch, because when you picked the door it was 33%
When you pick a door, there is a 1/3 chance you picked the car and a 2/3 chance you picked a goat. In either case, the host has at least one goat to show you, which he does. This does not affect the probability that your original choice was a car. If you switch, you are betting that your initial choice was a goat, and you have a 2/3 chance of being right, since the host revealing one of the goats has no effect on the probability that you chose a car. Nothing is a 50% chance.
[deleted] ยท -3 points ยท Posted at 16:36:46 on May 25, 2016 ยท (Permalink)
Only because we didn't have the info we get later.
It's still 50%.
Not switching is a choice, just like switching is. Both doors have a 50% chance. they always did, we just didn't know it yet.
66% chance you picked a goat -> switching gives you a car.
33% chance you picked a car -> switching gives you a goat.
Not switching means you're more likely to end up with a goat. Switching means you're more likely to end up with a car.
PRDX4 ยท 4 points ยท Posted at 21:06:00 on May 25, 2016 ยท (Permalink)
I GET IT NOW.
You're saying that the act of switching gives you a 66% chance of success. I think what I and others were hung up on is that we're counting the number of doors and the number of prizes. 1 prize out of two doors is 1/2, intuitively.
When you choose in the beginning you have a 1/3 chance. If you switch, what you're betting on is that your first choice was wrong. It's between the door you pick first and "any other door besides this one". After you make your choice, the dealer eliminates every thing you didn't pick except one, but your choice is still betting on getting it right the first time vs getting it wrong the first time.
Because while the two situations are congruent in some sense, in some sense there is a dissimilarity. I would wager that if you rephrased the question so that there's 100 doors, you pick one, the host opens 1 empty door and asks you if you want to stay with what you have or choose another door, people would be equally confused as they are with the 3 door version of the problem. Of course, in this variant, it still makes statistical sense to choose another door, as each one of those other doors has a slightly higher chance than the one you initially chose as well.
You're right in this case. The idea that having 100 doors illuminates the problem is something I feel to be a mental trap that prevents people from actually understanding the problem and frequently only fools them into thinking they do.
Having 100 doors means that the chance of randomly picking a door with the car and happening to be correct is low enough that you may as well assume that when Monty eliminates all the other doors, that it's more likely that he's deliberately chosen to eliminate all the other answers except for what you reasonably believe is likely to be the car.
The thing is, this logic doesn't actually apply to the original three door problem directly, as even if both you and Monty are actually choosing randomly (if the reasoning behind his actions is not specified), there's a decent chance that you'll end up in the situation specified by the original scenario. Then, if you suspect Monty is likely acting randomly, him revealing a goat actually provides additional evidence that your next choice is 50/50, which is less likely to be the case in the 100 door problem.
All of this is irrelevant if you know exactly how Monty must act beforehand though.
[deleted] ยท 1 points ยท Posted at 10:09:41 on May 26, 2016 ยท (Permalink)
The key is that Monty knows where the prize is, right? I don't know, I've had this explained to me so many times and I still have a hard time wrapping my head around it.
You're looking at the two doors in isolation and thinking each has a 50% chance. The problem is, you can't consider them in isolation because the host's actions (opening the other doors) has added new information that has to be considered.
The way I usually state it is that if there are X doors, your chance of choosing correctly on the first guess is 1/X. That means, crucially, that the chance you chose wrong is (X-1)/X. In the classic MH problem, it's 1/3 chance right, 2/3 chance wrong. By the host selectively opening doors, he's adding new information -- namely, a selection of doors that are now known to be wrong choices. It is that new information that changes things, because now the odds of you having chosen correctly never change even though there are now fewer doors left closed. The original odds remain 1/X, and the odds you were wrong remain (X-1)/X. And that's ultimately what you fight against at the end -- it isn't "is it this one door or that one door," it's "was I likely right when I guessed at first when there were X number of doors, or was I more likely to be wrong."
Of course, the MH problem as we think of it now technically wasn't how the real game operated. Sometimes he's open your door to reveal a win, or a loss, directly. Sometimes if you guessed wrong he'd open the winning door directly. They adjusted that in order to help control how much they actually had to pay out in prizes.
Dr-K-G ยท 1 points ยท Posted at 17:08:13 on May 25, 2016 ยท (Permalink)
Look at switching as betting on that your first choice was wrong. By switching you say "I think it's more likely that I got the wrong door the first try than that I got the right door and this is why I should switch".
The nice thing about the Monty Hall problem is that its so small you can actually just work out the possibilities to show that it works.
Lets say you pick door 1 and stick with it. There are thee options for what will happen:
The car is behind door 1 and you win
the car is behind door 2 and you lose
the car is behind door 3 and you lose
very simple 1 in 3 chance of winning.
Lets say you pick door 1 and switch. Your outcomes become
The car was behind door number one, he showed you either door 2 or 3 (it doesn't matter which) you switched to the other and now you lose.
The car was behind door number two, he showed you door 3, you switched and won.
The car was behind door number three, he showed you door 2, you switched and won.
2 in 3 chance of winning by switching.
The other way to think about it is that if initially pick a goat and switch, you will win. You will pick the goat 2 out of 3 times. The only way switching makes you lose if you happened to get the 1 out of 3 chance that you correctly picked the car the first time.
[deleted] ยท 1 points ยท Posted at 17:41:13 on May 25, 2016 ยท (Permalink)
If you land on the donkey he can only switch you to the car not another donkey. That was the part that constantly tripped me up.
During the initial choosing you have a 2/3 chance of picking a goat. He always opens a goat door. If you switch, odds are you will switch to the correct door, or rather the one you want, because of the odds in the initial choosing.
Actually, your original choice remains at 33.33...%
Consider this scenario. The setup is just like the Monty Hall scenario: three doors, one good result, and you choose your door randomly. However, instead of picking a certain loser to open, the host opens the first door that you didn't pick - door 2 if you pick door 1, door 1 if you pick 2 or 3.
1/3 of the time, you will lose as soon as the door is opened. The rest of the time, you will have a 1/2 (50%) chance of winning. But the total chance of losing is 2/3 of the time -- 1/3 + 1/2 of 2/3 = 2/3 -- whether or not you change your pick.
If both unpicked doors are opened at the same time in the above scenario, your pick still has a 2/3 chance of losing.
In the Monty Hall problem, the first pick will never be a loser. Although your first choice only has a 1/3 chance of winning no matter what (because you chose one door out of three), removing one door from consideration sets up a different problem with only two doors.
Now, if you can not change your door at this point, you are still playing the game where two out of three doors are losers. It doesn't matter what order the doors are opened, you are still playing a game where 2/3 of the doors lose.
If you stay with your first choice, it is the same as if you were not allowed to change doors - you still lose two out of three times. However, if you change your choice, you are playing a new game, where there are only two doors, and one of the doors has the prize. Instead of staying in the game where you lose more than you win, changing to the game where you have even odds increases your chance of winning.
I always felt that Monty Hall is so much more of a sticking point than other examples because of the extra ambiguity around the rules the host plays by.
It's a pet peeve of mine when people set up Monty Hall problems in an ambiguous way. For the problem to be solvable, it's not sufficient to say what the third party did - you need to also say what they would have done in each scenario.
boarhog ยท 1 points ยท Posted at 04:16:59 on May 26, 2016 ยท (Permalink)
For the problem to be solvable, it's not sufficient to say what the third party did - you need to also say what they would have done in each scenario.
In each scenario they would open a door that doesn't have the prize behind it. Can you explain what you're referring to?
It took me a while to get it, and when I did, I didn't understand why the explanations to the problem I had seen were so obtuse.
Basically, at the start you have three doors and a 66.66% chance of selecting the wrong door.
When asked if you want to switch your answer, you have two doors and so a 50% 66.66% chance of success if switching, vs a 33.33% chance of having selected the right door from the start.
If asked, "Do you want to stick with your 33.33% chance, or switch to the 50% 66.66% chance?" the correct decision is obvious.
edit I'm annoyed I got it wrong still after thinking I had sussed it...but the logic works out.
As others have said, increasing the number of doors makes it clearer. If there are 10 doors, you have a 90% chance of selecting the wrong door initially, so once given the choice to switch after all invalid doors are closed, the other door has a 90% chance of being the winning one, while you current door retains the initial 10% chance of being the right door.
Ah, I might be misremembering the rules as the other guy said, but I always thought they always got rid of a losing door. So at the end there is a winning door and a losing door.
So the 33% of the time you picked the right door the first time you will be switching to a losing door, the 66% of the time you will be switching to a winning door.
So if the rules are like that, you always switch. And have a 66% chance of winning that way.
Switching gives you a 2/3 probability of winning, not 50%. You are being asked to bet that your initial choice was bad (switch, 2/3 probability of winning, or that it was good (stay, 1/3 probability of winning.
It's also a little easier to understand if you start with a higher number of doors. Maybe there's 100 doors, you pick one, and he opens 98. It's much easier to understand there's a higher likelihood that you chose the wrong door initially, and apply it to the 3-door problem.
The birthday problem I am assuming is you only need 23 people to have a 50% chance that two people have the same birthday and the gamblers fallacy is that you believe your chances of winning go up the longer you haven't won bc eventually you've got to win sometime even though in reality you have the same chance of winning your first time as you did you last time.
Yeah that's pretty much the entire psychology behind casinos.
If people were rational, no one would gamble, because you always lose long-term.
[deleted] ยท 0 points ยท Posted at 16:34:47 on May 25, 2016 ยท (Permalink)*
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Barimen ยท 1 points ยท Posted at 17:01:59 on May 25, 2016 ยท (Permalink)
If people were rational, no one would gamble, because you always lose long-term.
"Intristic satisfaction" doesn't fall under rational. You win, your brain is flooded with nice, juicy and addictive neurochemicals and you are happy... for a moment.
And PessimiStick clearly said "long run". You're talking about short run. :)
He says rational people would not gamble (at all) because of the long-run consequences. He doesn't say rational people would not gamble only in the long run.
If your goal is to maximize satisfaction and gambling gives more satisfaction than not gambling, isn't the rational choice to gamble? Rational decision-making isn't really possible without some kind of a goal. Otherwise there is no way to distinguish rational from irrational choices. He's presupposing that the goal is to maximize profit, in which case long-run gambling is a poor strategy. But if intrinsic satisfaction per gamble outweighs the average cost then it could be a rational endeavor in the long run (it just generally doesn't, so it isn't).
Essentially yeah. Gambler's fallacy is people believing a string of one value must eventually break. Hot streak fallacy is people believing the exact opposite about the same situation, that a string of values are more likely to not break.
to be fair variance dictates that it gets less and less likely to lose AGAIN the more often you repeat throwing the dice. Their sample size is just too small for it to be of relevance
chetlin ยท 1 points ยท Posted at 16:30:31 on May 25, 2016 ยท (Permalink)
Is it also the gambler's fallacy when people say Chicago is "due" to get hit by a strong tornado or Florida is "due" to get hit by a hurricane this year because it's been longer than normal since the last time those things happened? Previous years really don't have much of an influence on this one.
there is no ELI5 for the Monty Hall problem... a simple explanation that will get you to grasp it simply doesn't exist. I hate going down the inevitable rabbit hole every time i rehash that problem in my head.
Sure there is: There are some doors, you get to pick one, then you get a choice. You can either open [your door] or [every other door].
The mechanics of playing are very simple but the gameshow trappings are very confusing. The host is only dramatically opening known losing doors from the [every other door] category for entertainment purposes.
The prize doesn't care whether he opens some and you open some, whether he opens them all or you open them all. Either way you're going home with what's behind your door or what's behind every other door put together.
I'm in no way an expert but I believe I understand it. When he tells you to open one of 3 doors, you have 1/3 chances to win (or 33%). But then he opens a not winning door, which leaves you with the one you picked and another door, now you're asked if you want to keep your door or change for the other one, but this time you have 1/2 chances to win (or 50%), 50% is higher than 33% so theoretically you have better chances to win if you switch, because when you picked your first door, your chances of winning were smaller.
The 3 door scenario doesn't really make it easy to understand, it's way better if you imagine it with 100 doors, say you pick one (that's 1% chances of winning) he opens 98 losing doors, that leaves you with 2 (50% chance), the one you picked and another one. Would you really believe you picked the winning door out of a 100??
yeah I was sort of joking, I understand the logic behind it. I think the part I struggled with (still struggle with) was that it seems that the whole problem hinges on the fact that it would have to be established that he is going to open a losing door prior to the game starting. If I was told that going into the game then I agree on the principal. I know people will say that doesn't matter. But that removes the concept of the switch offer potentially only being given if you picked the winning door, etc.. Definitely thinking from a different angle on that one beyond just pure probability analysis which isn't the point of the problem, but I feel like the math implies that the switch offer is always in play the whole time, every time, yet the question is phrased that it is introduced only after the selection is made. (if that makes any sense)
[deleted] ยท 2 points ยท Posted at 15:50:32 on May 25, 2016 ยท (Permalink)
A nice visualization and presentation of the false positive paradox, as well:
First one is the problem with the three doors and goats/cars behind them. Birthday paradox (not really a paradox) is that if you get 23 people in a room there's a 50% chance of two people sharing a birthday and the gambler's fallacy is assuming that if you flip a (fair) coin a hundred times and get heads each time, you have a better than 50% chance at a tails next time you flip it. Although if that happens, I'd tend to suspect the person who told me the coin was fair was full of it.
The false positive one doesn't seem that hard to grasp. If the likelihood that your test gives a false positive is greater than the actual percentage of positives, a positive is just numerically more likely to be a false positive. "3% of people are infected. This test screws up 10% of the time for the uninfected. A positive test is pretty unreliable".
[deleted] ยท 4 points ยท Posted at 15:37:16 on May 25, 2016 ยท (Permalink)
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lala447 ยท 3 points ยท Posted at 15:44:51 on May 25, 2016 ยท (Permalink)
Your explanation of the birthday paradox is slightly misleading. It implies that there is a 69% chance that a group of 23 has a shared birthday, while the actual chance is ~50.7%. It also implies that a group of 20 is sufficient for >50% chance, which is false.
It's easiest to think of it in terms of "the chances of two people not sharing a birthday." The first person is guaranteed a unique birthday for any of the 365 days: 365/365.
The second person has a unique birthday on 364 of the remaining days, so their combined probability is 365/365 * 364/365. Dividing by 1 = 365/365 to simplify things leaves you with just 364/365.
Then the third person can pick 363 of the remaining days, and so on:
which is equal (after dividing by 365/365 again) to
(364 * 363 ... (365-n))/(365n )
The numerator can be rewritten as 365!/(365 - n)!, leaving you with
365!/[(365 - n)! * 365n ]
which gives you the correct probability P(n) for a group of n people not sharing a birthday. The probability for that group having a shared birthday is then 1 - P(n) > 0.5 for n>22
Figure out the odds that n people do not share a birthday by looking at the number of possible days left that haven't already been "taken." For the first person, all 365 are available, so he has 365/365 available days: a probability of 1.
The second person has only 364/365 available days IF the first person has a unique day (P=365/365). So the combined probability of the first person having a unique day then the second person having a unique day is their product: 365/365 * 364/365.
The third person has 363/365 IF the first AND the second both have unique days (P=365/365 * 364/365). So their combined probability is 364/365 * 363/365 = (365 * 364 * 363)/(365 * 365 * 365) = (365 * 364 * 363)/(3653 )
As you can see, the numerator is following the pattern: (365 * 364 * 363 * 362 * 361 ...) while the denominator is simply (365 * 365 * 365 *365 * 365 ...). You can rewrite the numerator as 365!/(365 - n)! and the denominator as 365n to give you the equation P(n) to find the probability of a group of n people all having unique birthdays.
P(n) = 365!/[(365 - n)!(365n )]
So the probability of the opposite case, where at least one shared birthday exists, is 1 - P(n), which is greater than 0.5 for n=23.
there are perfectly good explanations for 'human intuition' in those cases. It has to do with the fact that the human brain is evolved to operate on conditional probability in the real world. For example, if you roll a die 100 times and you get head every time, conditional probability would tell you that the probability of the next one being head is very high, just as if you had dropped an apple and it fell to the ground 100 times it's a pretty good chance the next time you drop it it's gonna fall.
crh23 ยท 1 points ยท Posted at 16:07:15 on May 25, 2016 ยท (Permalink)
Of course! That is why the sorts of things that don't come up in nature (like a dude with cars and goats behind doors) are the things we struggle with.
I have to say. It took me a long time reading the Monty Hall entry to agree with the correct conclusion.
[deleted] ยท 1 points ยท Posted at 16:20:13 on May 25, 2016 ยท (Permalink)
Monty Hall isn't really that confusing imo. You initially had a 2/3 chance that the door you pick had a goat behind it, so once a goat is revealed, there is now a higher chance that the door you didn't initially pick isn't a goat.
I think what gets people is that once a goat is revealed, they stop thinking about the doors in terms of the initial situation.
Monty Hall's is one of my favourite math problems. So simple, yet so hard for people to grasp. It can be explained so easily by just checking the arrangement table. The reason this works is simply because the host never opens the door with the car in it. The behaviour of the host, just as the article explains, is what makes the door-switching strategy the most successful.
[deleted] ยท 1 points ยท Posted at 18:04:05 on May 25, 2016 ยท (Permalink)
The Monty Hall problem is my favourite. I actually learned about it through reading the curious case of the dog at night time.
bl1y ยท 1 points ยท Posted at 18:14:53 on May 25, 2016 ยท (Permalink)
Don't forget the puppy problem!
A person calls a pet store and asks if they have any male puppies. The clerk at the counter says there are 2 puppies, but they're in the back getting washed, so he calls to the dog washer a the back and asks "Hey, do we have any male puppies?" The dog washer checks and says "Yes."
Then the person on the phone asks "What about 2 male puppies?"
What are the odds both puppies are male?
Intuitively, we'd say there's a 1/2 chance. One puppy is male, and there's a 50% chance the other is male, so 50% chance they're both male.
In fact, it's only a 1/3 chance!
The combination for any 2 puppies is M/M, M/F, F/M, and F/F, and it's important to understand that M/F and F/M are not the same, and are two separate possibilities. It can help to name the puppies to make that clear -- Spot female, Rascal male, and Spot male, Rascal female are different.
However, knowing that there is 1 male puppy already eliminates the F/F possibility, leaving us with M/M, M/F, and F/M. These all occur with equal odds, so M/M is only a 1 in 3 chance, much less than the 1 in 2 we would have thought.
For instance, Texas has low high school graduation rates, overall. But, for whites, Hispanics, and African Americans, it has among the highest graduation rates for each race
rivade ยท 1 points ยท Posted at 19:48:50 on May 25, 2016 ยท (Permalink)
Can you explain why gambler's fallacy doesn't directly apply in the situation OP was describing with the meteor?
Nugz123 ยท 1 points ยท Posted at 20:26:29 on May 25, 2016 ยท (Permalink)
Flipping a coin 100 times vs asking a group of people to fake it.
The coin always has longer streaks because people faking it don't understand statistics / probability.
crh23 ยท 2 points ยท Posted at 20:39:42 on May 25, 2016 ยท (Permalink)
There are a set of tests of randomness for coin flips: on average, half are heads and half are tails (which humans simulate quite well), but also half of sets of two consecutive coins are the the same and half are different, and half of adjacent pairs are both the above, ad infinitum
I hear stuff like this all the time on the Weather Channel. If we experience a few days that are unusually cool or warm, then we can expect a few days to compensate because of "the law of averages".
Odesit ยท 1 points ยท Posted at 20:42:05 on May 25, 2016 ยท (Permalink)
I was about to post the birthday paradox here because I love it. It really goes to show how statistics can be confusing intuitively. Also I think it's great to win bets against people who don't know it. E.g. I bet you in this chamber of 23 people there's at least two people who share birthday. If this bet doesn't work, you double it in the next room you go to with 23 people eventually recovering your loss.
What he is calculating is 1 minus the odds of not winning on any of the attempts.
There are probable scenarios where you win 1 time, 2 times, 3 times, and so on. So to calculate the odds of winning at least once, the easier way than summing all of those possible winning scenarios is to find the odds of not winning, then reducing one by that value.
Say x = 100, so the odds of not winning 100 times in a row are (99/100)100
The compliment of that is simply 1 - (99/100)100 = 0.63397
I love all of these!
[deleted] ยท 1 points ยท Posted at 21:22:06 on May 25, 2016 ยท (Permalink)
From your first link:
[If] We get 43,200 bits of data a day, or 1.296 million a month. Even assuming that 99.999 percent of these bits are totally meaningless (and so we filter them out or forget them entirely), that still leaves 1.3 โmiraclesโ a month, or 15.5 miracles a year.
Ironic that this ignores the concept above. Should be like 0.8 miracles per month, no?
cool article except he's wrong about evolution. you can witness evolution in a human lifetime, just not human evolution. you can witness evolution in successive generations of fruit flies or nematodes or whatever. organisms where the time between birth and reproduction is very short.
I understand the math for gambler's fallacy...but I have to really disagree with what people usually understands it as. People usually understand it as that whatever number of tosses come next, you can't have more probability due to the previous records. (See /u/asdfqwertyfghj's explanation) However, that only holds true for the very next toss, because head/tail is always 50/50.
For example fair coin = 50/50 chance. Meaning, if in first 50 toss of are heads biased, then your next 50 toss will be tail biased to average out the toss pattern. Assuming this is a fair coin. If you say, no no no, that's gambler's fallacy, then you probably understood it wrong. It has to tail biased to average it out. If you continue to have head biased, then yea, your 100 toss is probably more like 75/25, then you can bet your next 100 toss will be tail biased. In order for the whole set to be averaged out to 50/50
IMO, gambler's fallacy only applies to the very next bet because regardless, head/tail is always 1/2 chance. However, if a gambler is looking at a set of data at a time, gambler's fallacy no longer applies to its full extent.
The thing about that though is people are often better at understanding the real world against statistics. Taking the monty hall problem, statistically it's a better bet to switch, but outside sterile statistics it actually is irrelevant. The prize has already been placed, it hasnt moved.
[deleted] ยท 1 points ยท Posted at 07:50:50 on May 26, 2016 ยท (Permalink)
Daniel Kahneman's 'Thinking, Fast and Slow' also has some great examples demonstrating poor human intuitive grasp of statistics. More from a decision-making and judgement perspective as in cognitive psychology, but still very relevant.
[deleted] ยท 4 points ยท Posted at 18:01:03 on May 25, 2016 ยท (Permalink)
That's because it is worded poorly. The right way to see it is, there is a 1 in N chance of an event occurring. The probably that the event occurs at least once in N attempts is about 63%.
If you think about the odds, what it means to have odds of 1 out of 100 is that out of 100 times it should happen at least once. That's what the odds mean: it happens 1 time out of every 100 times. So the idea that it's a different number is counter intuitive.
Yes, it should, the odds for each are 2:1 so you would expect each to come up once in two flips. In reality, since there is randomness, you would need to repeat the experiment many many (infinite) times to get that outcome of 50%. So what's the problem again?
Yeah, when I think about it, I think each time I do Y, there's a 1% chance that X will happen. So it's like how many times do you need to roll a 1d100 until you get a 1... As a tabletop gamer, it seems like this happens way more than 1% of the time, but really you could roll it 1,000 times and never see a '1' come up... I guess when you start adding up a bunch of 1% chances over time it averages out to 63%?? I dunno.
droodic ยท 3 points ยท Posted at 15:57:11 on May 25, 2016 ยท (Permalink)
I don't know why it's surprising to hear that to people who haven't studies statistics, hearing something having odds of 1 out of 100 would usually yield a 100% result if tried 100 times
yeah I'd think you just add the probabilities up. e.g. two 1:100 chances, 1/100 + 1/100 so 1/50 times you'd win. I think anyone claiming that reaching 63% as the answer is more intuitive then reaching 100% is either lying or desperately trying to sound smart.
You're the one that initially responded with a high-brow "It is?" like you are so surprised anyone wouldn't be as smart as you and realize this immediately. Why do you think the fact is the top comment on the thread? Perhaps because it isn't very obvious.
The original fact presented could easily be given as a textbook example of counter-intuition.
What are the odds of tossing a 6-sided die and getting a 1? 1:6, obviously.
What about if you get two throws and have to throw a "1" at least once? Majority of people would assume your odds would increase to 2:6. Intuition says that if you get double the chances, you would double your odds. Many people would apply the same logic to the 1:100 chance. The first probability site I pulled up reiterates that to be standard train of thought.
The probability of one dice being a particular number is 1/6. You would assume that it would be twice as likely that either of two dice being a particular number, or 1/3, but this would be wrong.
Secondly, people also may confuse probability of 1 (or 100%) to mean that if you do something with a 1/100 chance 100 times, and then repeat this process many times, you will win once on average in each set of 100 attempts. Hence why /u/droodic said it would "usually yield." I don't think anyone is claiming or thinks that it is guaranteed to happen.
[deleted] ยท 1 points ยท Posted at 20:40:32 on May 25, 2016 ยท (Permalink)
I'm not so sure you fully grasp what intuition implies. If you are applying things you've learned in statistics or math courses, or even thinking deeply into the problem at all, that is no longer intuitive thinking. I didn't say that "anyone that claims they agree that 63% makes more sense to them as the answer than 100% is lying." or "anyone that understands why it is 63%", etc. I said anyone that claims that their basic intuition (which implies instinctual thought, not having been instructed on principals of statistics or probabilites, and by definition, not applying conscious reasoning) would have led them to an answer closer to 63% than 100% is either lying or desperately trying to sound smart.
You use the Monty Hall problem as an example. So you are claiming you immediately knew the correct answer to the problem without even having to think it through? If not, then you prove my point that that problem is also counter-intuitive. Again, that doesn't mean that you don't fully understand it in and out, or that you couldn't figure it out after breaking it down, but then it ceases to be intuition that helped you reach the answer.
My opening line of the last message clearly was directed to a comment earlier in the thread which I wrongfully assumed was from you. I'm quite surprised your intuition didn't deduce that one.
Wow, so I have a 50% chance of growing wings and flying away right when I submit this comment? I like those odds.
_mainus ยท 1 points ยท Posted at 16:38:33 on May 25, 2016 ยท (Permalink)
I was thinking more along the lines of the top of a bell curve
lazyant ยท 1 points ยท Posted at 15:53:14 on May 25, 2016 ยท (Permalink)
Think about rolling dice and getting a '6', if you roll it 6 times you are not getting a 6 all the time, but only some of the time, if you bet 1-1 with a friend that he won't get it 1/3 of the time you would be ahead in the long term.
nejc311 ยท 1 points ยท Posted at 18:00:41 on May 25, 2016 ยท (Permalink)
It's only because we usually forget about the possibility of multiple successes is why it's counterintuitive. In the lottery example, there is a small chance that we win more than once. Hence more than 50% chance of winning at least once.
It's really not, if you understand how e arises from the process of interest compounding upon itself, in the limit that that process becomes continuous.
For a process where something is repeatedly increased by an amount proportional to itself (compounding interest), e arises in the limit of that process becoming continuous. This statistics problem is constructed such that the probability of failure is inversely proportional to the #of trials. The probability of failing each consecutive trial is then a process of repeatedly attenuating a term by an amount proportional to itself (like the opposite of interest compiling upon itself). Therefore when this process of repeated attenuation is taken to the limit of being continuous (# of trials -> inf), the term 1/e arises in the exact same manner that the term e arises in compounding interest.
just like how e arises in x=x' or how 1/e arises in x=-x'
[deleted] ยท 1 points ยท Posted at 18:43:36 on May 25, 2016 ยท (Permalink)
It's just because of doubles and triples of certain outcomes occurring. You wouldn't expect every possible number in a set of 10000 to come up exactly once in 10000 random draws. as the number of draws approached something like 100 septillion, yea you'd expect each number to be drawn roughly equally. But 10000 is a very poor sample size when there are 10000 possible draws.
UBKUBK ยท 1 points ยท Posted at 21:01:44 on May 25, 2016 ยท (Permalink)
What does your intuition say should be the answer?
Mesonit ยท 1 points ยท Posted at 21:30:34 on May 25, 2016 ยท (Permalink)
100%, because the phrase "1 in x" makes me think that I should expect it to happen once in x trials, at least if x were big enough. I know it's probably basic statistics, but it still made me think twice about it.
UBKUBK ยท 1 points ยท Posted at 22:15:37 on May 25, 2016 ยท (Permalink)
This way of thinking about it might help: On average a win will occur 1 in a million times. So if you did groups of one million trials over and over again, let's say 1000 times you would get about 1000 wins. But they would be occurring randomly so sometimes a certain group of a million trials might have 2 or 3 wins. This means that some other groups of a million trials must have no wins.
Yeah his lottery example was bad. In a traditional lottery, if you buy 1 million tickets when the odds are 1 in a million, you've got a 100% chance of winning assuming each ticket is different.
Scratch off tickets are better because the chance of winning is random for each ticket. If the odds of winning with a single ticket are 1 in million, and you buy a million random tickets, you've got a 63% chance of having purchased a winning ticket.
just plug the probability and #attempts into the equation and see for yourself. the probability is that 1/x in the parentheses, and the exponent is the number of attempts
If there's a 1 in a million chance of winning the lottery and you buy a million (random) lottery tickets, you have a 63% chance of winning.
This particular example is a bit misleading. A lottery might have 1 in a million odds because the only possible plays are 1-1,000,000. So if you bought every single possible number you'd have 100% chance of winning.
wait so if I have a 1 in 100 chance of unboxing a knife in cs:go and I open 100 boxes I have a 67% chance of actually getting it ?
I'm surprised since I came up with this in school and asked how to calculate my chances to get it since you obviously doesn't have a 100% chance of getting it with 100 boxes and he said that you can not calculate it but with each try I just have a 1 in 100 chance.
[deleted] ยท 1 points ยท Posted at 18:39:59 on May 25, 2016 ยท (Permalink)*
IANA math person, but that would only be true if there are more than a million tickets actually available. If you buy all the tickets, and there's 1 winning, your chance is 100%. right?
if you get a million randomly generated tickets for one lottery (or any ticket for a million different lotteries) then this works. If you purposely buy different tickets to use up each possibility, then it will be higher (or 100% if you buy every possible combo). The key word is "random"
the key word is random - yeah if you buy every possible combination then it's 100%. If you buy one ticket in a million different lotteries, or a million randomly generated tickets for any one in a million lottery, then it's 63%
We need to get a lottery pool going. Of course we'll probably get no where near 63% chance, but if we got 10,000 people to play and we hit the jackpot, that is 8,000 grand each. If we got 1,000 people to play, we could win 80,000 each.
Excellent! Of course if a thousand people did this they would win 1 each on average. 37% may not win any, but some people would win twice or more, so on average it will be 1.
[deleted] ยท 1 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
So you're telling me that there is a 63% chance that everybody gets hit by meteor and that there is possible for there to be a 63% chance of winning the lottery
mkid75 ยท 1 points ยท Posted at 16:30:57 on May 25, 2016 ยท (Permalink)
this lady's and gentlemen is how RNG in video games work. Well played good sir, well played.
Zman14q ยท 1 points ยท Posted at 16:31:54 on May 25, 2016 ยท (Permalink)
Does that 63% also include the times you got struck by a meteor more than once in the 10,000 attempts? Which basically, in the long run, makes up for the 37% of the time you weren't struck?
Is there any real world proof of this? Like can we calculate the odds of getting hit by lighting, then look at a large enough group of people and find that 63 of them were struck by lightning?
gnutun ยท 1 points ยท Posted at 16:33:00 on May 25, 2016 ยท (Permalink)
Piggybacking on /u/NoCanDoSlurmz's reply, I think it would be helpful to explicitly provide for the case of the event occurring multiple times in the description. For example:
[I]f there's a 1 in 10,000 chance of getting hit by a meteor if you go outside, if you go outside 10,000 times, you have a 63% chance of getting hit with a meteor at least onceat some point. If there's a 1 in a million chance of winning the lottery and you buy a million (random) lottery tickets, you have a 63% chance of winning at least once.
arxv ยท 1 points ยท Posted at 16:34:29 on May 25, 2016 ยท (Permalink)
in what way, if any, can this be applied to gambling?
Wow I might be retarded. I always thought that if I was trying to do something that had 1% chance of success statistically I would achieve it in 100 attempts. TIL
If you do it 52 times (with replacement and shuffling so there's a fresh start each time) then there's a 63% chance of pulling the ace of spades at some point in the 52 tries.
dangz ยท 1 points ยท Posted at 16:52:49 on May 25, 2016 ยท (Permalink)
Alright cool. Thanks! I was tripping out like "Did I understand it wrong my whole life."
It's used in physics for nuclear calculations and in electricity. (basically any exponential monotone evolution)
sapador ยท 1 points ยท Posted at 16:59:09 on May 25, 2016 ยท (Permalink)
When I was 12 and playing world of warcraft I thought its 50%. I have no idea but it made sense to me, until a friend asked me why. Then I tried (1/2)*(1/2) and it wasnt 50% :P
tdug ยท 1 points ยท Posted at 17:04:31 on May 25, 2016 ยท (Permalink)
That being said, the lottery thing is kinda meaningless since if multiple people win a jackpot, they split the pot.
Edit: Also, is there a formula to determine the distribution of the amount of times the event would occur?
I figured this one out one night. I was so pumped it was 1-1/e I made a Facebook post about it. :) Which is my second greatest maths accomplishment, the greatest being solving the switching zero coin flipping problem. (With a lot of help from wolfram ;) ) Which is far cooler
[deleted] ยท 1 points ยท Posted at 17:05:18 on May 25, 2016 ยท (Permalink)
LOL I love your edit. Why the hell would you even have to explain that? Some people....
Funny you should mention that. Not that long ago, I wondered – if drop rate for an item in a game is 1/N, what's the probability of still not getting that item in N attempts. That probability is ((n-1)/n)n, which approaches 1/e, yes :) About 36.79%.
It also converges fast. For N=2,3,4,5,... – corresponding to drop rates 50%, 33%, 25%, 20% – the probabilities of not getting the item after N attempts are 0.25, 0.296296, 0.316406, 0.32768, ...
iIsMe95 ยท 1 points ยท Posted at 17:12:18 on May 25, 2016 ยท (Permalink)
I've gone outside for roughly 7,308 days. How likely am I to be hit be space debris?
I haven't taken statistics in ages, so you'll have to excuse my ignorance, but I always thought it was a common misconception that the more you do something, the higher the probability there is of a particular event occuring. Using a coin flip as an example, if someone flips 10 heads in a row they might think that the next flip is very likely to be tails, but isn't it still 50%?
I discovered this by chance on my own while playing Pokemon. I believe the Masuda method yields a shiny Pokemon from breeding with 1/1365 odds. It took me around 1500 attempts, so I was slightly unlucky. I actually drew out the curve to see what I could expect.
In other words, if I picked a million truly random numbers, between one and a million, I'll likely get approximately 63% of the numbers?
Is this at all related to the birthday problem, what are the odds of two people in the room having the same birthday for any number of people in the room?
I once proved that without knowing about it and felt really proud of it. Now it just makes me feel like all the good proofs are taken! My teacher was impressed though, I think(hope)
There is a big mathematical difference between a 1 in 100 chance tried 100 times (99100) and a 1 in 1,000,000 chance tried 1,000,000 times (999,9991,000,000).
Doesn't everyone go outside at least 10,000 times in a lifetime?
perkco ยท 1 points ยท Posted at 18:18:21 on May 25, 2016 ยท (Permalink)
Can someone explain to me the implications of this for expected values? I would have thought that if I had a 1/x chance in each attempt (with a payoff of 1 if successful), and I did x attempts, my expected value would be 1 (i.e., 1/x * x). Does this mean that, instead, the expected value of x attempts is .63?
So what you're saying is that if I buy a million lottery tickets I will become a millionaire?
[deleted] ยท 1 points ยท Posted at 18:22:24 on May 25, 2016 ยท (Permalink)
There are a lot of interesting math shortcuts dealing with large exponents of numbers near 1 which you can do in your head with a little practice. They're the kind of shortcuts that make your friends think you're the next Feynman. MIT has an excellent (free) book and course online containing many of these "tricks."
[deleted] ยท 1 points ยท Posted at 18:26:19 on May 25, 2016 ยท (Permalink)
In the same vein is the game show statistic. The game is to guess which door the car is behind, door 1, door 2 or door 3. You pick one and the host starts opening the other doors. The 1st one has no car behind it. He adks you if you'd like to switch your answer. Should you? The answer is yes. You now have a 1/2 chance of winning instead of 1/3 chance. It's hard to wrap your head around this fact but it's true
[deleted] ยท 1 points ยท Posted at 18:27:24 on May 25, 2016 ยท (Permalink)*
It's a simplified version of the Probability Mass Function for the Binomial distribution. Have a look on Wikipedia and keep in mind that for this example k=0.
[deleted] ยท 1 points ยท Posted at 18:39:11 on May 25, 2016 ยท (Permalink)
So then what? I get a 1 in 1.58 chance that I'll get hit by a metior if I go outside 10,000 times. So if I go outside 15,800 times do I now have a new 63% chance of getting hit by a meteor? Am I going to dilute the possibility of ever getting hit by going outdoors more? How does anything ever happen?!
EDIT: oh shit this comment blew up and I remembered a way better fact later.
If you add up the numbers 1 to 36, it adds to 666.
AND if you draw a perfect pentagram, the internal angles of the star are all 36 degrees.
How the fuck did I not talk about my own damn number.
Eh, not really. It's =1 by definition. The factorial is used to calculate the number of ways a set of numbers can be arranged (permuted).
So, if you have a set of 3 numbers, [1,2,3] you can arrange them 6 ways (123, 132, 312, 321, 231, 213), so 3! tells you how many permutations or arrangements you can have. A set of n numbers can be arranged in n! ways.
if you have a set of 'no numbers', or as it is properly called the Empty Set, n=0. You can only arrange (permute) the Empty Set one way - [] so n!=0!=1
[deleted] ยท 1 points ยท Posted at 01:08:40 on May 26, 2016 ยท (Permalink)
im pretty sure a factorial is all the numbers below and including the numbers multiplied together.
That is the way you calculate it, but it doesn't explain why 0!=1.
[deleted] ยท 1 points ยท Posted at 21:57:29 on May 26, 2016 ยท (Permalink)
Number phile did a good job of explaining it. this link
[deleted] ยท 1 points ยท Posted at 23:00:00 on May 25, 2016 ยท (Permalink)
numberphile did an amazing job explaning why 0! = 1. It's because of a pattern in factorials.
5! = 6! / 6 = 120
4! = 5! / 5 = 24
3! = 4! / 4 = 6
2! = 3! / 3 = 2
1! = 2! / 2 = 1
0! = 1! / 1 = 1
factorial is the product of all the integers below and including a number. But a factorial can also be then number ahead divided by that number. Hope that explains why. If you still don't get it go to this link by numberphile youtube channel.
Or, stepping away from mathematical purity and into logic, factorials can be used to describe the amount of ways something can be arranged. A set with 0 items can only be arranged one way (as opposed to a set of 5 items, 1,2,3,4,5 , which can be arranged 4,2,3,1,5 for example) and the factorial mirrors this.
'this' is base 36 for 1375732, per Wolfram Alpha, which also gives 1375732! as 1.22433069887918754190508636513318769451534501450378357285932310011240528537021063229328167365626537612760027381027635721490513568578769889176366164801250721892503278930162368497443723597943081636085321499675375050080224972046615350639180719588150311524155989379588960968564907643809003381862707661500245161757608237729511162492680906126617328609184841959277430994780111890577964855088263106282897810276315011511287358861073115376746502352144636310โฆ ร 107847508
DearKC ยท 1 points ยท Posted at 20:18:09 on May 25, 2016 ยท (Permalink)
On the other hand, you could have put the arithmetic into your calculator. If your spm on a 10 key is fast enough, you get the # of seconds in a week: 3628800 and 10!: 3628800. Proof. IT's not good for understanding how it works, merely that it does work. but I'd argue it's faster than what this guy did :)
I was going to try to think of an example for my favorite maths fact, but /u/Mirrorboy17's proof depicts it better than any of the examples I had in mind could:
With virtually all math problems you work with, there are multiple ways to break the problem down into steps -- multiple paths to the solution you seek. But unlike a more subjective field, the path you take won't influence the solution; all techniques, assuming they are valid, will reach the same answer, every time. You can completely adapt your approach to your own preferences, and still arrive at the same answer as someone doing a completely different approach. Every valid approach is equally so.
Maths are the language of the universe, the one true objectivity, and the closest thing we'll ever see to absolute perfection. They're beautiful in their own way.
Yes! Exactly this! Back when I was in college I used to tutor math at one of the local public libraries (K-12 students). During my first week, there were a few times I noticed that a kid would solve a problem in a completely different way than I would do it. Because of this, I started having kids try to solve the problem from beginning to end to the best of their abilities then showing them where they went wrong instead of walking them through the way I would do it which could potentially just confuse them more. I always got really excited when a student and I would get the same answer using totally different methods. It was cool to see possible applications of concepts above their level too like when the younger kids had to add lots of numbers instead of just multiply or high school geometry problems that could be solved using calculus.
kyune ยท 1 points ยท Posted at 06:12:42 on May 26, 2016 ยท (Permalink)
Six weeks is Math's happy little accident. Bob Ross would be proud.
ewic ยท 1 points ยท Posted at 15:54:14 on May 25, 2016 ยท (Permalink)
Umm. I didn't take "proof" or "logic" or whatever. And certainly no advanced math courses in college. What exactly is happening here. Where are we getting 60 x 60 x 24 x 7 x 6.edit: Okay I got this, it's hours x seconds x minutes x days x weeks. It's 3,628,800 (seconds in 6 weeks), which happens to equal 10!, after I manually multiplied 1-10. But still confused on my part below
Why are we running a bunch of calculations to pull out numbers 1 through 10. What does that "prove" and what are these numbers sourced from (e.g. the 60 = 2 x 3 x 10)
Edit2: holy shit I get it now. That's weird and cool.
Wait so I never did high level math in school.... the ! operator just means multiple this and every real whole number before it? So 5! would be 1x2x3x4x5?
Yea I ended up reading some crazy shit with playing cards and 52!. Something about walk around the world emptying the ocean a drop at a time and stacking the paper for each ocean emptied and stacking it to somewhere in space and then I smoked a joint and brought my dog for a walk.
The definition of n! can also be written as n! = n*(n-1)!. By definition, 0! = 1 because it's impossible to have positive integers less than 0. Every other factorial can be found by using this as a defined value. This also makes it easier to see why the factorial for negative integers is undefined since it would necessarily be the case that 0! = 0*(-1)!. If (-1)! were a real number, this statement could not be made true no matter what (-1)! is; therefore, it must not be a real number.
[deleted] ยท 1 points ยท Posted at 00:13:44 on May 26, 2016 ยท (Permalink)
Coincidence. We already divided time into nice numbers with lots of factors like 24 and 60, we just happened to pick just the right nice numbers and pick 7 days for our week to fill in the gap.
And just to make it clear that the coincidence isn't all that unlikely: if our week only had 6 days, then 10! seconds would be exactly 7 weeks instead, and it would still look faszinating.
And there would be other fun coincidences for different numbers of hours per day or minutes per hour.
I think you'd have to go ask the ancient Babylonians or something, I think they started at least the 60 minutes in a degree/hour thing, probably also 24 hours in a day. 60 seconds per minute is a much more modern thing, but was a direct imitation of the minutes per hour. No idea about the 7-day week. Romans? Greeks? Babylonians?
Kind of a coincidence, but kind of not. Time bases were chosen to be highly divisible (e.g. 12 can be divided evenly by 1, 2, 3, 4, 6), a side effect of which being that they have many factors.
To get 10!, we need to find the numbers 2 through 10, or the factors of these numbers. That gives us eight 2s, four 3s, two 5s, and a 7. The 7 is easy, that's days in a week!
A day can be separated in 24 hours, which can be separated into three 2s and a 3. (5, 3, 2 left). Hours are separated into 60 minutes, which is two 2s, a three, and a 5 (3, 2, 1). Same can be said for seconds ( 1, 1, 0). That leaves a factor of one 2 and one 3 left. 2*3 = 6 weeks.
Basically, 10! is the first factorial that contains all of the factors needed to build up to a "number of weeks" value (to get that second factor of 5). Once you factor it all out, the remaining factors are the number of weeks you have. You can do something slightly less impressive with 5! being exactly 2 minutes, for example, since 5! contains all of the factors needed for a minute (2, 2, 3, 5).
lengau ยท 1 points ยท Posted at 17:08:17 on May 25, 2016 ยท (Permalink)
The choice of 6 weeks is deliberate to fit the one missing number in the factorial (6)
Can someone explain what just happened here? I understand how this works, but this isn't how I did it growing up. Is this the preferred method? It seems like a lot more effort to me.
I don't know about preferred, but I thought checking all the factors was brilliant. This is a great way to do it if you didn't have a calculator on hand.
And because it shows how they're equivalent without doing any real arithmetic, I think it's more intuitive.
THIS is what blows me away about math and numbers. Everything's modular, you can just break it up into different chunks to see them in a different way. Thanks for proving that the way you did, that was pretty cool.
I read all the comments and I'm still not sure if this is a correct way to prove the 10! or just a messy toss-around with the numbers that somehow turned out right.
[deleted] ยท 1 points ยท Posted at 19:17:43 on May 25, 2016 ยท (Permalink)
Isn't this the more complicated way of solving this? I would have just done 1 x 60 x 60 x 24 x 7 x 6 but I guess I did take longer to write down and keep track of where I was/use a calculator
[deleted] ยท 1 points ยท Posted at 20:34:53 on May 25, 2016 ยท (Permalink)
I also figured it out but I did it the lame way:
Calculator - 10!
Calculator - 60602476
Both equal 3628800.
[deleted] ยท 1 points ยท Posted at 20:42:16 on May 25, 2016 ยท (Permalink)
This actually demonstrates the reason we have 60 seconds in a minute and 60 minutes in an hour.
When the Babylonians wanted to divide up time, they wanted highly divisible numbers. 60 was chosen because it's divisible by 2, 3, 4, 5, 6 and all the cofactors.
in math "!" is the symbol for factoral. which is essentially how many different ways you can arrange a group of things. you can arrange a group of 10 objects 3,628,800 different ways. so 10!=3,628,800 and there are 3,628,800 seconds in 6 weeks: 6(weeks) x 7(days per week) x 24(hours per day) x 60(minutes per hour) x 60(seconds per minute)= 3,628,800
While this isn't a proof our friend /u/Gstreetshit will find that the exercise of laying out all the possible permutations of A,B,C,D with pencil and paper will make everything clear.
There are 4! = 1 x 2 x 3 x 4 = 24 possibilities. Try it!
You've got 10 "slots" to fill with 10 objects in any arrangement, and to make it easier we're gonna do them one at a time, starting with the left one.
For the first slot you can put any of the 10 numbers, so we have 10 ways to arrange the first slot.
For the second slot you put any of the nine remaining numbers. Meaning the first 2 slots can be arranged in 10*9 different ways.
For the third slot there are 8 numbers remaining, so the first 3 slots can be arranged in 10 * 9 * 8 ways
And you continue like this, and end up with 123456789*10 (EDIT: 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 formatting is a pain sometimes) in the end. This is what 10! means, and if you try putting in a calculator you're gonna find it equals 3,628,800
The ! symbol following an integer is called a factorial. It's really simple.
5!= 5x4x3x2x1
6!= 6x5x4x3x2x1
10!= 10x9x8x7x6x5x4x3x2x1
And so on. As you can see from the thread, these factorials can grow drastically in very few increments. 10! seconds equals six weeks while 14! seconds is over 2770 years.
If you're a physicist, you're probably more interested in the fact that ten pi million seconds is approximately a year, to within 0.5% tolerance.
Ten pi million = 31415926.53589... seconds
One year = 60 * 60 * 24 * 365.25 = 31557600.0 seconds
Difference = -141673.4641099982 seconds
Error = -0.0044
Percent = about 0.4% less than expected
Bob and Joe were sitting in their math class one day when their teacher suddenly shouts โPop quiz! If you donโt answer this question correctly, then you will fail the classโ
Both Bob and Joe are taken aback.
The teacher turns to Joe, โJoe! Quickly, how many seconds are there in six weeks?โ Joe takes a few seconds to think about it, and then with a smile on his face quickly exclaims, โthere are exactly 10!โ
The teacher then turns to Bob, โWhat do you think, Bob?โ Bob is perplexed with Joeโs answer. How can there only be 10 seconds in six weeks? However, not being great at math, Bob decides to agree with Joe and says, โthere are exactly 10 seconds in six weeks.โ
The teacher then turns back to Joe with a smile, โGreat work, Joe. You pass!โ Then she turns to Bob shaking her head. โBob, looks like I will be seeing you again next year. You fail.โ
Given how bad my maths is and the fact I barely passed at the lowest level, I genuinely thought you were just really excited about there being 10 seconds in a week and my thinking, "well I know that's not right.."
10! seconds
DoWhile ยท 2 points ยท Posted at 14:33:56 on May 25, 2016 ยท (Permalink)
It's not quite as math-y as the explanation of this one below, but there are approximately pi * 107 seconds in one year. That's accurate to within 0.5%, so it's perfectly acceptable when doing quick estimates of things.
also something i ended up at after thinking about this, is that if you take n!, then the number of times 2 is a factor of n! tends to n as n tends to infinity.
e.g. 2999987 is a factor of 999999!
You can do similar things with other prime factors, p;
pn/(p-1) is a factor of n as n-> infinity
so for the first few primes (p:number of times p is a factor); 2:n 3:n/2 4:n/3 etc
Am I the only one who read 10!, and yelled TEN in my head, as if it was meant as an exclamation point?
elee0228 ยท 4307 points ยท Posted at 12:34:05 on May 25, 2016 ยท (Permalink)*
International Paper Sizes (e.g. A4) use a 1:โ2 ratio. If you cut them in half lengthwise crosswise, the same ratio will be maintained. It's great for scaling up or down.
That, the fact that A0 has an area of 1 m2 , and that each subsequent size is just half of the previous one is all you need to define the whole series of sizes (A1, A2, A3, ...).
Yeah, seems silly at first, but what he/she meant is that paper stock density is defined in grams per m2 and knowing that A0 is exactly that allows for easy calculation of all other formats.
So we can easily calculate that single sheet of A4 is 5 grams, or a 96-page notebook weighs 240 grams. Or that two hundred blank A8 business cards made from 350g stock weigh 340 grams. It's cool when you work in printing-related industry :)
gnorty ยท 3 points ยท Posted at 23:33:32 on May 25, 2016 ยท (Permalink)
Plus, the weight of an A0 sheet of paper is equal to its density (in kg/m2 ).
Is "density" really the name for this? surely density is kg/m3. the weight of a piece of paper could be related to density (ie the fibres are closely packed with less air) but equally could be the thickness of the sheet (a very airy sheet 1mm thick might weigh more than a tight packed sheet 0.01mm thick.
If density really is the name for that, then OK I guess, but it does seem like a meaningless value
[deleted] ยท 1 points ยท Posted at 10:48:42 on May 26, 2016 ยท (Permalink)
It's how much paper (or cellulose, or whatever) goes into this paper. And because "3" is hard to compare, it's set it into some relation.
density is usually really good for this, but if you want to calculate "how heavy will this letter (package) be and how much postage must I pay" or want a tangible way of comparing paper, "grams per mยฒ" provides useful.
Of course "thickness" is technically wrong, but what should be meant in this case is "strength" of the paper, not unlikely in lack of a better english word, as the "a4"-denomination is commonly used in europe, but only to a lesser extent in the USA.
The further benefit of "grams per mยฒ" is the above demonstrated calculation of weight, an "Ax" size paper with "y g/mยฒ" will weigh y / 2x gram.
this comes in handy when some angry officer comes into your office and yells at you "give me 300 A4 pages, IMMEDIATELY!". no need to count that, just tell him bitch i got this, then give him (300/16*80)g of paper.
jf908 ยท 1 points ยท Posted at 15:55:51 on May 25, 2016 ยท (Permalink)
Doesn't that depend on the thickness of the paper?
The density /u/DCallejasSevilla is quoting is "mass per unit area," aka "area density." Regular "density" is "mass per unit volume." To get from "density" to "area density," you multiply by the thickness. That's how the thickness comes into play.
jf908 ยท 2 points ยท Posted at 16:30:19 on May 25, 2016 ยท (Permalink)
The B series is the geometric mean of the A series, where B1 is between A0 and A1. The C series is the geometric mean of the A and B series, where C1 is between A1 and B1.
Its not exactly that simple. If I told someone to make a piece of paper with an area of 1m2 without any other instructions, I'd probably get 1 sq. m of paper, which doesn't conform to AX ratios.
Right. But the parent comment to mine states that the aspect ratio is โ2 .
Put these two pieces of information together, and consider a rectangle (OK, I forgot to say it's a rectangle) with sides a and b.
The aspect ratio means that:
b = (โ2 ) a
The area gives usthat:
a b = 1 m2
solving for a we get:
a (โ2 ) a = 1 m2
a2 = (1 m2 )/(โ2 )= (โ(1/2)) m2
a = (1/2)1/4 m = 0.841 m
With the aspect ratio and the total area you get A0, with the third fact (that each subsequent one is half the area of the previous one) you can construct the rest.
Posters aren't usually made with standard paper. They're either on a glossy specialty paper or, for a presentation, they're going to be custom made by a printer.
marnues ยท 1 points ยท Posted at 21:47:28 on May 25, 2016 ยท (Permalink)
I can arrange a page many ways to be 1 m2. One of the dimensions or a ratio would be helpful too!
Yeah, it seems to be a pretty obscure fact. I knew of course that A4 was half the size of A3 etc. but the actual area of them being a proper number I had no clue.
[deleted] ยท 7 points ยท Posted at 22:12:45 on May 25, 2016 ยท (Permalink)
[deleted]
Ray57 ยท 6 points ยท Posted at 22:29:06 on May 25, 2016 ยท (Permalink)
I am all for the world dominance of the metric system
The Imperial system exists as "soft" protectionism for the US manufacturing sector.
It's a battle that can't be won by scientists, but by diplomats with trade deals.
It's not so nefarious as all that. Two two important things are true.
(1) Changing to the metric system is expensive
(2) US is principally a consumer, not a seller. The buyer gets to set the standards.
When the trade balance shifts (and it really will) US manufacturers will have to meet their buyer's standards if they want to compete. Everything will standardize through vertical integration simply under the drive of supply and demand. But it just isn't going to be be worth it to anyone to make the change, no matter how sensible it is from a maths perspective, until the cost of not doing it hits the bottom line.
Most scientists, engineers, and academics would prefer to use the metric system. It's not even trade deals or consumerism that prevents the switch; it's the sheer amount of infrastructure and existing machinery that was built using the imperial system. Specifically tooling for and maintenance equipment would have to be converted from imperial to metric which is just about impossible and ungodly expensive. The united states is proliferated with drill bits, end mills, material thickness, and fastener sizes in fractions of an inch without a metric equivalent. It seems that reddit believes switching to metric is much easier than it really is.
Ray57 ยท 1 points ยท Posted at 02:57:20 on May 26, 2016 ยท (Permalink)
Well that might be an argument. Except almost every other country from highly industrialised western countries to third-world shit holes have managed to do it.
Never attribute to incompetence that which is adequately explained by greed.
Aside from the UK in 1965, there hasn't been a metrication by a country that has been historically known for manufacturing in the past 50 years. My original point still stands that conversion to metric is extraordinarily difficult and expensive for the United States, primarily because we've waited so long. It's not as easy as telling teachers to stop teaching imperial; private businesses and whole industries have invested millions of dollars into tooling that would be obsolete after the switch. Everyone on reddit might be up for a switch, but the metric/imperial argument affects them so little compared to countless businesses and the entire country's infrastructure history and standards.
Ray57 ยท 1 points ยท Posted at 03:45:49 on May 26, 2016 ยท (Permalink)
Well then what about the UK then?
What magic do they have that you don't?
No-one says it is easy. We choose to do these things because they are hard.
[deleted] ยท 14 points ยท Posted at 17:28:33 on May 25, 2016 ยท (Permalink)
Not really metric, if you did it in furlongs it would be true as well. However, since 220 square yards of paper is a lot of paper, we use the meter which is large enough to be usable when cut in halves or quarters, but small enoughto be kind of absurd but still useful
It's more of a math thing than a metric thing
rtomek ยท 2 points ยท Posted at 22:53:59 on May 25, 2016 ยท (Permalink)
I wasn't aware the metric system considered fractions a thing
eh? Fractions and decimal points are just mathematical notation. It's certainly easier to use 0.5 m2, 0.25m2 and 0.125 m2, but nobody stops you from notating in fractions.
itz4mna ยท 3 points ยท Posted at 19:05:11 on May 25, 2016 ยท (Permalink)
Not really, it would be just as reasonable to define A0 as a square yard. It wouldn't break the scaling properties.
every little piece of the imperial system can be fixed within its little universe; but there is no overall connection with everything else like there is in the IS (which ISO uses in this case).
This is the hardest thing to explain to Americans: yes, inches work, feet work, cups and pounds and Fahrenheit. But there is no relationship between them, making any sort of work more complex than cooking a lot harder than it could be.
AshtarB ยท -4 points ยท Posted at 20:56:16 on May 25, 2016 ยท (Permalink)
The metric system isn't perfect, either, but at least it's an international standard. It's a large leap forward from Imperial, at least.
To begin with, it's based on 10, which, although adequate for multiples, doesn't really work for divisions of the base unit. You would expect a metre to be divisible by 3, but the decimal system doesn't really allow that. Base 12 would be better, but our number system is already base 10, so it would be more impractical.
Yes, some of these conversion factors are very close to a power of ten. There's the density of water at 999.972 kg/m3, and standard gravity at 9.80665 m/s2. It would make sense in that respect to use the decisecond, decimetre and kilogram as the base units to keep these as close to 1 as possible, or to use 98.0665 mm and 943.083 g to make them exactly 1.
Then there are the conversion factors that don't mesh well with decimal, like 4184 joules to raise 1 kg of water 1 Kelvin. Fahrenheit has its 0 and 100 points in a range comfortable for humans. Celsius doesn't, but it makes up for it by having 0 and 100 be the phase changes of water. But even across the earth's surface, gravity is much more stable than the boiling point of water, which can go under 80 ยฐC in more mountainous regions. It seems better to me to keep the freezing point at a round absolute temperature and let the boiling point be free.
But that's just an idealist's dream. SI is here to stay.
You can't make a system that has nice conversions for every physical scenario. It's impossible. And there is nothing scientifically special about water that demands we define units in terms of it. In fact, as you said, water is not perfectly consistent and is a terrible way to do science. Your system has to be arbitrary, but as long as it's based on something consistent, you're fine.
Everything SI has some physical definition, and it's not all about water. In fact, if anything has to do with water, it's because water is a common, stable substance that allowed scientists in the past, with their imperfect tools, to base units off of it. But now that we have better measurement devices and know that the properties of water change very easily, we've based the units on something else, something more consistent in nature.
Both the SI and the imperial system are based off of something consistent (or are in the progress of being so), which is why they both work. The problem is that the imperial system is literally defined in terms of SI units. A meter is defined in terms of the speed of light, but a foot is literally defined in terms of meters. Not only is it unnecessary, but it also takes away your ability to use a simple decimal system to scale your units or convert between different SI units (like meters and and newtons).
Finally, yes, the decimal system is imperfect. Base 12 is "better" (more convenient when working with certain simple fractions), but base 10 is definitely here to stay. And while base 10 isn't very nice when it comes to thirds, it's way better than most of the ugly imperial conversions.
AshtarB ยท 2 points ยท Posted at 04:55:11 on May 26, 2016 ยท (Permalink)
Yes. This was what I meant. The SI isnโt perfect, but itโs a lot more practical when actually doing calculations than the imperial system.
The only relationship with water is precisely "conceptual" definitions. A second is conceptually the 86400th part of a mean solar day, a metre is conceptually the ten millionth part of the distance from the poles to the equator, a kilogram is conceptually the mass of a cubic decimetre of water, and a kelvin is conceptually a hundredth of the difference between the freezing and boiling point of water at sea level.
The actual definitions have been refined several times, to keep up with the precision and accuracy that modern tools are capable of, but that obviously introduces extraneous conversion factors if you want to keep the units within the range of error of the previous definition.
But that doesnโt matter anymore. If a system is consistent with the physical world by itself, itโs that much better than a system defined in terms of another, and the SI is already here, and itโs an international standard, so trying to reform it puts you out of step with the rest of the world.
Those "conversion factors" are just as random as the random states/points you chose to look at them.
You chose to pick one specific gravitational accelleration out of the infinite values you could find for it just on this planet.
You chose one of the infinite densities that water can have. Sure, I get that you picked a popular one that water has for a very specific (randomly chosen) set of parameters. But even if you would define that to be exactly 1, a second later the very same water would have a slightly different density.
Same goes for the specific heat capacity you named for water for which you chose a value of 4184 J/kgK. water can have that value, but it is not a constant.
So what exactly would be the point of redefining base units just to get some derived functions to have a value of exactly 1 for a very specific set of parameters?
itz4mna ยท -5 points ยท Posted at 20:41:19 on May 25, 2016 ยท (Permalink)
I think the way we do it in the UK is pretty good, we use both depending on the situation. Kilometres are kind of a crap measurement for road distance, a car typically travels around 60mph or a mile a minute, the average man walks around 3mph or a mile every 20 minutes. In metric that works out to driving 100km/h so a kilometre every 1.7 minutes, hardly a convenient number. If want to design a car you'd use metric measurements. Imperial units which developed from real-life use tend to be much more relatable to humans than metric ones which were mandated by the intellectuals of the French revolution, which is why for human things like body weight and height are more often than not given in stone and feet in day to day life, if you're at the doctors getting a bone fixed then they'll use metric.
The other problem I have with the metric system is that 10 is a shitty choice of number to base a system of measure on. It only divides cleanly by 5 and 2. Compare that to say the foot of 12 inches which divides by 2, 3, 4 and 6. The base-60 measuring system we use for time which the French famously tried to get rid of is even better, 60 divides by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.
I won't defend Americans using volume measurements for literally everything in cooking though, that's just silly.
The strength of base 10 though is how easy it is to multiply and divide. Take a square metre. You know a metre is 100cm, so a square metre ought to be 10,000cm2. Which is easy to do and most people can somewhat easily do in their heads if they think about it. In a base 12 system though you'd run into all sorts of problems trying to convert, doing for example 120x120=14,400 and similar, which far fewer people can do in their heads.
Not really, units are human constructs and can be redefined. The second and meter were already redefined to natural and repeatable phenomenon, they were just refined very very close to their original values. Nothing is stopping us from base 10, or 100, time except convention.
[deleted] ยท 1 points ยท Posted at 11:24:26 on May 26, 2016 ยท (Permalink)
It's not the earth we have to change, but our way of counting time passing. You have to keep in mind that even with 10 hour days, it doesn't change the minutes or seconds.
1 hour = 60 minutes.
1 minutes = 60 seconds.
86400s in 24 hours. We could make one minute 100 seconds long, and an hour 100 minutes long, but then we would only have 8,64 hours in a day.
What if we change what a second is instead? Lets say we use the new Second (nS), which is slightly faster than the old second, so there is 100 000 seconds in a day (that way there would be 10 hours per day), the new second would be ca. 1,157 times faster than the old second.
The reason we count time as we dose is because of historical reasons and some old mathematics using 60 as a base (which is also why there is 360 (or 60x6) degrees in a circle. And changing it would mean changing all clocks, time measuring equipment we have worldwide. It could be done, but so far no one has agreed or suggested doing that.
itz4mna ยท -2 points ยท Posted at 21:37:04 on May 25, 2016 ยท (Permalink)
You'd have to be pretty awful at maths to not be able to realise 122 is 144 and therefore a square foot is 144 square inches. If people were taught from primary school how to do it they'd have no problem, I mean for most of our history we used ยฃsd money which is arguably harder to work with than feet and inches.
Lol, look at international tests and you'll see generally Europe is ahead of the US, by quite a gap as well.
[deleted] ยท 1 points ยท Posted at 11:29:01 on May 26, 2016 ยท (Permalink)
I think he was talking about people in US being bad at math, as in agreeing with you.
[deleted] ยท 3 points ยท Posted at 21:39:56 on May 25, 2016 ยท (Permalink)
All of those are only related to what you are used to. I can just as easily figure out how long a trip somewhere will take based on kilometers because I'm used to that. Using multiple units for the same thing is very counter productive.
And where I live, we talk about distance in time. I don't live thirty miles away from my parents. I live about forty five minutes away from them. Oh*o is about an hour away. I lived about fifteen minutes from school on my bike.
You're argument here is largely based on life experience. It's measures you have used for a long time that are familiar and comfortable to you.
I've grown up exclusively with metric measures. These are natural second nature to me.
Why divide your hour up to a third to get one mile? My average walking speed is pretty much bang on 5km/h. 1km every 12min. My car at 100km/h will cover 25km in a quarter hour. My point being that we can all find nice points on both scales that work for us in our everyday life, but these do not contribute to an effective argument for or against.
As it happens I quite like imperial. There's an extra mouth full in each beer pint :)
Thank you for explaining the way England uses the Imperial system. I always knew you guys used a sort of mix, but wasn't sure if it was just because of everybody around you using Metric. As an American, I recognize how much better the Metric system is in scientific applications, but all we've got over here are 2L bottles of soda.
Interesting with the stone measurement too. Over here we just use pounds for everything.
itz4mna ยท 4 points ยท Posted at 21:10:44 on May 25, 2016 ยท (Permalink)
No worries! Stone's only really used for body weight, I think it's from agriculture but that's all metric now. Most stuff's either given in kilograms or pounds depending on what you're buying and who you're asking.
Good thing we have computers and "ease of unit conversion" is kind of a moot selling point! The Imperial System has survived the ages in which it might have been killed, sorry.
Also, it has nothing to do with what area you choose for a piece of paper, which will likely never be subject to unit conversions.
Edit 2: I will buy reddit gold for anyone who can show a relationship between degrees Celsius and another SI dimensional base unit!
What is the relationship between Celsius and other SI units like: meters, liters, kilograms? There isn't one.
And I'm a chemist and use SI every day.
Edit: instead of downvoting I'd really like people to think back to their high school education. The dimension of temperature is not relatable to mass or length. Nor the other four base dimensions of current, luminosity, time, or moles.
Celsius came 50 years before the base ten metric system and 200 years before the SI system was codified...
We start with 1 meter, which was originally thought to be 1/40,000,000 the circumference of the Earth. This is a unit of distance. It is used in fractional sizes of the original (nanometre, micrometre, millimetre, centimetre, metre and kilometre are typical). Since these are all decimal fractions of the original, translation between them is trivial, and comes down to where you put your decimal point.
Lay two of those orthogonally and mirror across the endpoints' diagonal, and you get 1 square meter. This is a unit of area. As with the metre, it is also used in fractional sizes, typically square millimetre, square centimetre, square metre, hectare (10,000 m2) and square kilometres. Again, since they are based on decimal fractions of the original metre, translation becomes trivial and comes down to where you put your decimal point.
If you take the 1 meter square, and place another meter orthogonally to the corners, you end up with a 1 meter cubed box. This is a unit of volume. As with the others, it is based on fractions of the original metre, typically mm3 (1/1,000,000,000 m3), cm3 (1/1,000,000 m3), m3 and km3 (1,000,000 m3). And as with area, there is a unit that is atypical but still fractional, the litre, which is (0.1 m)3 or 1/1,000 m3 or a (10 cm)3.
And if you take the 1 metre cubed, and fill it with water, you have 1 metric tonne (1000kg). Divide each dimension by 10, or the volume by a thousand (0.1m x 0.1m x 0.1m = 0.001m3) and you've got a litre of water, which weighs 1 kg. Divide that by a thousand, and you've got a millilitre of water, which is of course 1g in weight and 1cm3.
Then get that Kg you just defined and accelerate it at a rate of 1 meter per second squared. Congratulations, you just applied a Newton of force. Then of course hold that Kg at a constant speed of 1 meter per second against the force of 1 Newton and you are exerting 1 Watt.
Then get that water you've been pushing around, freeze it at sea level and call that 0; now boil it at sea level and call that 100. Divide the resulting scale in 100 equal parts and you have the Celsius scale. Extend that down to -273.15, call that absolute 0, and you have Kelvins :)
I believe his point is that technically there isn't a better reason as to why water is used other than it being what we use. It's better than most options but still arbitrary.
That is close to my point. Celsius/centrigrade has no connection to the other units/dimensions in SI, no temperature scale does. But apparently you can't point that out without people getting mad.
If you took your Newton of force, and a gram of water, then moved the water over a distance of 4.182 metres (at NIST Standard Temperature and Pressure, and with zero losses other than into the water), you have raised the temperature of the water by 1 degree celsius (and expended 4.182 J, and 1 cal).
Take this interval and take 20 away from the starting temperature. You now have water's freezing point. Multiply the interval by 100 and add to the water's freezing point, and you now have boiling (at the NIST standard pressure). Take this 0-100 scale, and you now have Celsius.
EDIT -
An alternative is to climb vertically in the atmosphere until you reach the base of a cloud. For every hundred metres of altitude gain inside a cloud, the ambient temperature will drop 0.5 degrees Celsius (moist adiabatic lapse rate). Alternatively, if you are in a desert at sea level in the middle of summer (so a really dry air parcel above you), you will lose 0.98 degrees Celsius per 100 metres of altitude gain (dry adiabatic lapse rate).
Of course, if we're being entirely consistent, it's an effect of pressure, but altitude is much easier to measure given our starting point of derived values.
it kinda doesn't work tho. a standard architectural drawing size is 24x36, and a true half scale of that is a 12x18, which is a non-standard paper size. A1 to A3 scales perfectly.
Do people do architectural drawings on printing paper? I know nothing about that. Also the dimensions you listed aren't ANSI standard anyways, so it isn't surprising that half of a non-standard size is also non-standard.
I was just kidding, but as a civil engineer I can tell you that the common practice is to use 60x90cm to print blueprints, at least the ones we handled to our clients. The ones we used for revision were mostly A5 sized.
4 times actually. My point is that the ISO scaling has nothing to do with the SI base ten system.
And if you forgot my original point it is the same with the ANSI system. Double the width to get the new length.
atyon ยท 1 points ยท Posted at 22:42:48 on May 25, 2016 ยท (Permalink)
It can't be the same system, because the DIN/ISO system only works with a ratio of 1:โ2. With any other ratio, you can't repeatedly fold the paper to get two of the next smaller size.
If your aspect ratio isn't 1:โ2, folding just once will change the ratio.
I never claimed it was...Just that the 1/2x relationship with area also holds in ANSI printing sizes.
atyon ยท 1 points ยท Posted at 23:01:40 on May 25, 2016 ยท (Permalink)
Ah, the confusion starts because you talked about letter and legal, which have none of these properties.
The ANSI series (containing letter and ledger, but not legal) is actually interesting, because it alternates between two different ratios. Which isโฆ kinda neat, but not the same.
But that's not the point of ISO. The A-series sheets never change aspect ratio, meaning you can scale them up and down without any losses or distortions. However, going from 8.5x11 to 11x17 changes the aspect ratio, meaning that if you enlarge or reduce, either the image will be distorted or you will have blank spaces along one side.
For this reason, most photocopiers in the rest of the world have an 'A3->A4' button, useful for shrinking two pages of an A4 book side by side to fit on one sheet of A4 with no cropping or stretching. That is the whole point of maintaining the 1:sqrt2 aspect ratio
That is true, but I wasn't addressing that just the halving. Every two steps in ANSI has the same aspect ratio though.
I haven't had to photocopy and shrink enough things for a function like that too be useful, and with computer printer scaling it isn't an issue at all.
[deleted] ยท 1 points ยท Posted at 18:24:32 on May 25, 2016 ยท (Permalink)
A: 8.5" x 11" (letter)
B: 11" x 17"
C: 17" x 22"
D: 22" x 34"
E: 34" x 44"
If you fold a size B sheet in half, the result measures 8.5" x 11". This works for each of the larger sheets as well, making it far easier to stack multiple sheet sizes neatly than would be the case for the metric sizes.
Edit: found a better source showing it works for metric sizes too.
-KR- ยท 8 points ยท Posted at 16:07:12 on May 25, 2016 ยท (Permalink)
making it far easier to stack multiple sheet sizes neatly than would be the case for the metric sizes.
ISO 216 paper sizes are defined to the neared mm, so A4 is 210*297, then A5 is 148*210, and is rounded
Edit: damn you markdown, stealing my asterisks, and also, I'd imagine that the 0.5mm difference isn't much larger than the tolerances on manufacture either.
And the B sizes follow a similar pattern, with B0 being โ2 m on the long side and 1 m on the short side, with subsequent sizes halving in size every step.
Props for owning it. :-) and an upvote for your worthless karma!
markjs ยท 3 points ยท Posted at 15:54:24 on May 25, 2016 ยท (Permalink)
How does it not work for A3? The caveat is that the official A0 size has the lengths rounded to the nearest millimetre and the other sizes are then deduced from that. The formula gives a fairly accurate number but it gets less accurate the smaller the paper size.
Well, once you have the first size (A0, that is, or any other one. It doesn't matter), you can confirm just visually that the surface area halves each time you increase the number, and therefore doubles each time you decrease it.
Yeah! We had a printing paper business and we used to supply materials to the printing press in the area. We used to have 1meter iron racks in the shop to store reams of paper. A sheet from the ream of paper would get you 4 A/4 size papers.
CKyle22 ยท 1 points ยท Posted at 20:15:21 on May 25, 2016 ยท (Permalink)
Are there paper sizes larger than A0? What's the notation in that case?
markjs ยท 1 points ยท Posted at 20:55:59 on May 25, 2016 ยท (Permalink)
2A0 and then 4A0. Self explanatory how they work.
stm2a ยท 1 points ยท Posted at 20:21:35 on May 25, 2016 ยท (Permalink)
Is there an A-1 piece of paper?
markjs ยท 1 points ยท Posted at 20:56:21 on May 25, 2016 ยท (Permalink)
Double the size of A0 is known as 2A0 (and next up, 4A0).
And finally, each B, C, and D size sits at 1/4, 1/2 and 3/4 of the way between the corresponding pair of A sizes. This means that folded A1 paper fits easily in a B1 envelope, B1 paper in a C1 envelope and so on.
This was done to have zero waste when making paper sizes. Just manufacture A0 and you can make any other size. US sizes lead to a lot of waste and has to be pulped and recycled.
Still, A4 and A5 sure feels weird to read.
hazily ยท 1 points ยท Posted at 05:51:54 on May 26, 2016 ยท (Permalink)
By the same logic A0 has infinite size? Since 1/(2x0) = Inf...
markjs ยท 1 points ยท Posted at 06:19:29 on May 26, 2016 ยท (Permalink)
It's 2 to the power of x. And 2 to the power of 0 is 1.
boarhog ยท 1 points ยท Posted at 08:33:08 on May 26, 2016 ยท (Permalink)
Also, international envelope sizes, the so called C sizes will fit corresponding A paper.
C4 is for A4, C5 is for A5 and so on. I don't think there is a C0 envelope though.
FYI, letter is slightly wider and shorter than A4.
If you travel abroad with a North American duo-tang or folder, A4 paper WILL stick out the top. You'll be the laughing stock of all your European friends, I tell you!!
Edit: Apparently no one knows what a duo-tang is...
Also annoying when one wants to print pdf files laid our for letter on A4 paper (printers tend to be able to handle both, but I'm not sure letter-size paper is easily/cheaply available outside the US). The whole page will probably end up scaled down a bit so that it fits horizontally, and then you also end up with extra large white areas at the top and bottom of the page.
Never heard that term before, but after a quick search, a manilla folder doesn't appear to require hole-punching, so no, I don't believe a duo-tang is the same thing.
[deleted] ยท 20 points ยท Posted at 16:45:39 on May 25, 2016 ยท (Permalink)
1:โ2 ratio paper could have been done with any measures and isn't a part of the metric system, but I do agree that it's has some advantages over US letter size.
Ignoring your lameish joke (judging by personal taste and your downvotes), IIRC C4 is the envelope size that you can easily fit an A4 inside. C5 for A5 paper or A4s that have been folded in half are much more common though.
heliorm ยท 58 points ยท Posted at 15:22:40 on May 25, 2016 ยท (Permalink)
There is no A4 letter and A4 legal. The USA legal and letter formats were just overlaid on the graph for info.
Because Marge in Accounting would shit a brick and vote twice for Trump if we forced sensible ideas like A(x) paper and metric measurements into her stupid antiquated "system."
They'll throw you in jail for using an A4 for letters, obviously
[deleted] ยท 11 points ยท Posted at 15:31:53 on May 25, 2016 ยท (Permalink)
Holy fucking shit. I work with paper a lot and this image made all of these sizes click. Before, I'd just basically remembered proportions and the ratios of each paper relative to each other. Looking at the odd/even numbering - how in the fuck did I not notice this sooner?
I should say that I just kinda landed in a position that dealt with a lot of printing, so I never had an training in it. Just self-taught. And this is why being self-taught sucks. heh
gerryn ยท 10 points ยท Posted at 17:50:41 on May 25, 2016 ยท (Permalink)
Most likely because you are not thinking by default in metric. Everything in metric makes sense, not so much with imperial.
Toppo ยท 3 points ยท Posted at 18:32:21 on May 25, 2016 ยท (Permalink)
A-sizes are independent of metrics though, and only the size of A0 fits nicely to metric measurements. The same principle could be used with inches too.
gerryn ยท 2 points ยท Posted at 19:19:59 on May 25, 2016 ยท (Permalink)
Ah, good point. The cm measurement of an A4 for example are not "uniform" as one would see it.
The A4 size print measures 21.0 x 29.7cm, 8.27 x 11.69 inches
Doesn't fit into the "niceness" of 100, 10, 1, etc. Very true - I was mistaken. Thanks for your post.
A0 is one square meter, dividing down the dimension of the paper is still designed with utility in mind, rather than pure mathematics, because this is a situation where usability is more important than keeping to metrics.
So the area of each page is exactly half of the A before it, meaning they're easy to cut, and the dimension of the page is designed with usability, text count, and margins factored in.
gerryn ยท 1 points ยท Posted at 01:30:21 on May 26, 2016 ยท (Permalink)
Yup, for me it makes perfect sense, it just doesn't translate to the uniformality (yeah, I just made that word up) of metric - 100 10 1 :) I have no idea how feet, inches and shit work, all I know is how much 14 inches is, or 20 inches, or 27, from monitor sizes :D
It is awkwardly long, it's also a half cut of an incredibly common dimension of paper (foolscap) that was used in the 1500's onwards. Like most imperial things, it was chosen by chance and then used in the legal system until it became the norm. Because of the sheer number of legal documents written in legal size from then onwards, legal size was maintained in order to ensure backwards compatibility with previous documents, amongst other reasons.
I was so confused when I learned the US doesn't use the same paper size as the rest of the world. Why can't they be standard with anyone else on anything?
If you insist. How would you prefer to die, sentenced to walk 10,000 miles with only 8 fl. ozs of water? To be dropped 100 yards with a 200 pound weight tied to your leg? To be buried 6 feet deep? To be burned in an oven set at 500 degrees....Fahrenheit?
AHucs ยท 7 points ยท Posted at 18:15:27 on May 25, 2016 ยท (Permalink)
I love the irony of calling them "Freedom Units". The reason they're called "Imperial" is because they were the standard units of the British Empire (although at the time of the AR I think they were still just called English units).
AHucs ยท 4 points ยท Posted at 18:15:28 on May 25, 2016 ยท (Permalink)
I love the irony of calling them "Freedom Units". The reason they're called "Imperial" is because they were the standard units of the British Empire (although at the time of the AR I think they were still just called English units).
I see the sarcasm, but the american measurement system is actually great for engineering. You can divide measurements in half easier because it uses a binary like system. For example, in your head, take 1cm and divide it in half, then in half, and then in half again and what do you get?
1cm/2 = 5mm
5mm/2 = 2.5mm
2.5mm/2 = 1.25mm
1.25mm/2 = 0.625mm
0.625mm/2 = 0.3125mm
0.3125mm/2 = 0.15625mm
See how you start getting all these long numbers? Now take the good ol' American system and divide it in half.
1" /2 = 1/2
1/2" /2 = 1/4
1/4" /2 = 1/8
1/8" /2 = 1/16
1/16" /2 = 1/32
1/32" /2 = 1/64
Fellou ยท 3 points ยท Posted at 17:56:41 on May 25, 2016 ยท (Permalink)
Then you could say the same about dividing by 5 or 10 for metrics. The reason we use base 10 is that we write numbers that way.
Kered13 ยท 1 points ยท Posted at 22:05:22 on May 25, 2016 ยท (Permalink)
How often do you divide by 5? How often do you divide by 2?
We write in base 10 and that's bad enough, don't make us measure in base 10 as well.
Fellou ยท 1 points ยท Posted at 23:01:53 on May 27, 2016 ยท (Permalink)
I that base 10 is not the best base, 12 or 8 would be better. But what is wosre is having different bases in different things. That mean converting the numbers each time you do a calculus using different bases.
reytr0 ยท 6 points ยท Posted at 17:59:57 on May 25, 2016 ยท (Permalink)
Americans MUST stick with Standard. Too many of us are too stupid to change anything in their tiny little minds. Not all of us, just those who think that Donald Trump anything but a huckster out to destroy the nation with his racism and ignorance-is-cool kind of lifestyle.
Source: Ask a Trumpster if they'll switch to metric.
No not that portion. Metric is the better system, I was asking him to calm down in reference to his obviously inflammatory pro Trump rhetoric.
[deleted] ยท 3 points ยท Posted at 16:54:41 on May 25, 2016 ยท (Permalink)
I was actually responding to a comment way above ours. I don't like the way Reddit does this. The trees become far too branched and split in several areas. Hell, I don't even know who I was talking to. I just put my comment under yours so the single thread would continue outward rather than adding another split.
Ugh, I miss the days of forums where the next comment/post would simply fall below the one above it! :P
nivlark ยท 1 points ยท Posted at 18:20:21 on May 25, 2016 ยท (Permalink)
He's not actually saying that though:
those who think that Donald Trump [is] anything but
i.e. unless you are anti trump, you are too stupid to learn metric. (His words not mine)
Also the fact that they weren't the first to put people in space, the first to have a spacecraft reach the surface on another planet, or create the first probe to return direct measurements from another planet's atmosphere. Getting to the moon was a seriously big achievement, but a lot of the other advancements of the time are often overlooked.
[deleted] ยท 2 points ยท Posted at 09:11:20 on May 26, 2016 ยท (Permalink)
The Soviets were also the first to put a spacecraft in orbit around the sun, the first to land a spacecraft on the moon (ten years before Apollo 11), the first to take pictures of the far side of the moon, the first to take pictures from the surface of the moon, the first to put a spacecraft in orbit around the moon, the first to put a remote-controlled vehicle on the moon, the first manned space station, etc.
The US does not use imperial, the British did. The British codified their system of measurements into the Imperial System after the Americans had codified their US Customary System. British Imperial units aren't even the same as US Customary units.
nivlark ยท 2 points ยท Posted at 18:21:19 on May 25, 2016 ยท (Permalink)
As do China and Russia (who have also been to the Moon)
Which is a lot. It was enough to make transferring my resume over look like shit. It was a huge pain in the ass on most other documents too. It's a lot easier to present more information neatly and with good use of white space on A4.
latman ยท 1 points ยท Posted at 18:59:29 on May 25, 2016 ยท (Permalink)
itz4mna ยท 3 points ยท Posted at 19:04:19 on May 25, 2016 ยท (Permalink)
Not really, we still use Imperial for a lot of things in the UK like the roads and pubs. If you ordered 50cl of beer or a 250g steak in a pub you'd get a funny look as well.
We only used letter format since 1995? What a fucking joke. We were using that for hundreds of years. The Europeans roughly copied the same size, and used that for their system, which I agree is better.
I'm only stating a fact. Look at that guy and who so many times edited his comment to make it look like America only used the Letter format since the late 90's. We used that format way longer than they ever came up with some clever system on how to divide paper. I'm pretty sure the Chinese taught us all, but the Europeans are smug idiots.
I just learned the other day -- on Facebook, of all places! -- that the US standard geometry for a 45rpm "single" vinyl record is different than the world standard (which I had never heard of and which blew my mind when I guy posted a video of it): in the US a 45 rpm single has a "large" central hole about one inch (?) in diameter, whereas in the rest of the world it has the same "small" central hole (about 1/4 inch) as all the other (e.g. 33.3... rpm albums) kinds of records (which are the same in the US).
It's one of those "more hassle than it's worth" things. A4 is, mercifully, the same width as A (letter) size (edit: apparently A is slightly wider), and only about 20 mils longer, so there's no functional benefit to switching out, aside from perhaps a one-time stimulus boost to the binder industry as everybody suddenly needs slightly longer things to hold their papers in. And ANSI sizes scale similarly to the way that ISO ones do, so it's not like we don't also get the benefit of maintaining aspect ratios.
It's not actually the same width. Letter is slightly wider than A4.
lengau ยท 5 points ยท Posted at 19:58:24 on May 25, 2016 ยท (Permalink)
Actually they don't scale in quite the same way.
You double one dimension and not the other, but because it doesn't have an aspect ratio of 1:sqrt(2), the aspect ratio of letter is different from the aspect ratio of ledger/tabloid (secretly the same paper, just rotated). So if you want a double-size print of an A4 page, you can print it on A3 paper and it'll look fine. If you try to print a letter page on tabloid paper, it'll be stretched.
From my perspective, the rest of the world is non-standard!
Daimoth ยท 3 points ยท Posted at 15:21:18 on May 25, 2016 ยท (Permalink)
WE LEARNED IT FROM YOU!
Provided you're English, that is. We occupy a massive chunk of a continent, not nearly as much pressure from our neighbors to standardize. We have far more infrastructure built using the old system than any European nation. It's tricky.
I doubt they're English, an English person would know that England's system of measurement is closer to the US's than to mainland Europe's (and much worse than the US's. They could at least be consistent. That should be the number one priority)
nivlark ยท 2 points ยท Posted at 18:40:23 on May 25, 2016 ยท (Permalink)
Not really, we are taught fairly exclusively metric and the vast majority of things are measured in metric. There are a few weird exceptions though: road signs are still mostly in Imperial, beer and milk are still sold by the pint (an Imperial pint, which is different from the US pint), and older generations still measure their weight in stones and pounds.
[deleted] ยท 1 points ยท Posted at 20:05:23 on May 25, 2016 ยท (Permalink)
So what you're saying is... it's inconsistent.
[deleted] ยท 1 points ยท Posted at 20:39:23 on May 25, 2016 ยท (Permalink)
Because the system we established long before international standardization existed works for us, and because the US has the economic clout to sustain non-standardization, it continues.
No, the A4 standard has been around since the 1940s and was basically ubiquitous by the '60s. The US didn't make 8.5x11 the national standard until Reagan decreed it in the 1980s. Before that, the US had all sorts of nonstandard paper sizes for different applications.
Joke answer: Because of Lunar Lander Awesomeness, that's why!
Real answer: the USA is a huge market with very low barriers to entry, and thus suppliers and manufacturers don't feel much economic pressure to adapt. If I make something in a small town in the States, I can sell it across an entire continent, in a market with 300million people, some more than 3000 miles away, with no currency exchange, no import/export taxes, no language barrier, and no trouble about metric vs imperial units. Maybe it interferes me selling it in Finland, but I probably wasn't to be selling in Finland, so I don't care that much.
When the metric system was cooked up, units like ell (https://en.wikipedia.org/wiki/Ell) were completely nonstandard from one country to the next, which was a big problem for merchants across Europe. The metric system solved a real problem. But that problem wasn't as seriously felt here in the States, so the pressure to adopt metric wasn't as high.
I think a switch would be pretty painless, all told. They've been selling soda in two-liter bottles for decades, and I don't remember anyone eve so much as blinking about it. I suspect the same would be true of many other changes, and we could go metric without anyone really bothering about it, if only anyone could be bothered to do it.
I at least want the US to use 8 x 12. It would be useful for measurement. Every single piece of paper could be used for measurement. 1 foot? whole paper. 6"? fold it height wise. 4"? fold it width wise. To get the odd numbers you'd need two pieces, but it still works none the less.
There was a time you had to apply to the US Green Card Lottery on Letter size paper. Not being a 'rest-of-the-world-standard' this made it more difficult in some countries.
Although this was not the reason for Letter-size I guess it didn't hurt the INS at the time
[deleted] ยท 1 points ยท Posted at 17:53:04 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 18:20:44 on May 25, 2016 ยท (Permalink)
Uhhh because it's an American company?
[deleted] ยท 1 points ยท Posted at 20:26:18 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 01:09:34 on May 26, 2016 ยท (Permalink)
I've never even been to Europe so I don't really know what I'm talking about. I agree it should default now based on language preference or something I just think its silly that you are surprised an american product defaults to american standards.
[deleted] ยท 1 points ยท Posted at 11:55:06 on May 26, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 18:07:07 on May 26, 2016 ยท (Permalink)
Provided I could easily change it to English I wouldn't be like "WOAAHHH WHY DID DEY DO DIS????? HOW DARE THEY!". So... yeah.
This is actually a problem at my company. We're in Russia and the HQ is in the US, so a majority of documents we receive from there look wrong when printed out.
The US paper sizes are setup such that folding in half will result in a sheet that is the same size as the next step down. So a 11x17 folded in half becomes an 8.5x11.
leshake ยท 1 points ยท Posted at 20:13:39 on May 25, 2016 ยท (Permalink)
Because every lobbyist in the country would rush to Washington to save the publishing industry, the paper industry, the educational industry, and whoever else is set on the 8.5x11. I use Rhodia A4, but everyone else is content with whatever is lying in the printer tray.
There are plenty of Americans who think it's ridiculous too. At some point "special" becomes "stupid" and the USA seems to have trouble distinguishing the two.
If we weren't such a superpower when these things were being developed, it would be far more likely that we would have followed the forms of the rest of the world. But since we not only had the resources but also the patriotic spirit, we developed our own systems for a lot of things rather than fit in with the rest of the world. It really came down to "AMERICA!".
I can't believe I'm reading a thread about maths. I can barely do arithmetic. My favourite maths fact is that in the times table, multiples of 9 add up to 9. So 9x3=27 and 2+7=9. That's all I've got.
You are confusing Americans in general with American business. Many Americans are very nice and helpful. Texas for example. American business however is anything but nice and helpful. American business is all about separating people from their money in any legal way possible. And sometimes those limits get tested. We have also had many problems with monopolies throughout our history. We have a lot of stupid laws, because of how much big business gets into politics. The real reason is probably something to do with making more money. Thats how all things end up the way they do in the US. It's all about the money.
Had this "a-ha!" Moment where it all made sense... Then looked at the image and saw how our "standard letter" paper doesn't meet the rule... Classic America move
During freshman year as an engineering student we had a class that just covered drafting. This was the only thing I remember from that class.
gmtime ยท 7 points ยท Posted at 15:19:07 on May 25, 2016 ยท (Permalink)
A4
Also, A0 has an effective area of exactly one square meter. Since every A size up is half the size, A4 is exactly 1/16th of a square meter in area.
Also, sizes are rounded to the nearest millimeter.
Does that mean it's a 30/60/90 triangle if you cut it diagonally?
[deleted] ยท 2 points ยท Posted at 17:09:44 on May 25, 2016 ยท (Permalink)
Not quite. If you draw a rectangle with side lengths 1 and sqrt(2) then draw a diagonal, you'd get a right triangle of sides 1, sqrt(2) and sqrt(3) (which is found with the Pythagorean theorem).
The side lengths for a 30-60-90 triangle are(some multiple of) 1, sqrt(3), and 2, whichis close but not the same as the triangle from the paper.
Also, one of the angles of the triangle from the paper is arctan(sqrt(2)) (approximately 55 degrees), which is not 30 or 60 degrees.
It is, however, one of the triangles in the Pythagorean spiral.
Not only that, paper size A0 has a surface area of exactly 1m2 . When you know the paper weight, say 80 g/m2 then you know an A4 is 1/16th of that so 5 grams.
jfb1337 ยท 3 points ยท Posted at 15:29:53 on May 25, 2016 ยท (Permalink)
Also either A1 or A0 (can't remember which) is 1m2 in area
smmck ยท 5 points ยท Posted at 17:35:48 on May 25, 2016 ยท (Permalink)
And here I was thinking that defaulting to A4 was just annoying. My wife is going to be so ticked when I replace our printer paper at home with the mathematically beautiful A4 paper.
gdub695 ยท 3 points ยท Posted at 15:59:49 on May 25, 2016 ยท (Permalink)*
I don't know about our other funky sized paper, but ANSI standard sizes follow the same convention. Double the short side, keep the long side the same when you go up.
A is 8.5x11
B is 11x17
C is 17x22
D is 22x34
And so forth. I don't think I've ever used larger than those though
No worries, Just have to deal with this silliness all the time trying to print 34" prints on 36" roll paper or worse, vise versa. The fun of large format plotters, and a purchasing department that can't be arsed to learn the different sizes.
Yeah, but the whole point is that the ratios keep alternating, whereas with A-series paper, it is always 1:sqrt2 which means you can scale up and down with no distortions or blank spaces
When i first started my degree, one of the first problem solving tasks they gave us on the first day was to work out the ratio given the fact that if you fold A3 in half you get A4 and so on. Quite interesting how stuff like this always seems to come up
IMHO this is a stupid way to design sizes. Why do we need a magic ratio? Pick sizes that are ergonomic for common tasks. I'm thinking in particular of index cards : 3x5 cards cut in halves or fourths are great for language flashcards. DIN sized cards are terrible
A cool consequence of this is that if you fold the paper diagonally so that the short side meets up with the long side like this then the 'diagonal side' will be exactly the same length as the long side. It's easy to show this using Pythagoras: โ(12 + 12) = โ2.
01is ยท 2 points ยท Posted at 18:39:40 on May 25, 2016 ยท (Permalink)
For legal size they should use the golden ratio.
[deleted] ยท 2 points ยท Posted at 18:39:50 on May 25, 2016 ยท (Permalink)
I have layman's math skills, but I worked in a paper factory once and had to manage shipping. I'd like to add to this, if you multiply the sheet x and y in metres by the weight of the paper, that's how much it weighs. So for a ream of A4 (500 sheets) printer paper: .210m x .297m x 80gsm x 500 sheets, the weight of that ream is in grams, about 2.5kg. Typically boxed in 5's, that box of printer paper is then 12.5kg. Good for office workouts if the plastic shipping strap wasn't so lethal.
I also personally love that the B series. It is the same ratio, but the B0 sheet has a longer side that is 1m. It makes more sense to me than something with the area of a square meter.
Zelpa ยท 1 points ยท Posted at 21:49:50 on May 25, 2016 ยท (Permalink)
I also personally love that the B series. It is the same ratio, but the B0 sheet has a longer side that is 1m. It makes more sense to me than something with the area of a square meter.
You missed Ansi E = 34" x 44". These follows the same fold in half rule as international paper sizes. Makes folding large drawing to fit into binders and folders much easier. Any size drawing can be folded to 8.5" x 11".
Scumbag U.K. exports shitty Imperial measurement system and paper sizes to North America, then switches to more sensible Metric and 'A' system of paper sizes.
The UK never used Letter. 8.5x11 was standardised by Reagan in the 1980s. Britain had its own imperial paper sizes like Quarto and Foolscalp, but the UK switched to the ISO sizes back in the early '60s like most countries. 8.5x11 is all American
Wow, thanks for taking time to give me feedback! I finished my undergrad in math, but I still have a lot to learn :)
[deleted] ยท 2 points ยท Posted at 10:09:03 on May 26, 2016 ยท (Permalink)
Here is another (slightly messier) proof, but I like it because it sort of follows the logic of why this intuitively makes sense - that the ratio you multiply the smaller fraction by will be greater than 1 and vice versa.
[deleted] ยท 2 points ยท Posted at 17:31:50 on May 26, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 18:40:21 on May 26, 2016 ยท (Permalink)
Thanks! I'd never used the website before and tbh don't exactly set things out formally. This was pretty much just scribbling on scrap paper before I decided to type it up.
graaahh ยท 1 points ยท Posted at 12:51:16 on September 26, 2016 ยท (Permalink)
I know this is an old comment but I just ran across it and I don't understand your proof. I can follow it line by line and see that the steps you take are true, but I don't understand how it proves that (p+r)/(q+s) is between p/q and r/s.
DustyLenz ยท 1 points ยท Posted at 16:52:37 on September 26, 2016 ยท (Permalink)
I got pretty lazy towards the end. In the second to last equation, you can multiply by q(q+s) on both sides, then subtract pq from both sides, to get ps < qr. We're given that a < b, which is the same as p/q < r/s. That statement justifies why ps < qr, so we've shown that a < (p+r)/(q+s). I didn't show that (p+r)/(q+s) < b, but you can use the same trick by manipulating fractions. Does that help?
graaahh ยท 1 points ยท Posted at 17:06:38 on September 26, 2016 ยท (Permalink)
I think so. It seems like most of the proof you worked out just wound up proving cross-multiplication (i.e. that p/q<r/s is the same as ps<qr.) But I think I see where you're coming from - the unstated part being that it proves a<(p+r)/(q+s). I'm wondering now whether this would work with negative numbers or not.
DustyLenz ยท 1 points ยท Posted at 17:16:41 on September 26, 2016 ยท (Permalink)
Nono, I used cross multiplication to prove that a < (p+r)/(q+s) is equivalent to p/q<r/s. That should also answer the question about negative numbers; as long as a < b, I believe my proof should still hold up? It gets a little weird when you mix positive and negative numbers, so a more careful proof is needed for that.
graaahh ยท 1 points ยท Posted at 17:17:32 on September 26, 2016 ยท (Permalink)
Thanks for the help! I'm normally fine with this kind of stuff but it's been awhile since I had to read through a proof.
The assumption that b can be written as m/n + c, c an integer is incorrect. For example, let a = 1/3 and b = 1/2. There's no integer c such that 1/3 + c = 1/2. I think the proof will work without that assumption though. c will just be some funky fraction. Good work!
[deleted] ยท 5 points ยท Posted at 00:55:46 on May 26, 2016 ยท (Permalink)
this is a super under-appreciated comment. a part of my brain already knew this but i never really understood it. it has actual life application too, as interesting as the Fibonacci sequence is, i will never use it. this is sort of great when picking something like a socket size for a bolt.
The minus sign can be in front of the numerator or denominator, it's interchangeable. So it would be 1/2 + (-1)/2 = 0/2 = 0, which is the right answer :)
If we take two fractions, without loss of generality we can assume p/q <= r/s. From here we can derive the following relation: ps <= rq.
By adding pq to either side we get ps+pq <= rq + pq, which is the same as p(s+q) <= (r+p)q. Now divide everything by q(q+s) and you get p(s+q)/q(s+q) <= (r+p)q/q(q+s), which is the same as p/q <= (r+p)/(q+s). The right hand side of this equation is the sum of the the numerators divided by the sum of the denominators.
If you add rs to either side of the first relation (instead of pq) you prove that (r+p)/(q+s)<=r/s.
[deleted] ยท 1 points ยท Posted at 17:32:05 on May 25, 2016 ยท (Permalink)
Which one was Calc 2? Are you in high school? While we had algebra 1 and 2, in my high school, we just had AP calculus for calculus. In college there were separate classes for differential, integral, vector, and series calculus. None of them were ever called "Calc 2".
I just finished calc 2 at uni and it was a grab bag of series/sequences, vectors & planes, parametric equations, and trig integrals that make death appealing.
[deleted] ยท 4 points ยท Posted at 17:49:12 on May 25, 2016 ยท (Permalink)
When I first took it 7 years ago, calc 2 was integrals, reimann sums, areas, volumes, volumes on xy and on periods, and surface areas.
When I took if this last semester, they threw out all of the complicated volume and area questions and made us do sequences and series instead. I think the latter one as easier.
[deleted] ยท 2 points ยท Posted at 17:46:13 on May 25, 2016 ยท (Permalink)
At my university, we had cal 1-4...
Calculus 1: Foundations (differentiation and integration)
Calculus 2: Series and sums (including Taylor and Maclaurin series)
Calculus 3: Multivariable and vector calculus
Calculus 4: Differential equations
I'm somewhat assuming for those first two, since I took them in high school, but even at my high school that's how the designations for calculus 1 and 2 were.
Hmm, mine went: Calc 1-3, then Linear Algebra, then Differential Equations 1 and 2
[deleted] ยท 1 points ยท Posted at 17:57:53 on May 25, 2016 ยท (Permalink)
Even with AP calc, I took the basic ones in college because I knew I'd need it as an engineer. Anyway, my differential equations class was separate from the regular calculus sequence, just like numerical methods, discrete math, and linear algebra. You must have been on a semester system instead of quarters.
[deleted] ยท 1 points ยท Posted at 17:59:46 on May 25, 2016 ยท (Permalink)
Yep, in my opinion a quarter wouldn't have been enough time for most of these courses.
[deleted] ยท 1 points ยท Posted at 18:14:36 on May 25, 2016 ยท (Permalink)
It probably depends on you, the professor, and the classes you're taking at the same time. Did I say it depends on you? If you're anything like my students when I taught, a semester probably isn't enough for any given topic. The reasoning behind prerequisites was lost on them. Reading was a problem too. They would have done much better if they'd just read carefully. They couldn't read the assigned material, the homework problems, or the exam problems. Many will literally kill people after they graduate.
Your series calculus was probably similar to my calc 2. The calculus class I took in high school and Calc 1 in college were both differential and integral calculus together (the same class, in retrospect I should have clepped out of Calc 1). Then Calc 3 was 3d calculus.
Also, I really liked my Calc 1 and Calc 3 profs, and wasn't too thrilled with my calc 2 prof so that could be part of it too
Is it really as bad as they say? I have to take Calculus 1 next year.
[deleted] ยท 3 points ยท Posted at 17:43:40 on May 25, 2016 ยท (Permalink)
No. Learning it for the sake of learning it might suck though. I took AP calculus while I took trig based physics in high school because we didn't have AP physics. I saw how it was applicable and made everything easier... Differential calculus is essentially division and integral calculus is essentially multiplication. They're just in multiple dimensions and/or for curves. Vector calculus helps extended it into even more dimensions. My best advice is to find a good reason for it. Apply it. Don't let it just be abstract.
If you're solid in algebra and trigonometry, then you will be just fine.
[deleted] ยท 1 points ยท Posted at 19:50:49 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 21:19:12 on May 25, 2016 ยท (Permalink)
I'm pretty sure very few people will agree that Calc 1 was harder than Calc 3. I'm not sure what you learned exactly in those classes but Calc 3 was definitely far tougher.
I learnt about Taylor polynomials in middle school due to my TI-81 graphing calculator supporting that natively (up to 6 degrees or so) in it's version of Basic.
How do they get used in Calc 2 that's so traumatizing? :o
It depends on your major but I don't think it'll be a bad idea to do that. You just don't get the same rigor that you do in high school that you do in college.
its 5 hours a day, 4 days a week, for 5 weeks. I absolutely rocked calc 1, so i'm feeling confident, but I've been hearing a lot of bad things about calc 2 from my STEM buddies. I'm setting myself up for Linear this fall.
Every physicist, engineer, and mathematician should find the level of Taylor Polynomials taught in Calc 2 easy. It has useful applications in linear algebra, modeling, circuits, and so on.
Ok, so I am guessing you mean that given an explicit open form, it can sometimes be hard to write down it in a closed form where one has explicitly stated the n'th coefficient in the sum/product?
That I can agree with. If I find it too hard to find the explicit expression for the n'th coefficient, I'll just refer to an equation that yields it implicitly.
godnah ยท 1 points ยท Posted at 16:42:01 on May 25, 2016 ยท (Permalink)
It's related, but not the same. 1/(1 - x - x2) is the generating function of the Fibonacci sequence. For any sequence An (n = 1, 2, 3, ...) you can define a polynomial whose n-th coefficient is the n-th element of the series, so A_0 + A_1 x + A_2 x2 + ...
Using the recurrence relation of the Fibonacci numbers, you can then show that this polynomial sums to the function 1/(1 - x - x2).
Generating functions have a lot of uses. For example, it can give you a closed form for the Fibonacci numbers. Use the partial fraction expansion on the form 1/(1 - x - x2), obtain two terms that can be expanded as a geometric series, whose coefficients have simple closed forms.
Nah, in order to be a Taylor series, it would have to converge to a function in some neighborhood of 0. This is a generating function, which is a similar looking formal construct, but is different in all practical uses.
Edit: Ignore this hasty, completely false statement that I made. /u/YoungIgnorant below me has the right idea.
We may be working with different definitions of Taylor Series, but if you look at the definition here you see that the series in /u/redditsoaddicting comment is what you obtain by plugging in f(x)=1/(1-x-x2 ) with a=0.
Convergence of Taylor series is a separate issue. Every Taylor series converges at its center, though for some Taylor series this is the only place it converges (we say that those functions have radius of convergence equal to 0). There are even some Taylor series which do converge everywhere, but to a different function (see the example of the piecewise function f(x) given in here).
Functions f(x) for which the Taylor series at every point converges to f(x) in a neighborhood of that point are called analytic, a property which gives complex analysis much of it's flavor.
A Taylor series has a very specific definition. The coefficients of a Taylor series are generated from successively higher derivatives of some differentiable function (along with some factorials). What differentiable function has derivatives such that you get the coefficients described in the top parent comment?
I explained this in a comment above (including the subtleties of convergence), but if you look at the definition here you see that the series in /u/redditsoaddicting comment is what you obtain by plugging in f(x)=1/(1-x-x2 ) with a=0.
In other words, it's a Taylor series for the function f(x) = 1/(1-x-x2 ) centered at 0. In fact, any time you can express a function as a series of the form
f(x) = c_0 + c_1 (x-a) + c_2 (x-a)2 + ...
the series on the right-hand-side will be THE Taylor series for f(x) centered at x=a (which you can verify by taking derivatives on both sides to see that the coefficients match the form of the coefficients from the Taylor series).
Yeah, I could see this working the same way in other bases. That is, sub in 1/b and expand the polynomial all in terms of that base b. It would be interesting to see if it truly does.
The defining property of the Fibonacci sequence is that every number in the sequence is the sum of the previous two numbers. So, if you look at coefficients in the above generating functions, you see that f(x) = 1 + x f(x) + x2 f(x), which can be rearranged to give f(x) = 1/(1 - x - x2 ).
This is similar to a cool blog post I saw this year: https://mathwithbaddrawings.com/2016/03/14/the-pi-day-recipe-book/. I thought it had something about the Fibonacci sequence in it because I also remember looking at something rehashed to it this semester as well. This is a lot if cool things about pi!!!
You can prove this by showing 1+x+10x=100x. I can write the details later if you want, but this essentially boils down to the fact that the sum of consecutive Fibonacci numbers is the next one.
whebzy ยท 1 points ยท Posted at 13:18:29 on May 26, 2016 ยท (Permalink)
The point is that, since 13 follows 8 in the Fibonacci sequence, you already know that 13/8 is roughly 1.61, and therefore 8 miles is roughly 13km - no calculations are necessary.
For those who didn't follow what this means: you can (approximately) convert from miles to kilometers by taking your number of miles, (say 5) and just getting the next Fibonacci number (in this case 8).
This is of course a bit harder to do if you want to convert 6 miles to kilometers.
Not just that, but any sequence f defined by fixing f(1) and f(2), then defining all other numbers in the sequence as f(n) = f(n-1) + f(n-2) will have the ratio f(n)/f(n-1) approach the golden ratio as n goes to infinity.
rubelmj ยท 3 points ยท Posted at 16:28:52 on May 25, 2016 ยท (Permalink)
Another fun related math/biology fact: because it's the product of haplodiploid sexual reproduction, the number of ancestors a drone (male) bee has follows the Fibonacci sequence as you move along the family tree.
Every sequence is encoded in every transcendental number. At some point in pi, there exists a string of ones and zeroes that would, when converted into alphanumeric text, spell out the entire written works of mankind, in chronological order, from the beginning of the invention of writing.
And then in another spot, there will be a string of ones and zeroes that spell out the exact chemical composition for a drug that can kill cancer cells without killing healthy ones.
In another place, a string for code that creates a strong AI that follows Asimov's Three Laws. And another string that makes a strong AI that will kill all humans.
Infinite length means everything will eventually be found in it.
53504 ยท 1 points ยท Posted at 15:58:48 on May 25, 2016 ยท (Permalink)
Why is this your favorite? I'm not attacking. Just wondering. If you encode it like you say it's going to add up to something. Am I missing why it's particularly interesting?
[deleted] ยท 1 points ยท Posted at 16:05:21 on May 25, 2016 ยท (Permalink)
So you're saying increasing the circumference of a circle by 6.3m will increase its radius by 1 meter regardless of its initial size?
kDubya ยท 1905 points ยท Posted at 14:22:05 on May 25, 2016 ยท (Permalink)*
Yup, exactly.
*edit:
Ok everybody, here are some common responses, and below each is my response:
Hur dur, not exactly, pi doesn't equal 3.15!
No, it doesn't. pi doesn't equal 3.14159265, either, but it's good enough for the vast majority of cases and is plenty accurate. For a simple thought experiment like this, 6.3 is close enough to 2*pi and results in an extra 2.7 mm radius over the 1 m stated.
Wait, this must not work at any scale, right? What about a golf ball, or a bb?
It works at any scale. Wrap a carbon nanotube rope around a speck of dust. It still works, because it's a simple mathematical relationship between radius and circumference. For any change in radius, there will be a corresponding change in circumference that will be 2 * pi (roughly 6.3) times the change in radius.
Since circumference is equal to 2 * pi * r, it makes sense. If you increase the radius by 1 it's equal to 2 * pi * (r+1) which equals (2 * pi * r) + 2 * pi.
[deleted] ยท 301 points ยท Posted at 15:21:56 on May 25, 2016 ยท (Permalink)*
for fucks sake mate I'm studying for an integer (integrals? not really sure how it translates) test tomorrow, and I can't make a single one of them I was trying to escape to reddit but nooooooo, you just had to press my face in it huh?
....help me. I see k's and x's and square roots and /'s floating in front of me, they're laughing at me, mocking me, I should burn them, I should burn them all.....
[deleted] ยท 1 points ยท Posted at 22:11:20 on May 25, 2016 ยท (Permalink)
Yeah based on your response, you probably haven't learned how to integrate by parts yet and so you cant compute the integrals above yet.
I wouldn't worry about seeing stuff like that above on your test, but if you do there is a super easy way to evaluate the riemenn integral of the product of a function which is finitely differentiable and something like cos(x) or ex, which are infinitely differentiable. Look up 'integration by parts using table' if you're concerned.
Just saw this. Should be Pi*n, technically not part of the equation.
Edit: Also not too sure that the integrals gives the circumference either...you are integrating radius. (Also my calc/trig is pretty rusty, haven't had the need to use it in a long time haha)
MauPow ยท 1 points ยท Posted at 23:38:42 on May 25, 2016 ยท (Permalink)
As someone who didn't initially still didn't get it, thank you, I, a non-mathematician, totally understand your much longer equation like 2nd-grade English.
If you take the Earth, moon, sun variable out the equation, and imagine there is a single point with no radius, the rope makes a circle with a radius of 1m.
Put that into the 2ฯr equation to find how much rope you need, and it's about 6.3m.
The radius of the circle (Earth, sun, moon) is ADDED to this number, which means that the extra amount of rope you need is always the same.
Okay as some who got the equation but didn't quite understand it yet here's what my presumption was - the length of the rope which goes around the equator.
The length of the equator changes causing the length of the rope to change.
The math makes perfect sense, but would someone be able to explain it in a more physical way? Intuitively, it just seems like such a big sphere would need more than 6.3m to lift up the rope by 1m on all sides.
Imagine if the earth was a cube. The rope around the equator would then be a square. Obviously if you want to lift up one side of that square by one meter, you need to add two meters of rope (lengthen both adjacent sides by one meter). So to move the whole rope up a meter, you have to add 8 meters of rope, no matter how big the original square was. From there, it's not that surprising it works similarly with a circle.
I'm confused, that doesn't seem to hold up on small scale. If I have enough rope to wrap around a tennis ball, I won't need 6.3m of additional rope to make a 1m halo around it.
kDubya ยท 1 points ยท Posted at 17:53:05 on May 25, 2016 ยท (Permalink)
It holds up at any scale.
Tennis ball - 6.86 cm diameter, 3.43 cm radius
circumference = 21.55 cm
add 1 meter to radius
1.0343 m radius, 2.0686 m diameter
6.499 m circumference
6.499 - 0.2155 = 6.283 (2*pi = 6.238, not 6.3, that's just an approximation).
So if I wrap a string around a marble, adding 6.3 meters of string will give me exactly enough to create a ring around it that hovers one meter out? That is so crazy to think about.
[deleted] ยท 1 points ยท Posted at 18:08:03 on May 25, 2016 ยท (Permalink)
Would this hold true for something as small as a ping pong ball?
This is a good point about sig figs and tolerances
The earth is around 6,353 kilometers, to keep sig figs you only need Pi out to 3.141
Do you want to calculate earth to the meter? add three sig figs!
3.141592
Do you want to calculate it to the millimeter? add Three sig figs!
3.141592653
So on and so forth, atomic length is on the length of a picometer, ergo to calculate the circumference of the earth to an atomic length the value of pi you need is 3.141592653589793238462643383279502884197
Exactly. FWIW, I think knowing Pi to 30 something decimal places lets you calculate the circumference of the visible universe to within half the width of a hydrogen atom? And you need 60-something decimal places to calculate to within 1 Planck length.
Meaning that, not only does it work in meters, but increasing the circumference by 6.3 of any unit of measure will increase the radius by 1 of that unit of measure.
kDubya ยท 1 points ยท Posted at 18:00:00 on May 25, 2016 ยท (Permalink)
Well aren't you so smart. How dare we use 6.3 instead of 6.28318530717958. Increasing the circumference by 6.3 would cause the rope to hover 2.7 mm higher than exactly 1 meter. That ruins the entire thought experiment.
(minor elaboration: 3.15 is around 0.2676% larger than the actual value of pi, or roughly 1/370th larger. If a piece of paper money that was supposed to be 16cm long were 0.2676% longer than intended, it would be 16cm and 0.416 millimeters long)
Zhortsy ยท 0 points ยท Posted at 15:07:02 on May 25, 2016 ยท (Permalink)
Well, technically not exactly (6.3 m that is)... :P 2*pi :)
No, it doesn't. pi doesn't equal 3.14159268, either
Well pi doesn't equal 3.14159268 for a different reason though. Mostly because the last digit of your estimation is wrong. It should be 3.14159265 (rounding or truncating doesn't matter it's the same either way).
kDubya ยท 1 points ยท Posted at 21:43:42 on May 25, 2016 ยท (Permalink)
Whoops, I misremembered it.
Multai ยท 174 points ยท Posted at 14:41:09 on May 25, 2016 ยท (Permalink)
Since circumference is 2ฯ*r adding 1 to r will just add 2ฯ to the answer, which is about 6,3 of whatever r was (meters for example).
The algebraic calculations shown in a couple of the other answers pretty much prove it for any circle (r>0 at least), but for a concrete example, a circle of r = 0.5m would have a circumference of 2 ร pi ร 0.5 m = pi m or about 3.14 m, and for r = 1.5m you get 2 ร pi ร 1.5 m = 3 ร pi m, i.e. pi m + 2 pi m i.e. 3.14 m + 6.3 m.
Somehow if you increase the radius by 0.5 meters instead you get a circumference increase be 3.15... which is close to pi. Is the 6.3m number wrong or is it just a coincidence?
[deleted] ยท 1 points ยท Posted at 16:18:55 on May 25, 2016 ยท (Permalink)
If you increase it by 0.5m your answer will be exactly pi. Not a coincidence.
Now think about how much water it would take to flood a perfectly smooth earth with 1m of water and you understand why they push to make things like planes, tanks, pipelines, dams, etc bigger and bigger.
Domin1c ยท 1 points ยท Posted at 17:50:06 on May 25, 2016 ยท (Permalink)
So let's set up our problem: Let Ci be the circumference of the earth, and let r be the radius of the earth (or ball, or anything) PLUS the new amount that comes from the added circumference.
Turns off? What the hell are you talking about. The sun doesn't turn off at night. That's the most ridiculous thing I've read in a thread full of ridiculous shit.
So as you pointed out, there are times, usually in the morning, evening, or during a "solar eclipse" where we can see both the sun and the moon.
The first two examples are an example of "solar photon dilation" essentially, photons from the sun are accelerated so rapidly around the earth that you are actually seeing the future sun (the moon) at the same time. This, coupled with the earth's rotation, distance from the sun, and everything actually results in a rather seamless transition from the double-sun to the moon.
If the earth was even a meter away from where it is now in relation to the sun, then we would see a lag or a jump (depending on the season) during the day-to-night transition.
As for an eclipse, this one's easy. It's the sun taking a quick nap. It has a circular blanket to keep it warm.
This basketball star pulled off this amazing slam-dunk. So one sportscaster yells out, "I think he was in the air for like five seconds!" The other sportscaster, trying to be diplomatic but factual chided him, "I think it was more like two seconds."
16 feet high? That's a heck of a jump, it would smash olympic high jump records to pieces.
It's not a maths fact but rather a physics fact that IIRC the air time of a jump/thrown ball etc. (ballistic trajectory, without any aerodynamic effects such as aeroplanes and birds have) doesn't depend on the horizontal velocity but only on the initial vertical velocity, or optionally on the consequence of the latter, the height of a jump.
tael89 ยท -1 points ยท Posted at 18:30:50 on May 25, 2016 ยท (Permalink)
Yes, but the rope that is somehow on the surface, the materials designed that it is just barely surviving, may not survive 1 m above the surface where temperature is hotter.
I grabbed a rope that is 6.3 meters long plus the c of a golf ball. Put it around the golf ball but it's not hovering. Therefore you are all full of shit.
DrAbra ยท 9 points ยท Posted at 16:46:39 on May 25, 2016 ยท (Permalink)
It's probably caught in OP's moms gravitational field, she's probably on the other side of the planet.
Wait wait wait wait wait. 6.3 meters...for everything. Does this somehow go along with the top comment. The one talking about 63% chance of something happening?
ktkps ยท 3 points ยท Posted at 04:53:34 on May 26, 2016 ยท (Permalink)
We did it Reddit!
New answer to life the universe and everything = 63 or 6.3 or 63% etc
SOwED ยท 1 points ยท Posted at 18:34:47 on May 25, 2016 ยท (Permalink)
What about earth's topography? Wouldn't it be different since it isn't perfectly round?
SOwED ยท 1 points ยท Posted at 18:29:43 on May 25, 2016 ยท (Permalink)
It only works if you assume a sphere.
ktkps ยท 1 points ยท Posted at 04:39:55 on May 26, 2016 ยท (Permalink)
science works in a lot of ways - when we first assume certain things
SOwED ยท 1 points ยท Posted at 05:26:08 on May 26, 2016 ยท (Permalink)
Well, the whole planet thing is just a useful way to explain the concept, but it's not realistic on any planet that you can't circle around without maintaining constant radius. I'm not sure if the gas giants have this property or not, do you know? I feel like they don't exactly have a border on the meter scale.
If the value 6.3 remains constant for all of those, then it is independent of the circumference, yes? So it works for literally every round object.
But there must be a minimum, because obviously this theorem is false for the case of a tennis ball.
Or there is a discrete, finite set of circumference lengths that this holds true. In which case, where do we define the surface of the sun to be? Because there is no point of change of mass. It fades into the next phase of matter over many kilometers.
edit: raising it up a meter is the same as adding 1m to the radius. 2 * radius = diameter. pi * diameter = circumerence. you're adding 2 to the diameter, and 6.3 is nearly exactly 2 * pi. It makes sense. But is much less impressive now. :(
Bosck ยท 2 points ยท Posted at 16:23:54 on May 25, 2016 ยท (Permalink)
It doesn't depend of the radius. It is really strange, but it is true. Take a rope and try with a tennis ball. You will see that it is true even if it seems impossible
Lets use some /r/shittyaskscience
Being simply taller would not make you float, but if the rope was perfectly disributed around the world, the gravitational pull of the earth would force it to hold form (the reason the world is round in the first place) so surely as a result, if the rope was the right length and had perfect distribution of the force of gravity it would force the rope to be the exact same distance from the ground the whole way round.
Even a bendy rope could hover in obviously idealized cricumstances. After releasing the rope, its movement can't break rotational symmetry, therefore it cant fold and fall.
It could compress and fall down though, becoming slightly thicker.
Amp3r ยท 1 points ยท Posted at 01:30:31 on May 26, 2016 ยท (Permalink)
Are the ideal circumstances that it won't bend to the sides and fall on the ground as a snake shape?
No. The ideal circumstances would be that gravity is perfectly even everywhere. To make the rope bend to the sides there would have to be a sideways force. But gravity only pulls downwards. So unless the rope gets perturbed, it will hover.
Amp3r ยท 1 points ยท Posted at 23:53:35 on May 26, 2016 ยท (Permalink)
I don't think that is the case. Ropes aren't good at longitudinal compression forces which is what would be needed to keep it hovering. Something like a steel cable might work
Nope. If we assume the rope is perfectly round and can't just compress to a ring with smaller radius. (Idealized) gravity can't break rotational symmetry, therefore the rope would hover. It doesn't even nead to be spinning.
A regular, non-rigid rope would work fine if you spin it at sufficient (angular)velocity.
raddaya ยท 2 points ยท Posted at 15:28:10 on May 25, 2016 ยท (Permalink)
Ah, yes, I was mentioning lower down that the rope would need to be taut, though I was wondering about whether if it was needed or not. I suppose a physical definition of "taut" would be "rigid".
Let's assume the rope is a one-dimensional massive string. For a real rope, you're right, you can't separate bendiness and compressibility. But in that ideal case, where it is bendy but not compressibly, it would still hover, because the gravity cannot induce a movement that does not have rotational symmetry.
The answer is independent of the earth's circumference, because circumference increases linearly with radius.
In fact, replace earth's circumference with your waist. You will still need an additional 6.3 meters of rope to have the rope hover a meter from your body.
This realization blew out my pants more than the original fat.
dtn1496 ยท 2 points ยท Posted at 17:13:55 on May 25, 2016 ยท (Permalink)
The thing that gets me is that is sounds crazy but it's actually really simple math. A circle's circumference is 2piradius so increasing the radius by 1 increases the circumference by 2*pi (which is roughly 6.3)
h, my comment was also a joke but yours is better :p
bradn ยท 2 points ยท Posted at 16:24:51 on May 25, 2016 ยท (Permalink)
Most underrated joke I've seen in a while here!
3lbFlax ยท 6 points ยท Posted at 17:32:27 on May 25, 2016 ยท (Permalink)
Your momma is so fat one would have to add an additional 7m to the circumference of a rope around her waist in order to increase the radius of said rope by 1m.
Fact: You're so fat that it would take the same extra amount of rope to hover a meter away from your body as opposed to wrap around it, as it would to do the same with the entire Earth.
That makes no sense to me, if I am ~ 1m around, I would need a 1m rope to go around me. If I make the rope 7.3 metres long, it will be 1m away from me at all points...that sounds like it would be way further away from me than just 1m...and then taking a 40,075km rope, and making it 40,075.0063km, it would then be long enough to still float 1m about the earth?
1m from belly button to the centre of your mass (middle of your stomach? [radius]), resulting in a 6.3m rope. With the extension, that would be 12.6m rope.
Filobel ยท 1 points ยท Posted at 17:52:12 on May 25, 2016 ยท (Permalink)
This is true when dealing with the circumference of planets and large object but does it still hold true when dealing with even larger objects? Ex: Ya fat ass mamma
What is meant by hover a meter from your body? Does it mean that the rope's circumference will always be a meter away from the body or will it somehow gain anti-gravitational properties?
And so is the formula for the circumference of a circle but if they don't recall that then it's unlikely that your response will have any meaning to them. Your response was concise but it won't help someone who doesn't already understand.
I'm sure you're content with the anonymous validation you've received but that's an immature attitude and it isn't characteristic of an intelligent person. Pragmatism is important. Don't act like a mediocre person with a decent education and a big ego.
As I forgot to mention in my previous post with the links (but did mention in another post in this sub-thread), I was talking about the English-language spelling, which as pointed out in my source, was most recently defined as metre, with only the US measurements authority specifically deviating from that. Hence you get the irony of an American (presumably) complaining to people to speak English and write meter, when the current spelling (and I think this has always been the case for British spelling, compare theatre, centre) in English i.e. British English is defined as metre and only the Americans have officially declared otherwise.
Furthermore, official spelling may of course be different from common usage, which is pretty clearly meter in most international usage as well as obviously Americans.
Here's a good way to picture this. Imagine that instead of a circle of rope around the Earth, it's a square frame (figure 1). This square frame will only contact the Earth at four points, in the middle of each side. Now, imagine you want to get each point a meter off the ground. All you have to do is add a meter at each end of each of the edges (the yellow segments in figure 2) and the clearance of the square frame is increased from 0m to 1m. The total in this case would be 8m, but since it takes less rope (or frame) to make a circle, a circle would only need 6.3m.
The craziest thing about this is that the original size of the circle doesn't matter. Whether you're wrapping a rope around a car tire or the Moon, if you want to increase clearance by 1m, you need 6.3m of extra rope.
You can cut the earth in half and cause death and destruction by shortening the rope by the same length.
Oncey ยท 2 points ยท Posted at 15:07:49 on May 25, 2016 ยท (Permalink)
If you think about it, it becomes a bit intuitive. If you add 2m rope in 2 opposite places, then the rope in both middles is hovering 1m above the surface. If you add 2m rope in those middle places, then the places where you added the original rope are now 1m above the earth. That's 8m rope.
nnyx ยท 1 points ยท Posted at 19:02:11 on May 25, 2016 ยท (Permalink)
Holy shit thank you.
This makes it so much easier to wrap your head around.
SOwED ยท 2 points ยท Posted at 18:49:49 on May 25, 2016 ยท (Permalink)
That's not really the point.
[deleted] ยท 1 points ยท Posted at 19:01:55 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 19:14:32 on May 25, 2016 ยท (Permalink)
No, the point is that adding 2ฯ (~6.3) units to the circumference will increase the radius by one unit, regardless of the sizes of the radius or circumference.
It was an imperfect analogy to explain this consequence of the relationship between radius and circumference.
[deleted] ยท 1 points ยท Posted at 20:15:44 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 20:35:53 on May 25, 2016 ยท (Permalink)
I understand your question, but as I said, it's an analogy. Analogies are, by nature, imperfect.
If you actually did this on a perfect sphere the size of the earth (so no mountains or anything to convolute things), the rope would not hover.
The original comment just used that analogy as a short way to explain that the radius of the circle made by the rope would increase by 1 unit if the rope length were increased by 2ฯ units. It does not matter the scale. This is true of a marble and it's true of a sphere larger than the Milky Way.
[deleted] ยท 1 points ยท Posted at 20:45:15 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 20:55:09 on May 25, 2016 ยท (Permalink)
No, because gravity would pull the rope down. I suppose there is a size at which you could send the rope into a spin and it would orbit.
[deleted] ยท 1 points ยท Posted at 21:35:15 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 21:59:16 on May 25, 2016 ยท (Permalink)
That depends on the mass of the sphere and velocity of the spin. So, actually, given a high enough velocity, the rope could hover one meter above a perfectly spherical earth. Now that I've refreshed my memory on the orbit equation, the size of the sphere doesn't matter as long as the mass of the sphere is compensated for by the velocity of the rope. The limit of this would probably be the speed of light, assuming you could magically have the rope already spinning evenly.
In other words, for there is a 1:6.3 ratio between radius and circumference.
Edit: And to be more of a party pooper, I'm fairly certain a rope would crumple. Unless (this is pure conjecture) the rope in question was perfectly aligned across the equator, was arranged into a perfect Circle, had no momentum, and was completely physically uniform, with no defects. If this is all true than the G force of the rope would push inwards into itself, thus being supported. However, it come under the same issues as "trying to play pull with a rope". Or driving a truck in reverse, with more than 1 trailer. Every trailer you add makes the task of steering exponentially harder.
For people that don't understand, it might be helpful to think of squares as well. If you have a square with side length s, then the perimeter is 4s by adding up all the sides. If you want a square (with the diagonals lined up) that is at least 1 m away from the edge at every point, then you'd need to add a meter in length to the left, right, top, and bottom of the square. The new square would have side length s+2, and so the perimeter would be 4s+8. So no matter what side length you have, you'll get an increase in perimeter of 8 if you want to make a new square that encloses the old one at a minimum distance of 1 away (with the diagonals lined up) from the old square.
You did a copy and paste of my answer the last time this was asked and got much more karma. I don't really mind, but dang at least write it in your own words.
Makes sense. If the circumference of earth is 2 * pi * the radius of earth, adding one meter to the radius is just adding 2pi to the circumference.
C1 = 2 * pi * r
C2 = 2 * pi * (r + 1)
C2 = 2 * pi * r + 2 * pi
C2 = C1 + 2 * pi
C2 = C1 + 6.28
ktkps ยท 7558 points ยท Posted at 11:42:11 on May 25, 2016 ยท (Permalink)*
Hairy Ball Theorem: The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres.
English: It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.
Edit: found a funny version :
The hairy ball theorem of topology states that, whenever one tries to comb a hairy ball flat, one always misses a spot. Topologists, who can never say anything that simply, put it this way: "For every 2โsphere, if f assigns a vector in Rยณ to every point p such that f(p) is always tangent at p, then it is a bit surprising that the girl blinded me with Science!"
That topologists use such gassy English is an indication why they are not able to comb a hairy ball, either. They refer to the missing spot as a tuft, a cowlick, or The Latest Rage. The latter is a way of claiming they missed the spot on purpose. Yeah, sure.
Imagine all the air is moving east to west, like it's a spinning top. This creates two points, one at each the north and south pole. Now, on a straight line between the poles (a meridian), move the poles toward eachother a little bit. The lines the wind follows look kind of like the lines on a croissant if the poles were the points. Keep moving the poles together until they reach eachother at the equator, and you only have one point where there's a cowlick.
I don't understand how you would merge the two. Just before they move, when they are very close, there is wind blowing between them. How do you eliminate that wind?
Thraol ยท 16 points ยท Posted at 20:16:21 on May 25, 2016 ยท (Permalink)
Thanks. Although it still looks like 2 poles to me. The vectors coming in from the south don't diminish as they approach the center, so they must be going through and out the other side, which would cut the 1 pole in half to make 2.
It doesn't. It still looks like two poles arbitrarily close. There has to be one stream flowing between the two points, and bringing the poles together concentrates the vectors.
Bringing the poles together concentrates these vectors infinitely across that pole, yet that pole's vector is supposed to be zero.
That croissant analogy is a great way of visualizing the movement you described. I'm just learning about this now, after reading the Wikipedia article, so I'm definitely not an expert but your explanation seems to make a lot of sense.
Would it really work with wind though? I thought it only applies to 2 dimensional surface areas, but with wind there air currents that are closer to the surface of the earth and others that are higher up in the sky
The wind directions would change in this scenario though right? Or is there some way of getting the lines to stay pointed in the same direction and still end up with one point?
Thats pretty wild. And crazy that I actually somewhat get it.
Paladia ยท -2 points ยท Posted at 18:01:49 on May 25, 2016 ยท (Permalink)
Actual answer here...
As the wind can blow in different directions at different altitudes, you can't imagine it as a 2 dimensional sphere but rather a 3 dimensional one without a core, if you want an actual answer.
oighen ยท 1 points ยท Posted at 18:44:30 on May 25, 2016 ยท (Permalink)
It's all about the hairy ball theorem and that is about a two dimensional sphere, not a "3 dimensional one without a core".
Paladia ยท 1 points ยท Posted at 19:43:04 on May 25, 2016 ยท (Permalink)
Except we are talking about wind. And wind doesn't move two dimensionally and thus the hairy ball theorem doesn't apply.
oighen ยท 2 points ยท Posted at 19:58:46 on May 25, 2016 ยท (Permalink)
The wind was an analogy. The statement of the hairy ball theorem is about the two dimensional sphere. It's nice and helpful to visualize it using a ball with hair or the wind. You have to implicitly assume to be in the right conditions for the theorem to hold. If, as a first approximation, you think Earth's surface as a sphere and imagine to be able to talk about the wind's direction and intensity at every point then you are bound to have tornadoes. It's math, not physics, don't be a pedantic ass for the sake of it.
Paladia ยท 1 points ยท Posted at 20:28:38 on May 25, 2016 ยท (Permalink)
It's math, not physics, don't be a pedantic ass for the sake of it.
Don't go berserk and start throwing insults left and right just because someone points out the flaw in using the wrong theorem.
Forgive me for stalking your post history but I think I may have found a clue. Were you the guy I met on Omegle (like 4+ years ago) who got me into trance music?
IIRC, you can move the spots whilst still satisfying the conditions. By 'pushing' both of these spots together it's possible to only have one point of zero.
Get a rebids ball and comb all the hair uniformly away from one single point in all direction.
[deleted] ยท 1 points ยท Posted at 16:18:16 on May 25, 2016 ยท (Permalink)
I'm assuming combing all hairs clockwise or counterclockwise around the ball as if it were a vertical cylinder. Two spots would be on the top and bottom (ends of the "cylinder").
Imagine covering a sphere with a piece of stretchy fabric and gathering the edges in your fist. Now imagine that material as perfectly stretchy and thin, and you have it converging only at one spot!
Imagine a tennis ball. Pick any single spot on it and imagine a ripple going outwards from that spot, flattening the hairs it goes across. The ripple will go around the ball and come back together, closing on the other side and causing a single cowlick there.
Now, replace the tennis ball with the Earth and replace the hair flattening ripple with wind and presumably you get a single spot where there is no wind.
Now, I have exactly zero experience on this and don't fully understand it, however, that is how I imagine it might work.
As the others have said, that creates two spots. I think it's a common misunderstanding because of the name of the theorem. Obviously if you're working with an actual hairy ball, your solution creates a situation where the hair stands up in only one place. However, the theorem itself, simply stated as
"Every smooth vector field on a sphere has a singular point"
does not distinguish between the two points. In your case, there is one point which all nearby vectors point towards (the end of the ripple), and another point which all nearby vectors point away from (the start of the ripple). There's also a third kind of point possible, a point which all nearby vectors circle around (for example, the eye of a hurricane).
However, even though all of these situations act differently, the only thing that matters to the theorem is whether a single zero-vector (or point) exists, not the behavior of the vectors around it.
kazneus ยท 2 points ยท Posted at 18:27:23 on May 25, 2016 ยท (Permalink)
This is assuming we are talking about the surface of a sphere. However, that isn't true; there is depth to the atmosphere of Earth and therefore you have an extra dimension to deal with. So vectors that can't cross on the surface of a sphere can cross in the extra dimension...
but now I'm thinking that it might end up with at least one spot of zero wind by symmetry of vectors around it. Or not because you could define a vector within that field..
So you squish a torus around the earth such that the center of the torus becomes two columns of vectors at each poll - one pointing all up and one pointing all down. But that leaves the inside of the torus, which you could just define as a ring of vectors pointing clockwise or counter-clockwise in sort of an equatorial sense.
For any arbitrarily thin surface surrounding the Earth (but inside its atmosphere), there must always be at least one point on this surface where the component of the wind's velocity tangent to the surface is zero.
Better?
kazneus ยท 3 points ยท Posted at 19:26:47 on May 25, 2016 ยท (Permalink)
Yes.
For the record I wasn't trying to give you shit I was just extemporizing on the idea
It means that it's true at any given "layer" of the atmosphere. Every layer will have at least one cyclone (point of zero wind) at all times. These spots in each layer don't have to line up vertically, though, so in a macro sense it does indeed mean it's not true
And to clarify one point, "zero wind" in this case means "zero horizontal wind". Vertical wind is still completely possible, as the theorem would only concern the component of the wind that is tangent to the surface.
Fenring ยท 3 points ยท Posted at 15:25:30 on May 25, 2016 ยท (Permalink)
Yes. It's a theorem of topology, which means that it's true of things that can be bent or stretched into spheres without tearing. It would still be true if the Earth were extremely lumpy, like an asteroid, but not if the Earth were donut-shaped.
IIRC it's true on any "closed" shape. Topology classifies things in a really weird, and unintuitive way, so I'd be hard pressed to explain what that means in an ELI5 way. But here's the wiki on the topic, if you care to dig in.
SpiffAZ ยท 1 points ยท Posted at 15:24:43 on May 25, 2016 ยท (Permalink)
Something something "only if you don't blow it" something...
It's too early.
But as has been pointed out, this doesn't actually apply to the Earth's atmosphere as a whole, since the atmosphere has thickness and is not a 2d surface. It could apply to a surface drawn inside the atmosphere though.
Dumb question- what if you have this pattern where there is one spot with no wind, then make the pattern move offer the surface without distorting? Would that just perfectly sync with another area and so stop wind there too, or is there some long-winded maths explanation?
Yes, it would always cause another point to have no wind. At least if we make the simplifying but false assumption that the atmosphere has 0 thickness so the theorem applies.
As for the reason, that is a long winded maths explanation. The actual proof deals with transformations of vector fields (a example of which you actually just described),so if you can understand it, I'd take a look at the real proof. Otherwise, suffice to say that no transformation can be applied that leaves the vector field both continuous and without a zero vector.
Isn't this only true if you assume winds operate in two dimensions? If winds move other than parallel to the surface, you can have winds everywhere, I would have thought.
For a small enough measurement point, there will always be a zero-point for wind at every layer. This means that a human would still experience wind if he/she stood anywhere though (the body is way larger than the required measurement point).
Source: Hairy Ball Theorem
EDIT: I am wrong if you account for vertical vectors in three dimensions (which you should in the case of wind)
I'm not sure if this is true if you add in a third dimension - the "cowlick" can just be rising air. When you say "every layer" you're saying the layers are arbitrarily thin, i.e. have two dimensions. But if the vector at any given point in the layer can point "up" (which would only make sense if you have a third dimension), then you can avoid having zero points.
Doesn't hairy ball theorem only apply to even dimensional n-spheres?
LSeww ยท 1 points ยท Posted at 22:32:35 on May 25, 2016 ยท (Permalink)
It says that among all only even cannot have this fancy property.
2weirdy ยท 2 points ยท Posted at 15:32:49 on May 25, 2016 ยท (Permalink)*
Even if it counted up and down winds, you'd still have a limit to the distance you can go.
Edit2: My reasoning was wrong.ยจ
Edit3: New reasoning: The Hairy Ball theorem is actually a result of the PoincarรฉโHopf Theorem, which states that with finitely (zero included) many zero points in a vector field, the sum of the indices of the vector field is equal to the Euler characteristic of the space.
An index of a vector field only has a defined value at a zero point.
The Euler characteristic of a ball is 1. I checked on wolfram alpha, and honestly can't be bothered to learn more about it at the moment.
Therefore, there must be a nonzero amount of zero points in a vector field, in order for the indices to add up to 1.
I'm not sure what "limited" means in this context. In the classic example, the cowlick is not a zero point when you extend into a third dimension: the vector points "up", away from the surface. You have a zero point in two dimensions, but not in three (this is kind of the whole point of HBT - the cowlick is the non-zero point projection into the third dimension). Note that I'm calling the surface of a sphere a two-dimensional object.
2weirdy ยท 1 points ยท Posted at 17:13:58 on May 25, 2016 ยท (Permalink)
Limited effetively means finite sized space. Even if you extend into the third dimension, a 3-dimensional sphere is effectively the surface of half of a 4-dimensional sphere, like a circle(2d sphere) is the surface of half of a 3-dimensional sphere, and a line(1d sphere) is the surface of half of a 2d sphere. The hairy ball theorem applies to ALL of those, and therefore also to the 4d sphere surface, and thus also to a filled 3d sphere (ball).
Think about it this way. if you have air moving "up", you'll reach the edge of the atmossphere eventually. Unless you have an infinitely large OR looping space (such as a torus or donut), there will always be a zero point somewhere in that space.
Essentially, you can only have no zero points if you allow circulation into a dimension you're not using, in other words having circulation into nowhere.
Slime0 ยท 1 points ยท Posted at 18:43:32 on May 25, 2016 ยท (Permalink)
The theorem doesn't hold for a sphere in 4D space (a 3-sphere).
2weirdy ยท 1 points ยท Posted at 21:29:28 on May 25, 2016 ยท (Permalink)*
Right, missread that. Still, I can't imagine a non-vanishing continuous vector-field in a finite ball in 3 dimensional space. I can neither find proof against nor for whether or not it is possible so far. Might come back when I do so.
Edit: Alright. The Hairy Ball theorem is actually a result of the PoincarรฉโHopf Theorem, which states that with finitely (zero included) many zero points in a vector field, the sum of the indices of the vector field is equal to the Euler characteristic of the space.
An index of a vector field only has a defined value at a zero point.
The Euler characteristic of a ball is 1. I checked on wolfram alpha, and honestly can't be bothered to learn more about it at the moment.
Therefore, there must be a nonzero amount of zero points in a vector field, in order for the indices to add up to 1.
I've updated my previous post to reflect this new proof. So while my argumentation was wrong, my initial statement based on a hunch was right. Considering this is a reddit comment and thus not that important, I'd say good enough in this case.
That's assuming a form of two dimensional space on the surface of the sphere, though. The earth isn't a closed system, the energy that drives wind comes from an external source. The zero point for terrestrial wind could be miles above the surface. Imagine a blow dryer pointed at your tennis ball.
Ugbrog ยท 5 points ยท Posted at 15:07:26 on May 25, 2016 ยท (Permalink)
from wikipedia: This is not strictly true as the air above the earth has multiple layers, but for each layer there must be a point with zero horizontal windspeed.
But how thick are those layers? If they're arbitrarily thin, that's just another way of saying they only have two dimensions. If at a point, however, the vector points "up" (i.e. you recognise an extra dimension), it is not a zero point.
Ugbrog ยท 4 points ยท Posted at 15:19:19 on May 25, 2016 ยท (Permalink)
You do realize that you're arguing the premise, right? The point of the HAIRY BALL theorem is that you can't comb the hairs of the ball in the same direction. You end up with hairs pointing STRAIGHT UP. No one cares about the third dimension because IT WAS NEVER PART OF THE PROBLEM.
You do realize that you're arguing the premise, right?
No, I'm not.
I'm addressing a very specific claim, made above: "there is always a spot on earth where there is no wind".
My point is that this would only be true if you assume two dimensions. In three, it's not true.
Ugbrog ยท -2 points ยท Posted at 16:22:09 on May 25, 2016 ยท (Permalink)
Which is a pointless argument, since we are only discussing horizontal windspeed as described by the mathematical theorem that this entire discussion is about. But yes, he was incorrect in how he oversimplified the phenomenon. Good job.
It's not pointless, it's precise. What's pointless is your incorrect and oddly aggressive assertion that I was arguing the premise. And I mean it is literally pointless - you have contributed exactly nothing of value to this discussion.
Ugbrog ยท -1 points ยท Posted at 17:19:37 on May 25, 2016 ยท (Permalink)
It would have to be vertical. Suppose that, for every point on the surface of the earth, x, we have a 3D wind vector w(x), where w(x) is not orthogonal (entirely vertical) to the surface. We of course assume w is continuous. Now suppose for each vector w(x), we take the projection of w(x) onto the tangent plane to the earth at x. Call that projection p. Projections are continuous, so p is continuous. Then p(w(x)) is continuous. Since no w(x) is orthogonal to the earth, p(w(x)) is nonzero for every x.
So, we would have a function p(w(x)) which is continuous, nonzero, and tangent to the surface at every x. This is a contradiction to the Hairy Ball Theorem.
Well, sure, but for the most part the wind on earth moves parallel to the ground. The up drafts and downdrafts are either too small to be considered, or they are moving along the ground as well.
Right but at the hypothetical zero point you could just have rising air - the "cowlick" and so even theoretically, there won't be a zero point for wind.
that and there are nothing but flat topology on earth, but since there are mountains its dynamic enough that theoretically you can have ZERO places on earth without wind moving.
ydubs ยท 0 points ยท Posted at 16:13:10 on May 25, 2016 ยท (Permalink)
Well, don't forget that the second dimension is really a function of the third and fourth dimensions!
2= (34 )(34) - (43 )(43)
And that's my favorite math fact
[deleted] ยท 3 points ยท Posted at 15:03:16 on May 25, 2016 ยท (Permalink)
Amphidromes! I just learned about these. Where the tide barely moves.
The two point thing you may be thinking of is that there exist two points on the exact opposite end of the Earth with identical temperature and humidity (or any other pair of measurements like 2d wind direction and magnitude). It comes from the Borsuk-Ulam Theorem.
I want to say that it's more that the solutions for a single point is so special that they just don't really happen. And the poles don't have to be opposite to each other.
But it's been like 12 years since or so since I was into math, so things area bit fuzzy (pun intended).
c3534l ยท 2 points ยท Posted at 16:24:14 on May 25, 2016 ยท (Permalink)
There's also always two spots where the temperature is exactly the same.
potatan ยท 2 points ยท Posted at 18:39:55 on May 25, 2016 ยท (Permalink)
Correct me if I'm wrong, but that's only true for an instant in time. The thing is that wind is about movement, so it requires time to really mean anything. Like if you took a snapshot of the earth right now, at least one spot would have no wind. However, if you were watching a video of the wind on earth then that one spot could be moving around constantly which means it wouldn't be a stationary point.
Yes. Just for some instant, and the spot shifts anywhere. As other's have pointed out there's likely still updraft at this location, but that's not how wind speed is measured.
It actually doesn't. The earth isn't topologically equivalent to a sphere, it has a really really high genus (all the tunnels through mountains and even natural rock formations give the earth holes) so the theorem doesn't necessarily apply to the earth. It might do for the surface of Jupiter though!
This brings back bad memories of dealing with streamlines and stagnation points in my aerodynamics class.
[deleted] ยท 1 points ยท Posted at 16:35:33 on May 25, 2016 ยท (Permalink)
This assumes far too much about the earth, that wind is measured with large vectors for example (they are just approximations, each instantaneous location is too small to measure). Wind is movement of nitrogen molecules - there are at any given time almost uncountable numbers with common velocity values imaginable.
In other words, it is purely a hypothetical that is true of a mathematical model, but on Earth has no practical meaning.
This is not true, there need only be one spot with no wind tangential to the earth 's surface, it can and probably will blow upwards and downwards at that point.
Paladia ยท 1 points ยท Posted at 18:05:05 on May 25, 2016 ยท (Permalink)
This proves that there is always a spot on earth where there is no wind. (I believe it's 2 spots, but I can't recall)
No it doesn't as the Hairy ball theorem only applies to a two dimensional sphere. Wind blows in the third dimension as it can also change altitude, as well as blow in different directions depending on altitude.
How? All the wind on earth doesn't simultaneously travel in the same direction right? Isn't it in like 'pockets'? (me trying to remember 7th grade science class)
simuse ยท 1 points ยท Posted at 18:28:06 on May 25, 2016 ยท (Permalink)
I'm in my bathroom right now, and I can confirm : no wind.
yaosio ยท 1 points ยท Posted at 18:37:32 on May 25, 2016 ยท (Permalink)
What if I have a fan going in the spot where's there's no wind?
Also, it can be used to show that at any given moment, there are two points on the earth exactly opposite of each other which have exactly the same temperature and barometric pressure.
There's an analogous theorem in chaos theory: every iterated map that maps over itself must have a fixed point. When you make a smoothie, there's always some point that didn't move at all.
This is just dumb. Wind have different speeds and can move in 3 dimensions. It's flowing more like water. And then there's the size of the "spot" you're talking about.
[deleted] ยท 2 points ยท Posted at 15:50:11 on May 25, 2016 ยท (Permalink)
That it has different speeds and flows like water is irrelevant. That wind can blow up or down is true, so, interpret the statement as 'there is at least one spot on the earth where the wind is not blowing east/west or north/south (but possibly up/down).'
It's not dumb at all! It's both true and not at all obvious!
You can try to apply it to wind, but in a mathematical sense it doesn't prove that at all because the earth is (as far as I know) 3-dimensional which clearly doesn't meet the requirements of "even-dimensional n-spheres". I guess such details don't stop people from upvoting false facts though.
You're thinking of ambergris. Aphasia is a thing that gets set to stun in startrek.
desopez ยท -2 points ยท Posted at 20:11:38 on May 25, 2016 ยท (Permalink)
Your thinking of ambergris. Aphasia is a combination of a speech and language disorder caused by damage to the brain that affects about one million individuals within the US.
[deleted] ยท 2 points ยท Posted at 19:09:29 on May 25, 2016 ยท (Permalink)
You're thinking of Asteroidea. Apple is a mass of snow, ice, and rocks falling rapidly down a mountainside.
You're thinking of Atlantis. Astronaut is the study of movements and relative positions of celestial bodies having an influence on human affairs and the natural world.
You're thinking of... Wait I forgot what we were doing.
icanhe ยท 1 points ยท Posted at 17:29:52 on May 26, 2016 ยท (Permalink)
You're thinking of Oldsmobile. Auroras were made by Oldsmobile.
Source: owned one
Throtex ยท 2 points ยท Posted at 17:55:18 on May 26, 2016 ยท (Permalink)
lol I was waiting for this response after I realized the actual car connection
icanhe ยท 1 points ยท Posted at 17:58:50 on May 26, 2016 ยท (Permalink)
I don't know if you've ever seen/been in an Oldsmobile Aurora, but they were a joke of a luxury car. I was the 3rd owner of mine, a broke college student, and that thing handled like a spaceship.
Hysterical looking car, sometimes I miss its ridiculousness.
[deleted] ยท -1 points ยท Posted at 14:59:14 on May 25, 2016 ยท (Permalink)
You're thinking of Accord. Aurora is the main artery of the body.
Then the hairy ball theorem obviously does not apply and the hairless ball theorem comes into play which states that on any surface devoid of vectors, a cowlick becomes impossible and that Nair can cause irritation in sensitive areas.
You have started something beautiful my friend. The larger the group of people who manage to continue this correctly, the more I love it. This is why I reddit!
BAMFMF ยท 1 points ยท Posted at 22:48:16 on May 25, 2016 ยท (Permalink)
upvote for the edit.
[deleted] ยท 286 points ยท Posted at 13:17:53 on May 25, 2016 ยท (Permalink)
It's one of those ones that if you think about it, it intuitively seems almost certainly to be true. But I wouldn't even know where to start on the maths of proving this
Crandom ยท 168 points ยท Posted at 15:08:34 on May 25, 2016 ยท (Permalink)
Ah yes, half of my proof techniques in my Analysis homework. Mention a few definitions, a proof result from class, somehow connect the dots, and we're done!
[deleted] ยท 2 points ยท Posted at 19:05:36 on May 25, 2016 ยท (Permalink)
I recall my differential equations professor was very fond of that technique
Spogito ยท 1 points ยท Posted at 15:30:52 on May 25, 2016 ยท (Permalink)
As a lab monkey would use emiprical evidence from 30 different tennis balls and 30 different combs AND novelty sized versions too.
Source: my few memories of middle school geometry class.
c3534l ยท 39 points ยท Posted at 16:26:04 on May 25, 2016 ยท (Permalink)
From math exchange:
Assume there is such a vector field. Let vxvx denote the vector at the point xx. Now, define the homotopy H:S2ร[0,1]โS2H:S2ร[0,1]โS2 by the following: H(x,t)H(x,t) is the point tฯtฯ radians away from xx along the great circle defined by vxvx. This gives a homotopy between the identity and the antipodal map on S2S2, which is impossible, since the antipodal map has degree โ1โ1. Hence there can be no such vector field.
So I imagine you'd have to first start by looking up what homotopy means.
Basically, a homotopy is a smooth deformation of one function to another. It's somewhat similar to the "squish a donut into a coffee mug" concept.
Here's an ELI5 of the proof:
We'll do a proof by contradiction. Assume such a vector field exists. We'll use this field to deform the identity map into the "antipodal map" (which is just f(x) = -x). There's many ways to show this, but it turns out that no such deformation can exist. So if we can build one using this vector field, that vector field can't exist.
Given a point x, there's a non-zero vector v_x attached to it. Imagine you're an ant at point x, and you walk in the direction of v_x. You'll trace out an arc on the sphere, eventually making it back to where you started. Let F(x,t) be the location of an ant starting at x and walking for time t.
Note: we can pick whatever speed we want for our ants. Let's pick ants that walk halfway around the sphere by the time t = 1. This only works because v_x is non-zero for all x. If some v_x were zero, the ant starting at x would just stand there like an idiot, and never make it to the other side.
Now we can define the deformation we wanted. For each time t between 0 and 1, let f_t be the function that sends x to F(x,t). So f_0(x) = F(x,0) = x (because the ants haven't moved yet), and f_1(x) = F(x,1) = -x (because the ants made it halfway around). So as t slides from 0 to 1, our function f_t smoothly changes from the identity map to the antipodal map. That's the deformation we were looking for!
c3534l ยท 1 points ยท Posted at 18:31:08 on May 25, 2016 ยท (Permalink)
Sorry if this is a stupid rephrasing, but would that mean if such a hairy ball existed, our ant might wander in some direction and wind up facing the wrong way?
Not quite. The ants are points, so there's not really a notion of them facing the wrong way. The real issue is that if such a hairy ball existed, we'd have ants that could walk to the other side of the sphere in a continuous fashion (nearby ants take similar paths). It's a little surprising, but that can't exist; you must have ants that behave very differently no matter how close they start out.
For example, if every ant except at the poles walks to the right latitude, then walks through 180 degrees of longitude, you still have to figure out what to do with the polar ants. No matter which way you start them moving, they'll move discontinuously from their neighbors.
This boils down to the "there's no deformation from the identity to the antipodal map". If you want more intuition for that, note that the antipodal map can be deformed to a reflection across the equator (just rotate the ball). So it suffices to show that there's no deformation from the identity to a reflection, which is a little less surprising.
c3534l ยท 1 points ยท Posted at 19:39:39 on May 25, 2016 ยท (Permalink)
I'm learning topology right now, so that's quite helpful. I'm still building my intuiton about this sort of thing.
Imagine that you are walking in a loop on a flat surface with a wind vane pointing the direction of the wind at every point. Call the number of complete rotations the wind vane makes the winding number of the loop.
Cut the Earth into two halves along the equator and flatten the two hemispheres into discs without disturbing the wind pattern. Note that because of the way the two hemispheres were attached, the winding number along the loops forming the boundaries of the two discs always have a difference of two, which means in particular that they both can't vanish at the same time. Try making a picture to convince yourself of this.
If a loop on a flat plane doesn't enclose any point at which there is no wind, its winding number of the loop has to vanish. Because if it didn't, we could continuously shrink the loop to a point, which has winding number zero, and the winding number being an integer can't suddenly jump as the loop is deformed. (For the case when the wind at some point vanishes, the wind has no well-defined direction at that time and the above argument doesn't apply.)
It follows that at least one of the two hemispheres must contain a point at which the wind vanishes.
For those uninitiated, an n-sphere refers to the dimension of the sphere surface, not the dimension of the space that contains it. So a tennis ball is a 2-sphere, as it's a surface, not a 3-sphere. A circle is a 1-sphere, which is why you can define a nonvanishing continuous tangent vector field quite easily thereon.
"Hairs" in this sense refer to vectors tangential to the surface of the tennis ball.
English: wind has a direction, North/South/East/West and the wind pushes air along the surface of the Earth. Imagine hairs on the tennis ball as individual gusts of wind, the direction each hair is facing is the direction of said wind, and the length of the hair is how strong the wind is.
Consequence: the phrase "no non vanishing continuous tangent field" translates to meaning that there is no magic configuration of hairs (in terms of spirals along the surface of the tennis ball) in which everybody lays flat. There has to be a break somewhere, and in terms of wind (since the Earth is a closed system of wind-tangents) there must always be some point on Earth where there is no wind right now.
English: It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.
Though an actual tennis ball has a finite number of hairs and each hair has a non-infinitesimal width. I would kinda like to know if the details for the actual physical case have been worked out, and if it has any real connection to the Hairy Ball Theorem besides the superfluous similarity.
What does same direction mean here? If I have a tennisball in 3d-space, all the hairs point towards a single point in space? Or same direction along the 2d-surface of the ball?
The ham sandwich theorem states that given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n โ 1)-dimensional hyperplane.
English: You can cut a ham sandwich(any sandwich of n dimensions) in half and have with your friend.
Thinking about how 2D creatures would observe the passing of 3D objects, I don't believe this is true. I would expect a 4D object passing through 3D space to manifest as a pretty serious violation of the laws of thermodynamics (e.g. a planet growing out of nothing, and returning to nothing). Of course, the absence of evidence is not evidence of absence, but it's pretty compelling in this case.
It is true that time is a dimension, but it is not considered a spacial dimension as far as I know.
eoghanf ยท 1 points ยท Posted at 21:03:24 on May 25, 2016 ยท (Permalink)
Why even-dimensional?
ktkps ยท 1 points ยท Posted at 02:37:54 on May 26, 2016 ยท (Permalink)
You know how theorems state things considering a perfect backdrop? Thats the reason... You never question Pythagoras theorm asking what if one of the side is slightly bent...
eoghanf ยท 1 points ยท Posted at 06:27:25 on May 26, 2016 ยท (Permalink)
No. This is not the reason. Even-dimensional means "of dimension 2,4,6,8...".
Is the "comb" thing a simple way of illustrating the point, despite the fact that the teeth are parallel?
I imagine from any hair root as the center, the polar vector of each hair could be relatively identical. But you (obviously?) can't accomplish that with a comb because parallel teeth cause parallel hairs to have identical absolute Euclidean vectors over the curve created by the vector of the comb, not identical relativistic polar vectors (which definitively can't be equal).
These are called cyclic numbers. Part of my undergrad research were on these types of numbers. 7, 17, 19, and 21 23 are the first numbers that form cyclics. They are formed by n/p, where p is the full repetend prime used to form the cyclic (say 7) and n are all numbers p-1 (1, 2, 3, 4, 5, 6).
Some other properties include if you split the number into two separate halves, for instance split 142857 into 142 and 857, and add the two halves together you will get a number containing only 9's (142 + 857 = 999). If you split the number into thirds you will achieve the same result: 14 + 28 + 57 = 99.
If you multiply the base cyclic (142857) by the prime that produced it (7), you will get a number containing only 9's (142857 x 7 = 999999). Multiplying by a number greater than p, for instance 8, will give you the following: 1142856. You can then get back to the original cyclic by taking the right most p-1 numbers and adding the left over numbers: 1 + 142856 = 142857.
If we again break the number into two halves, square each half, and then subtract the resulting numbers, you will receive a permutation of the cyclic. Example: 8572 - 1422 = 734449 - 20164 = 714285.
There are even more facts to cyclics, but this Numberphile video can explain more!
Edit: Made a mistake on the squaring each half, you are suppose to subtract them not add them, thanks for pointing that out /u/DoubleFuckingRainbow
"I think that weird guy with the beard that always stands next to the water cooler finally snapped. He's going on about cycling numbers and repeating 9's."
Man that's some interesting shit. It always amazes me that these patterns exist. It seems to me like maths is something that just IS rather than our own attempts to describe the world we live in.
But then again I'm from a biology field so my understanding of maths has always been embarrassingly limited to simple statistical analysis!
It seems to me like maths is something that just IS rather than our own attempts to describe the world we live in.
And the stuff you're reading here is only the tip of the iceberg. The patterns just keep getting more profound and amazing the deeper you go.
But it's still a tough call to say whether maths is "something that just IS", because you could observe that the patterns of maths are just a product of the logic we use, which is, in fact, merely the logic we choose. Logic and maths are the same thing, really. And they're man made. The logic/maths we choose certainly seems to reflect reality, but perhaps they just approximate it. There's no way to say for sure. There are many logics that might accurately describe reality. Or the universe may even be inherently illogical. Maths/logic could just be a tale told by a race of idiots, full of sound and fury, signifying nothing.
What happens if we use any ther basis than 10? What numbers are cyclic? Are some numbers cyclic for many basis? If n is cyclic for basis a, is it cyclic for a*b or something?
Yes there are cyclics in other bases. I don't have my research available right now, but just pulling some information from Wikipedia you can construct the cyclics in other bases using the following method:
Let b be the number base (10 for decimal)
Let p be a prime that does not divide b.
Let t = 0.
Let r = 1.
Let n = 0.
loop:
Let t = t + 1
Let x = r ยท b
Let d = int(x / p)
Let r = x mod p
Let n = n ยท b + d
If r โ 1 then repeat the loop.
if t = p โ 1 then n is a cyclic number.
[deleted] ยท 1 points ยท Posted at 17:02:27 on May 25, 2016 ยท (Permalink)*
I used to do this stuff in school too, it's like a little game, finding little patterns in stuff. It's like doing puzzles but without being sure there is actually an answer.
This. I wish this playing-with-numbers attitude would be taught at school instead of rote memorization. It practically killed my math skills at a very early age.
I figured out the n/7 fractions as well around 10 by realizing with long division in my head that the remainder kept doubling (14, 28, 57 (56 Cary over the one from 114))
If we again break the number into two halves, square each half, and then add the resulting numbers, you will receive a permutation of the cyclic. Example: 1422 + 8572 = 20164 + 734449 = 714285.
I dont get the same result as you? i get 754613
EDIT: Its 8572 - 1422 and you get the right result
I didn't know most of those other facts, but they feel true to me without checking them, due to other things I know more about. In my case, that's generators in a finite field using modular exponentiation.
Slivlan ยท 3 points ยท Posted at 15:08:55 on May 25, 2016 ยท (Permalink)
Any idea about what are the requisites (I'm not sure that's the word I need, sorry, am not English) for a number to be cyclic?
Slivlan ยท 2 points ยท Posted at 16:12:48 on May 25, 2016 ยท (Permalink)
Bot now the number you get has to add up to bn -1 if you split it in half. And also all the other stuff. Is it that how you look for "new" cyclic numbers? Going through permutations that add up to 999...?
Well the multiply by 7 or splitting of the elements to form a 9's number is kind of trivial. Since you cant divide 1 by 7, you are always approximating it as close as possible to 1 which will be a long string of 9's. So wherever you decide to taper the division when you multiply by 7 you will get a string of 9's.
cboski ยท 1 points ยท Posted at 15:22:29 on May 25, 2016 ยท (Permalink)
How exactly do you conduct your research? Do you just grab random numbers and attempt to apply properties to them or is there a pattern searching/testing algorithm somewhere?
I did not unfortunately. I am now studying Nuclear Engineering. Friends of mine did go on to graduate school from Pure Mathematics though, which includes Number Theory and Abstract Algebra. They have told me that at this point they miss numbers!
I knew about the 7ths thing, but splitting and summing the string for an all-9's number just blew my mind. That kind of thing just feels too complex to work perfectly. Is there some elegant way to explain why this happens? Are there similar properties to numbers in other base systems? Would an analogous operation on cyclics in base N result in N-1 repeating?
I don't have my research available at the moment, I will have to dig it out when I get off work, but I was able to prove the string of 9's and why it will always work.
There are cyclic numbers in other bases, for instance in ternary both primes 2 and 5 form cyclic numbers, 1 and 0121 respectively. They follow the form (bp-1 -1) / p, where b is the base and p is the full repetend prime.
ademnus ยท 1 points ยท Posted at 16:06:24 on May 25, 2016 ยท (Permalink)
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
Multiply any number made of ones by itself. This pattern seems to go on forever. Is this a "cyclic number" or something else? I find it so interesting how the results follow this pattern where the middle numeral of the answer equals the number of 1s in the number (let's call it X) in the equation and it's a sequence of numbers that incrementally rise from 1 to X and back down to 1.
No this is some form of sequence. Cyclic numbers are formed from 1 prime number, such as 7. 11 would not be cyclic because:
1/11 = 0.09
2/11 = 0.18
3/11 = 0.27
4/11 = 0.36
5/11 = 0.45
...
These numbers would all have to be permutations of each other.
ademnus ยท 1 points ยท Posted at 16:18:05 on May 25, 2016 ยท (Permalink)
I've always found it so odd. Now to just wait for the day a gameshow host asks me "what's 111,111 times 111,111" so I can answer without doing math and collect my winnings! thiswillneverhappen
You are forgetting a zero! But yes I never knew about this one. This isn't a cyclic though, as 2025 isn't prime.
godnah ยท 1 points ยท Posted at 16:39:03 on May 25, 2016 ยท (Permalink)
These are called cyclic numbers. Part of my undergrad research were on these types of numbers. 7, 17, 19, and 21 23 are the first numbers that form cyclics. They are formed by n/p, where p is the full repetend prime used to form the cyclic (say 7) and n are all numbers p-1 (1, 2, 3, 4, 5, 6).
But can't any number be reached from another number by some kind of equation? Like if you want 22 and you are given the numbers 1000, 45, 56789033 and 39.876, you can get to 22 you can design an equation to get you to 22. I'm by no means fluent in maths, but I hear people talk alot about searching for repeating numbers and number sequences, but it seems that you can get to any number from any starting number by an equation. I'm not sure how to describe it, but it's like you can make the rules work in your favor to get the answer you are looking for.
Yes, that is by using any form of equation. This holds true for a set equation for all cyclic numbers. You can take any cyclic and perform the difference of squared halves and still receive one of the cyclics. I'm not squaring one, cubing another, dividing and then adding. It is a set formula that will always work.
I kind of don't understand your reply, or even my original comment to your comment, but what I was thinking of when I posted my original comment was the film "23." In that film, the main character became obsessed with the number "23" and went looking for it everywhere, and he seemed to find it everywhere and called it some grand conspiracy. But what I am trying to ask or talk about is... if you want to find a number, say 23, you can find it anywhere by using an equation tailored to that specific situation to get you to "23." So when people talk about number patterns and problems I have a hard time understanding or grasping the concept of there being things that haven't been solved yet, because you should be able to formulate an equation that gets you to your desired destination or "number." I am not even sure I am making sense at this point anymore.
Sampwnz ยท 1 points ยท Posted at 17:31:09 on May 25, 2016 ยท (Permalink)
Cline Butte, Crooked River Ranch Rim Repeater, South Madras, and Juniper Butte Round Butte.
Sorry, I run a WISP and we assign area numbers to different sites for MPLS tagging, vlans, and private IP ranges based on odd numbers (Evens for the backhaul links) so when I see a bunch of small, odd numbers my brain instantly reads geographic locations instead now. x3
Quigz ยท 1 points ยท Posted at 23:49:22 on May 25, 2016 ยท (Permalink)
Holy shit thank you so much. Like, I knew that 0.9 repeating = 1, but I never understood that 0.142857 repeating was 1/7th of 0.999999 repeating. I think I finally understand fractions now.
Tasgall ยท 1 points ยท Posted at 00:29:45 on May 26, 2016 ยท (Permalink)
If you multiply the base cyclic (142857) by the prime that produced it (7), you will get a number containing only 9's (142857 x 7 = 999999).
Ha - I figured this out, or a version of it, in high school: any number divided by a number of the same length consisting of only 9s gives you a cyclic version of that number. Ex:
142857 / 999999 = 0.142857142857...
or
123 / 999 = 0.123123123...
or single digits
7 / 9 = 0.7777...
The reason I figured that out of course was because arguing with the math teacher about the "fun math fact" that "0.9 repeating equals 1" was all the rage at the time, and being able to show that "x/9" = "0.xxxxxxx..." made it really easy to prove because the fractional form of 0.9999... would then have to be 9/9, which is 1.
Fun times, I didn't know it went deeper than that.
MJWood ยท 1 points ยท Posted at 12:55:24 on May 26, 2016 ยท (Permalink)
These are all just incidental features of using a decimal system, aren't they? There should be some sort of function of n, where n is your base number, that allows you to calculate cyclic features for any n - but I'm just speculating wildly here.
Wow I didn't know this. My interesting fact about sevenths is that you get this number .142857... by taking (7*2/100) + (7*22 /1002 ) + (7*23 /1003 ) etc...
I never realised that the result is cyclical though.
This is something that has always freaked me out about the n/7 series in particular. Obviously the last two digits '57' are off by one (7*23 = 56) so I guess it could just be a big coincidence. But is it?
If you haven't already done so, sneak a peek down to my post below where I explain that it isn't a coincidence at all and is a result of carrying. You can go a step further and sum the geometric series u/modernbenoni refers to and show directly that it is equal to 1/7.
It works because 7*24 is 112, so the 1 in the hundreds place carries and adds to 56. What I didn't know is that there were other numbers that produce this pattern too. I wonder if there are infinitely many? Are they all primes?
I used to teach commodities options trading in a trading pit to grad students. On day 1 I would have them memorize all the decimal equivalents of fractions from 1/2 to 1/16 (skipping 1/13 and 1/15 because they end up being fairly useless if you know everything else. It's a lot of fun to see someone who's lived a lot of life and studied a lot of math realize how powerful knowing these simple fractions are for estimating quantities on the fly.
One thing to add: 1/14th is just 1/2 of 1/7th, and since it doubles with every pair... 1/14th = .072856(rounding down to make a point here)
Gelnef ยท 1 points ยท Posted at 20:59:55 on May 25, 2016 ยท (Permalink)
If I was to teach math in school I'd make the kids learn decimal approximations like this. I keep them memorized as approximate factors of 100 or 1000, with two digit accuracy. And no, don't skip 1/13 (roughly 77) and 1/15 (a third of a fifth, roughly 67)! So, the list goes:
jorellh ยท 1 points ยท Posted at 15:02:44 on May 25, 2016 ยท (Permalink)
I don't like 1/7, it is the first "ugly" fraction to me in base 10
JJean1 ยท 1 points ยท Posted at 16:03:21 on May 25, 2016 ยท (Permalink)
But this fact should make it "not ugly". The first one I don't ever bother learning any decimal places for is 1/13. Even 1/11 has the nice form 0.09090909090909...
jorellh ยท 1 points ยท Posted at 16:47:18 on May 25, 2016 ยท (Permalink)
It gives the impression that nine of the numbers quite fit in so it keeps cycling the pattern. Almost ad if it would be nice in base 9
Holy cow! That's really cool, but how did anyone ever notice this in the first place? Was there just some guy dividing everything by 7 one day and was going over his answers and was like "waaaait a minute..."? I would never have spotted that.
That's actually exactly how I noticed this. Probably when I was in high school or even in late elementary school. If you use a calculator a lot, it's not that hard to spot it.
JJean1 ยท 1 points ยท Posted at 16:00:30 on May 25, 2016 ยท (Permalink)
I am a math instructor and I love using this in the few instances it comes up. Students are always amazed that I can instantly write down a lot of decimal places, but, unfortunately, they do not seem to care when I try to show them what I did. They just ask "Can't we just use the calculator?".
Divide 7 or its multiples end up with an integer, actually if you divide any number by anything buts its multiples you end up without an integer. In fact the exact same fact happens of 3, 9, 11, but they just have a much shorter string (1 for 3 and 9, 2 for 11)
I actually found this out myself when having sex because I do math to last longer in the sack. The harder the math the more you have to focus on it and the longer you last.
I started doing shit with sevens because I already got bored with primes, and powers of 2.
I think this is my favorite one cause its so easy (for me) to remember to do in my head despite looking difficult to normal people.
The number that repeats in the decimal is 7 doubled each time: .7 14 28 5(6 but it repeats to 7 here to start the loop over again)
Take the numerator and multiple by 10. Then divide by 7. What is the whole number part of the quotient? That's where you start the sequence. 2/7: 2 x 10 = 20 / 7 = 2.something = .285714285714....
This is true for all decimals. Well, not quite. Rational decimals will either:
a) Stop. e.g. 1/10.
b) Repeat the same number for ever. e.g. 1/3 (which is basically a cycle of length 1).
c) Form a cycle. e.g. 1/7.
Think about doing long division. Either you end up with a perfect remainder and stop OR at some point you'll have to do a division you've done already and the pattern will repeat from there. The length of the repeating string cannot be more than the value of the number. I.e. 1/7 must have a repeating string of length 6 or less.
g_h_j ยท 1 points ยท Posted at 17:46:00 on May 25, 2016 ยท (Permalink)
Hey! Hush hush! Dividing things by 7 in my head is my party trick, you're ruining things. For me and my obviously cool parties...
I figured this out when I was 7, messing around with my dad's calculator. And the next year I was looking at a map and announced to my 3rd grade class that South America and Africa used to be joined.
It's all gone downhill from there.
Qscfr ยท 1 points ยท Posted at 18:28:33 on May 25, 2016 ยท (Permalink)
I raced someone on a calculator to find 300/7 in my head once. I knew this fact, that 1/7 was .14285xxxx, and multiplied by 100 and then by 3. Was wrong on the 4th or 5th decimal point but got the approximate-enough answer in the same time. Had I known 3/7 was .428571 I would have been even quicker. So, TIL.
I remember being a lonely 7 year old kid with a calculator and figuring that out myself. Tried to tell my friends and teacher. Whoever understood it wasn't impressed.
YLXV ยท 1 points ยท Posted at 03:46:07 on May 26, 2016 ยท (Permalink)
my grade 7 math teacher showed me this one time and it saved me on a university math exam a couple months back
Edit: Wasn't really expecting this post to get noticed but it pleases me greatly that so many people are holding their phones while putting their fingers in awkward positions, probably in public.
I 19 most of you, the rest can have a heaping helping of 132.
**edit 2: For those complaining about hurt fingers/difficult positions: Really it is just about representation. If you need to know binary 8 or 9, you can visualize it by going left to right and saying " 0 ouch 000 ok that is eight; 0 ouch 00 ouch ok that is nine. " Even if you can't physically make your fingers make the numbers you can easily visualize the values using your hands.
Kind of reminds me of the phrase "Digital Rectal Exam"... It sounds super high-tech as if it uses some awesome computer-machine to scan your bowels similar to an MRI or X-Ray...
There are 10 kinds of people in the world. Those who understand binary, and those who understand ternary, and those who understand quaternary, and those who understand quinary, and those who understand senary, and those who understand octal, and...
Yup! I learned a lot about hexadecimal today. I wonder if I'll retain it...
Edit: It's been 21 days, which is ancient in internet times on askreddit. I haven't thought about hexadecimal since I wrote this. I retained nothing. But if you found this then you're some kinda weirdo historian who goes through internet comments. Hi! I hope it excites you to be found like this. I hope it's like 120 years later (June 16, 2136 by my calendar) and you can't believe this letter I wrote, apparently to you.
Although the joke sounds better this way, doesn't using 10 require 2 bits and therefore can have 4 different values assugned to types of people :p? (00, 01, 10, 11)
Edit: Yeah, I know how two's complement works. My comment was more joking than serious anyway. The only standard I've seen that uses a signed zero is IEE 754, the most common standard for storing floating-point (real) numbers.
I thought about that when I wrote the comment, but I decided against mentioning it as I reckon it does not widely occur in the field of finger arithmetics. But yes, If you're in a situation where it is useful, its inclusion would also reduce the effective range by one.
[deleted] ยท 1 points ยท Posted at 23:04:47 on May 25, 2016 ยท (Permalink)
If you want to you can count in one's complement or sign and magnitude. But two's complement gives you one more number to work with.
Are hands big endian or little endian? How can this be standardized? I think people will intuitively use big endian, but then there's always going to be "that guy" who wants to use little because that's what x86 uses.
I fear that righties and lefties will count differently.
Also, do you supinate or pronate your wrists?
And are we really going to be able to express the full bit code? Some of those ring-pinky combinations are a bitch.
Intrexa ยท 2 points ยท Posted at 15:45:55 on May 25, 2016 ยท (Permalink)
I think it's going to be a bit more nuanced than that. I think we can agree that it's a 5 bit byte, with a words size of 2 bytes. Well, start counting on your hands, palms facing towards to you. I personally start on my right hand, and go thumb to pinky, then move to my left hand, and start with my left thumb and work to the left pinky.
So the most significant bit is now in the middle, right next to the least significant digit.
How the hell does binary work? It looks like a bunch of ones and zeros, how can it mean anything?
SkyKiwi ยท 7 points ยท Posted at 16:24:53 on May 25, 2016 ยท (Permalink)
I don't really know how we manage crazy shit like storing multiple numbers in binary or making computers out of black magic, but a single number out of binary is actually pretty simple. Easiest way to explain is with examples.
0 = 0
1 = 1
Okay, that's fairly simple. Now how do we get a 2? We add another digit. Any digit in the "tens" position counts the amount of "twos" we have.
10 = 2
11 = 3
Excellent! So what's the next number? 4! No, not 24. Just 4. Starting with the ones, each digit is double what the previous was. So the third added digit (the hundreds) is four. The fifth will be eight. So on so on. Using this combination, you can make any number, as 1000000 will always be +1 higher than 0111111 (with as many 0's are 1's, respectively, as each other).
100 = 4
1000 = 8
10000 = 16
11111 = 31
100000 = 32
100001 = 33
100010 = 34
100011 = 35
[deleted] ยท 4 points ยท Posted at 16:30:16 on May 25, 2016 ยท (Permalink)*
Not sure if sarcastic or not, but it's just in base two, so I'll try to explain.
The first digit, furthest to the right, has a value of 1. If it is 1, then you add 1 to the total. If 0, you add nothing.
Each place value is a power of two, so: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. 2048, 4096, 8192, ect.
I like to think of it as a sort of 'gate' system, so to speak, and when counting, you have to have all precursor fingers up to be able to move onto the next one. When that one goes up, all the previously up go down. Sooo, for example:
00001 = 1
00010 = 2
00011 = 3
00100 = 4
00101 = 5
00110 = 6
00111 = 7
01000 = 8
01001 = 9
01010 = 10
01011 = 11
01100 = 12
01101 = 13
01110 = 14
01111 =15
10000 = 16
Tah-dah. \o\
Sorry for such a long comment.
Edit for values because yeah.
Nerdn1 ยท 2 points ยท Posted at 17:00:17 on May 25, 2016 ยท (Permalink)*
Think of it like "normal" decimal numbers, but you only have "0" and "1" digits. So you count 1, then when you add another, you can't use the digit "2", so you go to the next digit over which in binary is the 2's place (whereas it would be the 10's place in decimal). So two would be written 10 in binary. You go from there with each place to the left of being 2 times the value of the last (just like each place to the left in a decimal number is 10 times the last). So counting in binary works like this:
Binary: decimal ("normal")
0: 0
1: 1
10: 2
11: 3
100: 4
101: 5
110: 6
111: 7
1000: 8
1001: 9
1010: 10
We found that the easiest way to make compact memory is to store it in units that can be either ON or OFF, which we'll call 1 for ON and 0 for OFF. Since we're limited to 1s and 0s, binary is best way to store numbers.
While computers only store 0s and 1s, the hardware is designed to interpret those 0s and 1s as instructions and data. Normally you store instructions that tells the hardware what to do with the data and where it is. Depending on the instructions, a series of 1s and 0s could be interpretted as a number, a character, another instruction, a pixel in an image, or anything else on your computer.
Look at it like this. Imagine in base 10, you have a line of zeros. I'll just demonstrate using 5 of them (or 1001 in binary!).
0 0 0 0 0
Imagine the numbers 10000,1000,100,10, 1 underneath each zero from left to right. To generalize, for radix (number base) b, each subsequent zero represents bn-1. So ten thousand is 104, one thousand 103, one hundred 102, ten 101, and one 100. Two facts that will stay the same no matter what radix you're in. The very first placement (the far right zero) will always be one, because b0 = 1. The one right next to it will always represent the base because b1 =b. And since this is base 10, there are 10 discrete values any placement can take: the numbers 0-9.
For example, let's have a number: 28495. Each discrete value represents value*placement. Then we add all the numbers together to get the final answer. Visualizing it looks like this:
(2*10000)+(8*1000)+(4*100)+(9*10)+(5*1)
Knowing this, let's apply it to binary. Imagine that line of zeroes again, except have the powers of two underneath them. So 16, 8, 4, 2, 1. Since binary is base-2, there are only two discrete values a placement can take: 0 and 1. Imagine the number 10100 in binary. Again, visualizing value*placement, we get:
(1*16)+(0*8)+(1*4)+(0*2)+(0*1)
Adding it together, we get the number 20!
occam7 ยท 5 points ยท Posted at 13:55:27 on May 25, 2016 ยท (Permalink)
I just counted to 31 with no knowledge of binary! Awesome. Probably a good way to demonstrate how useful binary is to someone for computers if they don't understand it.
Nerdn1 ยท 2 points ยท Posted at 16:47:49 on May 25, 2016 ยท (Permalink)
I can see this now. Telling a class that computer memory units can only be on and off. Think of them as your fingers being up or down (we'll take out the thumbs because we tend to arbitrarily group the bits into sets of 8). We tend to just count the number of fingers, but that will only get us 0-8.
That does something, but we can do better. Hey look, we can look at the POSITIONS of the fingers and each can be up or down, sort of like "normal" decimal numbers. Oh well, we only have up and not up. Let's give it a try anyway, and have down be 0 and up be 1. So we can only count to 1, before having to shift over, so the 2nd place over is the 2s place rather than the tens place. We can just keep doing this (please just do 4 in your heads, okay kids). You'll find that with just 4 fingers, we can get 0-15, almost double what we did with 8 fingers previously. With 8 fingers we can get 255. Now THAT is what I'm talking about!
CHE6yp ยท 2 points ยท Posted at 15:00:51 on May 25, 2016 ยท (Permalink)
There is a page about it? I used to do this sometimes to let people know how thoughful i am...
[deleted] ยท 1 points ยท Posted at 16:02:22 on May 25, 2016 ยท (Permalink)
There isn't anything special about binary that makes this possible, other than it being simple to represent 0 or 1 by raised or unraised fingers. The real magic is that instead of simply counting raised fingers, you've added the positions of the fingers into consideration. If you also allowed fingers to be half-raised (bent at the second knuckle), you could use ternary and increase your counting to 59,048.
[deleted] ยท 1 points ยท Posted at 16:13:09 on May 25, 2016 ยท (Permalink)
In sign language you can count to like... Whatever you want, man.
Nerdn1 ยท 1 points ยท Posted at 17:07:22 on May 25, 2016 ยท (Permalink)
Each number above a certain point would need multiple signs to express. Finger binary goes higher if you insist that all numbers are static. If we allow more than one hand state for a number we can add an arbitrary number of hands of digits (if we want the start and end to be unambiguous, we could restrict one of the fingers for a start or end flag).
[deleted] ยท 2 points ยท Posted at 17:20:39 on May 25, 2016 ยท (Permalink)
Sign language would still be infinitely more efficient in everyday use.
[deleted] ยท 1 points ยท Posted at 16:17:34 on May 25, 2016 ยท (Permalink)
I can't do this because I can't lift my ring fingers independently.
My friend showed me how to do this, eventually I ended up learning the basics. It's super helpful, and it was great for my music theory class when I had to count above 5 often.
64 and 4096 if you include zeroes and count your wrists.
jewdai ยท 1 points ยท Posted at 17:12:24 on May 25, 2016 ยท (Permalink)
While a smuller number, but easier for beginners to do, you can count to twelve on one hand.
using your thumb as a means of keeping track of where you are, start with the base of your index finger moving upwards count your inner knuckle using your thumb.
It's actually a lot less stressful on your fingers. Think about the number 3 you either hold it by using your thumb, index and middle finger up and the rest down or using your index, middle and ring finger with your thumb holding down your pinky.
wheras using 12 based system you're just holding the "OK" gesture to mean 3.
Its really awesome how simple yet effective binaries are. I wonder if children who were taught to count this way on their hands would have been better at mathematics.
Like, they would still use the HinduโArabic numeral system as a main, but would count on their hands with the binary numeral system.
For years, I had a nervous habit of counting to 32 on my right hand (In a fidgety kind of way). But somehow, it never occurred to me to extend it onto my other hand.
[deleted] ยท 1 points ยท Posted at 21:07:37 on May 25, 2016 ยท (Permalink)
I didn't know this was a real thing! I 'invented' it when I was a kid (probably 5-8 years old, not sure); I didn't know what binary was, but I used two positions (up and down) of the finger to count to large numbers when I couldn't sleep :) So glad it's been named!
This is how I count things (that take time and distraction between items). Though, I push my fingers for 1 into my palm and let the 0 fingers relax, so that no rude gestures are formed.
I once sat on the steps out by the quad in college and made it all the way to 1023. It took me almost half an hour, and I'm pretty sure some people thought I was crazy.
You said you 19 most of us. That's ASL for love. Do you happen to know ASL or is that handshape actually just common knowledge? ASL is what I've always used to count on one hand.
Edit: I've completely forgotten that's also like a "rock on" symbol. Never mind, I'm dumb.
I tried to count binary on my fingers, but it was so painful. Trying to hold up my left pinky and middle finger, and my right pointer and ring finger at the same time strained my tendons. It works better touching a table with a finger for 1 and raising the finger for 0.
It's easier to keep track of numbers up to 100. Left hand fingers are 1 each, the thumb is 5. Right hand is 10 for each finger, and 50 for the thumb. It works like Roman numerals; you can even draw I I I I V & L X X X X on your fingernails.
Really it is just about representation. If you need to know binary 8 or 9, you can visualize it by going left to right and saying " 0 ouch 000 eight; 0 ouch 00 ouch nine. " Even if you can't physically make your fingers make the numbers you can easily visualize the values using your hands.
Tsunoba ยท 1 points ยท Posted at 04:15:30 on May 26, 2016 ยท (Permalink)
I was actually wondering about the purely physical aspect of it, since I'm perfectly find with representing it another way.
ktkps ยท 1 points ยท Posted at 05:00:57 on May 26, 2016 ยท (Permalink)
the wizard of 0s1s
boarhog ยท 1 points ยท Posted at 08:47:50 on May 26, 2016 ยท (Permalink)
You can count to 243 on one hand using finger ternary
kdsl2 ยท 1 points ยท Posted at 12:03:04 on May 26, 2016 ยท (Permalink)
If you use base 3 on your fingers you can get to 242 on one hand and 59048 on 2. It requires having a midway position between up and down, it is very difficult to do without the help of a prop such as a steering wheel or handle bar though.
Tm1337 ยท 1 points ยท Posted at 13:05:22 on May 26, 2016 ยท (Permalink)
Using decimal you can count to 10000000000 (10 ^ 10) with both hands.
But how do you know how much digits the girl knows? What if she, too, starts saying random digits to impress you? Then you'd be locked in an endless spiral of meaningless digits. Too messy, dude, better impress her telling her that you know the last digit of pi
This is why I have people bring it up on their phone so they can follow along. I do 50 decimal points currently and plan to eventually recite a few hundred at least.
deusset ยท 1 points ยท Posted at 20:17:52 on May 25, 2016 ยท (Permalink)
I'd give you gold but I'm going to start using this and I don't want other people knowing about it. Now, please present your arm for a routine dysentery inoculation...
[deleted] ยท 1 points ยท Posted at 21:02:12 on May 25, 2016 ยท (Permalink)
Except, we now live in the age of smartphones and she can check you as you recite
Thud ยท 1 points ยท Posted at 22:12:50 on May 25, 2016 ยท (Permalink)
Actually, it's impossible for most people to recite convincingly random numbers quickly. Try it out! I always end up stumbling or repeating a cycle of numbers.
Thud ยท 1 points ยท Posted at 22:14:00 on May 25, 2016 ยท (Permalink)
True, and I end up accidentally reciting the digits of e.
Have you tried doing that? Whenever I'm reciting pi and people say I could just be saying random numbers, so I challenge them to try that. It's really hard to come up with random numbers that quickly without repeating a number or a string of numbers. Of course, it's possible, but if the person is reciting what they know really quickly, then getting into random numbers will drastically throw off the rhythm/speed.
Technically you just need to memorize 1 more digit thanas many digits as the girl already knows. Then just recite random digits because who is going to check you?
It's pretty much impossible to make up random digits on the fly. I alway trip up really quickly or start repeating the same sequence. It makes it pretty easy to tell if someone has it memorized as they can recite what are clearly non-repeating numbers quickly. I could probably get away with making up a couple extra, but it would become noticeable very quickly.
When I started dating my GF, I was talking to her over the phone and told her that I head memorized pi to 100 digits, and she obviously didn't believe me. So I rattled it off, and then she realized I was probably just saying random numbers, so she told me to do it again, so she could write it down, so I did, she wrote it down, and then I repeated it again verbatim. She was incredibly impressed with my intellectual feat. It was probably about a year or two later when I told her that I just googled it and was reading it off my computer monitor.
Actually, this is a real thing. When my husband and I first started dating he would whisper pi in my ear. So sexy!
lengau ยท 1 points ยท Posted at 20:22:15 on May 25, 2016 ยท (Permalink)
The key is to start memorising pi way after the last calculated digits. I did so. I don't quite remember where it begins, but my favourite section of pi is:
Back in school aged 16 a bunch of us tried to memorize as many digits of pi as we could one evening (I know, freaking wild times). The next day we went up to our maths teacher expecting him to be impressed by our efforts. One of us had got up to near the 100 mark...
His response: Pi's an irrational number, so you have learned 100 digits out of infinity, 100/โ = 0, therefore you've learned absolutely nothing.
[deleted] ยท 24 points ยท Posted at 16:16:21 on May 25, 2016 ยท (Permalink)
That's....kinda awesome and educating, in a bit of a brutal and ham-fisted way. And I can totally see my physics teacher pulling something like that back when I was in high school. In fact, he loved messing with us...but somehow that only made us learn.
I've heard a vareity of numbers as far as how many digits are needed, but they all agree that to get near perfect accuracy you need less than 100 digits (and often quite a bit less).
[deleted] ยท 495 points ยท Posted at 12:32:23 on May 25, 2016 ยท (Permalink)*
I burrowed all the way down this thread to find someone calling him out on not using the Planck length instead of the radius of a Hydrogen atom. You, sir, are a gentleman and a scholar.
T_at ยท 15 points ยท Posted at 18:52:57 on May 25, 2016 ยท (Permalink)
Yeah, yeah... The 'give gold' link is right up there--^
(Just kidding - reddit gold has about the same practical use as string theory, so don't bother)
[deleted] ยท 1 points ยท Posted at 05:39:45 on May 26, 2016 ยท (Permalink)
You might be onto something, I've always felt like our universe was actually made of tiny Reddit Golds
I think the size of the observable universe is a fine measure for the large end, so that 8.8e26m. The plank length makes a lot of sense on the low end, so that's 1.616e-35m. You would need 63 digits for that.
Because we will never be able to observe more of the universe, therefore we won't ever need anything bigger, and you can't know the position of a particle smaller than a proton maybe?
But the observable universe is going to grow into that entire universe. And objects from the outer limits of the universe can move into the range of the observable universe -- we actually don't know what's in the range known as the observable universe right now.
Oh, also, Gravity has infinite range, right? That's pretty important.
lerjj ยท 5 points ยท Posted at 18:27:46 on May 25, 2016 ยท (Permalink)
It's not about range, it's about time. Something outside of the obervable universe can't have a gravitational impact because the time taken for the gravitational waves to reach us is longer than the age of the universe.
MrXian ยท -15 points ยท Posted at 15:02:41 on May 25, 2016 ยท (Permalink)
I think the point is that the other things you hear were just explained to be false.
ben_jl ยท 13 points ยท Posted at 15:14:36 on May 25, 2016 ยท (Permalink)
There are multiple ways to interpret things like the 'size' of an electron, and no obvious reason to prefer one interpretation over another.
Just go with Planck length, its the smallest conveivable thing our physics knows of at 10-35m. In the video he uses hydrogen atom with 10-11m and his 39 pi digits give him accuracy to 10-12m.
[deleted] ยท 11 points ยท Posted at 16:59:05 on May 25, 2016 ยท (Permalink)*
I know 3. Not 3 digits, just the number 3. Seriously, you get like 3% error just using 3. You don't even have to remember how much error it gives, because it's also 3. It's so great.
One must only remember that pi is 3. The maximum error using 3 for calculations is about 3%.
[deleted] ยท 1 points ยท Posted at 23:15:50 on May 25, 2016 ยท (Permalink)
Actually the percent error for using 3 as pi is 4.5070340357462%, using the first 1000 digits of pi from Wolfram Alpha and the equation for percent error.
[deleted] ยท 1 points ยท Posted at 23:56:03 on May 25, 2016 ยท (Permalink)
dang. Well your percent error on your error is 33%. See, easy.
[deleted] ยท 1 points ยท Posted at 00:02:22 on May 26, 2016 ยท (Permalink)
It's roughly 50%, not 33%
4.5-3=1.5
1.5/3*100=50%
[deleted] ยท 1 points ยท Posted at 00:25:45 on May 26, 2016 ยท (Permalink)
1.5/4.5 = 33%
[deleted] ยท 1 points ยท Posted at 00:34:11 on May 26, 2016 ยท (Permalink)
Percent error is from the actual value not the measured value...
[deleted] ยท 1 points ยท Posted at 00:42:01 on May 26, 2016 ยท (Permalink)
Which is 4.5!
[deleted] ยท 2 points ยท Posted at 01:23:26 on May 26, 2016 ยท (Permalink)
oh shit.
[deleted] ยท 3 points ยท Posted at 16:52:18 on May 25, 2016 ยท (Permalink)
sine cosine cosine sine 3.14159
rzezzy1 ยท 11 points ยท Posted at 14:57:17 on May 25, 2016 ยท (Permalink)*
Thing about that, though, is that elementary particles, such as quarks and electrons, are thought to be point particles with zero radius.
Edit: considering /u/beeeel 's reply makes my comment much more accurate. Please do so.
beeeel ยท 18 points ยท Posted at 16:34:21 on May 25, 2016 ยท (Permalink)
They also don't have a strictly defined position, just a probability distribution for the position function, so you could say that the radius is just the standard deviation of the position distribution for a given state.
rzezzy1 ยท 7 points ยท Posted at 16:38:21 on May 25, 2016 ยท (Permalink)
If the connotation was "you only need as many digits as you need to get the precision you want" then that's a pretty obvious statement.
But that's not what the comment said:
The most decimal places you could ever need is the amount that allows you to calculate a position on a sphere the size of the universe to within one radius of the smallest known particle.
So I was pointing out that this is a false statement, as there is the possibility of needing greater precision than the "radius of the smallest known particle."
Plancks are absolutes. I was writing it generally such that no material discovery could make it inaccurate. We don't know for sure that nothing is smaller than a planck. We do know for sure than nothing is smaller than the smallest particle (by definition of it being the smallest particle)
There's no physical reason to use more digits. You could do thought experiments that analyze if pi were 4, but that's outside the bounds of our universe.
meh100 ยท 1 points ยท Posted at 18:25:53 on May 25, 2016 ยท (Permalink)
Is it outside the bounds of our universe if it has mathematical applications?
Because a planck length is an absolute and I was writing it as generally as possible. We might discover a particle smaller than a planck length. We won't discover a particle smaller than the smallest particle.
The Planck length is not any sort of "smallest possible length". It's just a unit of length, like a meter or a mile or a light-year. Planck units are defined using basic physical constants like Planck's constant and the speed of light rather than having mostly arbitrary definitions like meters/miles/light-years, and it just so happens that 1 Planck unit of length is really small compared to 1 meter/mile/light-year. But it has no particular physical significance.
On the contrary, the Planck length is (within an order of magnitude) the theoretical smallest possible detectable length. (according to the Generalized Uncertainty Principle)
While there are some speculative physical theories which suggest the universe is "pixelated" in this way, nothing has been verified by experiment that gives the Planck length physical significance.
Unless you plan to do that in a simulation of the universe across time. I'm which case you'd have to multiply times the number of time steps to stay within the plank distance or something.
Assuming the universe is purely deterministic (which we know it isn't) then knowing position and velocity is enough. But since QM makes that harder, it isn't (as far as we know) useful to know anything more accurate than a few angstroms.
Pretty much. We know that quantum mechanics screws with the determinability of particles once they get down to the subatomic scale. This is the whole problem behind transistors right now. We can only work with particles over such small distances as defined on a probability space.
Plank lengths are about 10-33 M, and 39 digits of pi gets you about 10-12 M of accuracy (within one hydrogen atom), so as a ballpark, you'd need about 60 digits of pi to calculate the circumference of the universe to within one planck length.
Verify if you'd like to correct me. Numberphile showed the error of a truncated pi (pit ) to be pi*duniverse - pit * duniverse.
Depends on what the smallest particle is. If it turns out to be the size of a planck length then the number is around 40 digits. If the smallest particle is bigger, you probably don't need as much. If the smallest particle is smaller, you'll need more.
Not necessarily. If the smallest particle were the size of a planck length and the universe was the size of the observable universe, you only need a certain number of digits to calculate an object's position in the universe to within one planck length. If the smallest particle were bigger, you need fewer digits.
I'm assuming you didn't read surrounding comments and are referring to the theoretical uses of pi beyond calculating anything physical. Those things aren't "needs" per se because they don't give us any insight into the physical realm.
The most decimal places you could ever need is the amount that allows you to calculate a position on a sphere the size of the universe to within one radius of the smallest known particle.
What if I ask you to tell me the location of the center of that particle? That requires more precision than just being able to name a point which falls inside its area.
The center doesn't matter when you're on that small of a scale.
But locating said particle in the entirety of the universe does matter? Who's to say what matters and what doesn't?
You phrased your OP as if it was some kind of proven mathematical fact, but all it is is you saying to yourself, "this is all the precision I could ever fathom being necessary." You can't just discount greater precision as impractical when the example you used is already orders of magnitude beyond practical or useful.
Let me explain what I mean by my last phrase, as it can be a bit confusing to those who don't get quantum mechanics. Let's say I have some number x digits of pi. This lets me calculate, if I know the radius of the universe and some universal coordinates that I could define myself arbitrarily, the location of a particle to within one radius, somewhere on the scale below the size of a proton. Knowing x + 1 digits will not make my positional calculation more accurate because that particle could spontaneously disappear and reappear in another location. By using a more accurate value for pi, I'm attempting to give more credence to the position that I'm calculating, when in reality, I can't know for sure that the particle is at that exact point. Ever. By using x - 1 digits (or maybe x - 2 or 3) I'm intentionally saying "this particle is somewhere in here. Dunno where, but it's in there." That's the nature of uncertainty in an answer and you're simply being explicit with it. Either your tool can't give you more accurate of an answer or your answer inherently can't be more accurate. It's like saying you're 5'11.56789234197891234578964231978" tall. You may be right, but it isn't useful to be that precise since the value is changing literally every second. Since the distance the particle could tunnel to decreases exponentially, I can give a pretty narrow area with high certainty. It very very likely won't be found an inch away, for example. So very unlikely that it's not even worth considering.
And my example is so not "orders of magnitude beyond practical or useful." Do you know why the computer you're using doesn't run faster than it does? There are limits to how small we can make transistors for this reason. To say that an electron is on one side of a transistor with a gate about an angstrom wide is to ignore the possibility that it could be on the other side of the gate, having tunneled to the other side. You can no longer determine the position by a vector. You have to describe it by a probability of vectors (probably here, maybe over here, probably not over there, but possibly, etc)
-widget ยท 1 points ยท Posted at 20:34:38 on May 25, 2016 ยท (Permalink)
Well yeah, unless you have a customer that insists that's not sufficient.
Not quite. With certain mathematically operations you can easily massively exacerbate errors in numbers you use. For example the error in 3.1416 vs the actually value is quite a bit smaller than the error in 103.1416 and the actual value. So you could definitely end up needing a ridiculous amount of accuracy in strange mathematical circumstances.
Right, but you can also have math problems that treat pi as equal to 4. It's possible, but that doesn't necessarily make it useful for us to do. I was pointing out digits that are useful to us.
mc_nail ยท 0 points ยท Posted at 01:13:29 on May 26, 2016 ยท (Permalink)
but that doesn't necessarily make it useful for us to do. I was pointing out digits that are useful to us.
I think you misinterpret my meaning. I am saying that there are legitimate useful cases for using more digits of pi, or numbers so ridiculously large that they cannot represent physical quantities.
Saying "x digits of pi are sufficient to calculate any real world circle, therefore that is all that we will ever need for anything" is an extremely limited understanding of mathematics and its utility.
As a very simple example, consider the encryption used for sending this comment to reddit. 2048 bits represents a 617 decimal digit number. That is 10617 !! Why that is enormously more than there are atoms in the entire universe, you say. Nobody could ever possibly make use of a number that large....
And I think you misunderstand my initial statement. The number 22048 is not physically useful for us. And we don't use it for anything. Similarly, 40 ish digits of pi is sufficient because we don't need that value for anything physical. To insist that more accuracy is required for anything shows a gross misunderstanding of quantum mechanics.
mc_nail ยท 1 points ยท Posted at 02:16:59 on May 26, 2016 ยท (Permalink)*
You need to reduce your claim then. If you only want to claim the cases where pi is physically useful, that is a much narrower claim and you should state it as such. But further, your statements are still not clarified:
Similarly, 40 ish digits of pi is sufficient because we don't need that value for anything physical
There is a logical contradiction in this statement. You can't say "sufficient" as the claim, and imply that "physically useful" means sufficient. Since 22048 is not "physically useful" then 128 bit encryption is therefore sufficient for you?
More importantly, I would argue very strongly against the notion that using pi to calculate the circumference of a circle is the only physically meaningful utility that it has.
As a simple example, in 1995 pi was used to 200 digits in an Integer relation aglorithm to produce a new and very useful formula for calculating pi (along with numerous other mathematical constants of 200 significant digits each). This is the BBP formula. Without 200 significant digits of pi, humanity would never have been able to find this simple, elegant formula with its simple single digit constants.
The BBP formula is very useful in answering many questions. For example, before this many assumed that it was impossible to calculate the nth digit of pi without calculating all preceding digits. However, it is also arguable that it has physical utility. This algorithm allows us to use less physical hardware, for example.
Ultimately, we may find all sorts of other useful formula, using even more digits of pi. And these formula could answer very real and fundamental questions. Relativity, among other math, allows us to answer very real questions about what a distant stars chemical composition is. Many fundamentals of abstract mathematics were required to formulate relativity's elegant postulates. Integer relation algorithms might derive the next useful formulas that answer questions about dark energy or other difficult unsolved real world physical problems.
You seem to be a bit sensitive on this subject. I'll gently clarify.
Since 22048 is not "physically useful" then 128 bit encryption is therefore sufficient for you?
the number itself is not useful to us. The range it can be found in is useful to us simply because there are lots of numbers in that area. The fact that 22048 has any specific property (other than obviously being a power of 2. I assume we're talking about large numbers in the ballpark and not that specific value) is of no consequence to us other than being very big. Similarly, knowing that the next digit of pi is a 7 and not a 2 is of no consequence because any additional accuracy we gain from such a digit is immediately canceled out by the fact that anything existing at a spot with such higher accuracy could very likely spontaneously tunnel to another location within the realm of uncertainty provided by the next higher decimal place of pi.
I do find it funny that you're claiming the usefulness of pi is that it allows us to calculate more digits of pi. It's a little circular, but I'm not picky.
mc_nail ยท 1 points ยท Posted at 14:11:14 on May 26, 2016 ยท (Permalink)
Similarly, knowing that the next digit of pi is a 7 and not a 2 is of no consequence because any additional accuracy we gain from such a digit is immediately canceled out
I'm not sure if you didn't even read anything I wrote. You're back to thinking that pi is only a means to calculate a circumference? Remember, pi and e are intimately involved in many, many formulas, from trig, to simple harmonic motion, to the Schrodinger equation.
Sorry, I was just trying to figure out a situation where you can scale pi enough such that you'd need more digits.
And my initial point was not "we will never need more digits of pi for anything." I agree with you that we can gain theoretical insight into other fields and situayions by using more digits. But as for physical applications of the value there is no need for more digits.
In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
[deleted] ยท 1 points ยท Posted at 20:48:44 on May 25, 2016 ยท (Permalink)
Interestingly, it was actually Douglas Hofstadter (the Gรถdel, Escher, Bach: An Eternal Golden Braid author) who said this. There's no record of Feynman making a similar remark.
[deleted] ยท 8 points ยท Posted at 15:11:07 on May 25, 2016 ยท (Permalink)
There really isn't a practical reason to memorize any of it. We have calculators
I've never trusted Numberphile after they went ahead and didn't explain this video at all, other than calling it "mathematical hocus pocus" (which was said by a fucking professor who I would never take a class from). So now I have to deal with idiots trying to sound smart by passing this off as the sum of a divergent infinite series. For anyone out there that believed this to be true, the "sum" that they are talking about is not the "sum" you have encountered in school, it's a completely different thing.
That's a much better video. I hate the first one so much because I feel like it helps reinforce the idea that math is all "magic" and so regular people assume they will never understand it. Whenever I've tutored math I've always found that that people get so easily flustered and forget all logic. That first numberphile is the exact type of "explanation" that I think adds to that problem.
Size of the observable universe in Planck units goes to around ~1061, so another 20 or so should suffice.
[deleted] ยท 2 points ยท Posted at 15:31:22 on May 25, 2016 ยท (Permalink)
Yeah, I was guessing 20-25. But, at that point (or indeed, at the "proton diameter" point) we're already in the "you're just showing off" area, on the other hand....
Yes there is. We had a contest in my class during like 7th or 8th grade so I memorized 100 digits thinking I could win. This fucker memorized 101. I just quizzed myself and got 45 before I messed up. That double 9 got me.
wouldnt plank length make more sense then a hydrogen atom though ?
zarraha ยท 1 points ยท Posted at 16:46:42 on May 25, 2016 ยท (Permalink)
There's no practical reason to memorize more than 3 digits of pi. Anything that you need more precision on should be done with a calculator, which knows the digits.
That's interesting, but pi is used for a lot more than just geometry. I'm curious if there are any other applications that could potentially require greater precision. Maybe something in the computation/simulation world?
At my high school on pi day (march 14th) whichever student could recite the most numbers of pi won a free pie of their choice. There were also slices for whoever came close to the winner. As you can tell my school was pretty big on science and math (nerds) so to win you had to know at least 120 digits of the sequence.
I always figured that point where there are 6 9's in a row is enough.
rtomek ยท 1 points ยท Posted at 23:01:25 on May 25, 2016 ยท (Permalink)
So he gets his point across in the first 15 seconds of the video. Then he repeats his statement. Then he writes down 39 digits of pi. Then he repeats why. Then he says it again.
At that point I took my mouse over the video to see that it was over 5 minutes long, so I closed the tab.
Can anyone explain to me how people use computers to calculate Pi, or even how historic mathematicians did it? Are they using super accurate measurements of some kind of known perfect circle or something? How does this work?
The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
I've found there is no practical reason to memorize beyond 3 digits
[deleted] ยท 1 points ยท Posted at 07:24:16 on May 26, 2016 ยท (Permalink)
Yeah, but it's not like that's the only place in maths or science that pi crops up. There are a million uses for it and I'm willing to believe some of them need more precise measurements of pi.
[deleted] ยท 1 points ยท Posted at 07:26:00 on May 26, 2016 ยท (Permalink)
Greater precision is needed when orders of magnitude are further apart. And it's hard to get further apart on orders of magnitude than "size of the universe vis-a-vis quantum level".
yCloser ยท 1 points ยท Posted at 13:35:00 on May 26, 2016 ยท (Permalink)
Nasa says:
we use 3.141592653589793
source. So, 15 digits. If it's good enough for NASA, it's good enough for me
[deleted] ยท 1 points ยท Posted at 15:23:55 on May 25, 2016 ยท (Permalink)
Do irrational numbers even exist or are they a human abstraction to approximate the real world? If, when you zoom in far enough, everything in the universe is discretized into particles, then there really is no such thing as a perfect circle.
[deleted] ยท 4 points ยท Posted at 15:25:11 on May 25, 2016 ยท (Permalink)
Math is a language, really. It's a way to express what we see when we observe the universe, it's not an observation in and of itself.
It's also a palindrome! I didn't know there were any prime palindromes besides the one digit primes. Then again, I never really considered the possibility before.
[deleted] ยท 1 points ยท Posted at 23:09:23 on May 25, 2016 ยท (Permalink)
An easy way to check if something is divisible by three is to see if the digits add up to be a multiple of 3. (It's not as easy when you have huge numbers though.)
That is so great. 666 with 13 zeroes on each side and two 1 devil horns. and 14 digits on either side divided by 2 devil horns is 1/7th or 1 of the 7 princes of hell. Yay symbolic conspiracy math.
Bspammer ยท 1097 points ยท Posted at 16:48:39 on May 25, 2016 ยท (Permalink)
I mean it looks more amazing because of the % symbol, but really if you do it with actual numbers it's pretty obvious that 0.02*50 = 2*0.5. You multiply one number by 100 and divide the other by 100 so of course the total stays the same.
tommit ยท 45 points ยท Posted at 17:07:53 on May 25, 2016 ยท (Permalink)
Exactly. And when you look at it in fractions, it becomes even more clear imo.
(1/50)*2
(2/50)*1
(1*2)/50 = (2*1)/50.
Looking at it like this, it may actually not make it more clear for everyone, but hey it's just another intuition.
One that made me pause for a bit in trigonometry was that 1/sqrt(2) was the same as sqrt(2)/2. But of course, multiplying either of them by 1 = sqrt(2)/sqrt(2) and then simplifying leaves the other.
jyonsin ยท 3 points ยท Posted at 19:35:40 on May 25, 2016 ยท (Permalink)
I dunno what you're using to read reddit but those backslashes are to cancel the asterisks to stop them from italicizing the text. without backslashes, *with backslashes*. You shouldn't be able to see them.
Mine too! I mean I've known for a long time that multiplication is independent of the order, ab=ba. But for some reason I've never thought to use the fact to more intuitively calculate percentages.
[deleted] ยท 1 points ยท Posted at 20:49:43 on May 25, 2016 ยท (Permalink)
I can actually use this for work. I do a shit ton of math for work, I am 40, and I have used math most of my life for work, and I did not know this. Holy shit I am blown away
WTF, why didn't anyone teach me this?! This literally changes everything.
Edit: I get it, you guys are very impressed with your mathematical knowledge, and this concept should be "obvious". The point is that the association between cumulative multiplication DOESN'T necessarily easily translate into real-world applications like calculating percents. This concept wouldn't have over 5000 upvotes if people didn't agree, so get off your damn high horse.
Mac2492 ยท 11 points ยท Posted at 21:36:58 on May 25, 2016 ยท (Permalink)*
100% is the same as 100/100 or 1.0
50% is the same as 50/100 or 0.50
If you want to get 50% of 40 then it's just 50/100 * 40. You can simply reorder this to 50*40 (or 40*50) / 100, which is equivalent to moving the decimal point to the left twice. This gives you 2000./100 = 20.00 = 20. In some cases it's easier to simplify the fraction first. Here 50/100 = 5/10 = 1/2, so you can get 50% of something just by dividing that number by 2.
This operation works in reverse as well. If you want to multiply something by 25 you can instead multiply it by 100 and divide it by 4 (because 100/4 is 25). In other words, just divide the number by 4 and move the decimal to the right two times.
64 * 25 = 64/4 * 100 = 1600
You can calculate discounts pretty easily in this same manner. If a product is 30% off that's the same as saying it's 30% off 100%. This is just 100%-30% = 70%. You can now calculate the final price if you multiply by 70 and move the decimal point to the left twice.
30% off $95 = 70*95 / 100 = $66.50
Personally, I tend to ignore trailing 0s for quick mental math and put the decimal point back "logically". Why keep track of more digits when you don't have to? Let's say you want 40% off $95. 40% off means you want 60% of the original value. 95 times 6 is 570. You know it can't be $5.7 or $570 so the correct result is obviously $57 even if you forgot how many zeros were in the problem to begin with!
As a final tip, it's still manageable to calculate something like 45% of 75 mentally (though depending on the purpose you may just want to round). I'll usually tackle this by using the distributive property to turn the problem into 40% of 75 plus 5% of 75. For this I'll use the "ignoring zero trick", though feel free not to, to get 4*75 = 300 => 30 by logic. For the second part it's just 5*75 = 375 => 3.75 by logic (5% should be less than 40%). Add them together to get 33.75. It takes some practice, but my best advice is to use whatever shortcut helps you get the answer easily and accurately. Break the problem into pieces that you understand and don't listen if someone says there's only one way to solve a simple math problem. For example, if you are good at visualizing things then you can straight up picture
45
x 75
and use your mind like a chalkboard. If you're terrible at visualizing but good at recognizing patterns then you can transform that 75 into "3/4" and turn the problem into 45*3/4-- a fairly simple multiplication followed by a simple division.
How does this work?
45% * 75 = 45 * 75% = 45 * 75/100 = 45 * 3/4
As usual, you can ignore trailing zeros or percent signs and figure out where to put the decimal point logically. The final answer has to be remotely close to 50% of 75 (37.5). It can't be larger than 75 (337.5) or super puny (3.375) so you can deduce that the correct place to put the decimal point is 33.75.
It's disappointing that so many schools teach rigid, inflexible approaches to problem-solving that carry on to adulthood. For example, I do my arithmetic from left to right because reading the numbers left->right and solving the problem right->left makes me constantly forget and scramble digits. It's pointless to teach people the commutative and distributive properties without also teaching students how to adapt them into their own solutions and benefit from them. Tricks for doing higher math are fascinating, but it really hits home for me when some of the most basic properties of math are considered an eye-opener. It's really sad how cool so many things are and how uncool we end up thinking they are simply because of the way they're taught in school.
[deleted] ยท 3 points ยท Posted at 20:47:22 on May 25, 2016 ยท (Permalink)
Because mathematics education is almost universally awful, but that's not helped by the cultural attitude most seem to have towards the subject for some reason.
Arithmetic is to maths what spelling is to literature. If your art classes was nothing but how to apply primer paint from first year through graduation, you'd hate art.
[deleted] ยท 9 points ยท Posted at 19:44:01 on May 25, 2016 ยท (Permalink)
Maybe the next thing someone will teach you is the definition of literally
Interesting fact: Literally has been used to mean figuratively literally since the word started being used.
Of course I am using literally to mean figuratively here, but it has actually been used for a couple hundred years IIRC. I'll check for a...(edit) source. Not the best, but I have literally millions of other things to do.
[deleted] ยท 9 points ยท Posted at 22:32:39 on May 25, 2016 ยท (Permalink)
Why are there so many redditors who simply don't know this or they refuse to accept it's true.
MrFace1 ยท 5 points ยท Posted at 00:17:54 on May 26, 2016 ยท (Permalink)
It removes their ability to be annoying pedants. Can't have that.
There are many ways to say "figuratively", but only one word for "literally". If you lose its meaning, you no longer have a way to refer to or use that concept.
Pretty much this. Literally is the one word I'm happy to have policed, since all of its power comes from its unambiguity in principal. Even if it was used in a particular way before, it's better to make sure as few people use it figuratively in excessive ways as possible.
I think that someone needs to teach you the definition of definition.
Solkre ยท 6 points ยท Posted at 18:29:25 on May 25, 2016 ยท (Permalink)
It's like my teacher trying to explain the exact situations when you can, or can't use a comma. Then someone just tells you it's when you want to pause. It's correct often enough for me!
Yeah that's not always correct though. Especially in current vernacular where people abuse commas where they might pause if they were speaking, yet it does not apply at all in the same sentence when in writing.
Solkre ยท 15 points ยท Posted at 20:04:30 on May 25, 2016 ยท (Permalink)
The reverse of this is why Christopher Walken talks like that. He used commas his own set of rules, and when his teachers told him not to, he exaggerated his verbal pauses to match his comma rules. After trolling for a consistent while, it stuck.
kanated ยท 1 points ยท Posted at 22:17:51 on May 25, 2016 ยท (Permalink)
If you use percentages it's hard to figure out. If you just write 0.02*50 it's pretty obvious that that's the same as 2*0.5. Either way is equal to 2*50*0.01, you just choose which number to multiply by 0.01.
In algebra 2 I was taught what of in math means multiply and I thought "no way, Isnt it when you divide". But I have never found that rule to be wrong. So then when you find some percentage of something you just multiply the percentage times the thing. And due to the combative property either one can go first.
Imsdal2 ยท 0 points ยท Posted at 19:52:33 on May 25, 2016 ยท (Permalink)
No, it doesn't change anything. If it did, it wouldn't stay the same...
I'm sure there's a really good your-mom joke to be made here, but I can't quite put it together. sigh... I was so much more clever before you discovered this math fact.
[deleted] ยท 0 points ยท Posted at 21:58:22 on May 25, 2016 ยท (Permalink)
Know it by intuition?
rtomek ยท 0 points ยท Posted at 23:09:08 on May 25, 2016 ยท (Permalink)
Because the percent sign literally means that the number is a fraction with a denominator of 100. If you were taught multiplications of fractions in school, they taught you how to do this.
My girlfriend was taking an online exam while I was over, and was freaking out over percentages when I told her this. She looked at me like I changed her life.
To do these I usually just multiply one of them to 10 by some factor n (in this case, 2) and divide the other by the same factor. 2/2 = 1, out of the 100%
It's only easier if you have simple numbers like that. I would say 90% of 8 and 8% of 90 take an equal amount of work to figure out. But it's not really hard. Just take 1% or 10% and multiply. 10% of 8 is .8, 100 - 10 = 90, so 8 - 0.8 = 7.2.
[Sounds like an intelligent input, but in actuality a huge simplification of something that is super complicated that we don't know how to solve accurately yet]
[deleted] ยท 1 points ยท Posted at 00:44:27 on May 26, 2016 ยท (Permalink)
And the equals sign does not convey any gravitational effects.
Masstch ยท 1 points ยท Posted at 22:34:52 on May 25, 2016 ยท (Permalink)
KLaxxon alarm!! He said "about"! Security! We have a breach!This fellow used a vague number! You, sir, are no Enjuneer
ldr5 ยท 1 points ยท Posted at 12:55:36 on May 26, 2016 ยท (Permalink)
Reflux ratio of 1.4 is just the ideal starting point and it gets tweaked as you go through your calculations! Oh no what have I done, the world is going to collapse into a black hole and the sun is going to explode!!!!! ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ
I feel like that's why in the Civil/Structural field, when something loses serviceability: the ability to perform it's use, it's basically unfit.
The bridge may not collapse, but if it sways too much, it's no longer useful
rngtrtl ยท 2 points ยท Posted at 18:07:24 on May 25, 2016 ยท (Permalink)
yup. I am an EE in power transmission/distribution. We have so much slop built into our models for estimates it would amaze most engineers not in the power industry.
My first heat transfer exam had a question calculating heat transfer from a cat standing on a roof. Most of the class assumed the cat was a rectangular prism
No, they designed it to use helium which the us controlled, then some idiot said fuck it, put hydrogen in, it's lighter and will work better, then kaboom.
[deleted] ยท 5 points ยท Posted at 19:23:27 on May 25, 2016 ยท (Permalink)
Probably jeff from accounting said that helium is too expensive.
and the Hubble lens error, the Titanic, leaning tower of Pisa....
Tasgall ยท 2 points ยท Posted at 00:45:07 on May 26, 2016 ยท (Permalink)
Don't know about the Hubble or the tower, but the Titanic at least was a result of the company cutting costs, not flaws in the engineer's original design.
The pair 3 and 11 are Octimus Primes, that's similar. The pair 5 and 11 are sexy primes.
Tom2Die ยท 1 points ยท Posted at 02:26:19 on May 26, 2016 ยท (Permalink)
I know you're being facetious, but you might enjoy looking at Mersenne Primes, as they're found using a similar idea, just without the absurd conclusion. :)
I would think that a smart person would at least use numbers that are unlikely to result in coincidental confirmation, e.g. almost any two numbers that aren't 100 and 10.
57.72% of 364 is 210.1008
364% of 57.72 is 210.1008
Now I believe it.
scandii ยท 1 points ยท Posted at 21:29:29 on May 25, 2016 ยท (Permalink)
This helps with estimating percentages and fractions easily with "pairs"
4 and 25 are pairs. 1/4 is 25%, 4% is 1/25
5 and 20 are pairs. 1/4 is 20%, 5% is 1/20
10 and 10 are pairs as you pointed out.
The rest are close, and are good for quick estimations.
6 and 17 are pairs. 1/6 is 17%, 6% is 1/17
7 and 14 are pairs. 1/7 is 14%, 7% is 1/14
8 and 12.5 are pairs. 1/8 is 12.5%, 8% is 1/12.5
9 and 11 are pairs. 1/9 is 11%, 9% is 1/11
I use these all the time to make rough estimates and impress people. "We need 17% of these for this to work" "Ok then we need about 1 out of 6 of these to work" "how did you do that so fast?" Happens all the time.
If his comment was edited, it happened within the first few seconds because there is no mention the comment is edited. You posted exactly an hour after him. His comment was not edited after you posted.
This sounds really alien at first, but when you think about it it's easy.
You're just multiplying 2 things and those by 100 (because of %).
And of course: A*B*100% = B*A*100%
[deleted] ยท 213 points ยท Posted at 14:05:34 on May 25, 2016 ยท (Permalink)
That's what % means. "Per cent." Cent- is the prefix, or Roman word, or something, for "100," and "per" means "divide by." So, "per cent" is literally, "Divide by 100."
The one that blew my mind recently was that I was perusing a font and discovered that there's such a thing as "per mille" -- division by 1000 rather than 100 -- and that its symbol looks like the % sign except there are two zeros "under the slash." Hm, I wonder if I can type it here... Ah yes: โฐ
Mathematically it's easy, sure. But it's hard to grasp at an intuitive level, because x% of y always assume the existence of some y which does no longer hold if you switch.
Actually, if you think a little harder, you'll find that AB = BA is not that obvious, and we all accept it because we know it to be true from experience.
Holy shit, I had never realized this once in my life, and I just graduated from a math heavy major. It's so simple too, since all you're ever doing is using basic properties of multiplication: (0.01x)y=x(0.01y). I guess the percent part just threw me off thinking about it that way.
This is simple associative property, though it's useful in application:
(x * .01) * y = x * (.01 * y)
Aski09 ยท 1 points ยท Posted at 16:42:48 on May 25, 2016 ยท (Permalink)
If you want to know what Y% is of X is, PM me your Email and I will send you a file to download an app that does it for you. (It is made by me so please do ;))
DDRundo ยท 1 points ยท Posted at 16:56:02 on May 25, 2016 ยท (Permalink)
When I saw this I was think of Modulo, since in most languages it is used via the % operand. I guess you know you are a programmer when you see a % and think modulo instead of percent.
rawling ยท 1 points ยท Posted at 17:13:03 on May 25, 2016 ยท (Permalink)
This is just straight up practical. Much more useful than the hairy tennis ball thing a few comments up. Talking about hairy balls gets me on lists. This I can use.
The word "of" is basically equivalent to the multiplication operator.
Hence, the sentence "x% of y" can be written mathematically as: "(x)(0.01)(y)" and "y% of x" is "(y)(0.01)(x)". By the commutativity of multiplication these mathematical statements are identically equal.
Even though it's a really simple trick it's still a surprising revelation when put into that context. It's seriously cool that 2% of 50 is the same as 50% of 2, calculating tips will never be the same.
This is kind of how I figure out how much to tip at a restaurant. Instead of taking 20% of the total bill, you can just multiply the bill by 2 and move the decimal 2 digits over.
I study maths and this blew my mind for the two seconds that it took me to realize why this is true. Damn my maths brain always trying to proof things.
x% of y is (x/100)y ->
y% of x is (y/100)x ->
(x/100)y=(y/100)x ->
xy/100=yx/100 ->
Q.E.D.
amyberr ยท 1 points ยท Posted at 22:58:32 on May 25, 2016 ยท (Permalink)
I was really confused and excited until I realized you actually meant percent and not modulo. 7%4=3, and 4%7=4, so it doesn't work for both meanings of %, which is a bummer.
mr_ewe ยท 20 points ยท Posted at 16:39:57 on May 25, 2016 ยท (Permalink)
Is this something you have seen or studied before, or do proofs like this just come so naturally to some people?
beeeel ยท 31 points ยท Posted at 16:51:47 on May 25, 2016 ยท (Permalink)
Once you've studied maths and learned to see the patterns, it starts to come more naturally, but there is the argument that the only people who study maths are the ones who can see the patterns in the first place.
DWe1 ยท 6 points ยท Posted at 23:21:26 on May 25, 2016 ยท (Permalink)
Yes, besides learning a lot of useful things while studying maths, you also create what some call "mathematical maturity"; you will be able to grasp more and more complicated structures faster. I am at the end of the second year of my mathematics bachelor's, and if I would have to learn a completely new mathematical concept that is thaught at the speed of a first course for freshmen, I would probably be able to deal with it a lot faster than when I was a freshman myself.
It comes naturally, but it's a process and the whole proof doesn't spontaneously appear in our heads. When working with "digit problems" like this it's frequently very useful to break the numbers up into their digits, like instead of using the number 'ab' you work with a*10+b. You figure out that:
(10a+b)2 = 100a2 + 20ab + b2
(10b+a)2 = 100b2 + 20ab + a2
At this point it becomes obvious that it doesn't work with any number. For a2 and b2 to fit in one digit neither can be above 3, and for 20ab to be smaller than 100 you need ab<5. This basically only leaves a small number of numbers that it works with; 00, 01, 02, 03, 10, 11, 12, 13, 22, 30, 31.
In the specific example given we knew that a was always equal to 1, so the proof reduces to the one given above.
mr_ewe ยท 4 points ยท Posted at 19:37:52 on May 25, 2016 ยท (Permalink)
Just the star is what tripped. I haven't been in a math class or done any may beyond plugging numbers into pre build equations in almost 4 years. Coming up with 10a+B=ab wasn't where I went first.
I'm an undergraduate in physics with a minor in math, so I have a fair bit of experience in working proofs out. I don't think I've seen this particular problem before, I just tried working it out and it worked.
I've always had a knack for math, but I really think it's my experience with solving a lot of hard math problems that has made proofs like this easy to do. Nothing in this problem requires more than high-school algebra, but it might be difficult for a high-school student to prove this because they haven't been using algebra for very long. The more you study, the easier it is to understand how to connect the dots.
Generalising to base k (where k is a positive integer greater than 1) and any integer a,b (where 0 <= a,b < k):
The original number is (ak+b), and its square is (a2k2+2abk+b2).
In base k it is written left to right as "a2 2ab b2" if no carrying occurs.
The flipped number is (bk+a), and its square is (b2k2+2abk+a2).
In base k it is written left to right as "b2 2ab a2" if no carrying occurs.
Notice that they are flipped versions of each other. The no-carrying condition is true only when k is greater than a2, 2ab and b2 (e.g. in base 10 a=1,b=3 works, a=2,b=3 does not because 2ab=12>10)
Yep pretty much. That's why I emphasized that b2 < 10 and 2b < 10 (so they're digits), and then sorted the final answers by the place each digit is in (hundreds, tens, and ones).
hjqusai ยท 1 points ยท Posted at 18:09:26 on May 31, 2016 ยท (Permalink)
It's explained by math. If you do the multiplication the long way, you never carry a one over, so all the numbers kinda stay in their own place
AsterJ ยท -1 points ยท Posted at 18:40:51 on May 25, 2016 ยท (Permalink)
It's not that interesting
(x + y)2 = x2 + 2xy + y2
(y + x)2 = y2 + 2yx + x2
x10x ยท 2 points ยท Posted at 18:58:48 on May 25, 2016 ยท (Permalink)
To add to this, each unit (ones, tens, hundreds) does not overflow into the next as x and y are less than 4.
Generally speaking, the palindrome of the square of a number equals the square of the palindrome of the number if and only if the cross sum of the square of the number equals the square of the cross sum of the number.
It also works in other bases, not just base 10
For example, in base 8 (octal)
122 = 144
(This is 102 = 100 decimal)
But 132 fails because 32 > 8
In base 5
122 = 144
(this is 72 = 49 decimal)
In base 16 (hexadecimal)
122 = 144
(This is 182= 324 decimal)
In base 20 you also get
142 = 18G, where G (the seventh letter of the alphabet) is the symbol for 16. 1+8+16 =25 = (1+4)2
In base 30 you get
152 =1AZ where Z (the 26th letter of the alphabet) is the symbol for 25, and A is 10.
This is 352 = 1225 decimal. 1AZ= 900 + 750 + 5
1+A+Z = 1+10+25 = 36 = (1+5)2
And so on.
[deleted] ยท 2 points ยท Posted at 15:28:56 on May 25, 2016 ยท (Permalink)
Sorry but I don't see what's special about this. What is it?
derrman ยท 10 points ยท Posted at 15:38:18 on May 25, 2016 ยท (Permalink)
An even better way of phrasing it (than cutting the cake into an infinite number of even sized pieces, because each would be zero volume and questionable surface area.. lol!) would be:
Cut the cake in half
Set one piece aside and cut the other in half
Loop back to step #2 forever
Because then, like even slices of Gabriel's horn, each piece itself is relatively ordinary. :3
CMariko ยท 1 points ยท Posted at 00:17:45 on May 26, 2016 ยท (Permalink)
Brilliant
RulerOf ยท 1 points ยท Posted at 01:42:17 on May 26, 2016 ยท (Permalink)
So if I use a knife instead of a fork, I can eat an infinite number of pieces of cake?
Woohoo!
[deleted] ยท -1 points ยท Posted at 23:47:02 on May 25, 2016 ยท (Permalink)*
[deleted]
yohohoy ยท 2 points ยท Posted at 03:45:49 on May 26, 2016 ยท (Permalink)
C/p
its volume is an infinite sum that converges to a finite value. For example, cut the cake into a set of infinite slices. The first slice has volume 1, the second 1/2, the fourth 1/4, the fifth 1/8 and so on. Such a cake would have volume 1+1/2+1/4+1/8+1/16+... = 2, as the sum of 1/( 2n ) from n = 0 to infinity is 2.,
It's 3d so conceivably yes, practically probably not
LoLjoux ยท 21 points ยท Posted at 20:21:25 on May 25, 2016 ยท (Permalink)*
The premise is that as the horn tapers it goes to infinity in the x direction. To build it you'd need an infinite amount of space, and the ability to build infinitely small objects
So you're saying I need a better 3D printer? What if my new 3D printer isn't infinitely better than my current one but only infinitely approaches the quality of an infinitely better 3D printer? If only I had an infinite amount of money to buy it
You could conceivably create a larger gabriel's horn which converges along the same point and axis as the original, in which case the new, larger horn would hold a finite amount of paint, but would never fully cover the surface of the smaller horn. Which is insane. The function for the surface area of both diverge no matter how you arrange them.
eliasv ยท 42 points ยท Posted at 16:25:58 on May 25, 2016 ยท (Permalink)
Nah, if you cover the outside in any constant thickness of paint (i.e. what happens when you dip something in paint, roughly speaking) the new volume is infinite.
This makes sense, as the horn is infinitely long and converges to essentially a cylinder with a radius of 0. If you cover it in paint, that line becomes a shape converging into an infinitely long cylinder with a radius t, where t is the thickness of paint.
Nah, if you cover the outside in any constant thickness of paint (i.e. what happens when you dip something in paint, roughly speaking) the new volume is infinite.
OK, maybe this would make it more clear:
You can fill it with a surprisingly small amount of paint (depending on the dimensions, but you could build one that would hold exactly one gallon of paint, or one liter of paint if you're metric).
However, while you can completely fill the horn with a small amount of paint, you would need an infinite amount of paint to paint the inside of the horn.
If "painting" implies a constant thickness of paint, then you can't "paint" the interior at all, because at some point the layers of paint on the interior would need to intersect each other, and then further along, the walls of the horn itself. Alternatively, if "painting" only implies some positive thickness of paint at every point, you can paint either the outside or the inside by reducing the thickness of paint as you proceed down the length.
The OP definitely was phrasing it in physical terms, I think. From a purely mathematical standpoint it doesn't even make sense to think that it's weird that you can "fill" the horn but not "paint" it, because you're talking about completely different spaces. It is weird to discover that finite volumes can have infinite boundaries, but not in quite the same way.
The OP definitely was phrasing it in physical terms, I think.
The OP was phrasing it the way it is always phrased: in a way that "makes sense" to the layman and captures the oddity of an object with finite volume and infinite surface area. It's meant to be intuitive and surprising, not realistic.
From a purely mathematical standpoint it doesn't even make sense to think that it's weird that you can "fill" the horn but not "paint" it, because you're talking about completely different spaces. It is weird to discover that finite volumes can have infinite boundaries, but not in quite the same way.
I fail to see any difference between the former and the latter that would justify one being "weird" and the other not. The boundary of a domain tends to be in a "completely different space". Keep in mind that this statement is only meant to be weird for someone at the level of calculus. Past that it's just a fact of life.
The OP was phrasing it the way it is always phrased: in a way that "makes sense" to the layman and captures the oddity of an object with finite volume and infinite surface area. It's meant to be intuitive and surprising, not realistic.
The problem is that the intuition that people get from this seems to be a flat contradiction in terms -- if every point on the interior consists of paint, how can it be that the interior surface isn't painted? What people are trying to do here is explain that this isn't really a contradiction.
The problem is that the intuition that people get from this seems to be a flat contradiction in terms -- if every point on the interior consists of paint, how can it be that the interior surface isn't painted?
Well that's why it is never stated this way. It's always stated that you can fill it with paint but you can't paint the outside. It just so happens to be the case that the interior surface is the exterior surface.
It's supposed to be a very simple volume versus surface area comparison. It's not meant to be very nuanced and it certainly isn't meant to be deeply analyzed in terms of physical reality.
It's nothing more than a quip in a calculus text book.
It's always stated that you can fill it with paint but you can't paint the outside.
Except people quite readily make the intuitive leap that if the exterior is unpaintable then so should the interior be.
It's supposed to be a very simple volume versus surface area comparison. It's not meant to be very nuanced and it certainly isn't meant to be deeply analyzed in terms of physical reality.
It's a poor comparison that confuses people, and I'm trying to alleviate the confusion. Why is that a problem?
Except people quite readily make the intuitive leap that if the exterior is unpaintable then so should the interior be.
As someone that teaches calculus, I can tell you with certainty that "people" do not readily make that leap.
It's a poor comparison that confuses people, and I'm trying to alleviate the confusion. Why is that a problem?
It's not all that confusing, and I fail to see how anything you've said attempts to clarify anything. Finite volume, infinite surface area. That's all there is to it. What this "means" is that you can fill it (with something 3 dimensional), but you can't cover it (with something 2 dimensional). Paint is something that both fills (comes as a liquid) and covers. Nothing in our everyday reality is truly 2 dimensional, but paint comes damn close. Hence the comparison.
Very rarely you come across a clever student that does see the inherent flaw that filling it "should" paint it, and asks how it is possible to be filled yet not painted. To which I generally respond with "you bring me a real Gabriel's Horn and I'll buy the paint to show you".
eliasv ยท 1 points ยท Posted at 14:05:30 on May 26, 2016 ยท (Permalink)
captures the oddity of an object
I disagree that it actually captures it, though. There is no self-consistent interpretation which even makes sense, so far as I can see. To anyone who actually somewhat understands what you're saying it's going to add to the confusions and misunderstandings (just look at this thread), and for everyone else it's at best a false sense of understanding.
As I've said before, it's a matephor. It lends to understanding what is being said, and it isn't meant to be perfectly analogous.
And this isn't usually met with confusion from students (except for any confusion they still have from evaluating an improper integral itself, but that has nothing to do with the metaphor). Most understand what is being said by "can be filled, can't be painted". The only people "confused" by this are those trying to apply physical real-world properties to the 2D notion of a "painted" surface.
eliasv ยท 1 points ยท Posted at 17:00:48 on May 26, 2016 ยท (Permalink)
trying to apply physical real-world properties to the 2D notion of a "painted" surface.
Sure, that or self-consistent mathematical properties... It's confusing because it contradicts itself. It's objectively nonsense.
They are self-consistent mathematical properties. You are attempting to twist them into something that doesn't make sense for sake of argument.
The mathematician makes no claims to your interpretation of events. Thus he does not contradict himself. He simply says the volume of the solid bounded by Gabriel's horn (Vol in R3) is finite while simultaneously the surface area of the boundary (Vol in R2) is infinite. This is perfectly consistent.
If one tries to interpret "paint the surface" as covering the surface with a real-life 3-D substance, you're going to have a bad time, because mathematicians make zero claims to that effect. "Paint the surface" refers to a completely 2-dimensional phenomena.
At best one may attempt to 3D-ify the statement by "unrolling" the horn into a flat surface and attempting to paint it with "real paint" of a constant thickness (such that we may speak of volume in 3D) which, for some, is enough to remedy the "inconsistencies" in the metaphor. However, I don't like this interpretation because, while the paint is now "realistic" in that it has a minimum thickness on the surface (say, it has a constant width in the z-dimension) we still need to allow the paint to get arbitrarily small in the y-dimension. Which, again, can't happen with real 3D paint, so all we have done is push the goalpost.
So if you fill it with paint how is the inside not painted? I'm having trouble picturing this in my head. A 'full' container ought to have paint touching every part of its interior surface, otherwise how is it full? Unless some of the interior surface isn't adjacent to interior space? But then how is it an interior surface?
So if you fill it with paint how is the inside not painted?
That's why it doesn't hold up to realistic interpretation. Mathematically speaking, paint (the substance) taking up volume is drastically different than the same paint over a surface. Incomparably different.
[deleted] ยท 2 points ยท Posted at 22:26:41 on May 25, 2016 ยท (Permalink)*
The only thing I could think of that makes sense to explain this, is that at some point, the diameter of the inside of the horn would be smaller than the size of one 'paint' molecule, thus leaving every part of the horn, past that single-molecule-wide point without paint.
eliasv ยท 2 points ยท Posted at 13:53:23 on May 26, 2016 ยท (Permalink)
If painting really implies zero thickness then the only even vaguely consistent and logical way to resolve that is by saying you can paint the horn. You start with a non-zero volume of paint. Painting a given area reduces your total volume of paint by zero.
If painting implies zero thickness, then either you can paint nothing (because it doesn't really make sense to subtract an area from a volume), or you can paint the entire infinite surface. Just the same as with any other shape, in other words.
Well painting does imply zero thickness, because the property being described is volume in R2.
If you don't like the metaphor because that doesn't seem "interesting" to you, or you think it's a bad metaphor, that's absolutely fine, I'm just explaining what is meant by mathematicians when they say it can be filled but can't be painted. The metaphor's been around longer than I've been alive, so I take no offense to your opinion of it one way or the other.
If painting implies zero thickness, then either you can paint nothing (because it doesn't really make sense to subtract an area from a volume),
You aren't subtracting an area from a volume when you paint a surface.
From Wikipedia: [Since the Horn has finite volume but infinite surface area, it seems that it could be filled with a finite quantity of paint, and yet that paint would not be sufficient to coat its inner surface โ an apparent paradox. In fact, in a theoretical mathematical sense, a finite amount of paint can coat an infinite area, provided the thickness of the coat becomes vanishingly small "quickly enough" to compensate for the ever-expanding area, which in this case is forced to happen to an inner-surface coat as the horn narrows. However, to coat the outer surface of the horn with a constant thickness of paint, no matter how thin, would require an infinite amount of paint.
Of course, in reality, paint is not infinitely divisible, and at some point the horn would become too narrow for even one molecule to pass. But the horn too is made up of molecules and so its surface is not a continuous smooth curve, and so the whole argument falls away when we bring the horn into the realm of physical space, which is made up of discrete particles and distances. We talk therefore of an ideal paint in a world where limits do smoothly tend to zero well below atomic and quantum sizes: the world of the continuous space of mathematics.](https://en.wikipedia.org/wiki/Gabriel%27s_Horn)
That's why I love Maths, it can literally break your brain.
EDIT: many users were kind enough to let me know that my use of the world "literally" was inappropriate. I personally find it unhelpful to use the downvote button for punishing grammar mistakes, but I did get the point.
I'm sorry, English is not my first language... Where did I mess up exactly? I double-checked on Google translate to be sure and I thought it was correct
[deleted] ยท 2 points ยท Posted at 05:55:53 on May 26, 2016 ยท (Permalink)
I disagree the goal is to "sound smart" when you correct someone for saying their head "literally exploded". I simply think someone that says their head "literally exploded" doesn't know what "literally" means.
Is calling them out on it a dick move? Sure, that can be argued... but I don't accept that just because so many people make this mistake, it somehow becomes "correct" because language is "fluid" or "evolving"...
[deleted] ยท 1 points ยท Posted at 05:49:29 on May 26, 2016 ยท (Permalink)*
Saying a noise is the "loudest thing they ever heard" is an exaggeration and a subjective opinion, which is fine - no one can refute an opinion. But saying your ears "literally exploded" is not the same thing - it's objectively wrong and a misuse of the language. Yes, I understand that when enough people misuse a word that the word can take on that second, incorrect definition. But if you want to be more accurate, don't say your ears "literally exploded" unless, well,.. they literally exploded (in which case, get to a hospital immediately).
I don't know why people talk about painting the outside because the more mindbending fact is that you can fill it with paint but never cover the inside even though it's full and so there's paint everywhere inside but not all of the inside is covered.
My brain breaks every time I try to think about what that means.
You can paint the inside if you don't need a constant thickness. Think of it this way. Choose a thickness of paint. Go down the smaller part of the horn. Eventually you'll get to a point where the diameter of the horn is smaller than that thickness. Even if you make the paint thinner, you still can find a part with a smaller diameter. So it's never possible to paint the inside with a constant thickness. The tricky part is that the paint thickness has to get continuously thinner as you go down the tube, forever.
That logic still applies to the outside of the horn, if you're allowed to thin the paint rather than have negligible thickness then you can paint the outside.
HOW? If you fill it with paint, there's no space left inside, right? So the paint is touching all the inside surface. That's how filling something works, isn't it?
Because the volume is finite, so you only have a finite amount of paint in it but the surface is infinite so you cannot cover it with a finite amount of paint.
zuccs ยท 4 points ยท Posted at 15:19:34 on May 25, 2016 ยท (Permalink)
It's a mathematical object being related to a physical one (the paint). This means you can't try it in the real world. So the thought experiment is trying to make the idea of infinite surface area relatable by attempting to paint it. The mathematical idea that's interesting is the shape has finite volume (can be filled with a finite amount of something) but infinite surface area (can't be covered by any amount of anything).
[deleted] ยท 4 points ยท Posted at 18:03:33 on May 25, 2016 ยท (Permalink)
But why does it have infinite surface area ? it doesn't look infinite at all.
Yeah, when you get to this part of the fact it just becomes uninteresting when you're trying to apply it to real life topology. Like yeah, if I had a cup in the real world that held a liter of water, but the handle of the cup was infinitely large, then you could fill it with paint but you couldn't paint the exterior.
See where it gets really skinny, that keeps getting skinnier and skinnier the farther out you go and it goes out forever. Unfortunately there is no way to have a picture of the whole thing because, well, it's infinitely long.
[deleted] ยท -1 points ยท Posted at 19:43:08 on May 25, 2016 ยท (Permalink)
You are correct that the paint is a physical object and the horn is mathematical which makes the idea fall apart under scrutiny. However, the mathematical object DOES have finite volume and infinite surface area. The paint is just to try and help people understand what that means.
[deleted] ยท 0 points ยท Posted at 20:27:22 on May 25, 2016 ยท (Permalink)*
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Godd2 ยท 3 points ยท Posted at 21:58:54 on May 25, 2016 ยท (Permalink)
The volume is not calculated by numerical approximation. We can find the volume exactly. The integral of pi*x-2 dx from 1 to infinity is precisely pi*(-(infinity)-1 ) - pi*(-(1)-1 ). The limit as x approaches infinity of 1/x is zero, so the first part is zero, and we're left with -pi * -1, which is precisely pi.
As x increases, the shape's volume increases. Without knowing anything more about its shape, the only conclusion we can draw is that as x approaches infinity, the volume increases infinitely.
This can be shown to be false by counterexample. The area under the curve x-2 from 1 to infinity is 1.
In short, there exist functions which increase forever, but don't diverge. Any function with a horizontal asymptote which the function approaches from below is an example of this concept.
Also, the irrationality of pi is a red herring. While the decimal representation of pi requires an infinite amount of digits to precisely represent, pi is indeed finite. It is as finite as any other number between 3 and 4. In fact, if we took the integral of 4*x-2 from 1 to infinity, we'd get the exact answer of 4, and your argument would become "the digits of 4 go on forever, thus adding volume infinitely". But the digits of 4 do not go on. They stop after one digit.
[deleted] ยท 1 points ยท Posted at 23:05:44 on May 25, 2016 ยท (Permalink)*
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Godd2 ยท 2 points ยท Posted at 23:14:59 on May 25, 2016 ยท (Permalink)
after you have found the exact volume of the shape, you add one more segment
There are no segments to add if the exact volume has been found. The volume wasn't calculated by sitting there and counting segments and adding them to a running total. The integral was found by doing a constant-time calculation at the boundaries.
If you were correct, then integrals could never be taken, since there are an infinite number of infinitely thin rectangles to add up. But you only need to evaluate the antiderivative at two places and then take their difference to know what the total is. That's why we do F(b) - F(a). That's why the integral of x-2 from 1 to infinity is precisely 1, and I don't have any more work to do.
I'm happy you're asking these questions though, so that passers-by have the correct math to learn.
[deleted] ยท 1 points ยท Posted at 23:26:23 on May 25, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 23:52:46 on May 25, 2016 ยท (Permalink)
Alright, I'll give you an example that will hopefully help you understand this better.
Suppose you have a cake that has a volume of 1. You then take the cake and cut it in half. Then you take one of the halves and cut it again. Then you take the quarter and so on.. until you have infinitely small pieces.
Yes, in real world this would be impossible but not in the realm of math. Now suppose you want to add all the pieces together again. So you start doing just that. With each piece you add the volume gets bigger obviously, but originally the cake had a volume of 1 and that didn't change.
As you can see you can have infinitely many parts of something that add up to a finite value. It is determined by how quickly the parts shrink. For example this series: 1 + 1/2 + 1/3 + ... adds up to infinity. But this one: 1 + 1/2 + 1/4 + 1/8 + ... adds up to exactly 2.
[deleted] ยท 0 points ยท Posted at 00:06:39 on May 26, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:23:26 on May 26, 2016 ยท (Permalink)
Check this math... if you have an infinite number of tiny cake crumbs with measurable volume, the total volume is infinite. It doesn't matter that you knew how much you started with. But x + x + x to infinity = infinity. Mind bending.
Alright, check this out.
You have infinitely many cake crumbs, but each crumb is one tenth in volume of the previous one. Arguably they all have a measurable volume.
What happens though when you try to add them up. You claim that the volume should be infinite. Let's see:
1 + 1/10 + 1/100 + 1/1000 .... =
= 1.111111..............
This doesn't look infinite to me. It is 10/9.
Godd2 ยท 1 points ยท Posted at 00:42:28 on May 26, 2016 ยท (Permalink)
What's funny is if we didn't know which property we were measuring (volume or area) and we just knew that as X increases, so does Y, but X increases less each time, we would get one answer. Yet we seem to get 2 different answers by thinking "area" or "volume" which is why I disagree.
They're two different integrals. The volume calculation is the integral of pi*x-2 dx from 1 to infinity, and the area calculation is the integral of 2*pi*x-1 * (1+-x-2 )1/2 dx from 1 to infinity. Area and volume are two different things. The surface area of a cube with edge length 1 is 6, but its volume is 1. 1 does not equal 6. Do you have a problem with the difference between a cube's surface area and its volume? I would hope not.
(despite the fact that it is smaller than anything in existence)
This betrays a fundamental mistake. The mathematical conclusion has nothing to do with physical things in the real world.
I was expecting that answer, because the "exact volume" supposedly includes all of it (even though it's infinite).
There are an infinite number of numbers between 0 and 1. The length of a line segment from 0 to 1 is 1. Are you going to claim that it is more than 1 just because there are an infinite number of points there?
[deleted] ยท 1 points ยท Posted at 01:07:53 on May 26, 2016 ยท (Permalink)
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Godd2 ยท 1 points ยท Posted at 03:46:23 on May 26, 2016 ยท (Permalink)
I agree that if you have an infinite collection of "points", each with the same non-zero length, that the resulting length will be infinity. But the cake and the horn deal with collections where the size of each one is different. Namely, that the size of each one gets smaller and smaller as you go along.
Let's talk about the distance between me and the grocery store. It's one mile away. Let's imagine the point halfway there. We'll call it P_0. The distance from me to P_0 is one half of a mile, and the distance from P_0 to the grocery store is one half of a mile. Let's mark another point P_1. P_1 is halfway between P_0 and the grocery store. It's 3/4 of a mile away from me, 1/4 a mile away from P_0, and 1/4 of a mile away from the grocery store. We can keep naming points. Let's say that each new point is halfway between the old point and the grocery store. So P_2 is halfway between P_1 and the store, P_3 is halfway between P_2 and the store, and so on.
Since there are an infinite number of points between me and the grocery store, I can keep cutting the distance in half, and the resulting distance in half, and so on.
As a result, we have an infinite number of line segments. Here they are in a list
As you can see, each line segment is half the length of the previous. We also know that the total length is 1 mile.
So we have a case where we have an infinite number of line segments, and each line segment is non-zero in length. But their sum is a finite value.
So just because you add together an infinite amount of non-zero segments doesn't mean you get a total that is infinite.
We can think of it a slightly different way. Consider points A and B where A is less than B. There's a distance between A and B. If I move A toward B, but I move it such that A move less than the previous distance, A will still be less than B. If I do this again, but with the new distances, A will still be less than B. I would have to move A at least the distance it is away from B in order for A to stop being less than B. However, as long as A is less, there will always be a distance I can move A such that A remains less than B.
So, if we were to inspect the distances I move A over time, we would see a number that is getting smaller and smaller. This is why we can add up an infinite list of values that are smaller and smaller, and end up with a total that is finite. (Of course, we can end up with a number that is infinite too, if the "smaller and smaller" values are still too big. The next number just has to be smaller than the previous)
Here are some math questions to illustrate the concept:
If I add up an infinite number of non-zero lengths,
how big will the total be?
A. Infinite
B. Finite
C. It depends
The answer is C.
If I add up an infinite number of non-zero lengths that
are all the same size, how big will the total be?
A. Infinite
B. Finite
C. It depends
The answer is A.
If I add up an infinite number of non-zero lengths
which are getting smaller and smaller, how big
will the total be?
A. Infinite
B. Finite
C. It depends
The answer here is C again.
For the case of 1 + 1/2 + 1/4 + 1/8 + 1/16 + ..., the answer is 2, but for 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ..., the answer is infinity, so it depends on how quickly the successive lengths are decreasing.
Sorry but this isn't accurate at all. The fact that pi has an infinite number of digits does not negate the fact that it is a finite number. Involving pi in calculations doesn't make the result infinite or cause any paradoxes. What is making this possible is the fact that it is a purely mathematical object we are talking about. It cannot exist as a physical thing. So of course it is confusing to try and make it fit into our physical way of thinking about it. I'm happy to try and explain more if you have questions.
[deleted] ยท 1 points ยท Posted at 23:02:51 on May 25, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:01:14 on May 26, 2016 ยท (Permalink)
The increase in volume is really no different from the surface area that increases infinitely.
I'm sorry but you're wrong. The increase in volume is very much different from the increase in area. The area of the horn is defined by an integral of 1/x, while the volume is an integral of pi*(1/x)2.
This difference is enough to make the volume finite. And no, there is no paradox because of pi. Pi is no different from any other number.
[deleted] ยท 0 points ยท Posted at 00:16:09 on May 26, 2016 ยท (Permalink)*
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zedpowa ยท 2 points ยท Posted at 00:25:51 on May 26, 2016 ยท (Permalink)
Integral is just an infinite sum. When the parts it sums are small enough the result will be finite, simple as that.
[deleted] ยท 1 points ยท Posted at 00:26:35 on May 26, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:33:34 on May 26, 2016 ยท (Permalink)
Not always. As I explained before, the volume is given by a different function than the area is. As you keep adding smaller and smaller parts to the horn, both its area and volume grow slower too. But because they are defined by different functions they grow at different speeds. It just so happens that the area keeps growing infinitely while the volume never goes over a finite threshold.
You can't decide a proof isn't valid. Anyway, the beauty of math really hits when you understand these things which it's obvious you don't want to do. I tried.
Edit: A simple way to illustrate the problem is to imagine a number like 1.999999... that goes on forever with more nines. Is the number infinitely large as more digits are added? Technically yes because it increases forever. But also intuitively no, because it will never be as big as the number 2. That's the paradox. Complex descriptions of weird shapes and calculations of volume and surface area are just ways to make it more nuanced and maybe harder to detect the core paradox.
This is totally wrong. 1.999... does not get infinitely large. It is bounded by 2. If you claim it gets infinitely large then prove it, it goes against accepted mathematics.
[deleted] ยท 1 points ยท Posted at 00:30:10 on May 26, 2016 ยท (Permalink)
Godd2 ยท 2 points ยท Posted at 00:52:19 on May 26, 2016 ยท (Permalink)
If there are not an infinite number of numbers between 1 and 2, then there is some number that is closest to 2, but not equal to 2, correct? Let's call this number B, for Biggest Number Less Than 2.
If I take B, and find the average of B and 2, or (B+2)/2, I'll get a number that is larger than B, but less than 2. But B is the largest number smaller than 2. This is a contradiction, therefore, it is not the case that there are a finite number of numbers between 1 and 2. Thus, there are an infinite number of numbers between 1 and 2.
Is this convincing to you?
[deleted] ยท 1 points ยท Posted at 00:56:53 on May 26, 2016 ยท (Permalink)
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Godd2 ยท 2 points ยท Posted at 01:09:13 on May 26, 2016 ยท (Permalink)
If it really can go on forever, then yes I think I can come to terms with there being an infinite number of numbers between 1 and 2.
You seemed not completely convinced it was the case.
Also, it's worth noting that I'm not being as rigorous as I ought to be. There are sets where there aren't an infinite number of numbers between 1 and 2. In the set of integers, there aren't any numbers between them. But in the set of rationals and reals, there is an infinite number between them. In the set of complex numbers, being between two numbers doesn't have an obvious or natural definition, since the set isn't ordered.
My proof above only technically applies to the rational numbers, but could be used on the real numbers as well.
[deleted] ยท 4 points ยท Posted at 18:41:28 on May 25, 2016 ยท (Permalink)
Basically, it's like taking the integral (aka finding the area under the curve) of x-2 from 1 to โ. The answer is finite, and actually will be equal to exactly 1 if you work it out. Now, if you find length of the curve, you'll get infinity, because, well, the domain of the curve is pretty much infinite.
So let's say you revolve that entire segment from 1 to โ around the x axis. Now we are adding a whole new dimension to our universe, so basically the properties of the previous two calculations kinda jump up a dimension too. Long story. But basically, because the area was finite in 2 dimensions, the volume is also finite in three dimensions. Also, because the arc length was infinite in 2 dimensions, the SURFACE area is also infinite.
It extends forever, so there is no end to its surface. The only reason you can fill it with paint is because, since the object becomes narrower as it extends to the right, the volume is approaching a finite number.
A similar problem with a number series may make more sense. Such as:
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...
Try it in a calculator. The number gets infinitely close to 2 as you continue. In mathematics, this mean it actually is 2.
Now think of each of those numbers in the series as periodic measurements of the horn's circumference as you move to the right.
971365 ยท 3 points ยท Posted at 15:50:05 on May 25, 2016 ยท (Permalink)
Imagine a flat stretch of desert with a small hole in the sand. You could fill it up but not paint the whole place.
[deleted] ยท 8 points ยท Posted at 17:24:37 on May 25, 2016 ยท (Permalink)
Forget the outside, you can fill it with paint, but you will never have enough to cover the inside.
[deleted] ยท 1 points ยท Posted at 21:44:16 on May 25, 2016 ยท (Permalink)*
.
sikyon ยท 1 points ยท Posted at 21:49:46 on May 25, 2016 ยท (Permalink)
That's easy, you just have an infinitely long cylinder with a finite divot in 1 end. Fixed interior volume, infinite exterior surface area.
The more interesting thing is that you can fill it with paint but you will never have enough to cover the inside (except of course that paint has a finite volume).
So you're tellin me you can paint the inside of my trumpet, but not the outside?
If I didn't know better, I'd think this was a scam.
...okay you have yourself a deal.
[deleted] ยท 1 points ยท Posted at 23:34:10 on May 25, 2016 ยท (Permalink)
You cannot fill it with paint. Any physical analogy fails.
If you were to "fill it with paint", you'd be implying that an ideal liquid could travel an infinite distance in finite time. Which is impossible. If you state that physical matter has definite size, then you don't have infinite surface area.
I'm being pedantic as all fuck, I know, it just irks me that people seem to be unable to recognize that all physical analogies of Gabriel's horn fail.
Eh, I like the concept but I don't think that's very accurate. You're assuming you can't paint infinitely fast but I can if I just dip paint in and accept that the paint is covering the sides.
It's not a mathematical problem, just a language one but it irked me a little bit.
Mathematically, it's because its volume is an infinite sum that converges to a finite value. For example, cut the horn into a set of infinite rings. The first ring has volume 1, the second 1/2, the fourth 1/4, the fifth 1/8 and so on. Such a horn would have volume 1+1/2+1/4+1/8+1/16+... = 2, as the sum of 1/( 2n ) from n = 0 to infinity is 2.
Many infinite sums do not converge to a finite value (for example 1/1 + 1/2 + 1/3 + 1/4... does not converge). It just so happens that the volume sum converges, while the surface area does not. Gabriel's horn can be modeled by 1/x. This is a rough explanation, but because volume uses cubes, volume can be modeled by the sum of (1/x)2, which converges (sum of (1/x)2 is sort of like cubing). On the other hand, surface area doesn't. It can roughly be modeled by (1/x), which does not converge. Using the volume and surface area formulas in single variable calculus can easily show this.
https://en.wikipedia.org/wiki/Gabriel%27s_Horn#Mathematical_definition shows the calculus application clearly.
Edit: converge to an infinite value --> converge to a finite value
Ah, that helps, thank you. It's still a bit mind-bending, though, understanding the infinite surface but knowing there's a finite interior... Thank you!
The horn has a radius of 1/x, the volume of a slice is proportional to r2 while the surface area of a slice is proportional to r so the volume of sections approaches 0 faster than the surface area. When you integrate the volume equation from 1 to infinity you'll see that it converges to a finite number but when you integrate the surface area from 1 to infinity it will give an infinite result.
It does go on, but it gets smaller and smaller. These values are "small enough" to add up to a finite value. Some others are not - like the 1/2+1/3+1/4+1/5 mentioned above. Why some sums add up (or "converge") and why others don't takes an understanding of calculus, notably limits.
So pretty much any measurable amount of paint would fill up the smallest sections at the end? Even if it was infinite, the amount of paint required would be effectively zero?
Thinking of it in physical terms is a bit tricky, as it is impossible to actually construct and more of an abstract shape. If you put 1 volume of paint into the cone, it would fill up exactly half of it. Doing it again will fill up the whole thing. However, no matter how much paint you tried to put on the outside, you will never end up finishing the painting, never reaching the "end" of the tip. This is all because the sum of the volume converges, while the sum of the surface area diverges.
If you didn't understand the other explanations here's what I think is an easier one.
Surface area is in units squared, volume is in units cubed, this means that if something is decreasing in size it's volume is decreasing faster than it's surface area. If something is getting smaller at a fast enough rate, even if it goes on forever, it eventually converges to a finite number.
For instance, 1 + 1/2 +1/4 + 1/8+ 1/16... can be said to equal 2 if the series goes on forever.
The case of the horn is that the radius of the cone as the figure moves from left to right is decreasing, but not fast enough for the surface area to ever equal a finite number. However, the volume, which decreases even faster than the surface area, is getting smaller to offset the fact that it's going on forever and eventually reaches a finite number.
[deleted] ยท -1 points ยท Posted at 23:52:45 on May 25, 2016 ยท (Permalink)
What? I don't understand your point. Also some infinite can be bigger than other infinites. Like the real numbers are bigger than the integers, which are the same size as the natural numbers
Take the graph of f(x) = 1/x where 1< x < infinity
rotate that graph around the x axis, you have gabriels horn
integrate that object you produce to obtain its volume and it is a finite number. However the object clearly extends on to infinity as per the initial conditions of the statement, giving it infinite surface area
And not infinite volume? f(x) = 1/x will never reach the axis, so there will always be some space/volume, right? I understand the infinite surface area.
using the integral of the planar area (pi * r2 where r = 1/x) over the length of the trumpet ( lets say from 1 to a to give it any length right now) gives us the volume
V = pi * integral ((1/x)2 dx) from 1 to a
= pi ( 1-1/a)
and so for any a, this volume is finite
[deleted] ยท 2 points ยท Posted at 19:18:58 on May 25, 2016 ยท (Permalink)
Yeah, I don't get this either. Isn't pi, as an irrational number, technically infinite?
(Pardon my ignorance. I enjoy math and find it all fascinating, but public school let me down...)
What? Pi is not infinite. Pi has a value. It is a constant. It is irrational meaning it has infinite non-terminating non-repeating decimal places, but it does not have infinite value
If this still confuses you, remeber that pi can be approximated quite well as 3.14 or as 22/7. Replace pi with either of those values in my previous post and the result is the same
[deleted] ยท 1 points ยท Posted at 23:35:19 on May 25, 2016 ยท (Permalink)
Huh. I guess the irrationality is what confuses me. The fact that the digits go on and on is hard to wrap one's head around. Then again, I know I'm not alone in that thought. Thank you for helping!
if pi is 3.14xxxxxx where the x's go on to infinity, and lets say for our purposes we have no idea what these x are. In the largest case, every single x would be a 9, giving us 3.149999999999999999 repeating to infinity. This number is easily seen to be less than 3.15. The same can be done for the lower limit of 3.14xxxxxxxx being always equal to or greater than 3.14 no matter what x we chose. ( if all x are 0, we get 3.14)
So we know forsure the value of pi is between 3.14 and 3.15, despite the fact that it has infinite digits. The infite digits just let us understand precisely where between 3.14 and 3.15 pi actually lies on the "number line"
This is a great explanation, but one nitpick, IIRC...
In the largest case, every single x would be a 9, giving us 3.149999999999999999 repeating to infinity. This number is easily seen to be less than 3.15.
I'm pretty sure in that case it actually would equal 3.15. The logic holds however for any other example besides infinite 9s.
you are correct, technically if those 9's continued on to infinity, it would be impossible to pick a number between 3.14999999999 and 3.15 making them effectivley the same number
3 was easy by comparison. Diff Eq probably still not as bad as Calc 2 integration methods of "here's 5 techniques that take a page of writing each time, they can be used in any order, some multiple times, and you may or may not get a workable answer."
[deleted] ยท 2 points ยท Posted at 18:29:46 on May 25, 2016 ยท (Permalink)*
When studying for the exams, just do the review problems over and over and over until you know how to do them all...sounds stupidly simple but it's what I ended up doing to pass. The exam will be just like the review problems with different numbers.
The key is knowing how to do them, as in why you are doing each part. I have seen people do ok for a few small tests/problem sets by using the same systematic procedure to solve things. It doesn't help in exams though, they often will throw two concepts from review problems together into on question.
Well, black holes could qualify for this given the distortion of spacetime approaching a singularity. Ironically, these are more physically real than the infinite surface area objects (which can't exist in this universe, since atoms have finite size).
We build a Sierpinski pyramid out of toothpicks and beans at our last math lesson. The teacher wanted us to calculate the surface and volume, but nobody did, because we wanted to build a really large pyramid.
There is still volume, but the volume gets lower and lower.
It sounds unintuitive but you can add more and more and still get to a finite value.
Just as: 1+1/2+1/4+1/8+1/16+.... Equals 2
It looks like Gabriel's horn has infinite length as well. Couldn't you get infinite surface area and limited volume and length by taking a fractal/"infinite coastline" and giving it some depth?
Sorry if I sound like an idiot, I'm just some high schooler that likes math. But to my knowledge, if the smallest unit of space is a Planck length, then how can the cone keep getting smaller forever? Shouldn't the space inside the cone eventually be the size of a Planck length?
I was looking for this. This is still crazy to me.
MX72 ยท 1 points ยท Posted at 01:45:04 on May 26, 2016 ยท (Permalink)
So basically this is just some "math trickery" with no possible way for it to actually exist in real life.. Which in my opinion makes it false. I get it, the math says its possible, but in reality it is not.
I have looked into this...
The volume being limited makes sense...
But as the volume approaches its limit it approaches but never reaches the limit.
What happens when the volume of the horn is increasing by less than the size of a single atom?
While that increase is happening is the surface area still able to increase.
In short, could Gabriels Horn only hold in theory?
As far as I can tell, that's just an 'imaginary' object, which stretches on forever. So it's sort of cheating to say you couldn't paint it, because it doesn't exist to paint in the first place.
Like others have said you can't really "build" one, but there are real life examples where you can see this in practice. For example, what is the length of the coastline of the UK? You could measure in the perimeter and area with a milestick. Then you could measure them both with yardstick, the perimeter would be much larger but the total measured area wouldn't change that much. Then you could measure the coastline with a foot-long ruler. Again, the measured coastline would be much larger but the total area added would not increase in the same way. It's called the coastline paradox and sites like this might help explain it better than I did. I love fractals!
Yes, but technically it never becomes a "single" line, it becomes an infinitely thin and narrow tube that keeps shrinking as it moves toward infinity
[deleted] ยท -1 points ยท Posted at 17:27:58 on May 25, 2016 ยท (Permalink)*
First of all, lines don't have surface area, so no. Surface area is defined for 3D objects, and area is defined for 2D objects. A line is one dimensional.
Also, Gabriel's horn converges to a line (the x axis), but is never actually equal to it.
Gabriel's horn is defined to be the 3D shape you get from rotating the function f(x) = 1/x around the x axis with a domain of x >= 1.
If you know some calculus, it's actually not that hard to prove that this has a finite volume and an infinite surface area.
EDIT: I forgot to mention, Gabriel's horn is only one surface with these properties. However, the converse cannot be true. There is no object with infinite volume and finite surface area.
[deleted] ยท -1 points ยท Posted at 17:24:01 on May 25, 2016 ยท (Permalink)
Yea but things like this are so pointless. Doesn't exist in real life. It's just a limit that goes to infinity.
You're on a gameshow. There is one grand prize that you can win but it's hidden behind one of three closed doors. The other two doors have nothing. You are asked to select one of the three closed doors. Once you choose a door the host opens one of the remaining two doors that does not contain the fabulous prize.
The host then asks if you'd like to switch your choice to the one other unopened door. Do you switch?
Statistically you should because there is a 66.6% chance the other door is correct and only a 33.3% chance your door is correct.
Most people will argue, vehemently, that there is a 50/50 chance of having the correct choice so switching is irrelevant. But you actually had a 66.6% chance to choose the wrong door to begin with. Math-Magic!
The important thing is that the host knows which door has the prize and which door is empty. You pick first and have a 1/3 chance of picking the prize, and a 2/3 chance of not. Then the host picks a door and opens it, but he will never pick to show you the prize. So there's still a 2/3 chance that the prize is one of the two doors you didn't pick, since there's still three doors. The 1/3 probability of the door that opened goes to the third door that neither of you picked, because the host knows where the prize is and would never pick it. Since the door he picked is now worth 0/3, the door he didn't pick is worth 2/3 to add up to the 2/3 that those doors have, combined.
If the host picked first then you picked, there would be a 1/2 chance for both doors.
The 1/3 probability of the door that opened goes to the third door that neither of you picked, because the host knows where the prize is and would never pick it.
That's the crucial sentence right there. Thanks for the in-depth explanation.
Yep, the host is providing vital information by picking the door, not just crossing off a random 1/3 chance.
[deleted] ยท 9 points ยท Posted at 17:13:56 on May 25, 2016 ยท (Permalink)
Why doesn't the probability of the door that the host opened split evenly between the two remaining doors? I just can't wrap my head around the fact that if you take the situation as it is, it's a 2/3 chance if you switch, but if your choice were to get "forgotten" after the host opens a door and you have to make an independent selection from the two remaining doors, then it's a 1/2 chance for each.
It's a good question: someone else asked it as well, so check my response there. I walked through all the possible picks. Sorry on mobile so I don't know how to link it.
The crux of it is that you're right, if you forgot what happened before then you'd have a 1/2 chance with the he two remaining doors. The fact that you know something about the doors that were picked helps out.
It also may think of it by thinking of their loss rates. You have a 2/3 chance of losing with your first pick. The host then picks a door which is always a losing door. That gives the third door only a 1/3 chance of being a losing door. Yours has a 2/3 chance of being a losing door still. That makes your door twice as likely to lose as the third door, so you should switch.
[deleted] ยท 4 points ยท Posted at 17:57:03 on May 25, 2016 ยท (Permalink)
Couldn't you explain it by saying that the host is not only showing which door is a losing one but also showing which one is a possibly winning one ?
Or said otherwise he didn't choose to reveal your door as a losing one because it is your door while the third door wasn't chosen because it is possibly the winning one compared to the second door which is a losing one ? or is that faulty logic that has nothing to do with the real logic in action ?
Sure that probably works too. The crux of it is as you said that he's telling you useful information by picking his door. You know his door loses, so that makes the one he didn't pick more likely to be a winner. The hard part is understanding why the information doesn't apply to your door like it does to the third door. Like you said, the fact is that he only picks between the other two options, not yours.
Actually if he picked your door when you had an empty door he'd be better off, because you'd have two options to pick from with 1/2 chance each.
The way I prefer to explain it is that, if you initially choose an empty door, then the host HAS to show you the other empty door, since he can't show you the prize door. This means that, if you initially picked a dud (and there is a 2/3 chance you did), then there is a 100% chance that the remaining door holds the prize. This is why your chances of winning are 66% if you always switch, because if you picked wrong and then switch you are guaranteed a victory.
Thanks for the description, I'm finally starting to get it more.
So...
One thing I'm still working through is how the odds can change depending on the person picking the doors. By what I understand here, if we had the same situation occur, then they brought in someone from outside the studio who has no idea which door the 1st contestant chose, and only knows that one of the two doors in front of them has the prize, then they would have a 50% chance.
So does this mean that 50% of the time, they'll choose the 66.6% door, and 50% of the time they'll choose the 33.3% door, and then the average between the two percentages is 50%, so there's a 50% chance in total that they pick the correct door? Holy shit this is starting to click.
As fun as this math is, and all the media its featured in, isn't the real answer is that you SHOULD forget what happened before? Once the door is opened this is an entirely new instance, and the probability of the choices beforehand do not affect the probability of the second choice.
deong ยท 13 points ยท Posted at 20:56:26 on May 25, 2016 ยท (Permalink)
You're confusing independence of trials with prior knowledge.
Very often in statistics, you deal with independent trials. If you're playing roulette and the wheel has turned up red 10 times in a row, the odds of the next spin yielding red are still 1/2. One spin of the wheel doesn't have anything to do with the previous one.
In the Monty Hall problem, you only have one trial -- playing the entire game. The reason is because the outcome does depend on earlier actions. If the prize was under door number 2 when the host opened door number 3, there's a 0% chance that it will be under door number 1 when you open it. It's all one connected trial.
When the host opened door number 3, you didn't start a new game. You gained information about the current one. In the face of new information, you update your beliefs. In this game, you update them in what most people find a counterintuitive way, for sure, but you can't just assume that opening one door tells you nothing, or else you'd conclude that you should still have a 1/3 probability that the prize is behind door number 3 -- a door that's wide open with obviously no prize there.
It's the same instance, but you've learned more about your options. The probability of each door's having been the winner in the beginning was 1/3. That's still true. But now that you know something new, namely one door that the host picked and one door that they might have picked but didn't, you can use this information.
If it were the same instance and you forgot what the host did, then yes you'd have a 1/2 chance. But since the winning and losing doors haven't changed, you have more information than that.
The host will always open a losing door. That means if you choose to switch and lose, you must have had the winning door in the first place. What are the chances of that? 1/3. Therefore there is 2/3 chance you will win if you switch.
The crux is that he always shows you a losing door.
The chance doesn't change, it's that you get different chances if you follow different paths. If you look at the second half of the scenario independently, there IS a 50/50 chance of getting the door with the prize if you switch doors. However, if you include the first part, then the number of scenarios where switching doors is better is doubled.
Yes this is a bad example in my opinion. Since you don't open the door that you initially pick, you can't draw any conclusions from simply picking it and standing in front of it. The fact is the host is always going to open an empty door regardless of your pick. 50% chance for either your pick or the other one left.
Edit: I'm probably wrong.. its starting to make more sense to me the more I think about it.
You can think of it like this. If you have to choose 1 door out of 100 doors you have a 1/100 chance of choosing the correct door. After you choose a door all but 1 remaining door are opened. Given your original choice you had a 1% of choosing the correct door. So by switching you are more likely to choose the correct door
[deleted] ยท 1 points ยท Posted at 17:58:24 on May 25, 2016 ยท (Permalink)
No matter the number of doors, it still seems to boil down to one door vs. another. In your example, it intuitively seems like each of those two final doors have a chance of 1/100, or 1/2 when compared with each other.
In your example, it intuitively seems like each of those two final doors have a chance of 1/100, or 1/2 when compared with each other.
The important part is that the host knows which door contains the prize. You know with 100% certainty that the host will not eliminate the door containing the prize.
It's much easier to understand if you don't think of it as "do you want to switch doors?" Instead, think of it as "do you think you were correct on your first guess?"
Now, imagine that there were a million doors, and you get to choose one of them. Then, the host eliminates 999,998 doors from the equation. You're given the option to open your original choice, or open the other door with the knowledge that the host would never eliminate the door containing a prize. Do you think it's more likely that you correctly guessed the door out of a million? Or is it more likely that the prize-winning door was one of the 999,999 that you didn't choose?
Ulrezaj ยท 4 points ยท Posted at 18:13:30 on May 25, 2016 ยท (Permalink)
It's only 1/2 compared to each other if you didn't already know which door you originally picked.
We can make it more extreme if it makes it easier to understand. If there are a million doors, your chances of picking the right one are more or less zero. Now, the host opens 999,998 other doors and leaves 1 other door closed. Do you see now that it HAS to be that remaining door?
If you pick 1 out of 100 doors, you have a 1% chance of picking the correct door and there is a 99% chance the remaining group has the correct door in it. It necessarily has 98 incorrect doors and a 1% chance of having 99 incorrect doors. Seeing 98 incorrect doors doesn't change the odds of the correct door being in that group.
Here's another way to think of the 100 door variant. You choose Door A. Instead of opening 98 empty doors and leaving one mystery door. They take all the contents of those 99 doors and put them in one room and label that Door X. There's a 99% chance that Door X has the prize in it, because there's a 99% chance that it wasn't in Door A. This is exactly the same as the normal 100 door Monty Hall Problem.
That's not the correct probability space. I'll copy what I said in a different part of this thread
There's three equally likely situations the prize is behind Door A, B or C.
You can start by choosing door A (without loss of generality).
There's a 1/3 chance that Door A contains the prize. In that case the host will randomly reveal Door B or C to be empty. You will be better of staying with your first choice.
There's a 1/3 chance that Door B contains the prize. In that case the host will reveal Door C to be empty (they'll never open door B because the host knows where the prize is). You will be better off changing your choice.
There's a 1/3 chance that Door C contains the prize. In that case the host will reveal Door B to be empty (they'll never open door C because the host knows where the prize is). You will be better off changing your choice.
So 1/3 chance that your original guess was right. 2/3 chance that you would be better off switching.
The other scenarios will neve happen (guest will never open neither your door nor the prized one).
They will never happen, but you need to include them in your calculation of probability because you don't know which door definitely does not contain the prize until after you've made your original choice. The host opening the door provides you with additional information. The choice is not "should I switch doors?" The choice is "was it more likely that I was right or wrong when I made my original choice."
Sorry because I know you've got replies, but I want to throw my 2 cents in.
The host will always open a losing door. That means if you choose to switch and lose, you must have had the winning door in the first place. What are the chances of that? 1/3. Therefore there is 2/3 chance you will win if you switch.
JPK314 ยท 2 points ยท Posted at 02:48:32 on May 26, 2016 ยท (Permalink)
Let's expand it to 100 doors. You pick one door at random, and that door has a 1% chance of having the prize. The other 99 doors have a combined 99% chance of having the prize. At this point, would you want to stay with the door you picked, or all of the other doors where you get the prize if it's behind any of them?
Of course you'd choose the 99 doors. The host now opens 98 empty doors out of the 99. Would you want to stay with your 1% door, or the combined 99% chance of the other doors which is now down to only 1 door?
Imagine the question was now you pick one door out of a million doors.
Afterwards the host offers you the same choice, between your door and one other door, one of which is guaranteed to have the prize in it.
Your original pick had a one in a million shot at being right, but the host is now saying your door + this other door contain the winning door.
Would you still think its 50/50 in that scenario? You need to separate your original choice (which you knew was 1/million), and the new information presented, that your 1/million shot and some other door is guaranteed to be the winner.
Very easy to envision that same problem, but with 100 doors. If you pick a door at the beginning, and the host opens 98 other doors, then there's a 99% chance the last door has the prize. Your 1% chance at the beginning did not improve.
[deleted] ยท 1 points ยท Posted at 18:03:01 on May 25, 2016 ยท (Permalink)
If you want to see it in action, mythbusters actually did this one. Confirmed.
[deleted] ยท 1 points ยท Posted at 19:07:23 on May 25, 2016 ยท (Permalink)
I've read so many explanations and this one finally makes sense.
After all these years, I finally get it. What keeps breaking it in my head though: confronted with the choice to pick another door, doesn't that reset the chances to 50/50, or am I throwing information away?
We did this in math class in 8th grade. Playing the show host really helps make you understand it. As the host, you'll find that the majority of the time (66% of the time), there's only one door you can open because the contestant has already selected one empty door, so you have to reveal the only other empty door.
I found the best way to think about it is if you had 100 doors. You choose 1, Monty Hall uncovers 98 doors and then asks if you want to switch. Seems obvious that you would want to switch in that case. But when there are 3 doors, it becomes much less intuitive.
But why does the 1/3 probability of the door that opened go to the third door and not the one that I picked? That doesn't make any sense.
If the gameshow host is giving me the option of switching doors, then it's technically a new roll of the dice, no? I can pick, out of the two remaining doors, which one I want, and would that not make it a 50% chance of picking the right one? I can't wrap my head around this concept...
Let's say the prize is behind door A. There are three possibilities:
You choose door A. The host opens whichever of the other doors he feels like. You lose if you switch and win if you stay.
You choose door B. The host opens door C, leaving door A closed. You win if you switch and lose if you stay.
You choose door C. The host opens door B, leaving door A closed. You win if you switch and lose if you stay.
The reason it works is that if you choose either losing door to start with, the host is obligated to open the other losing door, and then switching guarantees you the win. It's only in the case where you actually chose the correct door to start with (a 1/3 chance) that switching makes you lose.
ovie707 ยท 1 points ยท Posted at 18:07:46 on May 25, 2016 ยท (Permalink)
This is the only explanation that actually made it less complicated. It also demonstrates why the extra 1/3 chance doesn't get distributed evenly between the 2 remaining unopened doors.
You picked a door at random and have 1/3 chance at the prize. If the host picked a door at random as well, then you could take his 1/3 chance and put it in half, 1/6 to each other door. That would give you 1/2 for each door, like you expect.
But the host does NOT pick a door at random. When he picks, you have 1/3 for your choice, 1/3 for the choice he didn't pick, and 1/3 for the door he picks. That last third becomes 0/3 (you saw nothing behind the door, so you know those odds). So you need to put it on a different door. His information doesn't tell you anything about your door, but it tells you about the door he didn't pick.
This means that while it is a new roll of the dice, you have extra information about one of the choices, namely that it wasn't one of the losing doors. It could be the other losing door, or it could be the winning door. But its chance of being the losing door just went from 2/3 to 1/3, while your door is still at 2/3 chance to be a losing door. Comparing your door to the third door, you'd half your chances of a losing door by switching.
There's three doors, so let's see how it plays, switching first then not switching.
1/3 time A will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks B. B has 0/3 chance to win.
You switch to C. C has 2:1 odds to win, because 1/3 chance to lose compared with 2/3 chance to lose.
You lose.
1/3 of the time B will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks C. C has 0/3 chance to win.
You switch to B. B has 2:1 odds to win, because 1/3 chance to lose compared with 2/3 chance to lose.
You win.
1/3 of the time C will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks B. B has 0/3 chance to win.
You switch to C. C has 2:1 odds to win, because 1/3 chance to lose. compared with 2/3 chance to lose.
You win.
Now the other option is to not switch.
1/3 of the time A will win.
You pick A. A has 1/3 chance to win.
He picks B. B has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You win.
1/3 of the time B will win.
You pick A. A has 1/3 chance to win.
He picks C. C has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You lose.
1/3 of the time C will win.
You pick A. A has 1/3 chance to win.
He picks B. B has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You lose.
So if you switch, you will win 2/3 games, winning each time you pick a losing door to start.
If you don't switch, you will win 1/3 games, winning each time you pick the winning door to start.
The door letters can be rearranged however you like. After all, it doesn't matter if door A is on the left, right, or center stage. Same for B and C, before or after you pick.
When you picked a door, you created two categories. You put your door in Category A which probably doesn't have the prize and you put all the other doors in Category B which probably does.
When the host gives you the option to swap, you're choosing between sticking with A (bad) or changing to B (good). The fact that a gameshow host theatrically walks along most of the B doors and opens them for you doesn't change anything.
Imagine you were given the option to stick with A or to go and open all the doors in Category B yourself instead of just the final one.
The key thing, here is that the probabilities don't change, ever. You simply start asking new questions or considering different doors.
It really gets obvious when you think in terms of "odds I was right to start," and, "remaining odds that it's any of the remaining doors".
Of course, with 3 doors, that logic doesn't occur to you because you're left with 1 door you chose and 1 door that's left unchosen. But with 4 doors:
you choose door 1, having a 1:4 chance of being right. Now the host reveals that the prize is not behind door 2. This tells you that the remaining 3:4 chance is evenly spread across the unrevealed 2 doors (each having a 1.5:4 chance of being the one, which is greater than the chance of your having been right when you started).
With 1000 doors:
you choose door 1, having a 1:1000 chance of being right. Now the host reveals that the prize is not behind door 2. This tells you that the remaining 999:1000 chance is evenly spread across the unrevealed 998 doors. Basically, you keep the same odds of having chosen correctly and the remaining chance is one-better than it was before the host revealed an empty door.
dv_ ยท 3 points ยท Posted at 17:07:21 on May 25, 2016 ยท (Permalink)
Another way to view it this:
There is only one case where you picked the right door from the beginning. In this case, the other two doors are equal - they both have no prize behind. In this case, it doesn't matter which one is picked by the host.
There are however two cases where you picked the wrong door. In these cases, the other two doors are not equal - one will have nothing behind, one will be holding the prize. And in these two cases, the host's pick does matter. (I agree that this is the heart of the whole thing - his pick is never random in these two cases.) And what's more, the host's pick gives you unmabiguous information, because in these two cases, you picked an empty door, he picked an empty door, so there is only one door left.
So, given that in 66% of all cases you get valid and unambiguous information from the host, it makes sense to rely on that information and pick the other door.
There are however two cases where you picked the wrong door. In these cases, the other two doors are not equal - one will have nothing behind, one will be holding the prize. And in these two cases, the host's pick does matter. (I agree that this is the heart of the whole thing - his pick is never random in these two cases.)
I still can't quite figure out how this trips people up. It's quite apparent that the two doors you're left to choose from are tremendously dependent on which of the three you picked originally.
dv_ ยท 1 points ยท Posted at 06:17:29 on May 26, 2016 ยท (Permalink)
Because we rely so much on the "common sense". And the human "common sense" is abysmal at statistics. We intuitively look at the two remaining doors and at nothing else, and conclude that it's a 50:50 chance.
The 1/3 probability of the door that opened goes to the third door that neither of you picked, because the host knows where the prize is and would never pick it.
No, it would be split between both doors left because either of them could still have the prize. The host is going to pick an empty door regardless of your initial pick.
If the host picked first then you picked, there would be a 1/2 chance for both doors.
Yes, but you aren't really picking first when you aren't told if your pick is correct or not. I'm no math teacher, but I feel it's wrong to draw conclusions statistically in this case.
Edit: fuck me, I think I understand now that I've read through more comment chains. Expanding the problem to a million doors instead of 3 helped me wrap my mind around it somewhat.
Sorry for the confusion! Maybe it would have helped if I added that the host will not pick the winning door, but he ALSO won't pick the door you picked. So you are picking first, only in that he won't pick your pick also.
Sorry but I actually don't remember that show well enough to answer. I think one important idea is to overcome your psychological fallacy of thinking the thing you "picked" from the beginning is the best. You may need to think logically to overcome the fear of uncertainty.
You also may want to consider whether you're happy winning 40% of your payout for sure rather than 50% chance of winning double. If I went on the show, I'd probably take one of the deals because I don't think having $1,000,000 is twice as good (or will make me twice as happy) as having $500,000. It may be twice as much money, but I won't get to play on the show again, so I'd rather take the guaranteed win.
The answer is, you really cant on Deal or No Deal until you get down to a few choices left. And even then, if the million is on the board, your case + 2 cases left, and you get any offer, you should take that offer and run, no matter what.
But Deal or No Deal is much more complex for most of the game because of the differing amounts of in each briefcase and the offers.
It doesn't work at all in Deal or No Deal. The host has to know the cases he is revealing isn't the "winner". If he's just opening cases at random (you selecting being random) then it doesn't actually work, and the last 2 cases are a 50/50 split.
If instead you selected your case and then Howie proceeded to open all the cases for you knowing that he wouldn't be opening the "winner" then you should switch cases when given the option because the "winner" has a very high probability of being the one Howie left remaining.
It's key that the host is knowingly avoiding opening the "winner" for the Monty Hall problem to be true.
and that they are only adding information to the doors you didn't pick. If the host randomly reveals that a door you didn't pick is empty (they have no knowledge about the prize) that gives you information about both the remaining door and the door you chose.
BigSpud ยท 2 points ยท Posted at 17:33:51 on May 25, 2016 ยท (Permalink)
Every time I read about the Monty Hall problem I promise myself I will memorise an explanation.
Haha I know what you mean! It took me a bunch of times to figure it out. If that explanation didn't do it, I replied in more detail to one of my other replies (sorry mobile, don't know how to link) that may help. It explains it in terms of your chance of losing and then walks you through how each scenario would play out.
It's easier to gain an understanding than to memorize it. The trick is to explain why the situation would be different if the host had no knowledge about the prize and randomly revealed door that happened to be empty.
I had to come up with like 10 ways to explain this because my co-workers couldn't wrap their head around it. I extrapolated and said "Let's say there's 1,000,000 doors. And you pick one. And the host opens 999,998 of the doors that didn't have the car behind it and asks you if you want to switch. Well, thinking of the 1,000,000 doors sitting there and every door open except the one you randomly chose at a 1/1M chance and one other one that we know only has a 1/1M chance of being random (since he would never open the door with the car behind it since he knows where it is)... I think everyone would make that switch.
Unfortunately, my manager refused to believe that The Monty Hall problem was accurate. So, we tried the game by him writing 1, 2 or 3 and then me guessing. Well, I won every single time by cheating (in an effort to prove the point, which I understand is cheap). I just watched how he wrote the number. If he made a single stroke, I knew he wrote a 1 and then I would say 2 or 3, he would open 2 or 3 and I would switch and get 1. If his hand moved at all when scribbling the number, I knew it was a 2 or a 3, and I would pick 1, he would open 2 or 3 and I would switch. I was like 12 for 12... he still refused to believe it worked. I left the company within two months...
Haha well it should work even without cheating if you play enough and approach 2/3 but sorry he never got it! Yeah that makes a lot of sense once you think of more doors and the host is opening lots of them. It really emphasizes how important the host's information is.
You have a 1/3 chance of picking the right door the first time, which means you have a 2/3 chance the prize is behind another door.
The host eliminates one wrong door of the 2 doors you didn't pick, but you still have that 2/3 chance the prize is behind a different door than you first picked except now you know which door of those other 2 was wrong.
last657 ยท 2 points ยท Posted at 21:08:17 on May 25, 2016 ยท (Permalink)
Another crucial point that is inherent to the problem but is often skipped over is that the host has to open another door independent of whether or not you picked the right door. If the host had the option of just opening your door and saying you lose if you pick the wrong door initially then him giving you the option to switch is a different kind of game entirely
Yup, the host has to open a second door, and he is not allowed to open your door. Of course that means he picks an empty door, rather than a winning door, giving you information.
last657 ยท 1 points ยท Posted at 05:30:50 on May 26, 2016 ยท (Permalink)
Yep. When I was younger it bothered me and I didn't get it. It was actually the 100 door example that finally made it clear to me. After that I became a little unnecessarily pedantic about the wording of it though. Its portrayal in 21 especially bothered me because they even directly addressed the possibility of it being a trick and dismissed it as unimportant. You can only garner that information when you know the rules of the hosts actions. If not the whole thing becomes a lot more complicated.
"The important thing is that the host knows which door has the prize and which door is empty."
This isn't quite correct, and I've seen it trip up people in the past. What matters is that the host picks a door that does not have have the prize. His knowledge makes no difference. It doesn't seem like an important distinction, but 3 separate occasions I've seen the requirement of knowledge cause confusion.
Interesting, thanks. I suppose you're right. They could always tell him off camera which door to pick, so then the host wouldn't need to know which door is the winner.
In any case though, someone needs to know which door is the winner, or else the host might accidentally reveal it, right?
Perhaps it depends on your audience, and maybe mine is pedantic :)
The minimum requirement is that the host always picks a non-prize door. The logistics behind this (knowledge, luck) do not matter.
No one needs to know the winner from the outset. What matters is that we as the contestant have the knowledge that the host picked a non-prize door. It is this knowledge that allow us to concentrate the probability of failure (1/3 + 1/3) behind the originally picked door.
The picking of the first door is just a mechanism; requiring the host to have knowledge casts him as an intelligent actor. I thinks this is the source of the confusion.
Fair enough! Haha I just feel like unless I'm misunderstanding you, someone's having knowledge of the prize door would be almost necessary. This is a television game show after all, so relying on luck or some other mechanism to pick a non-winning door would be unnecessarily complicated.
You're right of course that it doesn't matter how or why you were provided the information about the second door. An audience member could accidentally trip and knock over one of the doors, revealing nothing behind it. You'd still learn that nothing was behind it.
So if I make a game show and run it like this 1 million times, are you going to say, that because I swifted my opinion, that I would win roughly 666.666 times while losing only 333.334 times?
I'm not sure if you're the contestant or the host in this scenario, but yes. The contestant should win 2/3 games if they play with the better strategy of switching every time.
Of course the reality is that many people won't play with this best strategy. Plus, it isn't like the gameshow is betting that you'll lose, so they might be fine with 2/3 contestants winning.
You could run the same game as a betting game, just adjust the payouts to $0.45 and $0.55. You'd think you're winning by $0.05 (expecting $0.50 as break even) but in reality I'd be winning by $0.11 (knowing $0.66 is break even).
I know that mathematically this is how it works, but you could argue that you have always only had a 50% chance of picking the correct door.
If the host always removes one WRONG door, you are effectively only picking from 2 options anyway, regardless of what you choose. They will remove one incorrect option, so there is only ever two valid options. One correct, one incorrect.
You're right, if the host picked first, but in this game the host picks second and has to pick a door that is empty and not yours.
Try this way: I'll pick a random card and not show you, then put it back in the deck. Now you take a card. Now I'll discard all but one card from the deck, keeping my card if it was still there, or keeping a random card if you picked mine. Do you think your card is the one I picked first, or do you think the card in my hand is the one I picked first?
You're right that there are two options, but one of them is much more likely, because I added information by discarding cards AFTER you picked yours.
The assumption here is limited information from the perspective of the player and complete info on the side of the host. Practically, however, anyone who has watched the show more than a couple of times knows that the host will "burn" one of the two void choices no matter the choice of the player. Due to updating, one might argue that with this info on the hands of the player the probability transforms to a 50% one. In other words, a partially informed player knows that one of the two doors s/he didn't choose has an a priori 0% chance of containing the prize.
[deleted] ยท 1 points ยท Posted at 17:53:58 on May 25, 2016 ยท (Permalink)
I've seen it and heard it explained a thousand times, I can just never conceptually agree that the
1/3 1/3 1/3 Becomes 1/3 2/3
Like... The 1/3 chance is absorbed by the other....
Somehow I am still only to see a completely new math problem, that is mutually exclusive from the previous one.
Hi! Try my other post, unfortunately on mobile so I can't link. It's much longer and walks through the chances of all possible outcome, as well as comparing what happens if you switch or don't.
It also may help to think of your chances of losing, rather than your chances of winning (also in that post).
If you choose the wrong door he can only open the other wrong door, the only door left is the one with the prize, switch and win.
All you need to do is to pick a wrong door at the start.The chances of that happening are 2/3.
[deleted] ยท 1 points ยท Posted at 19:48:42 on May 25, 2016 ยท (Permalink)
But we are operating on the assumption that I chose a loser, which I am doing based on statistics...
So it's not "switch and win", it's "switch and probably win.", correct?
The host knowing which door has the prize is not important; in fact the host opening a door actually shows you no new information, since he is going to show you an empty door no matter what.
The host knowing which door has the prize is fundamental to the problem. If they randomly choose a door and it just so happens that the door is empty, then it's a 50/50 shot.
This proves my point. If they randomly choose a door then you have information to work with. But since the host isn't going to show you a door with the prize in it, you know he's going to show you a door without the prize, so which particular door he shows you does not help you or change your situation in the slightest.
It gives you information about the remaining doors that are left open. Let's say you choose Door A and the host knowingly reveals that Door B is empty. That gives you information about Door C, but not Door A.
But your selection is going to be between staying with door A, or switching to doors B and C. After you select door A, you already know that one of the remaining doors is empty, and it doesn't matter which one. He could show you door B or he could show you door C, (whichever is empty) and it doesn't change your dilemma. You already know your dilemma before he shows you a door. There's three possibilities after you choose a door and before he reveals: prize is in your door, prize is in unchosen door, or prize is in other unchosen door. At this point there's a 2/3's chance that the prize is not in your door and a 100% chance that the host will show you an empty door (that's part of the setup/rules). So he opens an empty door. Now we're to the dilemma that you knew you'd be in before he opened a door, before you even went on the game show. Doesn't give you any useful information. You are choosing between staying or switching, that's it. Sorry does that make sense?
I'm late to this thread, but you seem so close to understanding it, but not quite. You're either misunderstanding something or arguing a technicality.
But your selection is going to be between staying with door A, or switching to doors B and C.
That's not what happens in the game. It would be "staying with door A, or switching to whichever of doors B or C is still unopened."
He could show you door B or he could show you door C, (whichever is empty) and it doesn't change your dilemma. You already know your dilemma before he shows you a door.
That is true, it doesn't change your dilemma. You should still switch, no matter what door he opens. The math says you have a 2/3 chance of winning if you do. But if he opens door B, you will choose door C. If he opens door C, you will choose door B. The host has to open one of the doors in order to give you the information you need to choose the correct door. You can't choose both doors. At that point you've changed the game, and are talking about a different problem.
I mean yes which door he opens indicates which door you can switch to but statistically it doesn't matter. Even before he opens a door you are really choosing between having one door or having two doors. You already know one of the two doors is empty before he even opens one. Expand it to 10k doors, and you get to select between your door and the 9,999 other doors. Play the game a couple times and what's the chances that every time you play you've selected the right door? Very slim. Always go with the switch. Again, him opening a particular door doesn't give any useful meaningful helpful information. Edit: yes a technicality, but you can look at it like you are choosing between one door and two doors (or 1 door and 9,999 doors).
The opening of doors is the critical component here. Statistically, you know that you have a 1/N chance of having picked the prize at first, thus a 1-1/N chance of not having picked the prize. You already know this. The host opening all non-picked doors that do not contain a prize thus gives you a 1-1/N chance of getting the prize if you switch. That doesn't change with the opening of doors, correct. But he still has to do it before he lets you choose between switching or staying! This is the entire point of the game!
If you could start the game with picking a door, and the host says "alright, do you want to keep that door or do you want all the other doors?" -- that would be the situation you're describing. Statistically, they give you the same chance of winning if you switch/stay. But now you've reformulated the Monty Hall problem to take out the confusing part. Intuitively, in the situation I've just described you would obviously switch every time. N doors (for N>1) is better than 1 door. In the Monty Hall formulation, made evident by this thread, it's not immediately obvious that you should switch.
I mean yes which door he opens indicates which door you can switch to but statistically it doesn't matter.
It is determined in advance that you should always switch, if you want the highest probability of winning the prize. We agree on this. Statistically, you should always switch. So specifically which door he opens doesn't matter, no. But he has to open a door to let you know which of the remaining doors now contains the entire probability of "all other doors" having the prize. This is the entire point of the problem. If he doesn't, how would you pick which of the two doors to switch to? Because he still won't let you choose both of them.
You already know one of the two doors is empty before he even opens one.
But not which one. He won't let you choose two doors. He has to open one of them first.
Expand it to 10k doors, and you get to select between your door and the 9,999 other doors.
Again, no, you've changed the problem. The host has to open the doors before you can switch.
He is effectively giving you a door and thus it's equivalent to if he were to say "one of the remaining doors is empty, would you like to switch to doors B and C or stay with A?" Of course he's not going to let you have two doors directly but it's effectively what he's doing.
Edit: of course the way it actually is done makes it look like you have a 50-50 shot, which is why they make it a feature in a game show I'm 2/3 sure.
All of what I've been saying is to reduce the problem to what's really going on statistically as in why is it not 50/50, what's the trick etc.
He is effectively giving you a door and thus it's equivalent to if he were to say "one of the remaining doors is empty, would you like to switch to doors B and C or stay with A?" Of course he's not going to let you have two doors directly but it's effectively what he's doing.
Yes, that's effectively what he's doing by actually opening the empty doors. That is the point. Until he has actually opened the empty doors, he has not given you any advantage by switching.
Your last two posts here have not been wrong, per se, but you're talking about a different problem. You clearly understand the math that makes this work. I don't understand why you won't realize that the host knowing which door contains the prize and opening the ones that don't is the crucial part of this problem.
The host knowing which door has the prize is not important
This was your first comment in this thread. That is absolutely, entirely, 100% wrong. The entire problem works precisely because the host knows which door has the prize.
I'm not talking about him knowing whether it's not B or not C, I'm talking about the illusion that he is giving you information that helps your statistics. He is setting up your perceived choice sure but whether you end up getting to choose between A and B or A and C is the same. As given in an explanation of the problem somewhere, it's as if he is giving you the choice between A and BC
I'm talking about the illusion that he is giving you information that helps your statistics.
That's not what happens when he opens the door. It doesn't change the statistics you should take into account when making your decision, but it definitely affects your choice! It has to! He opens the door not containing a prize. You've already determined in advance that you should always switch, but you don't know which door to switch to until the host has opened an empty door.
but whether you end up getting to choose between A and B or A and C is the same.
Yep, it most certainly is. But you still can't make that choice until he's opened a door. A door which he must know does not contain the prize.
As given in an explanation of the problem somewhere, it's as if he is giving you the choice between A and BC
Yes, him opening the doors is what effectively gives you the choice between A or BC. That happens at the moment he opens the door not containing a prize. Not before. It is the action of opening a non-prize door that does that. You should still always switch. But you can't switch to the one remaining door before he has opened the one without a prize. This problem does not work at all if the host does not know which door contains the prize. You started this discussion by claiming that he host's information is not important, which is absolutely false. The problem doesn't work if the host doesn't know which door contains the prize.
I honestly don't know how else to explain this.
There's three possibilities after you choose a door and before he reveals: prize is in your door, prize is in unchosen door, or prize is in other unchosen door. At this point there's a 2/3's chance that the prize is not in your door and a 100% chance that the host will show you an empty door (that's part of the setup/rules). So he opens an empty door. Now we're to the dilemma that you knew you'd be in before he opened a door, before you even went on the game show. Doesn't give you any useful information. You are choosing between staying or switching, that's it. Sorry does that make sense?
That is from an earlier post of yours. How can you say that is not useful information? In your scenario, where you pick a door, and the host does not open more doors. What do you do? You claim it's irrelevant that he host opens more doors, because you already know that you have to switch. But which door do you switch to? There's still two unopened doors in addition to the one you initially picked. How can you know which one to choose? And how does that help your chances of winning? Yes, you should always switch. But you cannot switch until the host has opened the doors without a prize. It is the act of opening the doors that turns the problem into effectively choosing A or BC.
I swear I'm only continuing this discussion because I'm genuinely curious as to why you would claim the host's knowledge is irrelevant.
Lol I'm explaining why the host's action is designed as smoke and mirrors, why it looks like you have a 50/50 shot. I'm not talking about you and me who get the math. I'm talking about people who see the host do something and think it changes the stats.
But it does.... Opening an empty door changes the stats from 1/3 for each door into 1/3 for the door you initially picked and 2/3 for the remaining unopened door, as the set of unopened doors with a combined probability 2/3 is turned into a single door thanks to the host's knowledge. The statistics work out because you know the host will open a door without a prize. Which door it ends up being is irrelevant, but a door still has to be opened. The host doing something is the element that makes the math what it is. It does not work without that element.
The host knowing which door has the prize is not important; in fact the host opening a door actually shows you no new information, since he is going to show you an empty door no matter what.
You started this discussion with that claim, and you still maintain that the host's knowledge does not give you important information. Again, this is blatantly false. Super wrong. Entirely not correct. It is the complete opposite of that. It doesn't change your decision, but knowing that an empty door will be opened is what lets you determine that switching is the best decision in the first place.
You cannot possibly still claim that the host knowing which door has the prize is not important. You can't. Please.
That's not correct, because knowing which options are losses helps you to find the one that's a win. Seeing an empty door is just as important in probability as seeing a winning door.
You can calculate the probability of winning by subtracting the probability of losing from 1, the probability of all the possible outcomes or 100% of the choices. So for the first pick you have a 1-2/3 chance to win, because you have all of the possible options (1.00) minus the chances of losing (.33) and (.33). That's 1/3 just the same by counting losses as by counting wins.
The math is right, but the empty door doesn't tell you anything. He is going to show you an empty door no matter what. He doesn't even have to show you a door period.
AT-ST ยท 1 points ยท Posted at 20:46:49 on May 25, 2016 ยท (Permalink)
The host would also never pick the door that you picked. So really the 1/3 of a chance that belonged to the Host's door would get split to both the remaining doors.
Can you explain to an idiot why the 1/3 that now isn't the open door all goes to the third do and isn't split between your pick and the third door?
Obviously I get you start with:
1/3 (*empty*) and 1/3 (*your choice - always go middle!*) and 1/3 (*door three*)
Then he opens the empty door:
0/3 and 1/3 and 1/3 (+ the missing 1/3 that now isn't door one)
What I don't get is why that becomes:
0/3 and 1/3 and 2/3
As opposed to:
0/3 and 1/3+1/6 and 1/3+1/6
Obviously if nothing was said and he just continued opening doors you are still on your initial 1/3 chance but at the point he asks if you want to change your decision as long as you make a choice, be it to stick or change, that choice is now surely 50:50 whichever way you decide.... right?
I mean obviously not right or the problem wouldn't exist, but I can't get my head round why not, if you just put your fingers in your ears "la-la-lala-lala I can't hear you" you are still 1/3, but I can't see how the choice to stay or change have different odds once a door has been eliminated.
I don't follow his logic, maybe you want to explain it differently? It sounds like he's claiming that the eliminated door doesn't matter, but I say it definitely does, because you know the host will pick an empty door and never on with the prize. He gave a lot of examples of various things, but I don't see how any of them proves that you should disregard the information the host provides with his selection. Sure we could pick doors by throwing darts or rolling a die, but the host has to pick an empty door, so he won't do that.
Maybe I'm confused because it sounds like he admits to the truth/probability tables that explain the possible options and how switching doors is better, but then says they don't matter because it's now a new game. I explained the possible options in another post and how you can follow them to see that switching gives you double the chance of winning. There's an easily countable number of doors and options, so it's not hard to list them all.
Each door would be weighted equally in the new set, but only if you forgot that the host has to pick one that's empty. If the host picked randomly, your odds would change depending on which door he picked.
Just because he chose an empty door doesn't invalidate your choice.
If you have a sample of 3 doors, then remove a specimen because it was invalid, it doesn't change the results of the other two, it would remove it from the original sample leaving you with 2 doors or a 50/50 shot
You're right, that's how it would work if you were picking doors randomly and so was he, or if you walked into the studio after the host opened a door.
In this game though, the host knows which door has a prize, and the host is obligated to pick an empty door that you didn't pick. Knowing those rules gives you valuable information. From the host's action, you have learned that the third door is not one of the empty doors. It may still be the other empty door, or it may be the prize door. That's better odds than your first door has, since your first door had two chances to be an empty door rather than one.
Hm. I still feel like it's applying a reduction in value to your current door via increasing the value on the door left over, which is like changing the outcome, despite it already being fixed.
Think about it like this. Imagine he asked you to pick 1 door out of 100. He then opens up 98 doors except for yours and one other and one of them is right. Would you switch doors then, considering that you only had a 1% chance of getting it right in the first place?
The way I see it (and I've studied this problem multiple times before) is that it's irrelevant now that my chance was once 1%. My probability changes with each new door that opens up. When 98 are open, each door is now 50/50..
Please help me understand!
EDIT: I got it, and out of all the explanations, 3 really stood out. Those 3 people earned my precious reddit silver.
Korlus ยท 78 points ยท Posted at 16:19:50 on May 25, 2016 ยท (Permalink)
When he reveals the empty door, you are right that there are two options available, however you are mistakenly giving both of them an equal chance of being right.
Because the quiz host knows which door the prize is behind, by knowingly not opening it he makes it less likely you have picked the correct door.
I think it's easiest to understand if instead of trying to apply abstract logic, we instead walk through each scenario.
There are three doors - A, B and C. You pick Door A (leaving B and C). Now then:
The prize is behind Door A - the host can now reveal either door to you, and you would be wrong to swap 100% of the time.
The prize is behind Door B - the host MUST now reveal Door C, meaning if you swapped, you would win 100% of the time.
The prize is behind Door C - the host MUST now reveal Door B, meaning if you swapped, you would win 100% of the time.
Because you are now presented with three outcomes and two of them result in you winning, you win 66% of the time if you swap, and only 33% of the time if you keep.
I get that this doesn't explain the logic behind it, but people so often struggle to grasp the concept that it might even be right (Don't worry - it bothered many high level mathematicians at the time, so you are not in any way slow), I don't know why I have never seen it explained this way before.
I think the best explanation is for you to do a probability tree starting from the beginning and including all of the possibilities including which doors the host opens. It all collapses to the 66% and 33% given above.
This is an excellent explanation, however there is one issue:
by knowingly not opening it he makes it less likely you have picked the correct door
When you first pick the door, you have a 33% chance of getting it right. This never changes. What he does do, however, is condense all the wrong choices and the one right choice (assuming you didn't pick it) into a single option. This means that he has actually made it more likely that the other choice is correct.
But this is more of an error in your wording than your explanation.
jaaval ยท 64 points ยท Posted at 15:32:47 on May 25, 2016 ยท (Permalink)
You only win by not changing if you chose the right door to begin with. You win by changing if the prize was behind any of the other doors since the host opens all but one of them.
You are correct when the choices are independent. The explanation others are not clarifying is that in this case they choice is dependent on the previous choice so they are not independent of each other.
ds580 ยท 53 points ยท Posted at 16:11:51 on May 25, 2016 ยท (Permalink)
I finally get it. The trick to this is that the host will never open the door with the prize. The number of doors is irrelevant.
There's a 1/n chance you picked the door with the prize. There's a (n-1)/n chance that door lies in the group you didn't pick.
ASSUMING the host will never pick the door with the prize, when his group is down to one door, you can switch. The key here is that you aren't picking the odds of a single door. You're collectively picking the odds of EVERY door that you didn't choose, but all but one of those you know is empty. This leaves the final door with (n-1)/n probability of holding the prize IF THE HOST HAS PURPOSEFULLY AVOIDED THAT DOOR.
But it's only be 50/50 because (n-2)/n% of the time he'd open up the prize door and you'd lose. By knowing which door has the prize and avoiding it you're avoiding those (n-2)/n% of scenarios.
[deleted] ยท 1 points ยท Posted at 17:15:31 on May 25, 2016 ยท (Permalink)
How is it not clear that I meant to change the rules? I pointed out the part that made switching beneficial (which the person I responded to already highlighted, so that was really for emphasis) and then mentioned that if you changed that to an accidental reveal of the losing door the odds would become 50/50
[deleted] ยท 1 points ยท Posted at 18:01:15 on May 25, 2016 ยท (Permalink)*
I'm not interested in hashing out variants that attempt to justify 50/50 odds. That seems more the field of the psychology of math. I am interested in clarifying the confusion.
The variants of that give you the 50/50 odds illustrate that the hosts knowledge of the prize is the crucial part of the Monty Hall problem.
[deleted] ยท 1 points ยท Posted at 21:05:55 on May 25, 2016 ยท (Permalink)*
Once again you seem to be missing that a crucial part of the problem is in how you arrive at that second state. (Also the original problem is already counterfactual, the real Monty never allowed you to switch)
[deleted] ยท 1 points ยท Posted at 22:18:33 on May 25, 2016 ยท (Permalink)
Are you aware that it's possible to have variations on mathematical problems? Are you disagreeing with what happens in the Monty Fall variation? I have no idea what problem you think I actually have.
[deleted] ยท 1 points ยท Posted at 22:38:04 on May 25, 2016 ยท (Permalink)
That's messed up... the accidental reveal actually increase the likelihood that you picked correctly since there was a 50/50 shot that the stumble would reveal a car... since no car was revealed, it's likely both of the remaining doors actually contained goats, thus making it a 50/50 shot between the two remaining doors.
That one is extremely difficult to wrap the mind around... I think I still switch in that situation though.
So in this scenario these are the following possibilities:
Scenario 1: Pick L1 host falls and opens L2 . W remains.
Scenario 2: Pick L1 host falls and opens W.
Scenario 3: Pick L2 host falls and opens L1 . W remains.
Scenario 4: Pick L2 host falls and opens W.
Scenario 5: Pick W host falls and opens L1 . L2 remains.
Scenario 6: Pick W host falls and opens L2 . L1 remains.
So ignoring Scenario 2 and 4 due to them revealing the winner accidentally (and we know a goat was revealed) we are left with Scenario 1, 3, 5, and 6 where 2 out of 4 of them resulting in winning scenarios... 50/50.
When the host knows the outcome scenario 2 and 4 actually become 1 and 3 respectively causing the 66% win position.
Edit: This was just for me working it out, I know you get it... just needed to try and get a better view of what's going on.
[deleted] ยท 1 points ยท Posted at 18:29:44 on May 25, 2016 ยท (Permalink)
I did say I would still switch in the scenario... I am with you on this one, but the math definitely shows that if there is a possibility that he could have opened the car by accident (scenarios 2 and 4 on my list) that the chances are 50/50.
Given the knowledge that he will "accidentally" open the goat every time due to the scenario saying that that's what is the outcome gives it an unfair advantage since scenario 2 and 4 physically cannot happen (artificially giving additional weight to scenario 1 and 3) and turns this into the "Monty Hall" problem instead of the "Monty Fall" because the scenario you describe isn't actually random.
In theory, if it was truly random and I was knocked unconscious... 1/3 of the time I would be waking up to an open car door.
[deleted] ยท 1 points ยท Posted at 20:49:29 on May 25, 2016 ยท (Permalink)
You're wrong though... look at my scenarios. We agree that there are 6 total scenarios correct?
There is only 4 possibilities that could possibly result with a goat door being revealed right? Two possibilities being removed due to a winning door being opened.
So given that we know there are 4 possibilities, and we know that 2 of those possibilities result in losses... its a 50/50 shot! I've shown you the probabilities, where do you think I've messed up the math?
Edit: I am still going to switch in this situation since maybe the host knew and meant to do it, and since it's a 50/50 shot there's no downside to switching.
[deleted] ยท 0 points ยท Posted at 22:27:49 on May 25, 2016 ยท (Permalink)
Just checked this guy's history... he talks like he's coming straight from /r/iamverysmart.
Once you lay out the scenario it becomes fairly obvious that it's a 50/50 probability, I don't know why he's fighting this so hard.
[deleted] ยท 1 points ยท Posted at 18:25:19 on May 25, 2016 ยท (Permalink)
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rawling ยท 1 points ยท Posted at 21:03:08 on May 25, 2016 ยท (Permalink)
It does not matter if the host took a random walk before opening doors
If the host opened one of the two doors at random, and he happened to open one with a goat, your chances of winning if you switch (or don't) become 50/50.
[deleted] ยท 1 points ยท Posted at 21:11:54 on May 25, 2016 ยท (Permalink)
[deleted]
rawling ยท 1 points ยท Posted at 21:23:34 on May 25, 2016 ยท (Permalink)
OK, there are two possible states:
you pick the car door (1/3) and the host randomly opens one of the two goat doors (1) - 1/3 of starting probability
you pick a goat door (2/3) and the host randomly opens the remaining goat door instead of the car door (1/2) - 1/3 of starting probability
The two possible states that leads to you observing "the host randomly opened a door, and there was a goat" have equal probaiblity, so there is a 1/2 chance that you have the car and a 1/2 chance you will win if you switch.
The remaining 1/3 of the starting probability is lost to the impossible-given-what-you-observed state:
you pick a goat door (2/3) and the host randomly opens the the car door instead of the remaining goat door (1/2) - 1/3 of starting probability
[deleted] ยท 1 points ยท Posted at 21:37:02 on May 25, 2016 ยท (Permalink)*
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rawling ยท 1 points ยท Posted at 21:41:16 on May 25, 2016 ยท (Permalink)
If the host opens a door at random, it is more likely to be a goat in a you-picked-a-car universe than a you-picked-a-goat universe.
That means if the host opens a door at random and it is a goat, it becomes more likely that you are in a you-picked-a-car universe.
[deleted] ยท 0 points ยท Posted at 22:06:36 on May 25, 2016 ยท (Permalink)
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rawling ยท 1 points ยท Posted at 22:42:51 on May 25, 2016 ยท (Permalink)
I'm afraid you've lost me. By how, do you mean what are the numbers, or do you mean how is it possible that the host randomly opening a door and revealing a goat have any effect on the situation?
The difference is that in the original problem the second and third option lead to the same result (host reveals goat), instead of being split into two different results (host reveals goat vs. host reveals car).
[deleted] ยท 1 points ยท Posted at 22:21:04 on May 25, 2016 ยท (Permalink)
I'm not oversimplifying anything and I'm not losing any information, but if you still disagree feel free to give a none oversimplified explanation so that I can point out where you go wrong.
lazyl ยท 1 points ยท Posted at 17:37:21 on May 25, 2016 ยท (Permalink)*
That table is incorrect. The wiki editor must have misunderstood the paper he sourced for that information. If there are three doors, and you pick one, and then the host opens one of the two that you didn't pick revealing a goat, then the chance that the third door has the car is 2/3. It is irrelevant whether or not he knew where the car was.
I'll actually also explain why the intention matters. Suppose he revealed a door at random instead, and look at the odds before he reveals a random goat:
With probability 1/3 you chose the winning door, in that case the host will randomly open a losing door
With probability 2/3 you chose the losing door, in that case the host will open a losing door half the time and a winning door half the time, so each of those happens 1/3 of the time. (This is different from when he intentionally opens the losing door, in that case he will open a losing door 2/3 of the time in scenario two and a winning door 0% of the time).
Now suppose the host opens a losing door at random, there are two possible scenarios that lead to this and they were equally likely before he opened that lost door, so logically they are equally likely after he revealed that losing door and they remain equally likely until one of the two remaining doors is opened.
Each door has 1/100th probability of having the prize behind it. You choose one door. Now we separate the doors into two groups: "your door" and "the other doors". Each door has 1/100th probability having a prize behind it. Take what's behind your door, and put it in a one door building. Take what's behind the other doors, and put it in a 99-door building with 98 doors having cement behind them.
If asked to guess which building has the prize inside, which would you choose? The 1-door building has a 1/100 chance of the prize being inside, and the 99-door building has one a 99/100 chance of the prize being inside, even with 98 doors with cement behind them. Now Monty tells you he has opened the 98 doors in the other building that have cement behind them. This is no different that the normal situation, because monty is always choosing doors without the prize behind them. You know the other building has 98 doors with cement behind them. Opening and seeing them didn't affect the probability of something being inside the building. If given the option to open the door without cement behind it in the 99 door building, instead of the one door building, you should take it. Even though you have an option of two doors, one has a 99% chance of having the prize behind it.
The thing to remember here is the host knows which door has the prize behind it, the other 98 doors that he opened (imagine it all at once not one at a time) wasn't done randomly
I like to look at it this way, as it helped me get my head around it.
You split yourself into three alternate realities, in each one you pick a different door. Now, in all three realities, the prize is in door number three.
It's really important that you pick a door first and then are shown a door that is dud.
So let's play it out:
In reality A you pick door number 1. The host then shows you door number 2, knowing that it's the only empty door that isn't the one you picked. You're then asked if you want to switch?
No, you're good. Stick with your choice. You open door 1 and boo, you lose.
Reality B, you pick door two. The host shows you door 1, because it doesn't have the prize and you haven't picked it. Want to change?
No, you stick with door 2, and lose.
In reality C, you pick door three. The host can open either of the other doors as there are no prizes there, so he shows you door 1 as empty. Want to change?
No, you're fine sticking with your choice. Bam! You win, kudos.
In your three realities you just won 33% of the time.
The prize was in fact a time machine and you (or reality C you) use it to go back to the reality splitting moment, let's do it all again:
Ok, so same situation, three realities, the prize is in door number 3 in each one. This time we're going to switch in each reality.
So reality A plays out that you pick door 1, are shown the empty door 2, and then switch to door 3. Boom! Winner.
Reality B has you pick door 2, you're shown door 1 as empty, and then you switch to door 3. Awesomesocks, the prize is yours.
In reality C, you pick door 3, are shown an empty door 1, and then switch to door 2, which is empty so you lose. Darnit.
The point is that by switching, you won 66% of the time in the exact same scenario.
So though the initial door location and your first pick are two random factors, the rules of the game means that if you switch after being shown an empty door, you're 66% likely to be switching to the winning door.
a third of all contestants won't like the fact that they switched and lost, but the rest will be quiet happy.
(We're going to keep this as Y until the end as this term because this is a common term for both parts of the equation since exponents stay the same after being differentiated.
What we're doing first is rearranging AY + BY into (A+B)Y
Which looks like all of that out gives:
((32x-56) + (16x2 -56x+53)(4x-7))Y
Now we need to multiply out of all these brackets before we can simplify, like so:
We have some same order terms here that can be added or subtracted from each other, giving:
(64x3 - 336x2 + 636x -427)Y
Now, we want to simplify this further, but trying to figure out what divides into that could be a headache. However, we can cheat a bit and look at a few lines above, where we had (4x-7) as the 1st order differentiation coefficient. What's the bet that will divide into this monstrosity still?
Well dividing through with the 4x will make that 64x3 become 16x2 like we expect, and dividing the -427 by -7 will give you the +63 that you weren't sure where the hell it came from. The middle two terms also divide in and give you your result:
((4x-7)(16x3 - 56x + 61))Y
So we'll bring Y back into it's full form now:
((4x-7)(16x3 - 56x + 61))e2x2-7x+3
And there we have it. Let's leave it to 3 derivatives though, nobody needs a fourth derivative unless it's a full moon in November.
tl;dr Take out the common term (the exponential), expand, then simplify.
There are 100 doors. You pick 1. You're then offered the chance to switch to 98 99 of the others.
971365 ยท 3 points ยท Posted at 15:38:09 on May 25, 2016 ยท (Permalink)
I get the problem but why 98 others? Wouldn't it be like switching to the other 99?
[deleted] ยท 3 points ยท Posted at 15:46:59 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 16:05:51 on May 25, 2016 ยท (Permalink)
Here is the way I see it (in the original problem). When you first pick a door you have 66% chance of it not being the prize. So let's say that it's not the prize since that is most likely. That means the prize should be in one of the other doors. Well when the host opens up the other door he has to open a door without a prize meaning that if your original selection was 66% chance no prize then the other door shoild now have 66% chance being the prize
Putting it this way may actually confuse people more, because if N=3, you are switching to just 1 other door. One is open, and you had already picked another one. There is one choice left.
But that is incorrect, that one door has 2/3 winning probability.
Similarly, if N=100, and the host opens 98 doors, the remaining one has 99% winning probability, not 98%, or 0.9898...%.
You were much much more likely to have picked one that was wrong than the right one
You had a 99/100 chance to be wrong on the first pick, and now that 98 wrong options were removed and you know that you had a 99/100 chance of being wrong initially you can assume that you picked one of the wrong doors since the odds of you picking the right door initially was much lower than picking the wrong door
The odds actually don't change. There is the door you pick (1/100), the door that contains the prize (1/100), and all the other doors (98/100).
Since the host has knowledge of which door contains the prize, he will never open that door. IF he was truly opening the doors randomly, then your odds WOULD increase (with a potential that they drop to zero if he were to open the door with the prize).
So, are you willing to bet that you happened to pick the correct door when you were offered 100 doors?
If you were wrong the first time, you want to switch because the only remaining door has the car/money/whatever. You had a 2/3 chance of being wrong the first time.
You're thinking that his opening the one door and leaving the other means you're down to 2 options, but that logic stops making sense when you realze he's not opening a random door.
Imagine you took the same scene, played it out 3 times and opened all 3 doors. Two of those times, your picking a goat forced the host to show you the other goat, so those two times you only win if you switch.
Another way to think of it is chosing between your door and montys door. you will pick 1 door out of the hundred so you have 1% chance to get the prize. Monty will always pick the door that has the prize unless you have already picked the prize so he has a 99% chance to pick the prize since the only way he couldn't would be if you picked it. So then Monty gives you the choice of keeping your door or picking his door. Your door has a 1% chance and his door has a 99% chance. Does that help.
at the start you had 1% chance to pick the right one
at the end the other door has a 98% chance of been right because all the other doors were opened
the doors at the end would only be 50 / 50 if you didnt force one to not open in the first place by picking it if the host picked two doors at random (one been correct and one not) it would then be 50 / 50
but you picked one at the start and thus eliminated every single other door except (in 98/100 cases) the right one
its the same reason behind deal or no deal and why you always swap if you had a low number and a high number left, at the start you picked 1/28, at the end you eliminated 26 of them, and a high one was still left, either you got insanely lucky and picked the correct one out of 28
You gotta look at the total game and not the the new choice in isolation. It's 50/50 only if you have no other information. But you do have info: you know that your first door had a 1/100 chance of being right. If all other doors are closed except 1 unknown and the 1 you picked, and 1 of those 2 is absolutely the right door, then it's far more likely that the unpicked door is the right door.
Play the game 100 times. 99 of those times, staying with your 1st choice would be wrong. Only in that 100th game, you would be wrong to switch. So you have a 99% better shot at taking the option the host reveals, and only a 1% shot at taking the completely random door you started with.
Think from the host's perspective. The host sees you choose 1 door out of 100. 99 times, you'll choose wrong. 1 time, you choose right. After you choose, the host picks 1 other door for you.
99 times the host MUST pick the correct door. Only 1 time would the host get the option of trying to trick you by choosing an incorrect door.
Knowing that, you can alter your strategy because you have complete knowledge of the rules here. You don't have complete knowledge of the doors, but you should know that you have a 99/100 chance when you go with the host's "choice" (because he was obeying a certain rule that said you must have 2 choices and 1 of those must be the correct door).
Shrink it down from 100 doors to 3 doors and the logic still checks out.
My probability changes with each new door that opens up.
It hasn't though.
No new information is gained. Your probability starts as 1/100, the doors that are opened are always picked by the host to be goats (not selected randomly).
The intuition is that 2 doors means 50/50 odds. But this is easy to show as incorrect.
If in the game, instead, whenever you pick the correct door the host flips a d100 (without you seeing) and if it doesn't come up as 100 then he swaps what's behind the 2 doors (without you seeing).
It's easy to see now that it is not 50/50, almost every time you pick the car at first it is swapped. Even though there are 2 doors.
Maybe this will help your thinking for the Monty Hall problem:
Chosen door: Always Stick | Always Switch
Goat 1 Get a goat | Get a car
Goat 2 Get a goat | Get a car
Car Get a car | Get a goat
When a goat is revealed this does NOT change the probability that your chosen door is a goat. You had a 2/3 chance of selecting a goat, there is always an available goat in the 2 that you didn't choose, so showing you a goat tells you nothing about the probability of what you picked.
Here's another way of seeing why the idea that the probability changes doesn't work:
Say it's a billion doors. All across the world. A car is only behind one of them. The doors can detect what is behind them and be remotely activated to open.
One of the doors happens to be just down the road from you.
You want the car to be where you are, even though it could be behind any of the doors in the world.
So what you do is, you "pick" the door near you. You then press a button which makes all the other doors that aren't your door receive a command to open if they have a goat behind them, but one door other than yours has to remain closed. If the car is elsewhere it will be the door with the car, otherwise it is selected randomly which one will be kept closed.
Now, a billion minus 2 doors open. They all send information back verifying they have goats behind them.
One door, somewhere on the other side of the world from you let's say, is still closed.
So now it's 2 doors. Is there a 50% chance the car is behind your door?
If there is, that means that with a billion doors you can, every time, shift the probabilities so that there is a 50% chance it's behind whatever door you want. Isn't this getting close to teleportation?
You could have picked any of the billion doors to start with and there would be a 50% chance it would be behind that one once the other doors are opened. You basically have a teleporter that works 50% of the time.
When you picked 1 door out of 100, you had 1% chance of getting it right. When 98 doors were eliminated, the prize isn't randomly reshuffled behind one of the last two doors to reset the probability to 50/50....the prize stayed where it always was, so the door you picked is still 1% and the other door is still 99%.
I think where you're getting hung up is thinking of it like a coin flip. It's not that each 100 doors has a 50% chance of a prize behind it, you would need 50 randomly placed prizes for each door to be like a coin flip. It's more like rolling a 100 sided dice to roll a 1.
hrg_ ยท 1 points ยท Posted at 18:07:38 on May 25, 2016 ยท (Permalink)
You can think of it like this:
You have a 1/3 chance of picking any door at the beginning. Say you choose door A. This is the equivalent of saying there is a 1/3 chance you were right, and 2/3 chance you were wrong (there is a 2/3 chance the car is behind doors B or C).
So we have:
Door A = 1/3 chance of having a car behind it
Doors B & C = 2/3 chance of having a car behind one of them
Suppose the gameshow host opens door C, showing the door to be empty. The key thing to realize is that the above rule still holds true:
Door A = 1/3 chance of having a car behind it
Doors B & C = 2/3 chance of having a car behind one of them
However, this time, we just know that Door C is a 0/3 chance (by itself). So Door A has a 1/3 chance (this can't simply change just because a door was opened) and Door C has a 0/3 chance. So what does that leave in Door B? 2/3. Thus, we are left with:
Door A = 1/3
Door B = 2/3
Door C = 0/3
Should we switch our choice to Door B? Every time.
EDIT: I chose a poor example to try to get to the solution in two steps as there are at least two sticking points for most people.
Better example follows:
When choosing out of a hundred doors, you probably picked wrong. So, when you picked, you created one category of 'your-door' which is hiding 'probably-no-prize' and another category of 'every-other-door' which is hiding 'probably-the-prize'.
Of those two categories, one is better. You're given the choice of switching from the poor 'your-door' category to the better 'every-other-door' category, which you should do. The fact that a gameshow host walks along most of the doors in the better category, theatrically opening them one at a time is meaningless. It just serves to leave the show with a dramatic decision between two single doors.
What if you got to open all 99 of the doors in the better category? You'd do that instead of sticking with your one door, right?
This is wrong. You do not get two games, you get one. You get two probabilities: one where you don't know anything about any door, and one where you're given information about the doors you did not choose. It's the fact that the second one is a conditional probability that changes the answer. The condition is: You've chosen a door, and every other door than the "swap to" door is wrong.
Your example is also very confusing, because it would suggest that the second choice is 50/50, which is wrong.
That's not at all a good analogy. In the Monty Hall problem, switching is intuitively 50/50, but intuition is wrong. Comparing it to a switch to a coin flip game does not help overcome that intuition.
If there were 100 doors, and I got to pick one. Then the host opened a door and I got to choose whether to choose a new door or stay with my remaining door, and this continued until there were only 2 cups remaining.
Am I right to think that I should swap cups every time to have the highest chance of winning?
Instead of one door out of 100, maybe using the lottery will help some people. Suppose you buy a lottery ticket with the numbers 1, 2, 3, 4, 5, and 6. You don't watch the drawing that night, but instead, you have your friend come over and read the results in the paper. Your friend, who knows the winning numbers, then tells you "Okay, either you won, or the winning numbers are 12, 14, 22, 25, 28 and 39".
Do you now have a 50% chance of winning the lottery? If you had the opportunity to change your ticket to the other numbers your friend read out, would you?
There's three equally likely situations the prize is behind Door A, B or C. You start by choosing door A.
There's a 1/3 chance that Door A contains the prize. In that case the host will randomly reveal Door B or C to be empty. You will be better of staying with your first choice.
There's a 1/3 chance that Door B contains the prize. In that case the host will reveal Door C to be empty (they'll never open door B because the host knows where the prize is). You will be better off changing your choice.
There's a 1/3 chance that Door C contains the prize. In that case the host will reveal Door B to be empty (they'll never open door C because the host knows where the prize is). You will be better off changing your choice.
So 1/3 chance that your original guess was right. 2/3 chance that you would be better off switching.
For extra credit consider if the host doesn't know where the prize is and randomly opens a door to reveal that it's empty.
[deleted] ยท 2 points ยท Posted at 16:16:46 on May 25, 2016 ยท (Permalink)
This is a much better explanation, thanks.
I'm not terrible at maths but just couldn't picture why the 1/3 chance of the host's door went to the door her didn't open.
As someone else said. It's either in the door you originally chose or not. There's a 1/N chance it's in your door. If it's not in the door you chose it's the door the host left unopened which has a N-1/N chance.
Instead of using 3 doors, use 1000. You pick 1, monty opens up 998 of them so there are 2 doors left over: one that you picked and one that may have the prize unless you already picked the one with the prize.
That's pretty brilliant expansion of the logic to make it make more sense.
By the time he's picked 998 doors (knowing which one is the winner beforehand, and therefore not picking it yet on purpose), the chances of the one door neither of you picked having the prize is very, very high, because the odds of you picking the right door yourself, randomly, out of 1000 doors, right at the start, is insanely low.
So you switch, and are almost guaranteed to win, because he's basically shown you which door is the winner, unless you were just obscenely lucky with your first pick.
ASAPScience did a great video about it on YouTube if you still can't figure it out. It didn't really make sense to me for the longest time but as soon as I saw that video it clicked
On your first pick, you have 1/3 chance of picking the car, and 2/3 chance of picking the goat.
If you stick with the original door, then you still have your original 1/3 chance of having picked the car right the first time.
The only other door left then has the remaining 2/3 chance of being the car.
[deleted] ยท 1 points ยท Posted at 21:23:42 on May 25, 2016 ยท (Permalink)
There's a lot of good examples and descriptions here. My favorite way of thinking about it is:
You own Door 1 which has a 33.3% chance of being a winner. The host has the other 2 doors have a combined 66.6% chance. He opens one of them, which is a dud, so that doesn't change the odds that the host has a winning door. So the one door now has a 66.6% chance of being a winner, and you still have a 33.3% chance. He then offers you his door and his odds.
So, when you switch, you actually get pick the two doors you didn't choose, you get the dud the host opened for free, and you get the new one which has a 66% chance of being the right one.
When you switch, you actually get pick the two doors you didn't choose.
If I pick one of the wrong doors first round then the host will open the other wrong door leaving me only with the right door, thus if I pick the a wrong door the first round I will necessarily be presented with the choice to pick the right door the next round.
Similarly if I pick the right door in the first round the host will open one of the wrong doors leaving the other wrong door, thus if I pick the right door first round I will necessarily be presented with a wrong door in the second round.
To sum up if I pick wrong in the first round I will be presented with the right door and if I pick right in the first round then I will be presented with a wrong door. Since there is a 66.7% I chose the wrong door in the first round there is a 66.7% I will be presented with the right door. Since there is a 33.3% that I picked right the first time there is a 33.3% I will be presented with the wrong door. So the door I'm presented with will always have 66.7% of being right and a 33.3% of being wrong.
Just try it. Get a coin, 3+ cups and then turn then upside down. Now get your cat to pick a cup, flip an empty one and ask the cat to switch or not.
You'll see why its first guess is improbable and switching is good.
narrill ยท 1 points ยท Posted at 16:03:42 on May 25, 2016 ยท (Permalink)
The host reveals all but two doors, including the one you picked, and one of those doors contains the prize. So switching will win you the prize if you initially picked wrong, which is a 66% chance with three doors.
pnoozi ยท 1 points ยท Posted at 16:34:47 on May 25, 2016 ยท (Permalink)
It's easier to visualize with more doors
Imagine there were 100 doors, you chose 1, then the host eliminated 98 of them. Unless you got very lucky (unlucky?) and picked the prize to begin with, obviously the door he didn't eliminate contains the prize.
the playing card Monty Hall problem varient is better for understanding that.
suppose you want to pick the Ace of Spades from a deck.
You draw a card from the deck, but don't lock at it. Then the host locks at the rest of the deck and shows you 50 cards that are NOT the Ace of Spades. You now have the choice of the remaining card or the card you choose.
Of course you would flip in that place b/c well there was only a 1/52 chance you were right. There is a 51/52 chance that remaining card is the Ace of Spades.
Another key point is that the object you select is random. The ones the host throws out are NOT random, they are losers selected to throw out.
pjswmkj ยท 1 points ยท Posted at 16:55:19 on May 25, 2016 ยท (Permalink)
Think of it this way: the revealed door is part of your switched pick. Whichever door you originally pick, there is a 2/3 chance that one of the other two doors is the correct one. So pretend that you get to change your pick and can pick both those two other doors. You have a 2/3 chance of being correct, right? That is essentially what it happening: by switching your pick you are essentially just picking two doors, except they don't punish you for the revealed door being picked. There is a 2/3 chance that the switched door is correct.
If you think of each of the doors as having a 1/3 chance of having the prize, then that means that the two doors you didn't pick have a combined 2/3 chance of having the prize behind one of them. Now when the host opens one of those two doors and shows you that it's empty, the last door now has a 2/3 chance of having the prize, since you just found out that it wasn't behind the one he opened. Compare that 2/3 chance with the 1/3 chance you picked the right door first, and it's clear that you have a better chance of winning if you switch.
MedBull ยท 1 points ยท Posted at 17:07:37 on May 25, 2016 ยท (Permalink)
you actually had a 66.6% chance to choose the wrong door to begin with
That's really the meat of it. If the host reveals a wrong door every time, then either your door is right or his is. The above fact is still true, which means there's a 66.6% chance you didn't choose the right door.
You're on a gameshow. The grand prize is hidden behind one of 100 doors. You pick one out of the 100 doors randomly. The host then opens 98 of the doors, revealing no grand prize, and leaving you with two doors; the one you chose, and a single random door the host didn't open.
Which door would you choose now?
[deleted] ยท 1 points ยท Posted at 17:42:11 on May 25, 2016 ยท (Permalink)
The way the game is set up, Monty's proposition is equivalent to him asking whether you want to keep what's behind the door that you chose, or accept whatever is behind both of the doors you didn't choose. Now since at least one of the doors you didn't initially choose will have nothing behind it, Monty can always open such a door before offering you the trade; but he is still offering to let you switch from your first door to both of the doors you didn't pick. Hence it's always better to switch.
Someone else might have satisfactorily explained this to you already but imma give a shot anyway.
Okay so you've picked a door. Now there are 3 options.
Option 1: You've picked a door with a goat. The host reveals the other door with the goat, you switch, and you win a car.
Option 2: You've picked the other door with the goat. The host revels a goat, you switch and you win a car.
Option 3: You've picked the door with the car. The host revels either of the goats, you swap and you win a goat. Booo.
Now, 2 out of the 3 options you win the car. That's because the host knows where the goats are and always reveals the one you haven't picked. The only time you lose is when both doors are goats.
A lot of people try to explain it by using 100 doors and opening 99 of them. but I think its better to just look at the options.
The easiest way I found to get a grip on this problem is imagine there are 100 doors with 1 "winner" door. You pick 1 door out of them and the host (who knows what's behind each door) then starts systematically opening doors containing no prizes. Now there are only two doors left at the end, the one you picked, and one the host intentionally left closed.
Would you choose the one the host intentionally left closed? or the one you picked?
It pretty much comes down to that fact that before hand you KNEW Monty was going to reveal a door was empty. So the fact that he actually did reveal an empty door didn't give you any more information.
There's a neat probability proof for the problem but I think that's an easy way to explain the intuition behind it.
Now that you know that a door has been opened, and he did not reveal the prize, you know that if you picked the wrong door, and switched, you will win.
There were 3 choices:
Door 1 - The Right Door - You picked this, you switch, you lose.
Door 2 - A wrong door - You pick this, you switch, you win.
Door 3 - A wrong door - You pick this, you switch, you win.
You can easily see how many chances of winning you had if you switched, assuming a wrong door is revealed.
the other explanation was good, but i like to think about the larger option - so instead of 3 doors, there are 100. then the host reveals 98 of the doors after you choose one, and then asks you if you want to swap. of course you would say yes, because the chances you got the right door the first time is 1/100. the same principal works with the 3 doors.
When you pick the first door you have a 2/3 chance of picking the wrong door. If they opened an incorrect door and then opened your door without giving the option to change you would still be wrong 2 out of 3 times and correct 1 out of 3 times. By changing doors you now have a 1-1/3=2/3 chance of being right.
I wrote a simple Matlab code to prove this. I created 1000 cases with random numbers for the prize door and 1000 cases with random numbers for the door chosen. The number of wins when you switch doors is almost twice the number of wins when you stay with your initial choice.
If there were 100 Doors and behind one of them is A Million Dollars and behind the rest of them there are goats. You pick Door No. 42 then door No.25 Is opened to reveal a goat. Your chances of being right were 1/100 but now they are 1/99
Oh no. Not this again. I've never seen anyone explain at an ELI14 or less. Here's my attempt. (Assume the host MUST open a door after you've selected)
Choice 1: you have a choice between 3 doors, so there's 3 possibilities.
Select correct door
Select incorrect door X
Select incorrect door Y
Choice 2. After choosing a door, one of the other doors is always is opened by the host (it's always empty). You can do one of two things
STAY with your selected door
SWITCH to the other closed door
So there are only 6 possible sequences (3x2=6).
Let's just list them out along with their results:
Select correct door, STAY = win
Select Incorrect Door X, STAY = lose
Select Incorrect Door Y, STAY = lose
Select correct door, SWITCH = lose
Select Incorrect Door X, SWITCH = win
Select Incorrect Door Y, SWITCH = win
Now, you have no idea whether you selected the correct door or not, so you can't base your decision to STAY or SWITCH on that. Looking at the list of sequences though you see that when you SWITCH, you win 2 of 3 times. If you STAY, you only win 1/3. Try covering up the first "select" part of the sequences and it ends up looking like this.
It's much easier to visualize by adding more doors. So you pick 1 out of 1,000 doors. It's unlikely you've picked the right door. Now every door opens except for one other door.
I've given this explanation in a number of threads now.
It's easiest to think of this way :
Imagine these two scenarios, in one, you start by picking the correct door. In the other, you start by picking the incorrect door.
If there's three doors, obviously you have a 66% chance of picking the wrong door, and a 33% chance of the right door. So let's assume we say "switch doors" every time.
If you pick the correct door, there's two empty doors left. The host opens an (obviously) empty door, and you switch to the other empty door. You've lost. This happens any time you start by picking the correct door, or, 33% of the time.
If you pick the incorrect door, the host opens the only remaining empty door, and the only door left for you to switch to is the correct door. This happens every time you start by picking an incorrect door, or, 66% of the time.
The best example I heard is to scale it to 100 doors. If you pick one, and the host picks another, and asks if you want to swap to his, your door was 1/100, whereas his door now has 99/100 as one of them has the prize and he picked that specific door.
Here's a better explanation than the ones you've gotten so far.
I have 1,000 doors. Behind one door is a new car. Behind the others is nothing. I invite you to guess which door has the new car. You guess one randomly. That leaves 999 doors. I eliminate 998 of these doors as not having the prize; the prize is either behind the door you chose or the other one I left in contention. Which is more likely: you guessed right the first time randomly out of 1,000 possibilities, or that this other door I led you to has the prize?
[deleted] ยท 1 points ยท Posted at 23:37:32 on May 25, 2016 ยท (Permalink)
It's all in the fact that they only flip the empty door.
Imagine it this way: you select a door, they randomly flip one of the other two, no matter what's behind it. Then, you'd have 3 cases:
1/3 of the time, you select the right door.
1/3 of the time, you select the wrong door and they flip an empty door.
1/3 of the time, you select the wrong door and they flip open the door to the car.
In this scenario, if they flip open the empty door, then it's a 50/50 chance, and is what most people assume is going on. But, in the actual problem, in the 1/3 of the time case where they would reveal the car, they instead also flip open the empty door. So the 1/3 + 1/3 cases become 2/3.
The easy way to explain it is with more doors. Lets say there are 5. You are going to pick a door, I open 3 losing doors, you get a chance to switch. Lets assume the prize is in door number 3. If you pick a door and don't switch, you win when you pick 3 and lose when you pick 1, 2, 4, and 5. So you win 20% of the time. But if you pick a door and switch every time, you lose when you pick door 3, but you win when you pick 1, 2, 4, and 5. So you now win 80% of the time.
The key to the problem is if you switch, picking a loser = picking a winner every time. So because there are more losers than winners to start with, you want to bet on your first pick being wrong.
I know others have answered already, but it's much easier to imagine if you expand the number of doors to a million.
[deleted] ยท 1 points ยท Posted at 00:35:28 on May 26, 2016 ยท (Permalink)
I know this has been explained many times but really the best way to think about it is:
Imagine 1,000,000,000 options. One of them is a prize, the rest are nothing. You choose one at random. The chances of that being the prize are basically zero; if you guessed it you're insanely lucky.
The host, who knows which one is the winner, gets rid of all of them but the winner and another.
Would you swap?
If not, you're saying that you believe in your original 1/billion chance which is quite clearly nonsensical.
Engineer reporting in. Easiest way to explain this is by increasing the door count.
Imagine there are 20 doors. You pick door 4. They open every single door but door 4 and door 18, and ask if you want to switch. Well? Of course you do. What are the odds you managed to get it right? (for the record, the average person needs to get to 7 doors before they figure this analogy out. Furthermore, pigeons are not subject to the bias that humans have on the Monty Hall problem).
You only have a 1/3 chance in getting it right. Therefor 2/3 times you switch doors you will win.
Make a 3x3 table and put an x in the top left, middle, and bottom right squares where x represents the prize. Then play out the scenario and you will see that 2/3 times you switch doors you win the prize.
My favorite way to think about it is by writing out the three possibilities:
CGG
GCG
GGC
Now without loss of generality assume that I pick door one. Then I have a 1/3 chance of winning if I stay with my original choice (first arrangement) and I have a 2/3 chance of winning if I switch.
You choose one door at the beginning, there are two outcomes for this:
a) You picked the right door 1/3 chance for that
b) You picked on of the wrong doors 2/3 chance for that
The host eliminates one wrong door, no matter what you picked, you can now choose to either keep your door or swap it, if you keep it, no matter what, you have two outcomes:
a) You picked the right door and kept it, as I said before 1/3 chance
b) You picked a wrong door and kept it, as I said before 2/3 chance
Now you are given the chance to swap no matter what, as one wrong door is eliminated, swapping means you will swap to the right door if you picked one of the wrong doors in the beginning (As you had one of the wrong doors, the other on is opened by the host and you can only swap to the right one) or to the remaining wrong door if you picked the right one at the start (As you had the right one and one wrong one is out, you will get the other wrong door).
This leads to the knowledge that if you change your door, you are guaranteed to get the opposite of what you picked at the start (Wrong -> Right or Right -> Wrong), and since there is a 2/3 chance that you picked a wrong door at the start, there is a 2/3 chance to gain from a swap.
I don't know if this will help, but it's all about probability being king. If there are three doors, with one prize behind a single one, randomized each time you open one, you can choose a door as many times as you like and you will likely average a 33% success rate. No matter what, (outside of strange luck) having 3 doors gives you a 1/3 chance. So, let's say you choose door #1, which has a 33% chance, just like the others. THEN the game show host opens door #2, which is empty, and allows you to switch if you choose to. What are the odds now? Your door, #1 STILL has 33% odds while door #3 now has a 66% chance. Therefore, it would TECHNICALLY be safer to switch to door #3.
Edit: sorry, looks like door #3 actually has a 66% chance. I couldn't sworn that it was explained to me as 50%, but it's been awhile, and I very likely was remembering it wrong.
The last time this problem was posted on reddit, people got hung up on a detail that is essential to this problem, so I'm going to emphasize it:
The host HAS to open a door that does not contain the prize. He's not opening an empty door by accident.
Other people have posted explanations beyond this point, but keep the above fact in mind or else you'll burn a lot of unnecessary fuel trying to figure out why the switch makes sense.
[deleted] ยท 11 points ยท Posted at 18:02:47 on May 25, 2016 ยท (Permalink)
Interestingly enough, if you're describing a single situation ("you" on a game show) and Monty chooses and opens a door at random, then it is 50/50 to switch. So merely stating that he opens a losing door isn't enough, because whether he did so randomly or purposefully changes the answer.
Edit: to clarify, I could interpret "he opens one... that doesn't contain the prize" as a rule of the game or as a description of events and the difference matters.
[deleted] ยท 3 points ยท Posted at 21:59:41 on May 25, 2016 ยท (Permalink)
Well, it's obvious that he wouldn't pick the door with the prize behind it, because then the entire thing would fall apart. You'd know which door the prize was behind. It's implied by the rules.
It's implied but not explicitly stated, you could have the host randomly open a door and if it reveals the car then too bad, the contestant can't switch. You can still milk some drama from that outcome if you were really going to televise something like this.
[deleted] ยท 2 points ยท Posted at 12:00:19 on May 26, 2016 ยท (Permalink)
If that happens, then like you said, the contestant can't switch. Therefore that doesn't apply to the Monty Hall problem, because the problem wouldn't exist, the contestant would have just lost.
Right, this is not the Monty Hall problem, this is a variation, but in that variation you do not benefit by switching if the host reveals a goat (and the common explanation of the problem leave out to specify that the host HAS to reveal a goat, most of the time they state that he has revealed a goat (which is different because he could have done that by accident))
[deleted] ยท 1 points ยท Posted at 12:17:12 on May 26, 2016 ยท (Permalink)
You can't allocate the extra 1/3 to the door that's left over in case it wasn't specified beforehand that he was going to have to open a door after the first choice was made. This is in fact crucial.
Faugh ยท 0 points ยท Posted at 22:37:08 on May 25, 2016 ยท (Permalink)
The Monty Hall Problem wouldn't be a "problem" if people didn't explain the solution like fucking idiots.
It's also very important to know that the problem assumes the host ALWAYS opens a door and offers the switch. In the actual game on Let's Make a Deal, Monty Hall had the option of offering the switch or not, and frequently did not.
It's important that the host is intentionally choosing an empty door because it's the only way the probability of success from that door collapses onto the last remaining one, instead of being split evenly between your door and the other closed door. The whole problem is easier to explain using 100 doors, like other users have done to describe the problem more generally.
Changing the parameters of the gameshow, there are now 100 doors with 1 prize and 99 duds. I choose a door, the host opens 98 doors and leaves one closed. Imagine the two scenarios where:
a) The host randomly opens 98 of the remaining 99 doors and they all happen to be empty.
b) The host intentionally opens 98 doors he knows won't have the prize.
In situation "a", the host has eliminated 98 doors that aren't winners. However, the probability that the last remaining door has the prize is now 50%, and the chance your first choice has the prize is also 50%. This becomes obvious when you realize that your selecting at random and the host's selecting at random are functionally the same thing. If you decided to randomly open 98 doors and they were all empty, is there any reason to think either of the remaining two doors has a higher chance of containing the prize than the other? Choosing a door to keep closed at the beginning, then opening 98 of the remaining 99 doors would be no different than opening 98 empty doors initially, so why switch doors? If it makes no sense to switch doors when you're the only one randomly opening them, adding in a host makes no difference.
Now look at situation "b." You choose a door at random from a pool of 100. The host intentionally pulls out 98 of the remaining 99 doors which will be empty. In 99 out of 100 situations where you selected a bad door initially, the host is guaranteed to keep the remaining door closed because it's a winner. In 1 out of 100 situations where you had it right the first time, it didn't matter what door he left closed. In other words, it's because the host intentionally opened empty doors that the prize now has a 1% chance of being behind your initial door and a 99% chance of being behind the second.
[deleted] ยท 2 points ยท Posted at 20:06:49 on May 25, 2016 ยท (Permalink)*
Shit man. I first came across this problem 6 years back. I never understood it, though I understood the words. Yours is the most clear, especially that put another way in the last paragraph. That was the missing link in my understanding. I read that extending the scenario to a large number of trials makes it easy to understand, but their way of explaining was not exactly clear to me. Your version of the 3 million trials was perfect. I am saving this comment. Don't delete it.
[deleted] ยท -6 points ยท Posted at 22:18:50 on May 25, 2016 ยท (Permalink)
It's not. It works the same no matter what the host is thinking at the time, or what knowledge they are running under.
Notice that in that case the host does think about which doors he opens, if he doesn't think about it at all (and therefore could open the winning door by accident) then that changes the outcome.
[deleted] ยท 0 points ยท Posted at 12:15:50 on May 26, 2016 ยท (Permalink)
Did you read the entire comment? I went over this. You must throw out all results where the randomly picked doors lead to opening the prize winning door on accident, in order to fulfill the conditions of the problem.
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 2: Pick L1 - host falls and opens W.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 4: Pick L2 - host falls and opens W.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do you agree that these are literally all of the possibilities? Am I missing any? Or are any of these wrong?
Since we know that a goat door was revealed there are only 4 of the above scenarios that could have possibly happened:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do we disagree on this? Out of the original six scenarios these are the four possible positions that could possibly be true given that a goat door was revealed. Do you disagree with that? What other options could there be?
Of these 4 remaining options, 2 of them switching will result in a win, 2 of them switching will result in a loss. Switching is literally a 50/50 prospect.
If I am incorrect in any of my steps please tell me which step you think I made an error. Do you believe that the original 6 scenarios have different probabilities? Do you believe the 4 possible goat door reveals have a different probability? This is literally the probability tree for the scenario. These are the only possible options.
No, that's simply not true, the state is different, in one case you know the host had to reveal a goat, in the other case you lack that knowledge. That knowledge means you are in a different state.
[deleted] ยท 0 points ยท Posted at 13:05:51 on May 26, 2016 ยท (Permalink)*
If I know that a coin is biased then it doesn't change the fact that there are still 2 possible outcomes, but it does change how I should bet on it.
Let's go through the different possibilities when the host knowingly reveals a goat:
I chose the winning door, host reveals a goat by opening any door (happens in 1/3 of the cases)
I chose a losing door (happens in 2/3 of the cases), and the host reveals a goat (happens in 2/3 of the total cases)
Now let's see what happens when the host unknowingly opens a door, we can already deduce how likely each of the possible scenarios is:
I chose the winning door, host reveals a goat by opening any door (still happens in 1/3 of the cases, because this is not affected by the host only by my own actions)
I chose a losing door (happens in 2/3 of the cases), the host reveals a goat (in 1/3 of the total cases)
I chose a losing door (happens in 2/3 of the cases), the host reveals a car (in 1/3 of the cases)
Now we know that 3 did not happen, because a goat was revealed, but it's also clear that option 2 and option 3 were equally likely before the host opened a door, so if a goat is revealed there are two equally likely possibilities, either I chose a winning door (case 1) or I chose a losing door (case 2)
[deleted] ยท 0 points ยท Posted at 14:14:24 on May 26, 2016 ยท (Permalink)*
Please read the rest of that post (it in no way depends on my first sentence) and think about every step, try to identify the step where I make an error.
[deleted] ยท -1 points ยท Posted at 19:21:05 on May 26, 2016 ยท (Permalink)
Your response had nothing to do with irishsultan's post and it is clear you did not read it. irishsultan gave a correct explanation of why the probability in the "Monty Fall" problem is 1/2. You proceeded to give a somewhat incorrect explanation of the gambler's fallacy that had nothing to do with his post. Was a part of his explanation that you had trouble understanding? Have you looked at a computer simulation of this problem yet?
[deleted] ยท -1 points ยท Posted at 19:57:01 on May 26, 2016 ยท (Permalink)
Since you seem to think that Monty Hall and Monty Fall are identical, it might be time to look at that simulation again.
And, regarding my response you mention ... suppose for a second that the rest of their post were a wrongheaded approach to the the same answer given previously. Pedagogically, how should someone respond to that, given that the error is so fundamental?
Their post was correct, so this doesn't matter. If they were incorrect, you should point out exactly where they were incorrect.
Would you provide a spreadsheet of numbers highlighting an alternate interpretation?
What "alternate interpretation" are you talking about?
Or try to explicate the misunderstanding as problematic theorizing?
"explicate"? "problematic theorizing"? This is why you should be in /r/iamverysmart.
You seem to prefer both ... and it's because of that ...presuming you haven't read it... I'll recommend a classic intro theory book "How to Lie with Statistics" and be on my way.
I have taught undergrad probability multiple times. I don't need to read an intro stats book for laypeople.
The gambler's fallacy refers to the situation when you already know the probability distribution and you still try to use past events to predict a future independent event. When you do not know the probability distribution, you absolutely should use the previous results to place your bet, since these past results give you information about what the probability might be.
If you know a coin is fair (50:50), then even if you see TTTTT, there is a 50:50 chance that the next coin will be H or T, and you should not use the prior events to guess what the next flip will be. But if you do not know that the coin is fair, then the fact that you just saw TTTTT increases the likelihood of the coin being biased, and you should use this information to guess that the next flip will likely be T.
In any case, this has absolutely nothing to do with the Monty Hall or Monty Fall problems. In the situation where Monty randomly opens one of the two remaining doors and happens to reveal a goat, there is no advantage in switching doors, as a simulation clearly shows.
[deleted] ยท 0 points ยท Posted at 19:48:50 on May 26, 2016 ยท (Permalink)
That has no bearing if you cannot empirically justify it's intent to demonstrate the overall probabilities instead of the case specific ones.
What the fuck are you talking about?
I'll try to clarify myself once more ... even tho using prior, dependent probabilities to determine current probabilities is useful in confitions of possible states; when such priors are impossible given the current state, those priors are effectively zero.
This is just word salad at this point.
but sophisticated methods alone are insufficient to accurately model reality. In other words :P
Again, I have no idea what you are talking about. Are you claiming that if you performed this experiment in the real world, it would turn out differently than in the computer simulation?
This guy belongs on /r/iamverysmart so badly... or he's just trolling at this point.
This has been explained like a dozen times at this point and he's never once pointed out where he thought the error in the math actually falls instead just throwing out this nonsense.
[deleted] ยท -1 points ยท Posted at 20:05:07 on May 26, 2016 ยท (Permalink)
Will you please just look at my breakdown? Just show me where the error of my logic is. This breakdown should show you without a shadow of a doubt that the Monty Fall is a 50/50 scenario... it literally is the only possible outcome.
Here is a list of all possible outcomes:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 2: Pick L1 - host falls and opens W.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 4: Pick L2 - host falls and opens W.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do you agree that these are literally all of the possibilities? Am I missing any? Or are any of these wrong?
Since we know that a goat door was revealed there are only 4 of the above scenarios that could have possibly happened:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do we disagree on this? Out of the original six scenarios these are the four possible positions that could possibly be true given that a goat door was revealed. Do you disagree with that? What other options could there be?
Of these 4 remaining options, 2 of them switching will result in a win, 2 of them switching will result in a loss. Switching is literally a 50/50 prospect.
If I am incorrect in any of my steps please tell me which step you think I made an error. Do you believe that the original 6 scenarios have different probabilities? Do you believe the 4 possible goat door reveals have a different probability? This is literally the probability tree for the scenario. These are the only possible options.
Anyway, I pointed it out. It should be identical to Monty Hall. And I explained my argument, repeatedly. Sorry I couldn't be more clear about it.
IT IS NOT IDENTICAL TO MONTY HALL! Just look at a computer simulation. In the Monty Hall problem, there is a 2/3 probability of winning if you switch. In the Monty Fall problem, there is a 1/2 probability of winning if you switch. Do you think the computer simulation is lying? That I'm just getting really, really, really lucky with the random number generator?
How arrogant do you have to be to still insist that you are correct after seeing the simulation?
[deleted] ยท -1 points ยท Posted at 20:12:03 on May 26, 2016 ยท (Permalink)
I'm not using the program as a proof. I am well-aware of the mathematical proofs that the probability in the Monty Fall problem is 50%. I am using the computer simulation to try to convince you of the correct answer since you for some reason rejected irishsultan's correct proof.
Do you or do you not agree that the probability is 50% in the Monty Fall problem (where Monty randomly opens one of the two remaining doors and just happens to reveal a goat)? If you do not agree that the probability is 50%, what do you think is wrong with the simulation? Is there something wrong with the code?
Edit: Pynes is not a mathematician. His paper is incorrect and is not accepted by mathematicians.
[deleted] ยท 0 points ยท Posted at 17:14:40 on May 27, 2016 ยท (Permalink)*
There is no error. As I said, Pynes is not a mathematician. His paper was not reviewed by mathematicians. The paper did not appear in a math journal. His paper is incorrect, and no mathematician accepts his "solution." Unless you can find a problem with the simulation I gave you, the correct answer to the Monty Fall problem is 50%. If you believe the answer is not 50%, what makes you believe that you know more about this basic undergraduate probability problem than everyone with a PhD in the subject?
[deleted] ยท 1 points ยท Posted at 17:33:43 on May 27, 2016 ยท (Permalink)
Sure. You have already been given a proof that the answer is 50%. Then you were given a computer simulation providing experimental evidence. Those are the counter-arguments. In case you missed it, here is a proof written out in clear English:
You randomly pick one of the 3 doors. There is a 1/3 chance that you pick the door with the car, and a 2/3 chance that you don't.
Suppose you pick the door with the car - recall that this happens 1/3 of the times you play. Monty randomly picks one of the remaining doors and opens it. No matter which of the 2 doors he opens, he reveals a goat. So in 1/3 of all times that you play, you pick the car, and Monty reveals a goat.
Suppose you pick a door without a car - recall that this happens 2/3 of the times you play. Monty randomly picks one of the remaining doors and opens it. He has an equal probability of opening the door with the car and the door with a goat. So in 1/3 (2/3 * 1/2) of the times that you play, you pick a goat and Monty reveals a goat, and in 1/3 (2/3 * 1/2) of the times that you play, you pick a goat and Monty reveals a car.
To recap: In 1/3 of the games, you pick a car and the remaining unopened door is a goat. In 1/3 of the games, you pick a goat and the remaining unopened door is a car. In 1/3 of the games, you pick a goat and Monty accidentally opens the door with the car - we throw out these games because we are not in this situation in the Monty Fall problem. So we are in one of the first two cases, which both have a 1/3 chance of occurring. That is, they have an equal probability of occurring. There is a 50% chance that we are in each of those first two cases.
What about this do you not understand?
Also, you have still not answered my question: Why don't you believe the computer simulation? Is there an error in the code? Is the universe just playing a trick on us by giving us crazy random numbers millions of times in a row?
If you read the paper, the whole thing is going under the assumption that the fall is just a "tease" reveal since there must be a second part to make the offer to switch.
He concludes that if there is actually a chance that Monty could accidentally reveal the prize door that the odds shift to 50/50. The paper is literally just showing that the Monty Hall problem is correct.
without the assumptions it falls apart. So you can continue to disagree with us, or assume that the people that developed the problem know what they are talking about.
[deleted] ยท -1 points ยท Posted at 16:55:33 on May 27, 2016 ยท (Permalink)
Man, that paper literally says exactly what everyone is telling you. And I quote:
4.2 Monty Fall* and the 50/50 Answer
If, however, we remove the bad door tease reveal assumption from the Monty Fall problem, we get, what I will call, the Monty Fall problem. This version gives us an instance where the post fall reveal odds are 50/50.
The following is the case I claim Rosenthal wanted to present and solve with his proportionality principle. Monty Fall In this variant, once you have selected one of the three doors, Monty slips on a banana peel and accidentally pushes open one of the doors. In this case, like the others, you can only switch or stay after a reveal happens. If Monty reveals the prize accidentally through his fall, you can neither switch nor stay. This happens in 1/3 of the cases. Another way to think of this is to say that in Monty Fall, there is a non-zero probability Monty will reveal the prize, and this changes the problem dramatically. That is, Montyโs fall could open any of the three doors and in 1/3 of the cases his fall reveals the prize.
This immediately ends the game, but if we remove these prize reveal cases from considerationโthey are 1/3 of the cases remember, then yes, the odds after Monty reveals a door through an accidental fall where he opens randomly a door not containing a prize will be 50/50. When Monty falls and opens the contestantโs initial choice door and it isnโt the prize door, then game doesnโt have to end if Monty wants to give the contestant a choice of doors. If Monty does give the contestant a choice of doors after accidentally falling and opening the initially selected door that doesnโt contain the prize, then in those cases where Monty allows the game to continue, the odds are now 50/50.
Another way to think of this is to see that in half of the 2/3 cases you should switch in the original Monty Hall version, Monty, in the Fall cases, reveals the prize, accidentally, thereby ruining your 1/3 switch advantage. 1/2 of 2/3 is 1/3 and if the remaining two doors are equally likely now (1/3 each), then the updated probability really is 50/50. But this English explanation isnโt nearly as satisfying as the mathematical proofs; so letโs use Bayesโ Theorem and the general rules of probability to solve and explain both Monty Hall and Monty Fall.
Emphasis mine.
God I love when people supply papers that disprove everything they are saying.
Edit: Just read the rest of the paper... apparently he actually believes what you do. I don't see how because it can be shown mathematically incorrect and simulations can show it's 50/50.
[deleted] ยท -1 points ยท Posted at 17:35:28 on May 27, 2016 ยท (Permalink)
In cases where there is a non-zero probability Monty will reveal the prize, like Monty Fall*, the odds do in fact change to 50/50 after the fall reveal
There you go. When there is a chance that the host reveals the prize door, the odds go to 50/50. All the rest of his paper are going under the assumption that Monty couldn't reveal the prize door only doing a "tease reveal" since there must be a second part for the switch. That's just cheating though and turns the fall back into the hall.
dryfire ยท 2 points ยท Posted at 21:25:52 on May 25, 2016 ยท (Permalink)*
The host HAS to open a door that does not contain the prize. He's not opening an empty door by accident.
Exactly! This should be much higher. I have had to correct so many people who miss that when stating the problem.
Monty has to have a 100% chance of choosing a wrong door AND the person playing the game has to know it in order for them to know they should switch doors. That really needs to be emphasized in the problem or else people are just spreading confusion.
Vozor ยท 1 points ยท Posted at 23:02:54 on May 25, 2016 ยท (Permalink)*
The opening of the doors is irrelevant info, which confuses the reader. You get to choose one door or 2 doors where one is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
[deleted] ยท 0 points ยท Posted at 22:07:54 on May 25, 2016 ยท (Permalink)
Obviously the host opens the door with no prize. It wouldn't work otherwise. That's why the detail is "left out".
Even if he opens the empty door on accident, the percentage is still the same. Intent has nothing to do with it. What the host is thinking at the time doesn't change mathematics.
Even if he opens the empty door on accident, the percentage is still the same. Intent has nothing to do with it. What the host is thinking at the time doesn't change mathematics.
This is not true. The fact that he knowingly opens a door without a car is important. If you run this simulation many times with the host just randomly opening one of the two remaining doors, you will find that it does not matter if you switch.
[deleted] ยท 1 points ยท Posted at 12:01:57 on May 26, 2016 ยท (Permalink)
You are wrong. You are fundamentally misunderstanding why the Monty Hall problem works the way it does. I will try to explain, though I highly doubt this will convince you. Just try to stick with me on this.
To preface this, in order for the conditions of the Monty Hall problem to be met, the host MUST have revealed doors which don't have the prize behind them, because otherwise they'd reveal the door with the prize behind it and you'd know which door is the prize winner, defeating the entire purpose. So by the very structure of the game, this is the way it is.
What doesn't matter is the host being aware of what door is being picked. Lets imagine a scenario where you have a program running the Monty Hall Scenario, and after you chose a door, it randomly reveals the rest of the doors but yours and one other. For the sake of making this easy to understand, lets assume we're using 100 doors instead of just three.
So you choose a door, and then the program randomly opens 98 doors. Any time the prize door is revealed, you have to throw that test out, so you'll probably be doing this for a while. From now on we'll assume that every test we do is a functioning one (where the doors randomly opened don't contain the prize door, which would invalidate the scenario).
Eventually you choose a door out of the hundred, the program randomly opens 98 other doors, and just your door and one other are left.
What was the chance of you picking the right door the first time? Obviously 1/100. So, unless you picked the right door (1% chance of that happening) the "host" opening all of the other doors has essentially shown you the correct answer 99% of the time. The host's knowledge has nothing to do with it.
Fundamentally, this is a choice between opening the one door you originally chose, or opening 99 doors.
Let's bump this up a notch. Imagine there are a billion doors. You pick one. The "host" opens 999999998 that aren't your door or the prize door. Unless you have more luck than Fortuna, you didn't pick the right door. At this level, we can just assume you didn't pick the right door. What this means is that the host has opened every door but yours and the prize door. What this means is that the host has just shown you exactly where the prize door is. It doesn't matter what the host is thinking. It doesn't matter if the host knows or not, or is even self aware. It works exactly the same.
Alright, now to return to the original scenario. You have three doors. You pick one. The host randomly opens a door with no prize behind it. You choose the wrong door 2/3rds of the time. 2/3rds of the time, the host has just revealed to you the correct door. If you switch, you will win 2/3rds of the time. Essentially what you're doing is choosing between choosing the one door you originally picked, or choosing two doors.
Intent doesn't randomly change fundamental arithmetic. I can't believe reddit is this bad at math. And I can't believe people are "helping" other people to "understand" how it works by getting them to accept it through the wrong means. Even if you come to the correct solution, if you got there with the wrong methods, you're still wrong. None of you actually understand why the Monty Hall problem works the way it does, even if you accept that it happens.
I'm a mathematician, you don't have to explain it to me. What you are missing is that it absolutely matters that the host opens a door without a car on purpose.
So, unless you picked the right door (1% chance of that happening) the "host" opening all of the other doors has essentially shown you the correct answer 99% of the time. The host's knowledge has nothing to do with it.
Unless the host knows which door has a car, he will accidentally open the door with the car almost every time. This is important.
[deleted] ยท 0 points ยท Posted at 17:10:29 on May 26, 2016 ยท (Permalink)*
And if he accidentally opens the door with the correct prize, then it stops being the Monty Hall problem. People are saying that the host must be aware of what door is the prize door in order for the math to work, I'm saying that the math works if the conditions are met (doors other than the picked door and prize door are opened) regardless of whether the "host" has any knowledge. The knowledge allows the problem to work, the knowledge does not change the probability.
Edit: Also
Any time the prize door is revealed, you have to throw that test out, so you'll probably be doing this for a while.
So by your logic, if I asked the host to open the door and revealed a goat, instead of him "falling", then logically the last door suddenly jumps up in probability? That seriously doesn't make any sense... you may recognize this as the Deal or No Deal puzzle.
And if he accidentally opens the door with the correct prize, then it stops being the Monty Hall problem
Yes, that is correct. We've been pointing out the bit of the Monty Hall problem that makes it the Monty Hall problem. Many people are confused the first time they hear this problem and think it's 50/50, it's not. Part of the reason that people tend to think this is probably because their mental model of the problem doesn't actually match the actual problem, look at how many people responded with "now I get it", once it's pointed out that the knowledge of the host matters.
The knowledge allows the problem to work, the knowledge does not change the probability.
Without this knowledge you don't have the problem with it's standard set of assumptions, as a result you also get a different probability if the knowledge is lacking.
I don't think you should be correcting the logic when you're not grasping it. It's important that the first scenario is an "or" not "and" because it makes the hosts choice irrelevant to the outcome. Just look at the left two columns and ignore the host for a minute. There are only three doors. If you switch, two out of three times you will get the prize.
The choice of the host is simply there to allow you changing your choice to the opposite
If you pick the prize and change it you can only change to not picking the prize
If you don't pick the prize you will end picking it If you change
This said, you have 1/3 chance to pick the prize and 2/3 to not pick it as first choice
If you change it you will reverse the end result, so 1/3 of not winning and 2/3 to get the price.
I understand i am wrong, i was just explaining how do I see it
Still lost
Will drink a beer or two looking for wisdom
Oddtail ยท 12 points ยท Posted at 15:26:59 on May 25, 2016 ยท (Permalink)
The funny thing is, the Monty Hall problem's solution is so counterintuitive, a large number of people with scientific background get this one completely wrong. This included Nobel prize-winning physicists. In fact, some of them insisted on the wrong answer even after having been shown proof of the correct one.
Scott Smith, Ph.D, is probably glad he has such a common name so he can always claim that it was another Scott Smith who wrote that condescending letter.
dryfire ยท 3 points ยท Posted at 21:19:39 on May 25, 2016 ยท (Permalink)
The solution is only counter intuitive because you introduce a non-random factor into the middle of a seemingly random problem (Monty has a 100% chance of choosing a wrong door). If Monty is choosing randomly, and he chooses a wrong door then the you are back to having a 50/50 chance with the remaining two doors.
Vozor ยท 1 points ยท Posted at 22:59:43 on May 25, 2016 ยท (Permalink)*
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door and 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
[deleted] ยท 2 points ยท Posted at 23:56:21 on May 25, 2016 ยท (Permalink)
[deleted]
Vozor ยท 1 points ยท Posted at 11:41:58 on May 26, 2016 ยท (Permalink)*
Not at all. It's put in a way that is confusing to the reader, but the second question isn't about a door. The first question asks you to choose one object at random. You have a tiny chance of choosing the correct one. The second round starts. You pick between two sets of objects, the one you picked, and the ones you didn't pick.
The host asks if you want to switch to the other set, with a guarantee of getting the prize - so long as it isn't in the door you already have. Your chance of getting the correct one is now inverse of the original chance, where the first set has 33% chance, the second set has 66% chance of having the prize.
[deleted] ยท 1 points ยท Posted at 15:42:01 on May 26, 2016 ยท (Permalink)
[deleted]
Vozor ยท 1 points ยท Posted at 16:50:23 on May 26, 2016 ยท (Permalink)*
I'm sure we are arguing different points, so I apologize for not making it clear.
The door having nothing behind it is important information. That is true. But the question is posed in a way to make the contestant think he is choosing between one door and one other door. Which would be 50/50 probability
What is happening with the second question is that the contestant is choosing from two sets:
A door
A door, plus another door known to be empty
The important concept is that the first question is not the same as the second question, because it switches from "pick one" to "pick one or multiple."
That's the beauty of math. It works whether or not you believe in it.
And I don't mean that to be condescending. The Monty Hall problem sounds completely insane without some deep thought as to why your intuition is wrong in this case. But regardless of intuition, it is demonstrably a 2/3 probability.
I promise the logic is more simple than writing a program to prove it.
Three doors and you choose randomly. There is a 2/3 chance of getting it wrong. The host opens a door that you didn't pick that is the wrong door. If you swap your answer you're now placing your bet that you got your initial guess wrong.
The key is noting that you picked before he opened the door and that he opens a wrong door. This forces the probably of 1/3 as an original guess.
Maybe don't read if you're still confused
Also if he had a chance of opening the correct door, your chances would actually stay the same... Well, if you were willing to swap your answer to the winning door.
I cannot state enough that nothing anyone said would convince me until I tested it haha. It's pure ignorance, I get it, but I needed to see it for myself.
You have 1/3 chance of selecting door 1, and when you do, the host will show you one of the two wrong doors so you should stay with your door.
You have 1/3 chance of selecting door 2, and when you do, the host will show you the remaining wrong door so you should switch to the remaining correct door.
You have 1/3 chance of selecting door 3, and when you do, the host will show you the remaining wrong door so you should switch to the remaining correct door.
Notice that in 2 out of 3, scenarios, you should switch doors. Therefore switching doors gives you 66% chance of selecting the right door
Play the role of host and contestant. One if you hides an object under 3 cups, the other tries to guess where it is located.
Playing the show host really helps make you understand it. As the host, you'll find that the majority of the time (66% of the time), there's only one door you can open because the contestant has already selected one empty door, so you have to reveal the only other empty door.
Assume you choose the first door, and the host eliminates a door that both 1. does not have a car. and 2. you did not select. Here are all of the possible outcomes:
your door (1)
behind door 2
behind door 3
host reveals
results of staying with door 1
results of switching to other door
car
goat
goat
2 or 3
CAR
goat
goat
car
goat
3
goat
CAR
goat
goat
car
2
goat
CAR
as you can see, switching will result in a car 2 out of 3 times, while staying will result in a car 1 out of three times
Vozor ยท 0 points ยท Posted at 23:04:42 on May 25, 2016 ยท (Permalink)
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door or 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
Uilamin ยท 0 points ยท Posted at 23:51:03 on May 25, 2016 ยท (Permalink)
The simple explanation is that the host does not change the probability of it NOT being the door you chose by revealing a door.
What you know. 3 doors and 1 has the prize. You choose one randomly with a 33% chance of being right. There is a 66% chance of one of the other two having it. You are then told that the 66% chance is not 2 doors, but actually one. Do you switch for a 66% chance to win?
Sure! There is another famous one called the Achilles and the Tortoise. This is the idea of "will you ever catch up to an object?" Let's say you are running after a friend. You are faster than they are and you will eventually run to meet their position. However, in the time that you have run to meet heir position, your friend has since moved ahead a little. So now you must run to meet their new position. However, when you run to meet their new position, they've moved again. So when do you actually over take them? There are YouTube videos to visualize this one!
There is another called the Double Liar Paradox. This is a logic problem. On one side of a card the sentence says, "The sentence on the other side of this card is true." On the other side it says, "The sentence on the other side of this card is false." Can you figure out which is correct?
You can do a quick Google search to find more! Enjoy!
It's easier to think of when you increase the number of doors. If there are 100 doors, you have a 1% chance to pick the correct door first try. Then all the other doors are removed except yours and one other. Now it seems pretty obvious that there's a 1% chance you'll get it if you stay and a 99% chance you'll get it if you switch.
I like to think of it using cards. Let's say you are given a deck of 52 cards and you have to pick out the Ace of Spades. So you pick a random card but before it is flipped over someone who knows which card is the Ace of Spades flips over 50 of the cards which aren't the Ace of Spades, leaving two cards, the one which you picked and the one that the person didn't flip over. The card you picked had a 1/52 chance of being the Ace of Spades but this new card has a much higher chance.
Imagine the situation with a million doors instead. 999,999 have nothing, one has the prize. You pick one, and before revealing what's behind the door, the host opens 999,998 of the remaining doors, revealing nothing behind them. So now all that's left is your door and one other door.
And the question you have to ask is, "Even though there are only two doors left now, is there really any way the chance I chose the correct door in the beginning is 50%?"
[deleted] ยท 1 points ยท Posted at 21:49:40 on May 25, 2016 ยท (Permalink)*
Vozor ยท 0 points ยท Posted at 23:05:55 on May 25, 2016 ยท (Permalink)
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door and 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
Chance of prize behind each door:
1- 33%
2- 33%
3- 33%
You pick one -33% chance you got prize.
Host reveals WHAT HE KNOWS is incorrect door which had 0% of prize. This means the door that's left makes the rest of the total % chance of winning to your 33% door, which is 66%.
This is my favorite one for multiple reasons. It is a real brain wrinkler...but also...out of most of these it's the only one where I could see it coming in handy someday.
What always makes me mad is that when you bring up this problem on the internet you'll always have some people who'll tell you that this solution is wrong and that it's actually 50/50. It doesn't matter to them that the correct solution is accepted by basically every mathematician around the world, it doesn't matter that it's been proven time and time again that 50/50 is wrong. You can try to explain it as much as you want, they've already decided: they're right, and everybody else is wrong!
I was just thinking about this the other day and was wondering if I was misremembering, but you explained it just as expected:)
[deleted] ยท 1 points ยท Posted at 17:50:32 on May 25, 2016 ยท (Permalink)
This was actually a problem in one of my programming courses. We had to write a Monty Hall problem simulator, then add a class to record the statistics after n simulations.
I love this because its so counter intuitive that even PHD's were crying bullshit when it was first proposed.
There is something about the way probability works here that humans just reject. The vast majority of people when given this problem will not switch their choice. Even ones who should know better.
This one is easier to picture if there are say 100 doors. Still only one has the prize.
You pick one at random. It has a 1:100 chance of being the right one. Now the host eliminates all but two other doors. You now have your original pick and two more; one of which has the prize. Should you stay with your original that had a 1:100 chance or choose one of the new doors that has a 1:2 chance?
This comment has been overwritten by an open source script to protect this user's privacy.
bmmy9f ยท 1 points ยท Posted at 18:18:33 on May 25, 2016 ยท (Permalink)*
This doesn't make any sense to me. Wouldn't the odds just change to 50/50 when the empty door is revealed and choosing the initial door would give you a 50% chance?
How is this different then this example:
You are asked to pick a number for a dice roll, you pick 3. It is then revealed that the dice is actually a 5 sided die. Is it in your best interest to change your pick given the option of 6 is removed?
The answer is no. Your odds were 1 in 6 and they have improved to 1 in 5, the initial odds do no matter since the final roll will be random. Much like the door choice does not matter because the door that is empty will be random. Can someone explain how this is wrong? I really am curious.
Edit: just wrote a program to simulate this, it's 66.6% wtf.
I did a project for school on this in the 7th grade, even creating a small little game show setup with three doors and a prize that would slide behind each door, allowing for a rapid fire demonstration of the probability of winning when switching and sticking. After explaining why it works (and ending up with a mathematically sound result of like 13/20 wins when switching), he still didn't understand why it worked and gave me a fucking B for the project.
Granted this was for a science class, even though he said our projects could literally be on anything as long as we had some sort of scientific method involved, but still, the teacher should have been able to understand basic math and logic.
The only way I have ever been able to wrap my head around this is, when you initially make the pick, there is a 2/3 chance the correct answer is in the group of doors you didn't pick, and a 1/3 chance it's the one you originally pick. If you could, you would pick the two doors together over the one single door. Once the host eliminates a door, there is still a 2/3 chance that the prize is behind one of the doors in the pair. Switching doors isn't just picking between the last two doors, it's picking between a pair of two doors with a 2/3 chance of winning and one door with a 1/3 chance of winning.
I was thinking about this while watching Deal or No Deal last night. Some chick got all the way to the end with her case and 1 left held by the super sexy model, and she was soooo confident that her case had the million. But I was like, no it can't be because according to this logic (the one with the 3 doors as you explained) the likelihood that she chose the 1 million dollar case was 1/26 or however many there are in total, so when it comes down to it at the very end, you really SHOULD switch and 25/26 times you'll switch cases and win the million. Am I wrong in saying this? Maybe it's a different experiment.
btw, the girl on the show took the deal, gambling 500k is stupid.
That's actually the "Monty Fall" variant. Since she was randomly revealing cases (she didn't know where the prize was) it was a 50/50 shot that her case and the remaining case would contain the million.
for change in [False, True]:
right_count = 0
total_count = 10000
for _ in range(total_count):
answer = np.random.randint(3)
guess = np.random.randint(3)
opened_wrong_door = [door for door in range(3) if door != answer and door != guess][0]
if change:
guess = [door for door in range(3) if door != opened_wrong_door and door != guess][0]
if guess == answer:
right_count += 1
print("Change = " + str(change) + ", correct percent = " + str(round(right_count / total_count * 100, 2)) + "%")
People like using the Monty Hall problem as an example of a non-intuitive statistics problem, but I like asking people the following. Suppose there is a family with two children. One of them is a girl who was born on a Tuesday. What is the probability that both children are girls? For a hint, yes, the Tuesday bit does matter, and it's not because of some obscure statistics of people being more likely to be born on certain days. Assume uniform distribution of girls and boys and births per day of the week.
I remember my thrusters had an episode on the Monty Hall problem. I remember they had a right which simulated the problem a couple hundred times with the result of winning when switching to be 33.333%. My memory isn't too strong so I don't know if the episode had such a strong result.
Another fun fact:
If, in the Monty Hall Problem, the game show host opens a random door, instead of using insider knowledge to select a door, your odds do default to 50/50. Think about it this way:
o=your door
x=host door
In all cases, the third doorcontains the car.
Possible outcomes: (host selects a door)
ox- 33%
xo- 33%
-xo 16.5%
x-o 16.5%
Possible outcomes: (door is random)
ox- 16.5%
xo- 16.5%
-xo 16.5%
x-o 16.5%
o-x 16.5% (car is revealed)
-ox 16.5% (car is revealed)
We can eliminate the bottom two outcomes, since we know a car wasn't revealed, but our odds become 50/50 to stay or swap.
This is why Deal or No Deal outcomes are 50/50 to swap your case at the end, because you were selecting randomly instead of exclusively removing non-million-dollar cases
One of my relationships almost fell apart because of this problem. My boyfriend at the time just refused to believe me this is correct. We broke up like 4 months later for other reasons
When I was in highschool, my math teacher had us work it out by mapping out every possible outcome based on the variables of 'which door you picked' and 'which door protects the prize.' I found scenarios neither he nor the textbook accounted for and with my math it suggested the odds returned to 1/2, meaning it meant nothing if you switched.
My stats teacher had no response for it, and I've never found someone who can account for my results. I'm just waiting for some mathmetician to write a paper based on similar math to mine and get a nobel prize or something.
aonome ยท 1 points ยท Posted at 02:26:24 on May 26, 2016 ยท (Permalink)
Your math was wrong. If you write a program with all of the conditions applied and get 1/3 and 2/3 odds.
Oh, I never said it was right, just that I managed to come up with something my math teacher couldn't disprove. Says a lot more about my teacher than it does about me, haha.
The most intuitively obvious explanation I've heard is this: instead of 3 doors imagine 100 doors. You pick one, the host then opens 98 doors until just two remain. Then changing from your original pick seems obviously correct (at least to me)
Its funny seeing math I learned a month ago here .
[deleted] ยท 1 points ยท Posted at 01:00:41 on May 26, 2016 ยท (Permalink)
But you actually had a 66.6% chance to choose the wrong door to begin with.
jesus christ. i read the wiki on this every time it comes up. and i always ask someone to explain how it isnt 50/50. and for years, i have never gotten an answer, just accepted it as a fact. and in that one line, you have made it click in my mind instantly.
The Monty Hall problem is actually pretty elementary; it's very counter-intuitive, which leads to a lot of confusion, but the math is really pretty straightforward.
I like to explain it like this: What if there are a thousand doors? You pick one door at random, and then the gameshow host opens nine hundred and ninety eight doors, leaving one potentially correct, potentially wrong door and the one you chose, every other door is confirmed wrong. Do you switch?
Yes, because your chance was 1/1000 of getting it right with the door you have and, all things being equal, it remains so. Switching increases your chances to 1/2.
This is a common misconception. In the long term, yes, the odds are 66.6%. However, in this particular instance, without knowing the host's rationale for choosing the door he did, it could be anywhere from 50% to 100%. Still, it never hurts to switch (in the usual version of the game).
Edit: let me show you.
Suppose the host always opens the highest numbered door he can (he might be blocked because you chose it, or because it hides the prize). You pick door 1, he opens door 3. Your chance of winning if you switch? 50%.
Now suppose the host favors the lowest numbered door. Once again, you pick 1, he opens 3. Your chance of winning if you switch? 100%.
However, in this particular instance, without knowing the host's rationale for choosing the door he did
There isn't a rationale, the host always opens a door with nothing behind it. If you picked the correct one it doesn't matter which door the host opens because they're identical. If you didn't then the host only has the option of opening one of them.
Incorrect, see my edit. You are ignoring key information for the particular game you are currently playing: the door you chose, and the door the host chose.
I see what you're saying, but the problem doesn't cover which door the host will pick when there's two with nothing behind them, so the information is not available to the player.
No my version completely covers that. The subtlety is in saying "you have a 66% chance of winning if you switch!" That is not entirely accurate. Really, if you played the game 1000 times, you'd win by switching 666 times. But for a particular game, that percentage can vary quite a bit based on the host's strategy.
How does it? It's a 2/3 chance every time if you switch. If I write a program to simulate this and I run it several thousand times and everyone always switches then 2/3 of the plays will win, if I make them all stay then 1/3 will win.
That is not the same as talking about the odds of winning A SPECIFIC GAME. These are two different probabilities. Think about it this way: in my second example of my edit, FOR THAT SPECIFIC GAME, the odds of winning when switching are 100%. So, if you had a thing where you ALWAYS picked door 1, and the game producers had a thing where the ALWAYS put the prize behind door 2, then in that universe, SWITCHING WINS 100% OF THE TIME. When you say "2/3 chance of winning", you are implicitly assuming that each configuration of door choice and prize door is equally likely. Again, a valid assumption, but it DOES matter.
That is not the same as talking about the odds of winning A SPECIFIC GAME. These are two different probabilities. Think about it this way: in my second example of my edit, FOR THAT SPECIFIC GAME, the odds of winning when switching are 100%.
But you've changed the rules here, you added in new behavior the host has which is not included in the initial problem. You're saying there's possible scenarios where the player can know that switching will give them a 100% chance of winning right? But they could only possibly know that if they had the added benefit of knowing those secret rules on how the host picks when confronted with two empty doors.
Whether the player knows the host's strategy or not does not change the probability. If the host had that strategy, and the player swtiched, they win 100% of the time, regardless.
Ok I just understood the point of view you're coming at this problem from. I've not seen this type of view represented before in the Monty Hall problem and it's very interesting.
Most people assume that the player is whom we're calculating the probability for, and that the host chooses randomly when both doors are identical. You're instead assuming that the host has some fixed pattern by which it chooses the door to open, which of course reduces and increases the chances of the player.
I've not encountered your viewpoint of the problem before, it's strange because both your viewpoint and the normal viewpoint both lead to the same results but very few people pickup your point of view. I think you've picked up on a psychological viewpoint of the Monty Hall problem that hasn't really been explored.
It is actually detailed quite nicely on the Wikipedia page for this problem. The thing is, this is a poorly defined problem, so there are these implicit assumptions lurking everywhere. Thanks for the stimulating convo!
aonome ยท 1 points ยท Posted at 18:12:11 on May 25, 2016 ยท (Permalink)
Probability of winning and percentage of wins are equivalent here. The host's strategy is to remove an empty door which has not been chosen by the player, that's all there is to it.
No, it's not. Please see my edit, which shows that FOR A SPECIFIC GAME, the host's strategy does matter. Please see the Wikipedia article on this problem if you're having trouble understanding the (subtle) difference; it is explained in great depth there.
aonome ยท 1 points ยท Posted at 19:07:24 on May 25, 2016 ยท (Permalink)
I don't know what to tell you mate, I know the relationship between probability and percentage of outcome better than you do.
I'm sorry you cannot carry on an intellectual conversation. If you'd like to give explicit details about my construction that don't work, that's fine. Hiding behind boasts just wastes my time.
Thank you! I had this exact argument with my Philosophy class in college. Everyone in the class thought I was a moron for arguing that your choice doesn't really matter, in the context of the game. You have no idea WHY the host opened that door. Furthermore, your original choice is 33% accurate. Your second choice is 50% accurate. In other words, you're entirely justified, mathematically in sticking with your door because your second choice is a complete toss-up. If you play the game 30 times? Sure, pick the second door every time. If you play it only once? It's a toss up. The 66% chance for switching doors only comes into play as that 50% second choice gets averaged over time against the 33% first choice. People are confusing averages with one-at-a-time decisions. Averages are only useful for understanding populations, not random draws.
aonome ยท 1 points ยท Posted at 16:55:49 on May 25, 2016 ยท (Permalink)
What? It does matter. You should always pick the most likely door to be correct.
But the "most likely" to be correct only has meaning when you average many 1st choices and 2nd choices together and only if you make some false assumptions about the nature of the game. In any particular instance, your second choice is 50% accurate whether you stay with your first door or switch. The game isn't really "pick between 3 doors". The game is really "pick between 2 doors." It only appears to be a choice between 3 doors because the host has presented it that way. You do not have a 33% chance of picking the correct door on the first try. You have a 50% chance, because one of the empty doors was effectively off-limits, anyways. You appear to have a choice between 3 doors, but really you only have a choice between the 2 doors that the host does NOT pick. It just so happens that he reveals this fact later. The reason that simulations show a doubling of accuracy for switching is because they make the false assumption that you could choose any of the 3 doors. In reality, you can only choose one of two doors. The host simply changes which door he was going to make "off-limits" based on which door you pick, after the fact.
aonome ยท 2 points ยท Posted at 17:12:10 on May 25, 2016 ยท (Permalink)
Er, the average result is determined by the probability, not the other way around. This is a maths problem, not a scientific experiment.
But it's not. You're assuming that you have a choice between 3 doors. You really only have a choice between 2 doors. Simulations that seek to prove your stance make the false assumption that there are 3 doors, when in reality there are only 2.
aonome ยท 2 points ยท Posted at 18:02:58 on May 25, 2016 ยท (Permalink)
No, that's not how it works. You pick a door and have a third chance of being right. The chance that the money is behind any other door is 2/3.
Now, the host knows which door the money is behind. He purposefully eliminates one of the other two doors which is empty. He eliminated it because it was empty. In other words, whether or not the money is in the 1/3 chance set of doors or 2/3 chance set of doors is irrelevant, an empty door will always be eliminated from the 2/3 set.
This means that the 2/3 set only has one door but the probability has not changed. Again, I will say it so you definitely understand. The host deliberately removed a door that was empty and had not picked and the player was made aware of he fact that these two criteria were the reason for it being removed.
This is why you should switch.
If you do the math you should reach the conclusion that you should switch even though the end result is two doors to choose from. The mathematicians are right and you are wrong.
They're right because they are posing the wrong problem. They are making the assumption that you have a choice between 3 doors. In fact, you only have a choice between 2 doors. You already know beforehand that the host will eliminate one of the empty doors, whether or not you have chosen the door correctly. Doing it before or after your first choice is irrelevant. What if the host eliminated one of the empty doors before your first choice, and then asked you to choose a door? And then he gave you the option to change your mind. Do you switch? It doesn't matter. Either way you have a 50% chance of being right. This is what is happening with 3 doors only the host decides, after your first choice, which door to eliminate, instead of before.
aonome ยท 1 points ยท Posted at 18:23:17 on May 25, 2016 ยท (Permalink)
You're describing two different scenarios. Yes, after the host eliminates the door you have two choices. The key is that you have information because the door was eliminated while you had locked in a door and so if it is empty he can't eliminate it. If you don't pick a door first this is not case and the probability would be different.
f you run a simulation that does exactly what the Monty hall problem describes steo-by-step you will get the result the mathematicians predict. The whole scenario can be done mathematically and it is demonstrable with rigorous proof.
The fact that you think mathematicians who spend every day of their life working to further their understanding of this field are thinking about it wrong is quite funny though.
But it's only the illusion of new information. It's not really new information. You already knew beforehand that he would eliminate an empty door, so your first choice is really between the correct door and one of two empty doors. The reason the simulations behave as you describe is that they feed it the false assumption that you are choosing between three doors. You are not choosing between three doors. You are choosing between two doors.
aonome ยท 1 points ยท Posted at 19:04:39 on May 25, 2016 ยท (Permalink)
No, you are completely wrong. You don't understand what's going on here, i've explained it to you and you are relying in your intuition instead of math.
Please answer this though: do you honestly think that mathematicians that spend their lives studying these paradoxes are mistaken and that you, someone who definitely does not have a background in mathematics, are correct?
Rynyl ยท 894 points ยท Posted at 14:14:33 on May 25, 2016 ยท (Permalink)*
Graham's number iswas once the largest number used constructively in a math paper. It's literally unimaginably large.
morhe ยท 753 points ยท Posted at 14:25:00 on May 25, 2016 ยท (Permalink)
"Grahamโs Number is a number so big that it would literally collapse your head into a black hole were you fully able to comprehend it. And thatโs not hyperbole โ the informational content of Grahamโs Number is so astronomically large that it exceeds the maximum amount of entropy that could be stored in a brain sized piece of space"
quote stolen from somewhere on the internets
[deleted] ยท 114 points ยท Posted at 15:25:39 on May 25, 2016 ยท (Permalink)
Although true, this fact really really under-eggs it. 3โโโ3 is more than enough to black hole your brain even if your brain were the size of the universe and only contained information. Yet 3โโโ3 is NOTHING compared to 3โโโโ3, which is ABSOLUTELY NOTHING compared to 3โโโโโ3. Don't get me started on 3โโโโโโ3.....
...A long time passes...
...which is pretty much zero compared to Graham's number
marvin ยท 38 points ยท Posted at 17:57:51 on May 25, 2016 ยท (Permalink)
Graham's number to the power of Graham's number is bigger, though. Which is still smaller than the weight of OP's mom.
3โโโ3 is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to numbers the magnitude of 3โโโ3.
I know this is late, but yes it would be absolutely huge. 3โ3 is 27, 3โโ3 is 3โ3โ3, or 3โ27, or 7.6 trillion. 9โ9 is 387 million, so 9โโ9 is 9โ9โ9, or 9โ387 million. I can't get a good answer for what that is, but the number has 369 million digits in it, compared to 13 digits of 3โโ3. Add in another 2 levels and you've got an answer that's just too immensely large to imagine. And that's just 3โโโโ3, which is g0. If you followed through all the way to g64, or Graham's number, using 9s, you can't even imagine how much larger it would be.
more than enough to black hole your brain even if your brain were the size of the universe and only contained information.
I often wonder what size a black hole could get to before DE expansive pressure prevented it from getting any larger. I used to think it was "a hubble volume", but it turns out that the hubble volume is already influenced by gravity so the actual answer would be much larger than that.
But I can't get anybody better at math than me to run this question through the Friedman equations and poop out an answer. xD
[deleted] ยท 2 points ยท Posted at 14:59:11 on May 26, 2016 ยท (Permalink)
Why is this getting downvoted. That's a really cool thought
You cannot list all the numbers in the interval <0,1>. All these numbers have "0." followed by whatever string of digits (almost all infinite). If you tried to list all those numbers in order (like we did the positive integers), I could foil your dastardly scheme and come up with one you didn't list. I would just pick the first decimal place after the point to be different than the first decimal place of the first number you listed, pick a second decimal place different from that of your second number, pick a different third than your third, and so on forever. My number is not equal to any number on your list, which means your list wasn't complete to begin with, which means the number of numbers in that interval is "uncountable". That is a whole 'nother magnitude of infinity than the countable positive integers.
[deleted] ยท 2 points ยท Posted at 20:19:55 on May 25, 2016 ยท (Permalink)
If we both sat down and started taking turns listing positive numbers, you between 0 and 1 and me positive integers, neither of us would ever finish because both are infinite. I know for every single subsequent positive integer there's another infinite group of positive decimals, but that doesn't mean there are more positive decimals than positive integers because there will always be another positive integer
It all sounds fine if you talk about cardinalities, or bijections, instead of sizes of infinity. It all gets weird if you just want to say that one inifinity is bigger than another.
The whole point of cardinality is to generalize the notion of "size" to infinite sets. It's not the only possible way to do so, but it's a common and perfectly valid method of talking about the size of a set.
I don't argue there - but whilst one infinite set can be bigger than another, I find it's still odd to talk about an infinity being bigger than another. Sets being concrete, infinity just a concept.
dlgn13 ยท 0 points ยท Posted at 21:20:45 on May 26, 2016 ยท (Permalink)
Yep. And you can also talk about measure, but the measure of a countable set is 0, so the reals are still bigger.
[deleted] ยท 15 points ยท Posted at 20:37:39 on May 25, 2016 ยท (Permalink)
Put it this way, for every integer you write (1, 2, 3, 4, ...), I'll get write 1 over that number so: 1/2, 1/3, 1/4 etc
But I also get a while bunch of numbers in between those )eg 2/3, 3/4, etc
Thus I can match every number you get with a number I get, but I get an infinite among more in the middle of each of mine that you don't.
Actually, you are describing (positive) rational numbers, and the rational numbers are in a one-to-one correspondence with the positive integers using what's called the "diagonal method". Basically, rational numbers are x/y, where x and y are integers. List all the positive integers in a row, and repeat them in a column. Each intersecting cell is a combination of those headers, and corresponds to a rational number. You can zigzag in such a way that you will hit every rational number, eventually, and you can even calculate when you'd hit a given one first. I don't want to type up something to show you, but you can google it. =P
TLDR: (Positive) Integers are countable. (Positive) Rational numbers are also countable, via the diagonal method. Real numbers in any interval, however, are NOT countable.
[deleted] ยท 1 points ยท Posted at 10:26:59 on May 26, 2016 ยท (Permalink)
In fact, you can include imaginary and negative rational numbers, and draw it so that you have 4 quadrants, one positive real, one negative real, one positive imaginary, one negative imaginary, and spiral out from the centre, hitting every rational number.
That's a brilliant way to explain it, so much simpler than diagonalization. Uncountable vs. countable infinities was always one of my favorite date topics, I'm gonna use this to discuss it from now on.
This still doesn't show the difference between countable and uncountable sets. The same argument applies for the set of rational numbers between 0 and 1, which is countable.
Okay, here's the actual definition of cardinality for you: two sets are of equal cardinality if there exists a bijection between them. For finite sets cardinality is the same thing as the number of its elements. For infinite sets not so much.
A bijection in turn is a function that relates each object of the set of inputs to a unique object in the set of outputs, and each element in the set of outputs is related to an input. In other words, a bijection pairs the objects of two sets together.
Examples of bijections from the reals to the reals are f(x)=x, g(x)=xยณ, or h(x)=1/x when xโ 0 and h(x)=0 when x=0.
A bijection from the integers to integers divisible by two would be n(x)=2x. As this last example demonstrates, true subsets can have the same cardinality as the base set if both sets are infinitely big.
A countably infinite set is one whose cardinality is equal to that of the integers. Whole numbers are countably infinite. So are fractions. Real numbers are not, though.
One characteristic of a countably infinite set, S, is that for all its elements, x, there exists an integer, n, so that a subset of S with n first objects of it will include x.
The point of Cantor's diagonality proof is to show that it's possible to create a real number whose very definition is to not be included in the subset of n first objects for any integer n.
For fractions this kind of infinite goal post moving is of course not possible, as a fraction needs to be expressible as a division of two finite integers.
However, real numbers don't have this restriction. In fact, the completeness axiom gives real numbers freedom to be pretty much whatever they want as long as they are finite in size. This means that it is possible to make a real number that has infinitely many carefully chosen integers to screw up a bijection.
In short, Cantor's diagonal proof works because real numbers can be created using truly infinite goal post moving , and that in turn is possible because of the unique property of the real numbers known as the completeness axiom.
It's not so much about whether or not you can create a list. If you could write one integer a second forever (slow at the beginning, incredibly fast once you get up a few digits), you could not only guarantee writing another particular positive integer, you could actually tell me precisely when and where on the list it would show up. There is no such situation with intervals though - as I described, I could easily come up with a number guaranteed to be not on your list, even if you somehow wound up with a complete infinite list.
I see where you are comming from, I didn't understand this at all at first too.
the clue is that if you list ALL numbers between 0 and 1 and ALL positive integers, you can still always make a NEW number between 0 and 1, by taking the first deciman of the first number you listed, changing it, and using it as the first decimal of you new number. then proceed with the 2nd decimal, that way you create a new number between 0 and 1 that is different from ALL earlier listed number and thus can't be matched with one of the listed positive integers.
then you repeat this process infinitely many times and you have infinitely more numbers between 0 and 1 then positive integers.
maybe this will help: first you list both both the infinite sets and then they are equally big, but then you can make one infinity bigger, while the other infinity can't be made larger.
also YouTube is a great place to learn if you're interested
The diagonalisation is correct, but I'm not sure about the hint. You're not making an infinity larger, you're just proving the impossibility of a method to list all real numbers (you list them all, construct one not in the list, so you didn't list them all, but we could list all of the integers if we wanted).
When dealing with infinity sizes you do something called mapping. If, for every number in a set, it can be uniquely mapped to another number in another set (and vice-versa), then both sets are said to be the same size (in math it's called being one-to-one I believe) Example: the sets (3,4,5) and (6,7,8). 3 maps to 5 (and vice versa), 4 to 7 and 5 to 8. These sets have the same size.
Now we extend this to the negative integers as one set, and the positive AND negative integers for the other set. We say that every integer in the negative set can be expressed as an equation on the set of all positive and negative integers (I forget the actual mapping equation). Thus both sets have the same size.
When we look at the set of real numbers between 0-1 and all positive integers, there is now way to map them in both directions so one must be larger than the other. In this case, it is the one in which one element from one set has to map to multiple elements in the other set, which is the integers to real numbers.
So what you're talking about is the intuitive concept of how numerous something is, and what he's talking about is the mathematical concept, where an uncountable infinity "has" more numbers in it than a countable infinity. Basically there will never be a perfect metaphor to describe it, but ex: you can create a function that turns numbers in the interval (0,1] into any natural number (the function 1/x works for this), yet you can't write a function that turns natural numbers into the numbers in (0,1] (say you wrote it as 1/x again, any value such as 1/(1.5) would fail, and changing the number in the numerator just switches which values do and don't fail)
Why not just list out all the number you would do and divide them all by infinity? It's not in decimal notation, so you can't do that trick, but you get all the numbers just as well
I think a more intuitive explanation of what this means would be that while you can theoretically describe any arbitrary integer with a finite sequence of symbols, you cannot do this for arbitrary real numbers between 0 and 1.
If you think of any positive integer, you could theoretically write down its decimal representation. If you think of any rational number, you can write it down as a fraction. We even have ways of representing many irrational numbers, such as square root of 2, pi, etc... you could write down their definition, or maybe an algorithm that will compute their decimal representation up to arbitrary precision.
However, there are more irrational numbers between 0 and 1 (or any real interval with more than one number) than there are ways of representing things finitely. It seems counter-intuitive, and I suppose that's because the set of real numbers is really weird, we just don't think about it that much.
(By ways of representing things finitely I mean finite sequences of symbols chosen from a finite alphabet.)
[deleted] ยท 0 points ยท Posted at 19:31:00 on May 25, 2016 ยท (Permalink)
well saying "nearly all" is silly when there's an infinite amount
Careful with that. A countable infinity of positive numbers, more accurately
[deleted] ยท 67 points ยท Posted at 14:44:59 on May 25, 2016 ยท (Permalink)*
All that tells me is that no computer with the volume of a human brain can store Graham's number. What is the smallest such computer physically possible? That is, the black hole whose entropy equals that of Graham's number?
Are we looking at a stellar mass black hole? Supermassive galactic nucleus? Observable universe?
edit: Just reacquainted myself with the construction of Graham's number. The answer would be no. No, none of those would be even remotely adequate.
What is the smallest such computer physically possible? ... The answer would be no
Very well put. It is a stupidly large number.
prmcd16 ยท 2 points ยท Posted at 22:48:21 on May 25, 2016 ยท (Permalink)*
Think of a quantum computer the volume of a multiverse sized collection of multiverses whose bits are to the Planck volume what the Planck volume is to the computer's volume. Each bit can be in as many states as there are particles in this hypothetical multiverse. Now transform into a photon and whizz around a Planck volume at the speed of light. Each time you make a circuit, add a computer with as much storage as all the ones you have so far. Do this for around about the projected lifespan of the universe. Then get up, go outside, and do something useful with your life, because you haven't even managed to describe the number of digits in the number of digits in the number of digits in Graham's Number.
unampho ยท 8 points ยท Posted at 15:47:29 on May 25, 2016 ยท (Permalink)
room sized computers come back into style
oi_rohe ยท 18 points ยท Posted at 17:38:42 on May 25, 2016 ยท (Permalink)
They're already back in style, every business with a web presence interacts with them constantly, if they don't own at least one outright.
You would literally fill the universe with planck's constant sized atoms, and you are still like, 0.00000000000000000000000000001% away from Graham's number.
You underestimate Grahams number. You could not possibly write down the number of 0's to make that percentage accurate. You couldn't even write down the number of digits in the number of zeros needed.
[deleted] ยท 2 points ยท Posted at 19:21:23 on May 25, 2016 ยท (Permalink)
You couldn't even write down the number of digits in the number of digits in the number of zeros needed. You couldn't even write down the number of digits in the number of digits in the number of digits....
Heck, you couldn't even write down the number of times we would need to write down "number of digits".
You couldn't even write down the number of digits needed to write down the number of times we would need to write down "number of digits" in your explanation.
Although, if I just kept on going with the pattern in the previous paragraphs, saying that you couldn't write down the number of digits of the number of times needed to write "number of digits needed to write down the number of times needed to write down the number of digits" etc etc etc..., then maybe, just maybe, we can write down the number of paragraphs needed to fully express Graham's Number.
Ninja edit: I realize I just talked about them. I, of course, mean a specific one of them.
You have discovered the interesting number paradox. The smallest uninteresting number is itself interesting, because it is the smallest uninteresting number.
I do have a degree in computer science and quantum information theory and realized I just unintentionally got myself into pretty deep waters. To rephrase, what's the smallest number so that the definition would collapse the observable universe into a black hole? Well, fuck.
I mean, if you mean "literally write out all the digits" then sure, but that's true for like... pi.
But I can fully describe pi using clever mathematical notation. For instance, pi = 4 - 4/3 + 4/5 - 4/7 + ... which can be described very very concisely.
Similarly, the construction of graham's number can be described in (relatively) small terms.
The first number involved in calculating Graham's number is 3 ^ ^ ^ ^ 3. The second number has that many carrots between the threes. The third has the second number of carrots between the threes, and so on until you get to the 64th number. That 64th number is Graham's number.
For the record--to those that don't know--the carrots are not exponentiation. It's Knuth up-arrow notation. 3 (three arrows) 3 is a stupidly big number in and of itself. 3 (one arrow) 3 is 27. 3 (two arrows) 3 is 327. 3 (three arrows) is 3 (two arrows) (3 (two arrows) 3 ), or an exponentiation stack of 327 3's. 3 (four arrows) 3 is 3 (3 three arrows (3 three arrows ( 3 three arrows (... )and you repeat that cycle for 3 ^ ^ ^ 3. And that's not even close to Graham's number!
That is, in and of itself, incomprehensibly large.
So let's turn this around to that black hole, shall we? The Schwarzchild radius of a black hole is r = 2EG/c3, where r is the radius, E is the amount of energy in that radius, and c is the speed of causality, approximately 300,000,000 meters per second.
So when he says "What unit of energy are you using that has E in the Schwarzschild radius formula (r = (2 * energy * universal gravitation constant) / c3) equal to Graham's number?", it doesn't matter. No matter how small of a unit of energy you have, if that amount of energy is at all meaningful, the Schwarzschild radius of the resulting black hole is incomprehensibly larger than the 46,000,000,000 light year radius of the observable universe.
No, seriously.
Let's say you had a photon with a wavelength of light year. Yeah, that means its frequency is 1/31557600 Hz, or 3.16880878 * 10-8. Now, multiply that by Plank's constant (6.626070040ร10-34 kg * m2 * s-1 with some uncertainty), and you get a value that has an order of magnitude of -44. I don't care about that number, and neither should you, gentile reader. Compared to the order of magnitude of a 27-digit tall exponentiation stack of 3's (that first number involved in calculating the number of up arrows in Graham's number), it's nothing at all. Even dividing it by the 300,000,0003 m3*s-3that we get here (that's 3 ^ 24) doesn't save us. Nor does the incredibly small Universal Gravitational constant save us ( 6.674ร10-11 m3kg-2s-2). That still only a number with an order of magnitude of -79.
Fine. So we have G * 10-79 on one side of the equation, where 10-79 has so few digits compared to G that it makes no difference--and that's saying that the unit of energy we're counting Graham's Number of is equal to the energy in a single photon with a wavelength of a light year.
Now let's turn our attention to the radius of that black hole. The diameter of the observable universe is 8.8ร1026 m. That makes its radius 4.4 * 1026 m.
So choose your unit for energy. It doesn't matter. Whatever base unit of energy you choose, if you have Graham's number of it in the size of the observable universe, and you can write down its expression in terms of SI units (or electron volts) in any way, you get a black hole. The order of magnitude of Graham's number is just that big: no matter how small the thing you're counting is, Graham's number of it in the observable universe is a black hole.
jlcooke ยท 1 points ยท Posted at 17:06:28 on May 25, 2016 ยท (Permalink)
log(Grahams Number) =~ 3 ^ ^ ^ 3
Black hole entropy = (c * c * c) * Area / ( 4 * UnivGravConst * h-bar )
So Area =~ 3 ^ ^ ^ 3 * (4) * (6.67408 * 10-11 m3 kg-1 s-2) * (1.05457 * 10โ34 J*s) / (c * c * c)
So yeah, almost exactly equal to 3 ^ ^ ^ 3 ... in what units? Doesn't matter. Seriously, it doesn't.
Edit: Triple carot's ^ don't render as expected in reddit
Edit2: Added spaces to c * c *c ... when will reddit use LaTeX?
[deleted] ยท 5 points ยท Posted at 17:27:48 on May 25, 2016 ยท (Permalink)
log(Grahams Number) =~ 3 ^ ^ ^ 3
That does not seem right to me. Maybe you mean the iterated logarithm? Even then it seems too small.
[deleted] ยท 3 points ยท Posted at 18:58:02 on May 25, 2016 ยท (Permalink)
And that's g1. Graham's number is g64. For the record, g2 has g1 up arrows between the threes, and g3 has g2 up arrows between the threes. You get the picture. You can't write Graham's Number with Knuth up arrow notation.
it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space
Seems like if you converted all matter in the universe JUST to store Graham's number, each digit in one Planck volume, it still wouldn't be enough.
No, no, no ANYTHING with the volume of a human brain can store Graham's number. Not even packed atoms with their configurations arranged to match Graham's number.
crh23 ยท 17 points ยท Posted at 14:46:15 on May 25, 2016 ยท (Permalink)
Well, the entropy is clearly not that large, as we can represent it on a piece of paper!
Rynyl ยท 5 points ยท Posted at 14:31:33 on May 25, 2016 ยท (Permalink)
I didn't post this video in the top thread because I think the one with Ron Graham is better.
Umbrall ยท 8 points ยท Posted at 14:54:15 on May 25, 2016 ยท (Permalink)
Well the fact that we can write it down means it's fairly small. There has to be numbers that are close in magnitude to Graham's number, but admit no clean formula like Graham's number. These numbers could never hope to be described in any way by someone in the universe.
I mean, we can use variables or other non-numerical symbols to represent Graham's number when we write it down (aka I can say that Graham's number = X), but if you were to try to write out each digit in Graham's number for the rest of time, you'd run out of space in the observable universe, even if each digit only took up the space of a single atom.
Umbrall ยท 7 points ยท Posted at 15:51:34 on May 25, 2016 ยท (Permalink)
That's true. The point I'm saying is we can fit the decription of graham's number, as in the proof it appears in, or the 64th iteration of 3 โ x 3 etc. Most numbers the size of graham's number cannot have any kind of succint description like this even fit in the universe, not even considering digits. That we can write down what Graham's number is is a rarity.
fedd_ ยท 2 points ยท Posted at 19:16:43 on May 25, 2016 ยท (Permalink)
Wouldn't it be possible to write such a number in relation to Graham's number? Like Graham's number -1 or -("some fraction of g7") or whatever?
Umbrall ยท 2 points ยท Posted at 19:38:07 on May 25, 2016 ยท (Permalink)
Well you just wrote down what it was, so it definitely can't be in that case. We may certainly be able to write properties though, like saying it's approximately x/y of graham's number
fedd_ ยท 1 points ยท Posted at 20:08:35 on May 25, 2016 ยท (Permalink)
sounds like circular reasoning to me. although i guess I also can't challenge you to tell me a number you can't write down to prove me wrong either ;)
Umbrall ยท 2 points ยท Posted at 21:06:53 on May 25, 2016 ยท (Permalink)
To some degree it is. Pi is a relatively random string, but we've uniquely identified it. So it's not to say that there's anything special about the numbers, only that only so many can be written down finitely.
Look at it like a compression argument. We can't do better than assigning each number a given string. So suppose we're just using english letters and spaces. Then in n of these letters we can only describe 27n total numbers. So if a set of numbers is bigger than 27n, we certainly can't give them all a unique string.
Since Graham's number is so massive, we can't even get close to writing it down, but there has to be at least G - 1 numbers less than it. Since we know we don't have enough nearly space to write out Graham's number in the raw form, we can't have enough space to write out more than a tiny fraction of the numbers less than it since there's not enough possible strings for them. We can have large numbers be possible to write, but this just moves around the tiny fraction.
You'd also run out of time before the heat death of the universe, even if each digit took a nanosecond to write and you started at the beginning of time.
RiOrius ยท 1 points ยท Posted at 19:37:21 on May 25, 2016 ยท (Permalink)
In base ten, sure. In base Graham's Number, I can easily write it out.
marsten ยท 3 points ยท Posted at 17:55:50 on May 25, 2016 ยท (Permalink)*
Even 3โโโโโ3 is vastly larger than the Bekenstein bound for our observable universe. So there is no conceivable way that that number could ever be written down, let alone Graham's number.
That said, it turns out we know the rightmost 500 digits of Graham's number. It ends with a 7 for example.
To me, the fact that we can define and reason about numbers that are so large that they cannot even in principle be written down, is one of the best demonstrations of the power of pure thought.
There's actually nothing to worry about, because the actual information content of the number is quite small. It can be 'compressed' down to a fairly simple formula, or, more generally speaking, a fairly simple algorithm. I could write you computer code that, if run on a computer with enough RAM, would eventually output all the correct digits of the number and then tell you it was finished; and the code itself would be only a few kilobytes.
Most numbers are not like this. For instance, the average number ranging from G to 2*G (where G is Graham's Number) really does contain some colossal, ungodly amount of information that would collapse the observable universe, and cannot be (uniquely) generated by any concise algorithm. In fact, among all the integers, only an infinitesimally small fraction can be 'compressed' significantly the way Graham's Number can.
Well, actually there is something to worry about. Because it turns out that, although we can easily prove that almost all extremely large numbers contain extremely large amounts of information, it is impossible to prove (using the normal rules of mathematics) that any particular integer contains more than some particular finite amount of information. That is to say, there is a largest finite integer for which the normal rules of mathematics can tell us how much information it really contains, and said integer is much smaller than Graham's Number. (The amount of information it contains would still collapse the observable universe, though.)
Fudge89 ยท 1 points ยท Posted at 20:13:27 on May 25, 2016 ยท (Permalink)
Similar to how the number googolplex is impossible to write (physically, dunno about on computers or how that would work). The number of zeros it contains is more than the number of atoms theorized to be in the universe.
Graham's Number is scary as fuck. Reading the Wait but Why post about it really drove home just how mind-bogglingly, stupidly huge things like "infinity" really are.
That was a great read. I've seen several videos on Youtube about Graham's number, but none have been able to put it into the same sense of scale as this article has.
"Infinity" isn't huge. It transcends size entirely.
To say that if you think you can comprehend it, you can't, is an understatement.
It might be true, but it's also true for some finite numbers, like Graham's number.
Saying infinity is big is like saying red is big.
The colour red has no edges, as it is a concept, not a thing. Red is occasionally a useful concept when describing something. But red is not a thing.
Putting infinity into the same bucket as finite numbers is as wrong as putting colours and numbers together. Sure, you can colour by numbers, and sure, you can do useful maths with infinity. But you also get some really weird results.
This is absolutely true - the problem comes from a layperson's incomplete understanding of the scale of things that are finite and measurable.
Learning about large numbers like Graham's Number, TREE(3), etc. gives the average non-academic a profound adjustment to their perception of concepts like infinity when discussing things like religion, space, and so on.
To some extent, it could be compared to what astronauts have experienced with the Overview Effect.
You can say that infinitely-sized things are larger than any finite thing. They are big. Their bigness is on a different order, but it's still a measure of bigness.
I find infinities a lot easier to handle than stupendously large numbers. You can describe and reason about "the set of all natural numbers" fairly naturally.
Really Stupendously Huge Numbers are brainbreaking in a different way.
The car shot forward straight into the circle of light, and suddenly Arthur had a fairly clear idea of what infinity looked like.
It wasnโt infinity in fact. Infinity itself looks flat and uninteresting. Looking up into the night sky is looking into infinityโdistance is incomprehensible and therefore meaningless. The chamber into which the aircar emerged was anything but infinite, it was just very very very big, so big that it gave the impression of infinity far better than infinity itself.
Arthur's senses bobbled and spun as, traveling at the immense speed he knew the aircar attained, they climbed slowly through the open air, leaving the gateway through which they had passed and invisible pinprick in the shimmering wall behind them.
The wall.
The wall defied the imagination- seduced it and defeated it. The wall was so paralyzingly vast and sheer that its top, bottom and sides passed away beyond reach of sight. The mere shock of vertigo could kill a man.
The wall appeared perfectly flat. It would take the finest laser-measuring equipment to detect that as it climbed, apparently out to infinity, as it dropped dizzily away, as it planed out to either side, it also curved. It met itself thirteen light-seconds away. In other words the wall formed the inside of a hollow sphere, a sphere over three million miles across and flooded with unimaginable light.
Infinity isn't huge, it isn't a number. Saying things like this makes me think you're still of the 7 year old mindset where there is a biggest number and youre calling it Infinity.
I never knew someone could that emotional and use such hyperbole with numbers. Also, why call those intermediate numbers such silly things? Why not use one letter placeholders which is convention in mathematics?
[deleted] ยท 2 points ยท Posted at 19:18:09 on May 25, 2016 ยท (Permalink)
He talks about what it would be like to live a Graham's number of years, and how it is simply beyond comprehension.
But couldn't it be argued that any human who was been alive for some period of time, has also been alive for a Graham's number of finite units of time? A really small unit of time, but a finite unit nevertheless?
[deleted] ยท 7 points ยท Posted at 17:27:02 on May 25, 2016 ยท (Permalink)
Actually, there are a few larger numbers involved in serious mathematical proofs these days. One notable one is TREE(3).
lurgi ยท 5 points ยท Posted at 17:17:39 on May 25, 2016 ยท (Permalink)
Graham's number is an upper bound to a particularly funky math problem. It's not known precisely what the answer is, but we know it's less than Graham's number. For a long time it was suspected that the correct answer was... 6.
We now know that's wrong. It's at least 13.
aaaik ยท 6 points ยท Posted at 15:36:32 on May 25, 2016 ยท (Permalink)
Why are they trying to find a solution to the problem of same-coloured coplanar subgraphs? Does it solve some actual problem, or is it just a "hmmm... I wonder." kind of thing?
Most of the time, it's more of a "hmmm... I wonder." That doesn't it won't be useful though. Sometimes the problem ends up being generalized to some other problem, or perhaps the technique used to solve the problem becomes useful for another problem.
Here's a quote from Nobel-prize winning Scientist Richard Feyman that kind of describes his process:
"I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling. I had nothing to do, so I start figuring out the motion of the rotating plate. I discovered that when the angle is very slight, the medallion rotates twice as fast as the wobble rateโtwo to one. It came out of a complicated equation! I went on to work out equations for wobbles. Then I thought about how the electron orbits start to move in relativity. Then there's the Dirac equation in electrodynamics. And then quantum electrodynamics. And before I knew itโฆ the whole business that I got the Nobel prize for came from that piddling around with the wobbling plate."
[deleted] ยท 4 points ยท Posted at 16:06:04 on May 25, 2016 ยท (Permalink)
"hard" problems (look up np v p) are all able to be generalized into eachother. Put another way there is a relatively simple way to turn this problem into a problem about visiting all the cities exactly once in the shortest path, or finding the most efficient way to fill a knapsack, etc.
Alamo44 ยท 4 points ยท Posted at 17:38:17 on May 25, 2016 ยท (Permalink)
Took a class with him at UCSD. This guy is unbelievably smart, but at the same time very approachable. Told us about his friend Erdos the travelling mathematician, his trampoline skills, and how to flip a coin such that it always lands heads.
Not sure if anyone else found this interesting, but I'm all about Graham
b4b ยท 4 points ยท Posted at 22:18:55 on May 25, 2016 ยท (Permalink)
I thought Day9 plays StarCraft Brood War and Hearthstone :D
jlcooke ยท 3 points ยท Posted at 16:58:12 on May 25, 2016 ยท (Permalink)
There have been others larger then big-G - TREE problems etc.
G is still stupid big.
Kruki37 ยท 3 points ยท Posted at 17:06:13 on May 25, 2016 ยท (Permalink)
Graham's number is the largest number used constructively in a math paper.
It used to be, but isn't anymore. Not that it makes it any smaller though, obviously. When Knuth's arrow notation isn't enough and you need apply it recursively, you know something's going to be big.
It's way bigger than that scale. If we also considered the smallest unit of time, then every possible configuration of all the Planck size constants for every Planck second since the beginning of time, would still be dwarfed by G(2), never mind G(64).
For those who have taken in extremal combinatorics class, this is a pretty normal amount. Every once in a while, one of these coloring algorithms (like Graham's) is applicable. So we'll have a biologist come in asking how to simulate some extremal problem on a computer and we all just hang our heads and explain that it takes a stack of 2's 1/ฮต high, as ฮต tends to zero, iterations for this to work. Not exactly computable.
Graham's number is was once the largest number used constructively in a math paper. It's literally unimaginably large.
As explained by Ron Graham himself:
The Use of Graham's Number. Don't worry, it's surprisingly intuitive.
The magnitude of Graham's Number
As explained by Day9 (because it's really entertaining)
EDIT: Somehow, larger numbers have been used constructively. That blows my mind. Thanks /u/Kruki37
EDIT2: For those who hate watching videos and would rather read. Thanks /u/Mikebobble
FTFY
[deleted] ยท 2 points ยท Posted at 20:49:44 on May 25, 2016 ยท (Permalink)
[deleted]
Rynyl ยท 1 points ยท Posted at 21:30:02 on May 25, 2016 ยท (Permalink)
Yes, that would make it bigger, but the point is that Graham's number, at the time it was introduced, was the largest number used in a math paper constructively. It actually has a purpose (surprisingly).
As many have pointed out already, larger numbers have been used since then.
IsakMar ยท 2 points ยท Posted at 20:53:45 on May 25, 2016 ยท (Permalink)
I always thought googelplex was the largest number because mathmatician decided it was, and there was no point in going any further. Man was I (and my math professor) wrong...
My favourite thing about Graham's Number is that it's the upper limit on the answer the the problem - and the lower limit is 13 (I think). The answer is between 13 and a number so big that knowing every digit would cause your headspace to collapse into a black hole.
[deleted] ยท 2 points ยท Posted at 21:59:02 on May 25, 2016 ยท (Permalink)
Here's a trick for those of you that want to make big numbers - and by big I mean absolutely massive. No mere GrahamGraham nonsense here, no we are going so far beyond that that writing GrahamGraham as your largest number is like a child writing 9999999999999999999 as theirs.
We start with a pretty simple concept - repeated application. If f is a function that assigns one number to another, say f(x) = x+1, then we can just write f2 (x) to mean f(f(x)) = f(x+1) = x+2.
Let us use this notion to make an astonishing sequence, defined in the following way:
Define f[1](x) to be 2x, and then define f[n+1](x) to be f[n]x (x).
Not so impressive? Well we aren't quite done yet. There is one more step, we now make a sequence a1, a2, a3, ...etc. by letting an = f[n](n). If you aren't completely thrown yet, let me calculate a few of these.
a1 = f[1](1) = 2(1) = 2 (Difficult, I know)
a2 = f[2](2) = f[1]2 (2) = 8 (Bear with me, here)
a3 = f[3](3) = f[2]3 (3) = f[2]2 (f[1]3 (3)) = f[2]2 (23 x 3) = f[2]2 (24) = f[2] (f[1]24 (24)) = f[2] (224 x 24) = 224x224 x 224 x 24 ~= 10108 that is, a 1 followed by one hundred million zeroes - take that, googol!).
= f[3]3 (f[2] 21021 x 1021) ~= f[3]3 (f[2](101021 ))
=f[3]3 (101021 x 2101021 .) ~= f[3]3 (10101021 )
= f[3]2 (f[2]10101021 (10101021 ) ) ~= f[3]2 (1010...1021 )) (where in the ... we hide about 10101021 10s)
~= f[3](1010...1021 ) (where in the ... we're hiding the 10...1021 10s from last time)
~= 1010...1021 (where in the ... we're hiding the 10...1021 10s from last time)
Let's not go to a5, it may take a while. Suffice to say this gets past Graham's number in about 64 steps, and then a65 = f[65](65) = f[64]65 (65) ~= f[64]64 (Grahams Number) = f[64]63 (f[63]Graham's_Number (Graham's Number)) = ...
So yeah Graham's number pales in comparison to a65, which pales in comparison to a66, which pales...etc. If you want to go even further set b1 = a1, and b[n+1] = aa[n] n. Then b[64] = a(a(a(a(......a(64))...)) where we apply a a(64) times.
Even after all this, we're not one iota closer to the smallest infinity...and there are infinities far, far larger.
Archros ยท 2 points ยท Posted at 22:52:41 on May 25, 2016 ยท (Permalink)
Have you heard about Goodstein's theorem?
Rynyl ยท 1 points ยท Posted at 23:21:42 on May 25, 2016 ยท (Permalink)
I haven't, no. I'm not a mathematician, just an engineer
Archros ยท 2 points ยท Posted at 23:36:04 on May 25, 2016 ยท (Permalink)
After listening to the H.I. podcast because of GCP it's weird clicking on that and seeing Brady. Looks completely different than I pictured him. I knew he had a channel but just never thought to look.
I posted this earlier and it was buried, but another fact relating to large numbers that I find absolutely fascinating:
Goodstein's Theorem. Easily one of the weirdest theorems I know, and it at first seems very counterintuitive.
In layman's terms:
When we representing a number in a base (say 99 = 10200 in base 3) we are implicitly representing it as a sum of powers of the base, for instance
99 = 1โข34 + 0โข33 + 2โข32 + 0โข31 + 0โข30
= 34 + 2โข32.
A Goodstein sequence is defined as follows:
Start with any positive number n in any base b_0 > 1, and write out the base b_0 representation for n as a series as above. But don't just do that: every time you see a number greater than to b_0 in one of the exponents, also write that as a power series in b_0, and so on until all the numbers written down are at most b_0. So in our case (n_0 = 99, b_0 = 3) we have
99 = 33+1 + 2โข32.
This is called the hyper-base b_0 representation of n.
So starting with n, we write it in hyper-base b_0. Now comes the cool part: every time you see b_0 in the expansion of n, replace that with b+1. Note that "usually" this will dramatically increase the value represented. After doing this, subtract 1 to obtain a new number n_1, and if n_1 is positive, rewrite the number in hyper-base b_1 = b+1.
So in our example, we have
n_1 = 44+1 + 2โข42 - 1 = 1055
= 44+1 + 42 + 3โข4 + 3
in hyper-base b_1 = 4. We now just repeat this process. For instance, we have
n_2 = 55+1 + 52 + 3โข5 + 2 = 15688,
n_3 = 66+1 + 62 + 3โข6 + 1 = 279991,
et cetera. As you can see, these numbers increase quickly.
On the other hand, Goodstein's theorem states that no matter what our initial base is -- you could start with 1,000,000 in base 2, of you like -- the sequence will eventually terminate, i.e. n_k will equal zero for some finite k.
Somehow, once these numbers get big enough, their structure is exhausted, and they stop increasing, so we then simply subtract 1 until we reach 0.
On the other hand, the time it takes for the sequence to terminate is generally enormous. Indeed, the function giving the number of steps to terminate starting with n_0 in base 2 increases at a very rapid pace. For instance, if we start by writing n_0 = 4 in base b_0 = 2, the sequence takes 3โข2402653211 - 2 steps to reach 0, while if n_0 = 12, the number of steps needed is more than Graham's number.
But the real punchline is that while this theorem is true (according to standard set theory), it cannot be proven using the standard axioms of arithmetic. In a sense, the function described in the above paragraph grows too quickly for first order arithmetic to prove that it is finite for all n (note that it n price the function is finite for each n, by simply writing out the whole sequence, but this is quite different from proving the statement for all n simultaneously.)
I'll be real, those arrows were sort of confusing. But when he wrote out the 327 / 33333333 / 33333333 / and onward (at the 4:10 mark), I let out an audible groan.
h-jay ยท 1 points ยท Posted at 16:05:46 on May 25, 2016 ยท (Permalink)
This made me feel like we're all presumed illiterate. While my 5 year old appreciates YouTube very much, it's my duty to rescue those of us who'd rather read about it.
[deleted] ยท 3 points ยท Posted at 16:47:37 on May 25, 2016 ยท (Permalink)*
Some people prefer videos and learn better from them. I generally prefer to read about things too - and I do appreciate the article post - but there's no reason to be a condescending ass about it.
h-jay ยท -1 points ยท Posted at 17:57:33 on May 25, 2016 ยท (Permalink)
Some amount of condescension is necessary to indicate that it's in nobody's interest for the video-only reality to become the new normal. It is, in a lot of ways, extremely inefficient: in terms of the time needed to produce the content, the bandwidth needed to process and transmit it, and the time needed to receive it. Sure, you can watch at 2x and skip around, but in way too many cases it takes a rather long video to explain something that a few paragraphs would do at most.
Clack died. Now it's the "best of car talk". Or, to use their language:
Ha ha ha ha my brother ha ha He flat died! ha! ha ha! Doesn't anybody screens these calls! ha ha ha ha You can't do it, unless the number is 2! ha ha ha ha ha ha. My brother! ha ha ha Picov Andropov!!
And I heard it this morning on Car Talk thanks to NPR Onetm
The app you can download from your phone's app store that lets you listen to everything from the comedic game show "Wait wait, don't tell me" to the gritty frontline reporting in the new podcast "Embedded," all on the go whenever you want! NPR Onetm
Public radio at your fingertips.
ktkps ยท 377 points ยท Posted at 11:55:34 on May 25, 2016 ยท (Permalink)*
With Reddit, you end with a space
Then put one more in the same place
So your lines run together
Like birds of a feather
And you don't put your palm on your face.
(A little clumsy, I'll admit.)
[deleted] ยท 2 points ยท Posted at 21:11:21 on May 25, 2016 ยท (Permalink)*
If you stick a stock of liquor in your locker
Be sure to stick a lock upon your stock
Or some joker who is slicker's
Gonna trick you of your liquor
If you fail to lock your liquor with a lock
gileso ยท 1 points ยท Posted at 01:39:28 on May 26, 2016 ยท (Permalink)
There once was a man from Belair,
Who was fucking a girl on the stair,
The banister broke,
So he quickened his stroke,
And finished her off in the air,
Edit: I'm the person the reddit limerick was about
There once was a man from Madras,
who boasted two great balls of brass,
when in stormy weather
they'd both clank together
and sparks would fly out of his ass.
There once was a man from Nantucket,
With a dick so long he could suck it!
He said with a grin,
Wiping spunk from his chin,
"If my ear was a cunt I would fuck it!"
ktkps ยท 1 points ยท Posted at 05:03:31 on May 26, 2016 ยท (Permalink)
Checks out as per the definition in wiki:
A limerick is a form of poetry, especially one in five-line, predominantly anapestic meter with a strict rhyme scheme (AABBA), which is sometimes obscene with humorous intent. The third and fourth lines are usually shorter than the other three.
[deleted] ยท 2 points ยท Posted at 16:30:38 on May 25, 2016 ยท (Permalink)
Our chem teacher liked to quote this DDT limerick:
A mosquito was heard to complain
That a chemist had poisoned his brain
The cause of his sorrow
Was paradichloro
Diphenyltrichloroethane.
Godd2 ยท 2 points ยท Posted at 10:51:26 on May 26, 2016 ยท (Permalink)
It's a trick on the listener of the riddle. You use a couple words that rhyme with beach, and the you describe a desert. The listener then gives an answer of beach, because you've tricked them.
Ahh ok. It still kinda describes a beach though? I think I was largely confused though because I was trying to find something dirty in it given the rest of this thread.
I've always seen "log" refer to the log of base 10.
Al2718x ยท 1 points ยท Posted at 00:59:07 on May 26, 2016 ยท (Permalink)
Yeah that's common in high school because of our base 10 number system (1 plus the floor of the base 10 log is the number of decimal digits in a number), but there is nothing special about 10, so very little serious mathematics is done with base 10 logarithms.
Oh, I was just pointing out another definition of log. It all depends on the context. My attempt at a joke.
If you're in number theory, log(x) means ln(x) and nothing more. If it's basic algebra, log(x) is base 10, if it's complex analysis, log(x) takes on infinitely many numbers (even the image of a real number is a set of infinitely many complex numbers).
Interesting. I've finally reached a point in my math studies where I use log to mean ln. I'm a C.S. major but the more math I study the more I love it. I'm thinking of double majoring. I'll be starting my sophmore year this fall and will already be taking linear.
Emm03 ยท 1 points ยท Posted at 01:35:17 on May 26, 2016 ยท (Permalink)
Could also be:
the LN of the cube root of e
which might flow a little better (although, admittedly, I'm fairly good at math but fairly shitty at poetry)
[deleted] ยท 1 points ยท Posted at 07:29:12 on May 26, 2016 ยท (Permalink)
To make it flow better, you could use "three pi on nine." It's not the most common way of saying it, but I've definitely heard it used. (Mostly by Australians)
He's this older guy, but genuinely damn brilliant at maths and chess, and he has a reputation for giving nicknames. I'd found this limerick, and no-one in my class was impressed by it, but he was nearby, I told him, he found it very amusing and lo and behold, next time he took the register he said rapper in place of my name.
xereeto ยท 2 points ยท Posted at 01:07:58 on May 27, 2016 ยท (Permalink)
<\br>
Reddit doesn't use HTML markup... and that's not even valid HTML markup anyway. To make a new line you can either end your line with two spaces followed by a newline
Like this, or use two newlines
Not a limerick, and I can't remember what this equation is for, but
b-a/(2k) goes perfectly to shake that by Eminem. It's where Nate Dogg comes in, at 0:53
https://www.youtube.com/watch?v=WrjwGPb0Hvw
The Fourier Transform of a Gaussian is another Gaussian.
cthulu0 ยท 376 points ยท Posted at 14:40:26 on May 25, 2016 ยท (Permalink)*
I actually have a patent of an audio signal processing circuit that makes use of that fact. Note: I did not patent the fact that FT(gaussian) = gaussian. You can't patent math.
Edit: In fact if you have an iphone5 or 6, or an ipad or ipod or mac, this patented design is processing your audio. Its not everyday you can say that something you designed is in a hundred million devices.
Are you sure? I kinda want to try. Like all of math, the concept of math. "A novel method of determining rigorous quantitative relational properties of entities"
Yeah, but that lawsuit didn't hold up in court, and Apple lost that patent. Really, patents are like contracts. They don't mean much until you take it to court, then they're actually scrutinized.
You can't patent laws of nature. Pretty sure math is in the same vein.
NNNTE ยท 1 points ยท Posted at 00:38:02 on May 26, 2016 ยท (Permalink)
Those were design patents, not utility patents! the requirements for each are a bit different.
[deleted] ยท 14 points ยท Posted at 18:58:32 on May 25, 2016 ยท (Permalink)
The Supreme Court decided this a few years his, more generally about Algorithms. It was mainly due to the insanity of the start up bubble but it applies also to maths. They are still patentable but only under very specific conditions; the new way of doing it is linked to a new physical thing (eg, if it's only possible to utilize this equation in a specific new circuit you invented), or the new algorithm legitimately revolutionizes the field of intended use (eg, you find a new way of adding that makes existing processors execute operations 10x faster). Very few algorithm patents have been granted in the u.s. since then, single digits if I'm not mistaken
You can certainly mathematical steps. Creative Labs screwed John Carmack by patenting Shadow Volumes. And what is drawing graphics except calculating a bunch of math.
cthulu0 ยท 8 points ยท Posted at 19:50:51 on May 25, 2016 ยท (Permalink)
Well it is established now as of 2016 that you cannot patent abstract ideas. And math is about as abstract as it gets.
Unfortunately inventors get around this loop hole by describing a system that implements the mathematical method. So they technically patenting the embodiment rather than the algorithm.
Unfortunately the patent office is fooled repeatedly by such a trick.
Also this Carmack stuff probably happened 2 decades ago before the Supreme Court camed down on these shennanigans.
The patent system is idiotic and needs a serious overhaul if not outright elimination.
Patents do not need to be eliminated. If someone put forth the resources to develop a concept, then they should have the right to produce it exclusively. However I do agree that it needs a massive overhaul, especially where software is concerned.
cthulu0 ยท 1 points ยท Posted at 14:50:10 on May 26, 2016 ยท (Permalink)
Well European Union has the common sense to disallow software patents because software basically is applied math.
Too bad the US doesn't follow suit. But it won't happen anytime soon. It would require an act of Congress and Congress is full of lawyers. Lawyers would be the ones most hurt by an overhaul of the patent system.
You sound like a person who might work for the Telos Alliance.
cthulu0 ยท 6 points ยท Posted at 20:00:15 on May 25, 2016 ยท (Permalink)
Actually work for Cirrus Logic based here in Austin.
Had to google Telos Alliance. Sounded like a guild in some multiplayer online game :-)
fireatx ยท 1 points ยท Posted at 09:34:06 on May 26, 2016 ยท (Permalink)
Hello fellow Austinite! Got any opportunities for a desperate CS undergrad? ;)
Just kidding (mostly). But really, it's cool to learn about tech companies in our city. I tend to forget how tech-oriented it is here. Also cool to learn about your patent!
cthulu0 ยท 1 points ยท Posted at 14:44:38 on May 26, 2016 ยท (Permalink)
Thank you!
Yes Austin is not nicknamed Silicon Hills for nothing.
cthulu0 ยท 1 points ยท Posted at 19:44:48 on May 25, 2016 ยท (Permalink)
See my replies to other commenters that asked something similar.
zesn ยท 2 points ยท Posted at 18:33:34 on May 25, 2016 ยท (Permalink)
Complete newb about to study electronics with music. Tell me more about this circuit please?
cthulu0 ยท 10 points ยท Posted at 19:43:24 on May 25, 2016 ยท (Permalink)
Asychronous sample rate converter implementation for use on an integrated circuit. Different audio sources use wildly different sample rates. You need to be able to play an audio source data recorded at one sample rate on a system that uses another sample rate. Or you might need to mix different audio sources together which used different sample rates.
rtomek ยท 1 points ยท Posted at 23:21:23 on May 25, 2016 ยท (Permalink)
In your case, it is every day that you can say that! Which kind of mind bogglingly, is also true of a whole lot of engineers, from electronics to cars.
I have a job lined up at Western Digital when I graduate in June, and it's a bit crazy to think that a few years from now hundreds of millions of devices using systems I worked on will be storing billions of dollars worth of data (assuming I do my job well if course).
cthulu0 ยท 1 points ยท Posted at 14:43:08 on May 26, 2016 ยท (Permalink)
Yes you are totally correct of course. In fact that is why we get into engineering: not for the money necessarily ( though you can live very comfortably and even be rich), but rather for the fact that you can creatively design stuff that will benefit millions of people.
Glad to see you are on the verge of starting a promising career.
physchy ยท 1 points ยท Posted at 21:58:49 on May 25, 2016 ยท (Permalink)
For you? Yes it is every day
gart888 ยท 1 points ยท Posted at 22:47:41 on May 25, 2016 ยท (Permalink)
How rich are you?
cthulu0 ยท 1 points ยท Posted at 14:39:06 on May 26, 2016 ยท (Permalink)
I am squarely in the 1% maybe even 0.1%, but that is not saying much. So are doctors and lawyers and small business owners.
Unfortunately I don't get paid by commission.
gart888 ยท 1 points ยท Posted at 14:46:38 on May 26, 2016 ยท (Permalink)
Top 0.1% would give you an annual income of $1.6M. Congrats!
cthulu0 ยท 1 points ยท Posted at 14:54:54 on May 26, 2016 ยท (Permalink)
Ok I guess I am in the top 0.4%. Still fairly content.
gart888 ยท 2 points ยท Posted at 14:57:18 on May 26, 2016 ยท (Permalink)
I bet. How did you come about inventing/patenting that circuit?
cthulu0 ยท 1 points ยท Posted at 15:28:59 on May 26, 2016 ยท (Permalink)
Hard to answer that question without knowing what your educational background is.
gart888 ยท 2 points ยท Posted at 15:41:30 on May 26, 2016 ยท (Permalink)
I've got a masters degree in applied science.
I'm not asking how /i'd/ go about it though. I'm asking how you did it. Were you working for yourself? Was it a weekend project? Was it a project at a university?
cthulu0 ยท 1 points ยท Posted at 15:57:54 on May 26, 2016 ยท (Permalink)
I was (an still am) working for a company that designs integrated circuits. So though I am the inventor, the company owns the invention. So I obviously did not have to spend my own money on lawyers fees or patent application and maintenace fees.
And the invention was for use in a specific product line but was a side project I was working on unbeknownst to my manager.
It took at least a week to show the algorithm would work in MATLAB. It took several months to implement it in actual working silicon. But once that was done and the area was optimized, other managers of other IC projects realized it would benefit their projects also.
Ironically the solution was not fully trusted by our biggest customer (a "fruit" company based in California if you catch my drift). They needed convincing and demanded we show them details. We were apprehensive because they showed a tendency to think that because they were footing the bill, they could co-opt our intellectual property as their own.
My name is on a patent but it's both unused, useless and beyond trivial. I like self-repeating equations (quines, exp, ...), this is of much coolness.
cthulu0 ยท 2 points ยท Posted at 14:35:26 on May 26, 2016 ยท (Permalink)
Yes self-reference is cool. I'm a big fan of it. Its what allowed Kurt Godel to formulate his revolutionary incompleteness theorems.
Of the 13 patents I have, I can say the majority of them are either useless and trivial or that I am not particularly proud of them. The gaussian one is only one of two I am really proud of. Unfortunately as an engineer you have to play the patent game to advance in your career.
I don't see a reason to think that a complicated macroscopic system has to look anything like the underlying quantum mechanics. In fact, quite often the math for macroscopic systems looks nothing like the math for quantum mechanics. For example, diodes exhibit strongly non-linear behaviour even though they're based on quantum mechanics, which is a linear theory.
I think the connection has more to do with the notion of linearity/superposition. It's amazing to me how that idea ties together so many subjects that seem completely unrelated at first glance.
It's only exactly an eigenfunction if you choose the variance appropriately. If you choose an arbitrary variance then you get back a Gaussian with a different variance than the one you started with, thus its not exactly an eigenfunction.
If you were to plot a gaussian (a bell curve) with a height of 1, and then draw an infinite number of cosine waves whose height and frequency are the Y and X of the gaussian plot, then add up all of those cosines, you would have the gaussian.
Crysist ยท 0 points ยท Posted at 20:14:40 on May 25, 2016 ยท (Permalink)
Just curious, isn't that what the FT does? Split a wave up into an infinite number of waves that add up to the original? Why is the original fact noteworthy?
because the fourier transform/series describes the distribution of the amplitudes of the waves with respect to frequency, whereas the original describes the shape with respect to some other variable (for example, time).
This blew my mind when I first learned it, and at some point I had the necessary knowledge and intuition to have that "ah-ha!" moment, but that's lost now.
The most I can remember is that the FT of a "skinny" Gaussian is a fat one, which I can intuitively understand if I think of the first Gaussian as the amplitude of a signal in the time domain and its FT being the frequency response, i.e. the shorter a pulse gets, the wider the bandwidth it occupies.
You can take it to the extreme and consider the Dirac Delta function, whose Fourier transform is simply 1, and vice-versa. And what is the Dirac Delta, but an infinitely thin Gaussian?
jusjerm ยท 11 points ยท Posted at 16:32:40 on May 25, 2016 ยท (Permalink)
mokojin ยท 1 points ยท Posted at 23:14:54 on May 25, 2016 ยท (Permalink)
What I found even more interesting is that the Fourier transform of a narrow Gaussian is a wide Gaussian!
Heisenberg's uncertainty relation makes use of this, as the real space and momentum space are connected via the Fourier transform, meaning that you just cannot have arbitrary narrow gaussians for both of them.
(sorry for poor English, studied physics in Germany)
That property actually does come into play. The derivative of a Gaussian contains another Gaussian term, which is used in the derivation, which you can see here.
[deleted] ยท 0 points ยท Posted at 16:16:24 on May 25, 2016 ยท (Permalink)
[deleted]
Gnzzz ยท 7 points ยท Posted at 16:28:15 on May 25, 2016 ยท (Permalink)*
If I remember correctly, the Fourier transform of the Dirac-Delta is a constant, not another Dirac-Delta. The real part at least, the phase / imaginary part is an exponential of the shift.
Correct! Using the unitary Fourier transform in ordinary frequency, the Fourier Transform of delta(t) is 1.
However, the Gaussian principle is also tangentially related. If you consider a delta function as the limit of a normalized Gaussian as the width goes to 0, the Fourier transform is a Gaussian whose width goes to infinity, (i.e. a constant).
It's cool until you study the complex plane, then it just makes sense...
ben_jl ยท 380 points ยท Posted at 14:05:56 on May 25, 2016 ยท (Permalink)*
Even more generally, you can derive this solely by considering the definition of exponentiation. The two essential properties of the exponential function are ea * eb = ea+b and (ea)b = eab. When extending to the complex numbers, we want to make sure that ez satisfies these two relations and matches the usual definition when z is real.
From this, you can show that the only definition that fits is ea+i*b = Aea{cos(b)+i*sin(b)}, where A is a constant 1+iB, with B an arbitrary real number. We then choose B=0, and obtain Euler's Relation. No complex plane necessary.
Edit: This also demonstrates that Euler's Identity is ultimately arbitrary, as the value ei*pi is dependent on our choice of B. It only equals -1 when B=0, and we could make it equal any value we want on the unit circle just by changing our choice of B.
[deleted] ยท 217 points ยท Posted at 14:24:58 on May 25, 2016 ยท (Permalink)
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ben_jl ยท 61 points ยท Posted at 14:37:09 on May 25, 2016 ยท (Permalink)
Perhaps, but that clouds the (for me, more interesting) fact that the relationship comes from what the exponential does: namely, turning multiplication into addition. The other derivations make it seem almost like a coincidence, at least to me.
I first saw it being explained with a complex plane, and it really wasn't very clear. Later I saw it being derived using the Taylor expansion for ex, and it was much easier to understand. But I think one of my math lecturers said that the Taylor expansion method wasn't really a good proof, and only a way to remember the formula.
Thanks for this. I've always thought of the complex plane as a somewhat artificial construct, a useful one to describe certain real-life phenomena like "reactive power" in electricity, but nevertheless a made-up idea. The problem with that was that Euler's relation seemed to make "i" much more fundamental than this, but your explanation points out that it's not really.
but the complex plane only makes sense after you've been told about that sin/cos relationship.
how you go from e(j*w) to cos(w) + j*sin(w) is the amazing part. differential equation is one way. i've heard it can be shown via taylor series as well.
For Taylor series, just plug ix into the Taylor series for the exponential. The even terms for the Taylor series give you the Taylor series for cos(x), the odd terms give you isin(x).
by the way, I sometimes find myself deriving trig identities from the Euler formula. Once you're comfortable with j*j=-1 and you know two formulas (sin x, cos x) you can obtain all kinds of stuff. Euler formula and Pascal triangles FTW!
I'm missing something, I don't see the differential equations? Do we use d/dx ex = ex along with the properties of exponents he mentioned to construct them?
The second derivative of exp(ix) is -exp(ix). This is the differential equation for a harmonic oscillator (or spring if you like), which admits sinusoidals as solutions.
Differential equations was the first place I saw it proved. Happily reading along in the textbook about some random concept, "oh and if you just manipulate this and that, you derive this famous equation. But back to solving differential equations..."
[deleted] ยท 4 points ยท Posted at 14:37:50 on May 25, 2016 ยท (Permalink)
Sorry, what are the steps to arrive at the second paragraph?
ben_jl ยท 7 points ยท Posted at 15:03:27 on May 25, 2016 ยท (Permalink)
The majority of the work is done by the condition that the complex exponential f(z) = ez when z is real. Note that this implies that f(z)=eRe{z}g(Im{z}), where g(0)=1. From here, you have to obtain some conditions on g. Specifically, you take derivatives of the relations given by the properties of the exponential, and solve the resulting differential equations for g. The intricacies of that last step are a tad involved for a reddit comment (a lot of symbol formatting I'm not too keen on) - the first chapter of any complex analysis book (or googling 'complex exponential definition') will have the details.
The best way (or at least "coolest" way) to see this is using Taylor Series, works out really nicely. You see how cos and sin relate to e, you get Euler's Formula, and then you get Euler's Identity.
zarraha ยท 1 points ยท Posted at 16:48:41 on May 25, 2016 ยท (Permalink)
And because it's arbitrary, it's not as profound as everyone seems to think it is.
[deleted] ยท 1 points ยท Posted at 16:58:38 on May 25, 2016 ยท (Permalink)
3Blue1brown has a great video on this that completely skips the calculus and shows the underlying intuition.
What? Those properties of exponentiation are obvious in much simpler ways that don't require any knowledge of trigonometry, e, i, calculus, or taylor polynomials.
JesusK ยท 1 points ยท Posted at 19:30:23 on May 25, 2016 ยท (Permalink)
And that kids is were springs come from!
dh363 ยท 1 points ยท Posted at 19:56:25 on May 25, 2016 ยท (Permalink)
The fact that it satisfies these relations while being the only reasonable way to define the exponential function is beautiful though.
CCNezin ยท 1 points ยท Posted at 23:15:08 on May 25, 2016 ยท (Permalink)
I wouldn't say that choice is arbitrary. What about the motivating definition from the addition of taylor series of cos z and i sin z ?
I've never seen euler's formula including an A=1+Bi where B is arbitrary before, so your edit paragraph does not make any sense to me. I've known Euler's formula to be e^a+ib = e^a (e^cos (b) +i sin (b)). I also don't understand, even if A is included, how adding a complex part (B equals a real non-zero number) can make e^i pi be any number. Would you care to explain?
This reminds me. While analyzing Spirograph a couple of years ago, I discovered something interesting. Unfortunately the details are now very vague in my mind, but I think it was something like, if you draw any arbitrarily-chosen Spirograph pattern in the complex plane, sized (scaled) such that the outermost-extremal points ("tip" of a "petal" or "loop" or "cusp") lie exactly on the unit circle, then each of those outermost-extremal points is a complex Nth root of 1. For all I know, this could be a well- and long-known result, but it's new to me!. (At the time, I was able to compute, from the numbers of teeth in the "ring" and "moving gear" used to generate the Spirograph pattern, the value of N... and there were some other interesting properties, such as that, in emulating Spirograph in software, using non-integer ring and gear sizes (number-of-teeth being proportional to circumference which can be a real number) is simply equivalent to using very large integers -- the more decimal places, the larger the integers. You can thus very easily generate Spirograph patterns that will entirely fill the circle they occupy, given any specified pen thickness -- but can never truly computer-generate patterns that really entirely fill the circle in the true mathematical sense, because computer numeric precision is limited. To generate a Spirograph pattern that truly fills the circle, you would have to use the exact values of irrational numbers like e and pi.... i.e. infinite numbers of digits...
In the process of all the above, I also independently discovered what turned out to be the well-known relation LCM(a,b) * GCD(a,b) = |ab|.
It is still mind blowing that one equation is so simple & elegant and yet includes the big hitters:
0 - the first real "mathematical concept" - how can you count nothing?
1 - the most basic number.
e - transcendental number - a logarithm found many places in nature.
pi - another transcendental number that everyone knows and loves - again many places in nature.
i - a complex number that loops back to 0 - how do you count something that does not exist?
It also includes the operators =, +, *, ^ exactly once each.
can you please elaborate / link me to the resources that will allow me to gain this sort of understanding of the complex plane?
ben_jl ยท 6 points ยท Posted at 15:08:38 on May 25, 2016 ยท (Permalink)
Not OP, but I strongly recommend (at least the first chapter of) Visual Complex Analysis by Tristan Needham. You can find a PDF online pretty easily. Its a great first semi-rigorous introduction to complex numbers that gives a lot of intuition for the complex plane.
A tldr version would be if you imagine a circle with exp(j*theta) describing a unit vector from the origin to any point on this circle with theta being the angle. If theta is pi, then the vector is basically -1. -1 + 1 is 0.
I think it's even cooler when you understand where it's coming from. The historical significance of the discovery was one of the first steps to understanding the complex numbers as a plane, so rather than looking at what we have now and saying "yes, that just makes sense", I prefer to look at the beauty of the equation from the standpoint that this equation was one of the first steps to extending our understanding of numbers as we know them.
[deleted] ยท 7 points ยท Posted at 17:01:33 on May 25, 2016 ยท (Permalink)
I strongly disagree when people say that this theorem is trivial if you know what it means. I think that this idea is popular because in every text on complex variables the defintion of eix is given as cos (x) + isin (x). But that just buries the real theorem, which is that this definiton allows us to extend the exponential function analytically to the complex plane, with all the expected algebraic properties of exponential function still holding. That part is actually a fairly nontrivial theorem, and in my opinion a pretty surprising result.
[deleted] ยท 1 points ยท Posted at 22:50:39 on May 25, 2016 ยท (Permalink)
eix is given as cos (x) + isin (x)
This part is actually useful for stuff like phasor analysis
Of course it just makes sense - it's a mathematical fact, so you can prove it sensibly!
It's still cool that these constants that arose from seemingly disjoint areas of analysis - arithmetic, trigonometry, and exponentiation - are connected in this way. It's a bit like the 9-point circle in geometry. Of course it makes sense - you can even demonstrate its necessity with simple algebra - but it's still cool.
I kind of thought it made sense with Taylor series, what other insight do you get from complex analysis?
redzin ยท 0 points ยท Posted at 17:31:33 on May 25, 2016 ยท (Permalink)
That is the only way it makes sense. The complex plane makes use of Euler's formula from which Euler's Identity can be easily proven, but proving Euler's formula is the difficult part.
No, it isn't. A much more intuitive way to think about it is to use the definition of ex as (1 + x/n)n as n tends to infinity.
So ei*pi is (1 + i*pi/n)n as n tends to infinity.
1 + i*pi/n looks like a rotation of pi/n. Do that n times and you get a rotation of pi, which takes you to -1.
redzin ยท 2 points ยท Posted at 18:34:51 on May 25, 2016 ยท (Permalink)
1 + i*pi/n looks like a rotation of pi/n
I'm not sure I understand what that means. If you're talking about the complex plane (which it sounds like you are) then please understand that the only reason the complex plane can be related to complex exponentials is due to Euler's formula, which can be proven. Euler's formula is not a definition.
(1 + ipi/n)n is 1 + ipi/n multiplied by itself n times. In the complex plane, multiplications by complex numbers (of size 1) are rotations. So multiplying by 1 + i*pi/n, n times, means rotating by the angle of that complex number, pi/n, n times, which means rotating by pi.
redzin ยท 1 points ยท Posted at 19:15:54 on May 25, 2016 ยท (Permalink)*
In the complex plane, multiplications by complex numbers (of size 1) are rotations.
That's the part I was missing. Been too long since I did this sort of thing. Also, I've never seen Euler's identity derived this way. Pretty cool.
... one more thing though. The size of 1+i pi/n is not 1, so why does it remain normalized?
Edit: Oh, right. The limit takes care of normalization.
You can see Euler's formula this way too, just plug in a value other than pi and the same type of argument works. cos@ + isin@ is of course just the point on the unit circle at angle @.
I used to think that this identity (or more generally ei*x = cos x + i sin x) was very arbitrary and obscure, and I couldn't understand why mathematicians would appreciate it so much. Then I learned about analytic continuation and power series and realized how beautiful it was !
redzin ยท 2 points ยท Posted at 17:40:49 on May 25, 2016 ยท (Permalink)*
The idea of the complex plane is based on Euler's formula from which Euler's Identity (OPs equation) can be easily proven (just set x=pi).
Proving Euler's formula is non-trivial though. You need to Taylor expand ex, cos(x) and sin(x), then Euler's formula becomes apparent, but it's certainly not obvious until you see the proof. And even then it's still kinda "magic". Why is Euler's formula true? ... it just is, because it can be proven so.
kyred ยท 2 points ยท Posted at 15:14:04 on May 25, 2016 ยท (Permalink)
What's more fun is ei*pi/2 = i
"i" defines itself.
c3534l ยท 1 points ยท Posted at 16:29:45 on May 25, 2016 ยท (Permalink)
It didn't make sense to people for a very, very long time. They didn't have quite the understanding of things as we do nowadays.
MrJoo ยท 1 points ยท Posted at 18:10:41 on May 25, 2016 ยท (Permalink)
It's cool because it exhibits the three standard operations: addition, multiplication, exponentiation, e & ฯ as the two big constants as well as the multiplicative & additional identities, 1 * 0. All this and nothing extraneous.
Jack-90 ยท 1 points ยท Posted at 18:51:56 on May 25, 2016 ยท (Permalink)
Understanding it made it cooler to me. But hey...
jyonsin ยท 1 points ยท Posted at 19:40:16 on May 25, 2016 ยท (Permalink)
Yo, it's still cool, because it uses the five most important numbers in math. The most beautiful equation.
chiagod ยท 1 points ยท Posted at 22:37:09 on May 25, 2016 ยท (Permalink)
It's cool until you study the complex plane
I can see a mathematician, clad in a flamboyant cape, open a closet door from which emerges a most unnatural light....
"Hold my calls. I'm off to study the complex plane!"
Six months ago, I'd have said that you've got some funky notions of complex algebra.
Now, I just finished a graduate leveling class in theory of complex variables, and I'm convinced that I don't understand complex analysis or algebra at all. That class was just brutal, even more so than PDEs.
Euler's Identity unifies several different aspects of mathematics - the natural logarithm, complex numbers (i.e. real and imaginary), and trigonometry (this particular example is a special case of complex analysis, the more general version involves sine and cosine). So you've got several different fields of mathematics all brought together...and it's relevant to all of them.
The other user who responded to my comment gave a response that was more adequately dumbed-down for me, but Iโm definitely saving this comment so I can revisit it when I understand the concepts better!
I appreciate the explanation. But I must apologize โย it goes waaaay over my (borderline innumerate) head. :P
S'right. Too many years of math classes at university. Thanks for the gold!
[deleted] ยท 75 points ยท Posted at 11:16:06 on May 25, 2016 ยท (Permalink)*
It is usually considered elegant, or aesthetically pleasing as well. The reason for this is, that it links 5 of the most important constants in math and physics, (0, 1, e, pi, i), with exactly one addition, one multiplication, one power operation and an equality.
That makes sense. I realized the importance of โe,โ โ๐ ,โย and โiโ, but I definitely missed the significance of โ0โ and โ1,โ along with the nature of the operations used in the equation.
Mark7A ยท 3 points ยท Posted at 15:10:18 on May 25, 2016 ยท (Permalink)
It's funny, at one point the concept of zero didn't exist.
I wonder what people in the future will think of our math.
I wonder what people in the future will think of our math.
I'm pretty convinced that future math historians will marvel at our obsession with limits, and laugh at the gyrations we went through to deny the (to them) obvious existence of infinite and infinitesimal numbers. Limits were required in the 19th century to place analysis on a rigorous mathematical footing, as mathematicians couldn't find a way to make infinitesimals rigorous. However, in the mid-20th century that changed. (Search for non-standard analysis or hyperreal numbers if you want to know more.) The intuitive infinitesimal approach that was used for centuries (even by Newton and Leibniz) can now be treated with as much rigor as you like.
However, we continue to cling to our limits, often accompanied by arguments that infinitesimals aren't "real" - which is exactly the claim that was made about irrationals, negatives, and so-called "imaginary" numbers.
ben_jl ยท 5 points ยท Posted at 13:50:05 on May 25, 2016 ยท (Permalink)
Really, the more impressive fact to mathematicians is the general Euler relation: ei*x = cos(x) + i*sin(x). The Euler Identity is just a special case of this. And not even a particularly interesting one at that; once you understand the relationship between complex exponentiation and the unit circle, its essentially a tautology.
[deleted] ยท 1 points ยท Posted at 14:05:41 on May 25, 2016 ยท (Permalink)
I fully get what you're saying, and I agree that the whole concept of the complex exponential is more impressive. Although I still find the identity quite beautiful on its own, partially for the properties the identity specifically exhibits that I mentioned above.
But of course you are right, the general case is more impressive.
This equation fails to relate the five most important constants of analysis and the three most important operations. It's elegant, but it isn't beautiful.
guthran ยท 0 points ยท Posted at 17:17:51 on May 25, 2016 ยท (Permalink)
I disagree, if you're considering 0 to be the other most important constant and subtraction/addition to be the other most important operation, this equation could be expanded to something like "ei*tau = 1 -/+ 0" and your complaint is now invalid
Elegance in an equation to me seems to be a matter of it simplifying an otherwise complicated concept and doing so in a straight forward easy to use expression.
I don't get whats so elegant about this. It kinda makes a statement about complex numbers.
I explained this above, but Euler's Identify showcases how several different mathematical systems interact and relate to each other - not just complex numbers, but natural logarithms and complex analysis too.
sin and cos are the only two solutions where y'' = -y. Which is also true of eix
That is a confusing statement to make. If they're the only two solutions then saying its also true of eix only makes sense if we've already accepted that the two are equivalent, but the the whole point was establish their equivalence. Thus begging the question.
They are not the only two solutions. However every solution can be written as a sum of those two solutions (non-trivial result). I.e. C * cos x + D * sin x
For a given initial condition, such as y(0) = 1 and y'(0) = i, the solution has to be unique (also non-trivial result) so therefore since
both cos x + i * sinx and exp(ix) solve the equation for that initial condition they must be equivalent due to uniqueness.
[deleted] ยท 2 points ยท Posted at 19:40:56 on May 25, 2016 ยท (Permalink)
So cosx and sinx are an orthogonal basis for the space of solutions to that differential equation? It's cool to realize that linear algebra explains a lot more than just matrices and vectors!
As far as I know, orthogonality requires that you define an inner product. Haven't really thought of an inner product in that specific case. A vector space doesn't require an inner product to be defined.
They are certainly a basis for the vector space "solutions to that differential equation".
[deleted] ยท 2 points ยท Posted at 20:15:26 on May 25, 2016 ยท (Permalink)
There was some other argument that I read on /r/math I think, but it wasn't completely rigorous because the usual dot product on Rn doesn't extend to Rinfinity. But the gist of it was to take the coefficients of each from its Taylor polynomial. Then, since cosx is even and sinx is odd, the 'dot product' would be zero. Dunno how to rigourize that, but it'd be nice to cause I thought that argument was neat.
OHHHHHHH. and this is why Fourier decomposition is a thing!
Yeah, my intended point was just that establishing the equivalence was sort of the important part, and glossing over it was a (non-trivial result) or related doesn't really accomplish the goal and certainly no better than using a taylor series expansion would.
[deleted] ยท 1 points ยท Posted at 16:57:54 on May 25, 2016 ยท (Permalink)
I think you have to establish that sin and cos solutions are linearly independent, which isn't hard, and then i think you have to prove that sin and cos span the solution space. Once you do that you can express any solution, such as eix as a linear combination of sin and cos.
But i'm not actually super robust at these forms of rigorous mathematical analysis being more of a physics type person, and off the top of my head I don't know how you prove the spanning.
I said this to someone else, but there's some theorem in solving second order dfferential equations that the general solution is equal to a linear combination of two specific solutions or somehting. Can't ever remember the name of it or the exact particulars
Anaract ยท 3 points ยท Posted at 16:05:55 on May 25, 2016 ยท (Permalink)
I had an interview recently where I was asked to solve for the square root of i.
Mind was blown for about 20 seconds, then I started going through Euler's and it was pretty simple. Interesting, though. Certainly wasn't expecting that
there's some theorem in differential equations that says the general solution to a second order DE like this is a linear combination of two independent specific solutions or something.
I wish I remembered that theorem. Someone mathsy help?
ben_jl ยท 2 points ยท Posted at 14:16:35 on May 25, 2016 ยท (Permalink)
You don't even need Taylor Series! In fact, that method misses the essential point, and makes the result seem like a pure coincidence. Euler's relation, fundamentally, is the only sensible extension of the exponential function to the complex numbers. No calculus necessary.
Well, it really depends how you define cos and sin.
Most calculus courses define them as such:
cos(x) := Re(eix)
sin(x) := Im(eix)
Or like this (which is pretty much the same as above):
cos(x) := 1/2(eix + e-ix)
sin(x) : = 1/(2i))(eix - e-ix)
Hence eix = cos(x) + i*sin(x) does not have to be "proven".
So it follows directly by definition.
The real question is: Why is sin(pi) = 0 and cos(pi) = -1 ?
The thing is: that is how calculus classes define pi! (Kinda...)
pi/2 is the root of cos in the interval [0,2]. And that is kinda annoying to show that it exists and all...
Or another way to look at pi is:
We show that:
|eix| = 1 for all x
(not that easy to show, I believe...)
and that it is periodic (and maybe properties...). We then define 2*pi to be the length of the period ("circumference"). Then it is easy to see why eipi = -1
So it's all not that easy, actually.
Bobius ยท 1 points ยท Posted at 15:36:52 on May 25, 2016 ยท (Permalink)
Another fun way.
Use the quotient rule with f(x) = cos(x)+isin(x) aand g(x)=ei*x
Find that [f(x)/g(x)]' is 0, so f(x)/g(x)=a constant
sees "Hence, eiPi = -1 + 0i = 1 And therefore: eiPi + 1 = 0" well 'scuse me sir you appear to have a little bit of a smudge on your screen lemme ru--- wow what is this symbol is it magic will it take me to narnia will it make the world forget the prequels?
I just read the wikipedia article and I cannot for the life of me discern why everyone is literally jizzing at the sight of an equation.
When you multiply some fancy numbers you get 0-1? How that revelation can be described as "filled with cosmic beauty" is beyond me. Mathematicians are weird.
[deleted] ยท -1 points ยท Posted at 11:50:35 on May 25, 2016 ยท (Permalink)*
I've never understood how this works with logs though. For example I know that ln(1)=0. But if eฯi=1...
jfb1337 ยท 2 points ยท Posted at 15:24:55 on May 25, 2016 ยท (Permalink)
The complex logarithm is really a multivalued function, like the inverse trigonometric functions. So you add on 2*pi*i*n where n is in Z, or just take the principle value where -pi < Im(log(z)) <= pi
[deleted] ยท 1 points ยท Posted at 14:28:25 on May 25, 2016 ยท (Permalink)
The reason I like this so much is that two irrational numbers, which means that they have an infinite amount of decimal, combined with an imaginary number can form a negative integer. It's one of those things that really fascinated me in math class.
This boggled my mind for so fucking long, I even complained to the professor that it doesn't make sense. Turns out instead of a plus, I mistakenly wrote a minus on my notes.
I like phrasing it "ii=ei*pi ". That way it sort of rhymes.
atakomu ยท 1 points ยท Posted at 16:28:44 on May 25, 2016 ยท (Permalink)
It's even more fascinating when you think about what are e i and pi. Pi is some number we invented to be able to calculate pi. i is another one we invented to be able to get roots of negative numbers and we mostly use e to do differential calculus. But all those numbers together are in this nice equation.
Math is probably one of the things that is transcended over to the aliens and we could "talk" about it with them.
Captain obvious to explain me what is cool here ? :(
ythl ยท 1 points ยท Posted at 18:01:47 on May 25, 2016 ยท (Permalink)
I discovered this by accident playing with my Ti-83. I was just messing around with the baked in constants, and when I tried epi * i, and saw "-1" I was baffled and amazed. I showed my high school math teacher and he attributed it to a glitch in the calculator.
A single equation that makes much of trigonometry trivial. It's awesome because a lot of things that are really complex to do with trigonometry just sort of fall out when you approach it using Euler's theorem.
[deleted] ยท 9 points ยท Posted at 16:57:27 on May 25, 2016 ยท (Permalink)
I was about to say that if you're remembering 6 digits anyway, you might as well just go to the 5th digit of pi. Then you're off by less than .00001. ...but then I saw the % sign!
The only time you'll ever care about the tiny fractions of error between them, you'll be doing computational solutions anyway. So just use the simplest thing.
The others aren't perfect circles, pi is for a circle and it's an irrational number which can't be expressed as a fraction (whole number in integer numerator and denominator).
For example, if you have a regular hexagon where each angle is (360/6) = 60ยบ and each side is the same length, then "pi" = circumference/diameter is 3. As you increase it to a bigger regular n-gon, you get closer and closer to the real value of pi.
Zavant ยท 2 points ยท Posted at 20:03:51 on May 25, 2016 ยท (Permalink)
I think you meant to say, that 22/7 and 3.14 are off by 0.005%. It's impossible for 3.14 to be off by 0.05%, as the two first digits of pi are 1 and 4. If it was off by .05%, the actual digits of pi would be either 3.09 or 3.19.
[deleted] ยท 1 points ยท Posted at 10:13:18 on May 26, 2016 ยท (Permalink)
pi99.95%, or pi\0.9995 = 3.1400. So yeah, it's 0.5%.
Zavant ยท 1 points ยท Posted at 10:28:32 on May 26, 2016 ยท (Permalink)
Ah well apparently i'm bad at noticing the % thing, even though i wrote it myself. I was thinking about the digits themselves and not a percentage difference. Oh well.
My HP 48SX always just carried the pi symbol through the answer. That was annoying at times so I usually just typed in 3.14159 by hand (because that's oh so accurate).
My ti-84 plus uses 3.1415926535898, it also does integrals, derivatives and graphing, which are all very important things that a $20 calculator wont do.
edit: did a dumb
Thraol ยท 3 points ยท Posted at 20:30:38 on May 25, 2016 ยท (Permalink)
Not to be pedantic or anything, but there's an extra "4" in that number that shouldn't be there (3.14159265435898).
What's your point? All computers with finite bit storage must use numbers that have a finite size/precision, aka approximations when it comes to irrationals.
Thank you for stopping on a digit where the next digit isn't 5 or higher. Whenever anyone rattles off an approximation of pi, and i know the next digit is a 7, I really want to tell them, "Well, if you're going to stop there, then your last digit is off..."
That irks me too, I actually wanted to stop on the last 5 of "535" but then realized it would round up, and then just kept going until the next number no longer rounded it up, which turned out to be another five digits. No problem, random citizen!
Well they're rattling off digits. If they say "I don't know any more digits" then obviously they wouldn't round up the last one because they don't know what the next one is. They know there's another digit, they said all of the other digits up until that point, which is what they were trying to do. What's the problem? You're just being fussy.
I'm someone who's memorized around 100 digits of pi. I did it in middle school and 28 years later it's still stuck in my head.
What part of this doesn't scream "fussy?"
Have you ever actually said this, because that's a sad math fact.
Kayyam ยท -1 points ยท Posted at 15:33:21 on May 25, 2016 ยท (Permalink)
I don't get it. The same logic that make you round up at 7 makes you round down at 3, so why is the last digit off when it's a 7 and not a when it's a 3 ?
[deleted] ยท 1 points ยท Posted at 15:37:19 on May 25, 2016 ยท (Permalink)
[deleted]
Kayyam ยท 9 points ยท Posted at 16:06:54 on May 25, 2016 ยท (Permalink)
You don't round down. You never round down.
5.6732, rounded to 4 significant digits -> 5.673
You just rounded down.
[deleted] ยท -2 points ยท Posted at 16:15:51 on May 25, 2016 ยท (Permalink)
[deleted]
Kayyam ยท 7 points ยท Posted at 16:23:17 on May 25, 2016 ยท (Permalink)
I mean, you had an initial number, now you have a new rounded one and it happens that it's inferior to the initial one. I don't think it's a matter of perspective.
What is the difference between accuracy and efficiency?
xeow ยท 1 points ยท Posted at 19:54:30 on May 25, 2016 ยท (Permalink)
Accuracy here is how close the computed ratio is to the real value of ฯ. In the code, I defined accuracy as 1 โ error, where error is defined as the absolute value of ratio and target (the target being ฯ in this case).
Efficiency here is how much information is packed into the digits for the level of accuracy. If two ratios are equally accurate, the one with fewer digits is more efficient. In the code, I defined the efficiency as -log10(error) / ((1+log10(numerator)) + (1+log10(denominator))). There might be better ways to rate the ratios, but that's what I used.
fyi1183 ยท 3 points ยท Posted at 17:38:22 on May 25, 2016 ยท (Permalink)
In general, the trick to getting surprisingly accurate rational approximations of irrational numbers is to cut off the continued fraction. This is where the examples for pi come from.
Neat fact: using continued fractions, if your denominator happens to be k, you get accuracy better than O(1/kยฒ).
Bmandk ยท 2 points ยท Posted at 17:30:17 on May 25, 2016 ยท (Permalink)
Yeah, but the operation is almost as long as the number of digits of pi it gets you, and then you have to actually do the operation to get the digits. Better just to memorize the digits. I memorized the first 25 as a kid and it didn't take me very long.
EDIT: I get it, duodecim is "12." But the numbers of the months don't match up with their names now, and maybe in the future there will be a bunch of silly month-names in between December and Duodecember, like "Drumpf" or "Half-Life 3."
bl1y ยท 10 points ยท Posted at 18:30:30 on May 25, 2016 ยท (Permalink)
Duodec is 12, not 22. Don't you remember the children's rhyme?
Or the 7th day of the 22nd month if you're American.
[deleted] ยท 4 points ยท Posted at 15:53:48 on May 25, 2016 ยท (Permalink)
Well, the 22th of July is the day the right-wing psychopath Anders Behring Breivik killed 77 people in and around Oslo.
So I have a feeling this day wouldn't be very popular in Norway.
eeeebbs ยท 3 points ยท Posted at 17:32:20 on May 25, 2016 ยท (Permalink)
It's also my birthday :):
twbk ยท 2 points ยท Posted at 16:45:04 on May 25, 2016 ยท (Permalink)
My thought too. I think we'll stick to 3.14, or the third of dodecember or whatever the fourteenth month is called.
I had a math teacher once whose answer key for a test was done using 3.14. I used the pi button on my calculator for calculations and she marked half my test wrong. I had to sit down with her and basically re-type each question into my calculator to show her why my answers were slightly different... :/
jusjerm ยท 7 points ยท Posted at 16:31:30 on May 25, 2016 ยท (Permalink)
It is possible that you were instructed to use 3.14 as an approximation in the test directions. My time as a teacher assured me that words written in bold between tests questions might as well be invisible.
This is (maddeningly) done because certain standardized tests ALSO tell you to use the 3.14 approximation rather than pi
If you can memorize 3.14 adding two digits is reasonable. 3.1416 (3.14159) will probably cover all situations outside of space travel to sufficient accuracy.
I had a middle school teacher who told me something like that ("Pi is pretty close to 22/7! Neat, huh?") and I forgot about half of that ("Pi is pretty close to 22/7!"), so when high school rolled around I had a hard time figuring out why everyone thought pi was such a big deal. It's just a dumb magic fraction, right? Nooope.
The fastest known algorithm for calculating the value of pi uses an infinite sum. The more terms you include, the better the approximation, essentially. Including the first two terms of the sum is enough to get an approximation with a relative error of just 0.0000000000000000000000000001 percent.
I divided by zero once. It was pretty cool at first but then the room started to spin and my hands got all clammy. I had to call my friend over, I told him what I did and he was real dissapointed but of course interested in what it was like.
you should probably see a doctor to make sure your liver is still on the left side of your body. last time my friend did this, he ended up in a parallel universe where everyone's internal organs were reversed.
AnonZak ยท 3 points ยท Posted at 22:09:34 on May 25, 2016 ยท (Permalink)
You made a crucial mistake when you attempted to go at it yourself. I wrote a program to constantly divide by zero in my stead. I'm still trying to close the portal to hell...
Nope. Take a pie and cut it into one piece. That means you now still have that same lie. Dividing by one (or multiplying by one) is the math equivalent of sleep.
Dividing by zero is asking to cut the pie into zero pieces. No matter how many times you cut, you will still have not-zero pieces. Dividing by zero is bad and doesn't work and is bad.
Dividing by zero is performing an operation, though. It's not about being Zen - it's about understanding what the operations mean at a fundamental level. Dividing (or multiplying) by one is doing no math on the pie. That's why 1 is the multiplicative identity.
Had an argument with my mate about dividing by zero, he was convinced it equaled infinite, I was like wtf mate, we're both doing a degree in astrophysics, you should know this :/
In the real numbers the limit doesn't even tend to infinity, it doesn't exist. In other number systems though 1/0=infinity. An example is the extended complex plane.
The limit doesn't exist strictly speaking, but approaching from the left will make it tend towards -infinity and from the right +infinity, so you can say approaching from either side will tend towards positive or negative infinity.
It tends to infinity, the limit doesn't exist. The limit itself doesn't tend to anything, strictly speaking, but both of those are true. Some people are fine with saying the limit is infinity.
Oh, you're right. I thought the argument was over whether the limit exists at infinity or does not exist, but the limit as x approaches 0 of 1/x doesn't exist.
Doing it the right way, you can. Mathematicians do it all the time, it's just that arithmetic with infinity has a lot of special cases so it's harder to teach to nonmathematicians.
q3w3e3 ยท 1 points ยท Posted at 16:47:39 on May 25, 2016 ยท (Permalink)
I suck at math, but I would think it would just be zero. 1/2 (1 divided into two parts) is .5. 1/1 (1 divided into one part) is 1. So 1 divided into 0 parts seems like it should be 0. Where does the tricky part come in?
0/0 is not defined in any context I know of. However it is true that as an indeterminate form is can be any real number.
Adarain ยท 12 points ยท Posted at 16:39:58 on May 25, 2016 ยท (Permalink)
The nice thing about math is that it's really hard to break. You can define 1/0 to be whatever you please and then see what happens. For example, if I define 1/0 = q (a number I just invented), then what is q+1? Let's see...
q+1 = 1/0 + 1/1
Well, that is a bit unfortunate, we can't really sum those up... though... we allow division by 0 now, right? And it ought to work like any other division, so let me just expand that...
1/0 + (10)/(10) = 1/0 + 0/0 = (1+0)/0 = q
So q+1 = q, and the same proof can be extended to any q+x for x =/= q.
What about q+q? That's easy, 1/0 + 1/0 = 2(1/0) = 2q
So q behaves like we'd expect when we add it to multiples of itself.
If you play around a bit more, you'll find that our q acts just like 1 did before, and 1 (and any non-q multiple of it) acts like 0 did before. So we just created two parallel number systems that can be converted in between by dividing by 0. Neat, huh? (Also, I wonder whether this has any other neat properties that I missed. I haven't really experimented with this very in-depth)
Yup, even if you only look at logical inconsistencies in q and not real numbers, you can show that anything involving q breaks communitiviy and distributivity.
The nice thing about math is that it's really hard to break.
The awful thing about math is that it's really easy to break and have everything look like it still works on the surface.
[deleted] ยท 1 points ยท Posted at 19:43:42 on May 25, 2016 ยท (Permalink)
Not really. I'm only assuming the "facts" that /u/Adarain has given (in addition to, of course, a few axioms of arithmetic); namely that there exists some number q equal to 1/0, and division by 0 works "exactly the way any other division should"; that is, if a/c = b, then a = bc.
If you're going to call me "presumptuous" because division by 0 doesn't work "exactly the way any other division should", then you're merely stating my conclusion, so your comment is useless.
Or you could at the rule "you can't multiply by 0" in your system if you want to get creative.
Or we could just add the rule "you can't divide by 0". Oh wait...
Anyway, multiplying by 0 is useful and intuitive. If I have 9 people, each with $0 in their bank account, then they have in total 9*0 = $0. It's dividing by 0 that isn't. "If I divide $100 between 0 people, how much does each person (who doesn't exist, since there are 0 people, but must exist for anyone to "get" anything) get?"
If we wish to go deeper into theory, we must have multiplication by zero in order for the real numbers to be a field (which has nice properties). Division by zero instead wouldn't allow such nice properties.
But the main reasons we work in the "don't divide by zero" system are that it reflects real life, and that it lets the real numbers be a field. This is far better than your "don't multiply by zero" system.
Tobl4 ยท 2 points ยท Posted at 17:46:27 on May 25, 2016 ยท (Permalink)
So I don't think this checks out as a closed field. You could obtain any scaling of q that you wanted for q/0 by swapping out other numbers for the 2 and 1 there.
Tobl4 ยท 1 points ยท Posted at 22:01:26 on May 25, 2016 ยท (Permalink)*
Now I'm wondering, can we just introduce the q down there? Because in that case it seems like it would also be true that
Yeah, everything you just said is correct in the sense that, given the rules the guy above defined, you can correctly derive these (all contradictory) results.
This is because he mistakenly thought that because nothing immediately broke when trying to do a few quick algebraic examples on 1/0, that treating 1/0 as a valid mathematical construct is an ok and "non-math-breaking" thing to do, when it in fact is not. These contradictory results are exactly why 1/0 is not defined in the real number system. Actually any one of them is sufficient to prove that we "broke math" by assigning a distinct real value to 1/0.
For binary logic a->b is exactly the same as b/a if you assume division by 0 gives you 1. (You only get false for 1->0)
I created an entire class of algebraic objects around this idea called implication rings.
Now you have some incredibly wacky axioms you have to define to make things nice and neat and I don't really want to pore through my dissertation to enumerate them.
Of course these things aren't rings at all but I got them pretty darn close.
Haha I'm an idiot, I read that as "if you assume 1/0 gives you 1", and I thought "man, I swear 0->0 is 1 but 0/0 is undefined..." until I reread what you said.
That's really neat though. How did you come up with the idea, was there a real application, maybe computer related? Out of curiosity's sake, is there a specific interesting yet accessible axiom you'd like to share? I'm an undergrad just getting into math and I've been dying to take topology, so I'm drooling when I see someone with something interesting to say lol.
I'll PM you the relevant portion of paper tomorrow.
Honestly I don't know precisely what good these algebras are. I'm a teaching mathematician so I really just shelved the idea. The real key is understanding the homomorphisms between them. Perhaps there could be applications in logic, unfortunately I'm not an expert in that.
A lot of topology you can sort of self teach, basic topological proofs are incredibly good for building a good abstract mindset.
Awesome :) I'm a computer engineering student so whenever I hear "binary logic" I perk up a little. I found a pretty awesome old little topology book abandoned in the attic of my college's main building so I've been able to tide myself over for now.
[deleted] ยท 4 points ยท Posted at 15:35:00 on May 25, 2016 ยท (Permalink)*
[removed]
aonome ยท 1 points ยท Posted at 15:43:14 on May 25, 2016 ยท (Permalink)
he probably means that if you divide a number by any number and it gets smaller and smaller it gets closer to infinity. For example if you divide 1 by 0.1 you get 10, if you divide 1 by 0.01 you get 100, and so on...
edit: On many calculators or even computational engines, if you input something like 1/0 you will get infinity, or close to infinity. For example on Wolfram alpha you will get close to infinity
2nd edit: And after many years I've actually found something that will prove that it is never actually infinity (The more you know) :P https://www.quora.com/Is-1-0-infinity
aonome ยท 1 points ยท Posted at 18:25:07 on May 25, 2016 ยท (Permalink)
It seemed like he was agreeing that you can't divide by zero in standard arithmetic but it didnt make much sense is all.
This is actually true, doing it the right way, you can divide by zero. Mathematicians do it all the time, it's just that arithmetic with infinity has a lot of special cases so it's harder to teach to nonmathematicians.
this reminds me of a funny story. 4 years ago, i wanted to try acid for the first time, so i called up a buddy who gave me a pack, and told me to ONLY EAT ONE first and test it out, and soon you can increase your dosage, forgetting to tell me how long it would take to kick in. so i got back home, took one, and waited 5 mins, nothing happened. took another, waited 5 minutes, still nothing. i told myself fuck it, ill take another two. another 5 minutes passed and i was like fuck maybe im immune to acid. so i ended up googling how long it would take to kick in, and i got the answer, it was 30 minutes! so i decided to divide 30 by 4, coz i was guessin it would take 1/4 of the time to kick in coz i took 4! i took out my calculator, missed the 3, typed in 0/4 instead, pressed equals and
Zolden ยท 1 points ยท Posted at 16:23:24 on May 25, 2016 ยท (Permalink)
I once divided by O, and notging happened, but everyone was under impression, that I perfirmed division by 0. One lady even passed out.
c3534l ยท 1 points ยท Posted at 16:28:50 on May 25, 2016 ยท (Permalink)
I had a finance professor yesterday assert that you can't divide by zero because the answer is infinity and infinity is impossible. Then he went on to reason about a formula where he divided by zero and argued the solution to that one part was "some impossibly big number." These are the people running our stock markets...
I mean, as long as no one is watching so that no one could determine who did it.
zarraha ยท 1 points ยท Posted at 16:54:55 on May 25, 2016 ยท (Permalink)
I divided by zero once. Then I wrote down an equation which was false, and used regular algebra rules to turn it into another equation which was also false, and then wrote down 1 = 0, which is false.
You just have to do it really really fast so that the Intergalactic Police can't spot you
onzie9 ยท 1 points ยท Posted at 17:55:25 on May 25, 2016 ยท (Permalink)
Division by 0 is actually perfectly possible in some areas of math. We usually dress it up, though, depending on the application. Localization is a fancy way to divide; while localization at 0 (dividing by 0) isn't wildly useful, it doesn't necessarily break anything, either.
Provided you're not a pure mathematician, and that you know what you're doing, you can divide by 0 quite easily. You just have to make sure you're dividing 0 by 0.
A friend of mine once tried to turn in a math assignment he didn't do by burning a large hole in the middle of his paper with a lighter and pretending that he tried to divide by zero.
[deleted] ยท 1 points ยท Posted at 18:25:38 on May 25, 2016 ยท (Permalink)
Don't do it! You will awake the Old Ones!!
There are things man aren't meant to know!
You will doom us all!!!!
Nerf190 ยท 1 points ยท Posted at 18:26:33 on May 25, 2016 ยท (Permalink)
Since there seem to be people good at math here, isn't x-0 always just equal to one? I haven't done math in a long time but I thought this was true.
x-0 is indeed 1 for all real numbers x. How does that cause problems? Even if you think of x-0 as 1 / x0, which I'm assuming is what is causing you confusion, that still evaluates to 1/1 = 1.
My calc professor had a very bad burn scar covering about half his face and started off the semester by telling us the story of how he got it. He said he was a young boy doing math homework in his basement and tried to divide by zero.
the relativity fanboys sure do it a lot. you get all kinds of awesome stuff like black holes. they get "infinities" somehow. even as a school kid I learned you can't divide by zero. it isn't infinity, it is undefined
[deleted] ยท 1 points ยท Posted at 21:00:41 on May 25, 2016 ยท (Permalink)
If I had 6 pieces of pizza divided by 0 people wouldn't I just have 6 pieces of pizza? I've never understood why X/0 isn't X. I know it isn't, but it doesn't make sense.
You actually get โ when you divide by zero (if you take the limit).
i.e. If you take 1/0.1 you get 10,
1/0.01 you get 100,
1/0.001 you get 1000,
and so on.
Take a decimal so (infinitesimally) close to zero, like 0.000....0001, and you're gonna get a HUGE number. That's why dividing by zero technically gives you infinity.
b4b ยท 1 points ยท Posted at 21:56:10 on May 25, 2016 ยท (Permalink)
Don't drink and derive!
labdog ยท 1 points ยท Posted at 22:24:43 on May 25, 2016 ยท (Permalink)
You can divide by 0 in JavaScript. The result is Infinity or (-Infinity) depending on sign of the number divided by 0. I think it may even give correct results with very small signed numbers used as "positive and negative almost zero". And you can do it even when everyone is watching. This is possible because JavaScript just assumes the result of division by zero is equal the result of division by "positive almost zero". With this assumption the operation (and estimated answer) is correct. It behaves pretty nicely with estimating limits. And it's pretty intuitive that numbers exceeding maximum or minimum variable value are substituted by Infinity and (-Infinity). Statements made with such notation are almost obviously true. If you divide by a number sufficiently close to zero - the result will surely overflow the variable. This overflow is really a nice feature to have. In computer programs there a limits to any value. If you apply Infinity values to comparisons - you end up with the limit values. So you get pretty deterministic operation without hardcore math involved.
1/0 = infinity. Zero is simply infinity-1. In this way you can perform all mathematical operations involving zero and infinity with no information loss.
askold9 ยท 1 points ยท Posted at 02:24:04 on May 26, 2016 ยท (Permalink)
When I divide by zero I try to LIMIT myself
[deleted] ยท 1 points ยท Posted at 03:30:51 on May 26, 2016 ยท (Permalink)
Dividing by zero makes me better at my job actually
Late to the party, but you actually need to divide by zero in some cases when finding limitations in the case that x approaches infinity - keep in mind this does not mean dividing by zero equals infinity. Also, you don't actually write down you are dividing by zero because that is illegal and wrong - but you have to mentally do it to find the limitation.
mepwwn ยท 1 points ยท Posted at 23:56:37 on May 26, 2016 ยท (Permalink)
I love that Reddit can go from 0 to Monty Python in less than 2 comments regardless of what the original comment was about. Hmm maybe that's my math fact to contribute.
We accept them as our new overlord?
I mean thinking logically, we have little chance against someone who can use magic, when we on the otherhand only can use pitchforks and torches
Sinetan ยท 6 points ยท Posted at 12:57:37 on May 25, 2016 ยท (Permalink)
What's the airspeed velocity of an unladen swallow?
I understand that, but I had never heard the term until the card. I haven't researched all that much Greek so it was a new word for me. I was just wondering where u/banfromallsubreddits had heard the term from originally.
Dunan ยท 2 points ยท Posted at 15:32:43 on May 25, 2016 ยท (Permalink)
Illuminati confirmed
Ah, you see the connection with the sum of the digits of the year of the Illuminati's founding, '76. How could you possibly have known I was a member of-- wait, the Illuminati are a myth. They disbanded long ago. If they existed. Which we don't. ...I mean, they don't. Shhhhh.
Dunan ยท 2 points ยท Posted at 20:12:45 on May 25, 2016 ยท (Permalink)
Wasn't there a guy in the movie City Slickers who could the number of letters in phrases effortlessly? I hope it was the Jon Lovitz character. That guy is always hilarious.
Dunan ยท 1 points ยท Posted at 21:59:31 on May 25, 2016 ยท (Permalink)
It looked for a moment like the phrase might happen to have 13 letters, and I thought "eleven plus two", let's see, 6, then 4, then 3; it works! And since "twelve plus one" has the exact same letters (only in a different order) it has to work too. ^_;
I've always thought 12 and 11 were the most magical of numbers. The 11 multiplication trick...time is divided into 12 months, 12 hours,
I was 11 the first time I hid a body, and 12 the first time I killed a man in cold blood.
Time traveled or figured it out rather. How would he hide a body if he didn't kill anyone? This guy ain't no joke so it's not like he hide a body his friend killed, no he figured out time travel and covered up his own murder.
A friend once designed a base-12 digital clock. It used the standard 7-segment LED digit displays, and he had to invent glyphs for the eleventh and twelfth digits, i.e. those coming between "9" and "10," base 12. I found his solution to be genius: for the eleventh digit he illuminated the bottom horizontal bar and entire upper half of the 7-segment cell, and for the twelfth digit he illuminated just the middle and bottom horizontal bars. The genius part was that if you tilted your head to the left :-) these were literally a tiny "10" and "11", coming right after "9," exactly as they should.
and when you turned 13, discovered that 3 inch stick between your legs has the power to give you pleasure, repeatedly, the blood letting ceased. right?
Dernom ยท 3 points ยท Posted at 14:51:36 on May 25, 2016 ยท (Permalink)
But that's not what OPs comment said, it said to take 12+1 and swap the 2 in 12 with the lone 1, so in the case of 13+4 you swap the 3 and the 4 to make 14+3. And you can't rearrange "thirteen plus four" to "fourteen plus three"
Brio_ ยท 7 points ยท Posted at 14:58:58 on May 25, 2016 ยท (Permalink)
You gotta say it with an accent. Fourteen plus thir.
Well, sure, it's a fact about a set with a very particular definition.
Here are more general formulations that avoid your objection.
"let {A} be the set of integers whose numeric and named representations in (given language) both participate in anagrammatic arithmetic"
Similarly, "let {E} be the set of integer arithmetic equations whose numeric and (given-language)-named representations both exhibit anagrammatic arithmetic"
Nigel Tufnel: The numbers all go to eleven. Look, right across the board, eleven, eleven, eleven and...
Marty DiBergi: Oh, I see. And most amps go up to ten?
Nigel Tufnel: Exactly.
Marty DiBergi: Does that mean it's louder? Is it any louder?
Nigel Tufnel: Well, it's one louder, isn't it? It's not ten. You see, most blokes, you know, will be playing at ten. You're on ten here, all the way up, all the way up, all the way up, you're on ten on your guitar. Where can you go from there? Where?
Marty DiBergi: I don't know.
Nigel Tufnel: Nowhere. Exactly. What we do is, if we need that extra push over the cliff, you know what we do?
Marty DiBergi: Put it up to eleven.
Nigel Tufnel: Eleven. Exactly. One louder.
Marty DiBergi: Why don't you just make ten louder and make ten be the top number and make that a little louder?
Nigel Tufnel: [pause] These go to eleven.
[deleted] ยท 1 points ยท Posted at 17:39:08 on May 25, 2016 ยท (Permalink)
I bet someone was really high and was testing all sorts of anagram combinations to come up with that.
Jerzeem ยท 1 points ยท Posted at 21:23:55 on May 25, 2016 ยท (Permalink)
This would be less fascinating if the names of some our numbers weren't stupid. Let me explain what I mean. We have the names of the digits, right? One, two, three, four, five, six, seven, eight, nine, ten (and zero.) Then we have place values, ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc.
For numbers that have place values of ones, you just use the digit name. For numbers that have place values of hundred and higher, you the digit and place value (one hundred, two thousand, three million.)
But we have special names for the numbers with ten as their place value: twenty, thirty, forty, etc instead of two ten, three ten, four ten. And even more special names for the numbers between ten and twenty: eleven, twelve, thirteen, etc.
If we called the eleven, "one ten one," (and called the other special numbers similar things) a lot of math would become somewhat clearer when it's being taught (if more verbose.)
But then 12+1 = 11+2 would just be written as, "one ten two plus one equals one ten one plus two." And that makes the fact that the letters are the same less interesting...
You can cut a sphere up into pieces, and then reassemble those pieces to get two spheres which are exactly the same as the first sphere.
It sounds impossible, but the following analogy might help:
Imagine you have a dictionary where every string of letters is a word, so the dictionary lists all strings of letters. So AAAA is a word, WXYZ is a word, even ZZZZZZZZ.........Z is a word. Now because the dictionary list all possible words, it also lists BAAAA, BWXYZ, BZZZZZZZZ.........Z, CAAAA, CWXYZ, and so on.
So, if we take all the words that begin with the letter B, we can remove the first B from all of those words then we will have a list of all the words in the original dictionary.
If we do this 26 times, we'll get 26 copies of our original dictionary, plus A,B,...,Z left over.
Infinity is weird.
[deleted] ยท 54 points ยท Posted at 15:33:38 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 16 points ยท Posted at 16:12:33 on May 25, 2016 ยท (Permalink)
Choice is only weird in the case of infinite sets. Finite choice is perfectly well behaved and provable from ZF
Hmm, I think axiom is choice is what solves it, to me it's the property of infinite sets to be divided into two and still be the same size that's weird.
I don't think so... But this stuff gets really counter-intuitive.
In my mind, infinity-infinity=0 but then if I have an infinite set of items and remove an infinite number of the items in that set, I would still be left with an infinite set by definition... I think.
[deleted] ยท 5 points ยท Posted at 17:45:46 on May 25, 2016 ยท (Permalink)
infinity-infinity=0
Here's the thing though, infinity isn't a number. You can't do arithmetic with it.
if I have an infinite set of items and remove an infinite number of the items in that set, I would still be left with an infinite set by definition
Not exactly. That's true for some infinite sets (in fact, it's true for an infinite number of infinite sets).
Let's say you have the set of all integers. Now remove the set of all even numbers. You're left with the set of all odd numbers which is still infinite.
But what if I have the set of all even numbers and I remove all even numbers from the set? It's still an infinite set removed from an infinite set, but now the set you're left with has size 0.
Now let's say we have the set of all natural numbers. Our next set is the set of all natural numbers, and then we add -1 to the start of it. Now if we remove everything in the first set from the second, we're left with a set of 1 term: -1.
Basically, infinity isn't a number and you have to define what type of infinity you're looking at when you do stuff with it.
Yeah, an infinite set of size one... Haha. That's what is so frustrating about the concept of infinite things.
[deleted] ยท 2 points ยท Posted at 19:57:50 on May 25, 2016 ยท (Permalink)
an infinite set of size one
The thing is after removing an infinite amount of values (all natural numbers) from that set (all natural numbers and -1), it's no longer infinite. It has a size one so it, by definition, is no longer an infinite set.
So, how much in can an infin ite if an infin can fin ite?
Lol, sorry. I'll see myself out.
Dr-K-G ยท 1 points ยท Posted at 17:23:06 on May 25, 2016 ยท (Permalink)
What do you mean?
[deleted] ยท 3 points ยท Posted at 17:32:50 on May 25, 2016 ยท (Permalink)
If there are an infinite number of rooms in the hotel and each room is full, one guest leaves and the manager moves every guest down a room. Is the hotel still full?
Dr-K-G ยท 2 points ยท Posted at 17:35:37 on May 25, 2016 ยท (Permalink)
A bowling ball does not have an infinite series of points, so therefore it is not a true sphere. In fact, nothing in the universe is a true sphere. This theorem has nothing to do with what can be done in the physical universe. But when you think about it in terms of purely mathematical objects, it's actually pretty clear that it is true and isn't quite as counter-intuitive as it originally seems. It's only counter-intuitive when dealing with physical objects because it can't actually be used with them.
More correctly, you can't break anything up into an infinite series of points. The problem is not the unreality of spheres, but the unreality of points, particularly infinitely small ones. The fact that the Plank volume is the smallest meaningful space possible pretty much rules out mathematical points.
It does, but it also breaks down before that with atoms. Breaking an object down smaller than that fundamentally changes what it is. It's probably fortunate that this isn't possible in real life though. Life is complicated enough already without duplication glitches.
[deleted] ยท 1 points ยท Posted at 02:09:57 on May 26, 2016 ยท (Permalink)
A bowling ball does not have an infinite series of points, so therefore it is not a true sphere.
Fucking thank you. This is the sentence that helped my poor brain stop falling apart. The concept of a "true sphere" being an "infinite set of points" and this paradox using this concept of a true sphere was completely lost to me, but knowing this makes the whole thing a lot easier to digest conceptually.
It doesn't show that at all. Just because you CAN do strange things in math doesn't mean that you cannot limit yourself to a certain subset of math and describe all physical things without any weirdness.
It's called a paradox because of the naive notions of measure beforehand made it a paradox, if we allow for the axiom of choice then it fixes the paradox. This is further complicated by the fact that die-hard set theorists look at the axiom of choice with extreme suspicion.
An implication of the axiom of choice is that every set is well-ordered. This means we can well order the real numbers, but it's been shown we can never explicitly give an example of such an ordering. The axiom of choice is a Pandora's box of logic. The day is saved by the fact if we extend our usual axioms to include the axiom of choice then if we arrive at a contradiction then it would have been there regardless of the axiom of choice being there, so it is nice in some respects, pathological in others.
[deleted] ยท -1 points ยท Posted at 17:29:31 on May 25, 2016 ยท (Permalink)
A paradox is something that is simultaneously true and false, a self contradicting statement. The Banach Tarski result is a theorem that is simply true in the framework of ZFC - which almost all mathematicians work under.
Paradoxes don't have to be both true and false. The important part of a paradox is that you start with logical premises and reach a seemingly illogical conclusion. The conclusion can be perfectly valid and still be a paradox. Look at something like Simpson's Paradox - nothing about this is "simultaneously true and false," but it's a paradox nonetheless because the conclusion doesn't appear to make sense given the premises.
a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true.
dh363 ยท 1 points ยท Posted at 20:06:08 on May 25, 2016 ยท (Permalink)
Paradoxes are not precisely defined, and one of its technically correct uses is something that is true but just seems false or unintuitive.
dh363 ยท 1 points ยท Posted at 20:03:57 on May 25, 2016 ยท (Permalink)
Paradox means seemingly contradictory or senseless but logically true and sound, so this is actually one of the few things people call paradoxes that actually is one.
Yes. The second is identical to the first. And so on.
971365 ยท 1 points ยท Posted at 16:14:55 on May 25, 2016 ยท (Permalink)
Infinity is weird..
natziel ยท 14 points ยท Posted at 15:44:02 on May 25, 2016 ยท (Permalink)
It really doesn't have anything to do with infinity. The pieces of the sphere (which are finite in number) have 0 measure (in this case, the measure is 3 dimensional volume), so it doesn't make sense to reassemble them into a shape with nonzero measure, hence the contradiction. Or you can explain the contradiction by rejecting the axiom of choice, lol.
Another example of measure theory is when you have a real number line from a to b. Suppose you pick a random number between a and b. There is a 100% chance that you pick an irrational number, because the Lebesgue measure (the length of an interval) of rationals is 0 (as with any other countable set), and the Lebesgue measure of [a, b] is a-b. So the probability of selecting an irrational is (L([a, b]) - 0)/L([a, b]), or 1. The probability is exactly 1, not 99.9999% or anything like that. Pretty neat.
[deleted] ยท 25 points ยท Posted at 16:12:20 on May 25, 2016 ยท (Permalink)
None of the pieces will have zero measure. They all have either positive measure or nonexistent measure. Banach Tarski works by the existence of nonmeasurable sets, and that has everything to do with infinity. Choice is only weird in the case of infinite sets. Finite choice is perfectly well behaved and provable from ZF
I'd say it really has to do with infinity. The point of measure theory (very roughly speaking) is to say how "big" sets are, and as you've said that's tied with their cardinality (e.g. countable -> measure 0). Without a proper understanding of infinity and set theory even the definition of measure (or of real numbers for what it's worth!) wouldn't make much sense.
Maybe my point of view is a bit skewed because that's my area of interest though!
can you explain in layperson's terms how exactly there's a literal 0 chance of picking a rational number? does this have anything to do with cardinalities of infinity?
natziel ยท 3 points ยท Posted at 18:23:45 on May 25, 2016 ยท (Permalink)
So, you understand that if you have the set of numbers between 0 and 4, your probability of picking a number less than or equal to 1 is 1/4, because (1-0)/(4-0) = 1/4. More generally, the probability of selecting a number in a subinterval within an interval is the quotient of their lengths.
So, the probability of selecting a rational would be the length of the rationals over the length of the reals. So, all that's left is to show that the length of the rationals is 0.
Because the rationals are countable, you can enumerate them such that Q = Union({q_i}, i = 1, i -> infinity). Pardon the notation. Since the length of each {q_i} is 0, the sum of the lengths is 0, so L(Q) = 0.
So, the probability of picking a rational is 0. Ergo, the probability of picking an irrational is 1-0.
There is 0 chance of picking any one number. There is an infinite amount of real numbers between any two reals a and b. If you pick at random from that interval the probability of, say c, being picked is 1/infinity which is zero. Any time you pick any number at random and actually get a number back is fucking spectacular given that there was literally zero chance for that number to be picked
dh363 ยท 2 points ยท Posted at 20:08:03 on May 25, 2016 ยท (Permalink)
So it has everything to do with infinity because the whole reason the axiom of choice gives you this weird is if you accept infinite choice. The axiom of choice on finite sets doesn't lead to anything weird.
It's something that, in theory, happens when infinity "is allowed to occur", so it's misleading to use terms like "cut up spheres" which are physical terms. It's not something that's physically possible.
Right yea, that's what I meant by mentioning non-measurable sets. I guess it would be better to say volume is not relevant so it doesn't prevent this unintuitive behavior from happening as it normally would.
Also, it becomes extremely obvious and not at all counterintuitive when you consider it this way: Take a ball (a solid). Represent it as an infinitely dense point cloud. Select half of the points by some method that results in the selected points being distributed uniformly throughout the ball. Move the selected points as a group to another location. You now have two infinitely dense point clouds the same shape and size of the original.
Okay I get your dictionary analogy, and how infinity works.... I just don't see how that applies to one sphere being cut into pieces and then reassembled into two spheres exactly the same as the first. I don't see what that has to do with infinity. Spheres have finite volumes and dimensions. And if it were some sort of infinity example, wouldn't you say you could cut up one sphere into pieces that could be made into an infinite number of other spheres of the same size as the first?
Pair the dictionary metaphor with the fact that circles and spheres are of an irrational circumference and surface area respectively, and you can put together how a sphere can be copied.
trey3rd ยท 1 points ยท Posted at 21:30:30 on May 25, 2016 ยท (Permalink)
How does removing the first a from aaaa make that a word in the dictionary? Am I missing a step?
Wouldn't you have a list of all the original words, minus one letter (the B?)
b4b ยท 1 points ยท Posted at 22:25:20 on May 25, 2016 ยท (Permalink)
So, if we take all the words that begin with the letter B, we can remove the first B from all of those words then we will have a list of all the words in the original dictionary.
What you wrote does not make sense. If you take out the first later of "BAAAA" and get "AAAA" you will never get "AAAAA" (5 letters "A"), you basically only get words that are 1 letter shorter.
I dont know why you are getting upvoted, I guess a wikipedia link + random nonsense, makes the nonsense legitimate.
So, your analogy isn't exactly what's going on. If you replace A through Z with 0 through 9, then what you're essentially saying is take the numbers 1.something, subtract 1 to get .something, and multiply by 10, and you get all the numbers from 0 to 9 again. Multiplying by 10 doesn't preserve volume. The paradox is that you can break a sphere into pieces, and then put the pieces back together in a way that only uses rotations and translations (which preserve length and volume) and the two spheres have the same volume as the original. The resolution of the paradox is measure theory. The idea is that you have to break up the sphere into sets that have no volume. So you have a set with volume V, then several other sets (the pieces) which can have no volume, and then a set with volume V' where V != V'.
I've heard it several times before, but this is the first explanation that really clicked! Like the first time I heard of Cantor diagonals. I guess with infinity, everything comes down to mapping like this.
imtn ยท 1 points ยท Posted at 02:14:11 on May 26, 2016 ยท (Permalink)
The last time I read about this, I realized that it was because the sphere used for that paradox is infinitely dense.
Crucially, into finitely many pieces (in finitely many operations). Otherwise someone might just think it's not much different than applying f(x) = 2x to [0,1].
Nlelith ยท 1 points ยท Posted at 09:40:34 on May 26, 2016 ยท (Permalink)
The really astounding thing about the Banach-Tarski Paradox is, that even though it deals with "infinities", it staes that you actually carve the sphere into a finite amount of pieces to double it.
[deleted] ยท 1 points ยท Posted at 13:46:31 on May 26, 2016 ยท (Permalink)
That is ... a really bad analogy. Furthermore, Banach-Tarski is only valid if you accept the axiom of choice.
Okay, my point being that B-T isn't a "fact" like many of the other comments are. It requires more than our standard assumptions in ZF (but yeah, sure, people are mostly fine with AC nowadays, and the facts on this page all rely on axioms too, so aren't really facts at all, because they are based on underlying assumptions and oh my god nothing is true anymore).
Start by picking your favorite spot on the equator. You shuffle the deck of cards once every second. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.
Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time youโve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits havenโt even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still wonโt do it. There are still more than 5.385e67 seconds remaining. Youโre just about a third of the way done.
To put it otherwise if someone makes you a wager where they shuffle two decks and if the cards are in the same order they get to kill you and if not you get a dollar you play that game until you're richer than Bill Gates.
If someone bets you they can shit wooden nickels, it's probably because they have a technique for shitting wooden nickles.
[deleted] ยท 30 points ยท Posted at 20:23:05 on May 25, 2016 ยท (Permalink)
One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you're going to wind up with an ear full of cider.
Old Guy: "Betcha twenty bucks I can't bite my right eye." New Guy: "You're on." Old Guy takes out his glass eye and bites it Old Guy [as he's putting his eye back in]: "Double or nothing says I can't bite my left eye." New Guy: "You ain't got two glass eyes. You're on." Old Guy removes his false teeth, uses them to 'bite' the other eye
A drunk walks into a bar with a friend and goes to talk to the bartender. Drunk: "Betcha twenty bucks I can bite my right eye." Bartender: "You're on." Drunk takes out his glass eye and bites it Drunk [as he's putting his eye back in]: "Double or nothing says I can bite my left eye." Bartender: "You ain't got two glass eyes. You're on." Drunk removes his false teeth, uses them to 'bite' the other eye Drunk: That's $40. Alright, last one. I'll bet you double or nothing on the whole tab that I can stand on my stool and piss into this glass on the bar without spilling a drop.
Now at this point the bartender is suspicious but finally agrees. The drunk stands on his stool, pisses all over the bar completely missing the glass and the bartender jumps with joy. When he turns to the drunk he notices the drunk is also grinning. Bartender: Why are you so happy? I got my money back. Drunk: I bet my friend $100 that I could piss on your bar and you'd not only let me but be happy that it happened.
Hand shuffles are never truly random. Many people don't cut between shuffles and the top card will always be in the top 10% of the deck afterwards, it really limits the shuffle. Same reason why when you play poker with friends better cards end up showing more often later in the game (lower card values are folded first putting them lower in the deck).
mr_ewe ยท 3 points ยท Posted at 16:13:44 on May 25, 2016 ยท (Permalink)
I just watched a YouTube video about this a few days ago.
That isn't true for card games like hold'em where lots of cards are folded and burned from all around a physical table, where the first cards don't necessarily go to the bottom of the deck when retrieved.
You can confirm for yourself, take a deck of cards and add one card that has a different color back to the top. Shuffle the deck a few times (try to do it the way you normally would) and see where the card you put on top ends up. It will never, ever be on the bottom if you did the test honestly, and usually in the top 10%. Showing that hand shuffles are not random.
aegluc ยท 1 points ยท Posted at 17:42:12 on May 25, 2016 ยท (Permalink)
Assuming you are shuffling perfectly (One card from Side A, one from Side B, one from Side A, etc) and do just five rifle shuffles, the card that started on top can end up anywhere from Slot 1 to Slot 32.
Again, once you do 7 rifle shuffles, it has proven to be mathematically random.
That's not really what chaos theory deals with in a mathematical sense. But yes, you could get extremely unlucky. The odds of that are small. Really really really really small.
That's not what chaos theory says. Chaos theory describes systems where an arbitrarily small perturbation in the starting conditions can yield arbitrarily large changes in final conditions; and also describes attractors and suchlike systems.
It doesn't say anything that would lead you to conclude that two independent card shuffles are more likely to come out the same than you would expect by chance alone.
So which theory is it that concludes anything could happen at any time.? Isn't there an infinitesimal chance that the cards could just disappear also?
I remember reading about if you were to spend all your time pushing against a wall, there's a chance, at one point, you may push through it..
Maybe mathematically, but first of all decks don't start in a random order, and second, people don't shuffle randomly so the chances are still slim, but not ridiculous.
I know you're getting meta but that's a rule of thumb and the term "arbitrarily large," which is relevant there is meant to be vague enough to imply whichever number is big enough to make the statement true. 50 makes this work for most real life probabilities but definitely not something as minuscule as what we're talking here.
What their equation meant is that if something has a 1/x chance in happening and you do it x times the percent chance it happens will be 63%
There are a couple of places I've heard that. I learned something very similar to that from my Stats teacher in highschool before I ever saw it on Vsause. That is a mindbogglingly large number that actually influences our everyday life.
I first read it here...don't know which one was first though
Deasy_ ยท 11 points ยท Posted at 13:58:30 on May 25, 2016 ยท (Permalink)*
That was first, I remember finding that out then seeing the VSauce video uploaded like a week later!
EDIT: I'm not saying VSauce copied it, just pointing out the coincidence for me in learning of the fact then VSauce uploaded the video talking about it
This is an example of something that is so blatantly the work of a single person (or group) but yet people for some reason don't feel the need to cite that one person. I understand if you don't cite someone if you coincidentally happen to come to the same solution as them. But that is not the case here. Nobody else is just going to happen to come up with the conclusion that you need to start walking around the earth and removing drops of water from the Pacific Ocean and then stacking sheets of paper to the moon and filling the ocean back up and reaching the sun then unstacking the papers and repeating thousands of times.
In order to even recite the fact with as much accuracy as done here, you'd need to look it up anyway! So he didn't even pull it out of memory and say "I don't remember who came up with this." He found a source for this fact which is not common knowledge and then didn't cite the source that he just found.
Vsauce gave the original creator full credit. /u/canyoutriforce is just some dude on the Internet reciting a math fact. Just like most other people in here.
[deleted] ยท 4 points ยท Posted at 13:49:49 on May 25, 2016 ยท (Permalink)
Funny enough I said that I was facsinated by supertasks and cited a source of information: a vsauce video and got downvoted for it. This guy quotes a vsauce video verbatim giving no credit whatsoever and gets 1900+ upvotes.
People never fully comprehend the almighty power of putting ! at the end of a number. Like, you've got the number 100. That's a normal sized number, not too big. But look what happens when I put an ! at the end. Rounding up to one significant figure it becomes 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(That's 1 followed by 158 zeroes for the curious)
[deleted] ยท 75 points ยท Posted at 14:18:08 on May 25, 2016 ยท (Permalink)
10 unquinquagintillion
[deleted] ยท 66 points ยท Posted at 14:58:02 on May 25, 2016 ยท (Permalink)
I see you have been playing AdVenture Capitalist
cwf82 ยท 6 points ยท Posted at 17:32:41 on May 25, 2016 ยท (Permalink)
All I know about large numbers (I.e. beyond quadrillion) comes from AdCap
I was going more for the fact that 9.332...*10X rounded to one significant figure is 9*10X . Rounding it to 10*10X or 1*10X+1 is... well, less correct, and as my old maths teacher would say, is a crime worthy of being sent to Maths Prison.
Not that it's overly important, of course, it's just the idea of rounding up to a significant figure is weird in my head.
jelloey ยท 3 points ยท Posted at 15:49:00 on May 25, 2016 ยท (Permalink)
I have a very high level of knowledge in scientific fields and I'm currently working on a mathematical paper that may change the world, I think I can round numbers
9.3 is closer to 9 than to 10, as simple as that
_kst_ ยท 2 points ยท Posted at 02:31:54 on May 26, 2016 ยท (Permalink)
Part of me just wants to have another reason to chuckle when I see "omg!!!" or something. Like, "hey, depending on your values for o, m, and g, that's probably a danged big number."
Factorials are numbers just like anything else so you can do anything you can do to a number. For example, 5! = 120; 55! is just 5120. 5!! is 120!. (5!)! is also 120!.
_kst_ ยท 1 points ยท Posted at 02:35:54 on May 26, 2016 ยท (Permalink)
I wonder how awkward it must have been to be sitting at your office desk, typing "0", with a gaze that could set a stack of papers aflame, all-the-while counting every single one. "...101...102...103..."
I put it at the end of all my sentences! That way people hear me and know I'm serious!
nnyx ยท 1 points ยท Posted at 19:28:45 on May 25, 2016 ยท (Permalink)
I think it's less that people don't understand factorials (although I'm sure plenty of people don't) and more no one understands numbers that are even remotely close to that big.
Even imagining what 1000 of something looks like is hard without breaking it into smaller pieces.
Once you get past a million or so, in most peoples minds, it only registers as "really big number".
[deleted] ยท 1 points ยท Posted at 20:42:25 on May 25, 2016 ยท (Permalink)
(That's 1 followed by 158 zeroes for the curious)
That is 10158, just to give a perspective there are ~1080atoms in the observable universe.
kyune ยท 1 points ยท Posted at 06:26:32 on May 26, 2016 ยท (Permalink)*
Factorials are difficult to relate to--even if you're familiar with binary powers (2x), conceptually making the jump to factorials is difficult to understand without a math background. And even if you did, you quickly end up with numbers that are practically unintelligible without crafted stories and analogies.
A significant figure is the first digit after a zero and every subsequent digit, as I was taught.
You, sir, have a lot more significant figures.
1 x 10158 seems about right though.
klod42 ยท 1 points ยท Posted at 10:29:43 on May 26, 2016 ยท (Permalink)
One of my professors used to say "Exponential growth is intuitively ungraspable" (I can't translate it better). Factorial grows even faster. We can't even really comprehend how fast the number grows when you keep adding zeroes to it, let alone factorial.
100! is far more than number of atoms in observable universe. Many, many orders of magnitude larger. To my knowledge, no physical size exists that would be described by such a number. But it's still less than number of ways to shuffle a double deck of cards.
saab121 ยท 1 points ยท Posted at 13:47:59 on May 26, 2016 ยท (Permalink)
JTswift ยท 214 points ยท Posted at 14:12:22 on May 25, 2016 ยท (Permalink)
I know 52! is a big number (as you typed), but this one is just really hard to fathom.
Steps around the world, drops in the Pacific Ocean, then pieces of paper to the sun. It's all so absurd that it kind of fails in its intent, in my opinion. It's almost like trying to imagine infinity.
If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
JTswift ยท 5 points ยท Posted at 15:02:55 on May 25, 2016 ยท (Permalink)*
So, each person can shuffle a trillion packs of cards at a time?
Just change it to a trillion of these galaxies and only one deck per person and you'd have the same thing
Crully ยท 0 points ยท Posted at 17:47:10 on May 25, 2016 ยท (Permalink)*
Is that the total shuffles for the number, or does that take into account the fact that working with random numbers you would hit a collision before you get to the final number.
Sorry not a mathematician, what I mean is on a smaller scale if you had to pick a random number between 1 and 1000, you wouldn't need 1000 goes to get a number two times.
Edit: Why I'm downvoted, I'm just asking a question because I didn't understand the above post, this is the AskReddit sub right?
Yeah, it's easier to say something like: if you shuffled a deck of cards randomly a billion times a second since the beginning of the universe, you'd still today only be a little over a third of the way through the possible combinations.
Another fun math fact involving powers: when we ran out of IPv4 addresses, and came up with IPv6, we really fixed the problem. IPv4 addresses are a 32 bit number, and IPv6 addresses are a 64 bit 128 bit (oops) number. This means that there are 4.3 billion IPv4 addresses in total, but there are more IPv6 addresses than there are atoms in the observable universe.
Teo222 ยท 10 points ยท Posted at 16:38:10 on May 25, 2016 ยท (Permalink)
Actually we fixed it by 25 orders of magnitude more than you think. It's 128 bit..
You could easily give each user a 32 bit segment and still have no problem at all, fitting all devices
shinyM ยท 4 points ยท Posted at 16:59:22 on May 25, 2016 ยท (Permalink)
I was trying to explain this to co-workers who didn't quite understand the magnitude. They just believed that the number of addresses went up by a power of 6.
I explained to them like this:
Our current IPv4 internet has 232 addresses -- including the ones already reserved. IPv6 has 2128 addresses. an IPv4 /30 block (1 network address, 1 broadcast address, 2 usable addresses) is akin to an IPv6 /126 address.
So -- an IPv6 /96 block is the size of our current IPv4 internet.
a /95 block is 2 IPv4 internets.
a /94 block is 4 IPv4 internets
[...]
a /64 block is is 232 IPv4 internets. Meaning that if every single IP address in an IPv4 block had its own separate, full IPv4 internet -- that's the number of addresses you'd have.
... and then their heads would explode when we advised that we were designating /48 blocks to our enterprise customers. :)
I think we'll have enough addresses for a little while...
Yeah, but when IPv4 first came around, engineers across the globe would tout "you'll never need more addresses than this. This is good."
Then, whaddaya know, we ran out of IPv4 addresses ahaha. Now this isn't to say we're poised to build and connect more devices than there are atoms in the observable universe, but virtualization is only getting more popular. It may not be within our lifetime, but we will run out of IPv6 addresses as well.
Every virtualized system will require at least multiple atoms to track its state. That's not going to be what does us in. What does us in is people handing out /32's to ISPs and hosting companies, probably.
The point is that there is no way to represent this number in a way that makes sense to you. I've read, can't remember where, that numbers above 1 million are basically impossible for the human brain to actually conceptualize so we just generally imagine it. Assuming that's a low ball estimate and we can really imagine a million millions (also known as 1 trillion) then you would still need a trillion trillions. Times a trillion trillions. Times a trillion trillions(almost, a bit shy).
What I'm saying is that there is no way to make this description make sense because it its orders of magnitudes larger than our ability to even comprehend a number. To make this understandable would require cutting it up into steps less than a million, which would be a 16 part process that would get confusing very quickly because, again, the numbers just stop meaning anything to you.
You could make it make sense just by using concrete measurements like time and distance alone. I don't know how many drops of water are in the Pacific ocean, a drop of water is a subjective unit of measure and the Pacific borders other bodies of water
The problem is those numbers wont mean anything to you. As another reply stated "1 million seconds is 11 days. 1 billion seconds is 31 years." As you can see, moving up an order of magnitude makes a big difference. Now you need to move up another 19 times. The numbers are just too big to do anything meaningful which is, again, the whole point.
JTswift ยท 3 points ยท Posted at 15:39:46 on May 25, 2016 ยท (Permalink)
1 million seconds is 11 days. 1 billion seconds is 31 years.
SKR47CH ยท 1 points ยท Posted at 15:45:16 on May 25, 2016 ยท (Permalink)
Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.
I've heard it put more simply, just that it's a statistical near certainty that no two shuffles have ever been the same.
I've interpreted this to imply that shuffling isn't really that important, and when I deal at poker night I typically just cut it once, fold it into itself, and cut it again. That adds enough uncertainty and I'm pretty sure that the odds of ever seeing the same deal come out of two deals in a night, or even in the course of our three month tournaments, are astronomical.
Another way to think about it is to consider the fact that every time you shuffle a deck of cards there is a nearly 100% chance that the resulting order is completely unique in human history, assuming a legit, random shuffling.
[deleted] ยท 1 points ยท Posted at 03:09:32 on May 26, 2016 ยท (Permalink)
Let's say there are 7 billion people on Earth. Now, for each person, you make a tiny model of the Earth, complete with 7 billion tiny model people. This is the second iteration of "people" and it contains about 4.9E19 model people. But that's not enough, so in every model, you add 7 billion even tinier Earths, with their own people. That's the third iteration.
It takes SEVEN ITERATIONS to get to a number of people that's larger than 52!. Almost exactly 10 times larger, in fact. This isn't a very good cue, I suppose, but it's a really difficult number to visualise however you go about it.
necrow ยท 16 points ยท Posted at 13:57:16 on May 25, 2016 ยท (Permalink)
I like this so much better than the original. Ive always hated that one cause it adds so many unnecessary steps and details.
[deleted] ยท 2 points ยท Posted at 14:38:55 on May 25, 2016 ยท (Permalink)
The number of possible outcomes is approximately the same (1068) as the number of atoms in our galaxy.
Start by picking your favorite spot on the equator. You shuffle the deck of cards once every second. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.
Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time youโve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits havenโt even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.
So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still wonโt do it. There are still more than 5.385e67 seconds remaining. Youโre just about a third of the way done.
ktkps ยท 1 points ยท Posted at 06:21:15 on May 26, 2016 ยท (Permalink)
If we had a road to the sun and we got in a car travelling at 65mph toward the sun we'd burn up before we got there. But if we couldn't burn from it we'd die of radiation poisoning. But say space relating things couldn't kill us we'd still die of old age.
I honestly couldn't believe it, because it sounded so absurd. I fired up Wolfram Alpha to proof your calculation.
We shuffle the deck every second. So the ammount of seconds it takes us to go around the earth will be equal to the number of times we shuffled the deck. We move with the speed v of 1m/1billion years. Our distance s is the length of the equator. Formula is t=v/s, which leaves us with 1.2638057ร1024 shuffles for "running" the whole distance once.
Every time we do that, we remove one water droplet from the pacific ocean. We assume that one water droplet has a volume of 50ยตl (0.05ml), I couldn't find a value on Wolfram Alpha for that. To get the number of times we have to remove a droplet, we take the voulme of the pacific and divide it by the volume of a water droplet, which leaves us with 1.32ร1025 number of times to empty the ocean.
Last but not least we put papers on top of each other for every time we emptied the ocean. To get the number of papers we need we divide the distance from sun to earth by the thickness of paper. This leaves us with 1.492ร1015 papers.
Because we have to complete one task to take a step in the next one we mulitply the value of every task. This leaves us with 2.488ร1064 shuffles after building the tower once. If we do that one thousand times more now, we will end up with 2.488ร1067. Because this was just one third of the whole way, we also multiply by 3.
I always liked QI's illustration of the number better:
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second with each pack, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
[deleted] ยท 1 points ยท Posted at 14:17:00 on May 25, 2016 ยท (Permalink)
This means that every time you shuffle a deck of cards, that order has never existed before in the universe.
Even if everyone who ever lived had each shuffled a deck of cards once a second for the entire age of the universe, the odds would be against a single replicated order.
Take one step every billion years.
Every time you go around the world, buy a lottery ticket.
Whenever the lottery wins the grand prize, drop one grain of sand in the Grand Canyon (USA).
Whenever the Grand Canyon fills up, empty it and remove one gram of mass from Mount Everest.
When Everest is flattened, rebuild it.
Yeah, but i'm not playing a game where suit matters, so honestly I don't care about how the unique arrangement of suits. So for all 13 card values we have what 4! ways of arranging them in the deck and we compound those to be 13*4! ways to permute the deck into equivalent states. Well that gets me down to about 2.5*1065 nearly three orders of magnitude. That's still a lot to worry about, so well maybe all I'm a lazy black players and all I care about is face cards. so let's say 10,J,Q,K,A. Then 2-9 can be permuted freely so that's another 8! . Now I'm down to like 6*1060 . Which is still a whole mess of ways to assemble cards. Its gone down by a factor of like 10,000,000 but I'm still in a losing battle.
The possible permutations of a deck of cards (52!) is roughly equal to the number of atoms in the Milky Way galaxy.
52! = 8 x 1067
mass of Milky Way = 6 x 1045 g
atoms/g (~75% hydrogen) ~ 1 x 1023
atoms in Milky Way ~ 6 x 1068
Pyran ยท 1 points ยท Posted at 16:41:52 on May 25, 2016 ยท (Permalink)
Or put another way, every time you shuffle a deck of cards you put them in an order that has never before been seen anywhere in the history of the universe.
This is obvious, but still a cool fact: When you shuffle the deck of cards and deal, it is almost certain that a deck of cards has ever existed in that order before or ever will again.
Combining this with thedeejus post above, if you were to actually do all of this (shuffling cards every second while slowly circling the Earth, draining the Pacific, and stacking paper toward the sun 3000 times), the probability of reshuffling at any time back to a deck like new (unshuffled) is approximately 63%.
My mind is blowing up today.
That makes me wonder what kind of example the guys would come up with to picture how many type of Magic The Gathering decks and shuffles you could play with (the game got ~15.000 different cards).
WG95 ยท 1 points ยท Posted at 18:57:55 on May 25, 2016 ยท (Permalink)
My favorite algorithm (on a computer) for shuffling a deck of cards is fairly simple and produces a truly random order where every one of the 52! possible orders is possible and equally likely.
Put the cards in an array.
Iterate through the positions in the array from left to right.
At each position, randomly select an index between where you are now and the beginning of the array (inclusive).
Swap the card at that random position and the card at the current position.
(Linear time complexity and the shuffle is done in place with no extra storage space.)
colbymg ยท 1 points ยท Posted at 22:03:37 on May 25, 2016 ยท (Permalink)
You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years.
at that speed, plate techtonics would play a larger role in your travels than walking ;)
tojoso ยท 1 points ยท Posted at 22:07:55 on May 25, 2016 ยท (Permalink)
There are 52! ways to shuffle a deck of cards.
80658175170943878571660636856403766975289505440883277824000000000000 ways.
I've heard it put this way: for any given shuffle of a deck of cards, it is more likely than not that it is the first time the cards have been shuffled into that order.
Wow that's insane. I remember hearing that there is an extremely high chance that when you shuffle a deck of cards, that that combination has never been made before. Interesting stuff!
Start by picking your favorite spot on the equator.
What if we don't have one?
[deleted] ยท 1 points ยท Posted at 23:06:02 on May 25, 2016 ยท (Permalink)
The way I came up with to explain it to someone is that if you made a path equal in length to that number (in metres) then the diameter of the whole observable universe would be a tiny, insignificant blip on that line
Trofont ยท 1 points ยท Posted at 01:20:44 on May 26, 2016 ยท (Permalink)
The version I heard: A trillion galaxies, each with a trillion stars, each with a trillion planets, each with a trillion people, each with a 1000 decks of cards, each shuffling every deck every second since the dawn of time. There would still be combinations that never existed.
0kZ ยท 1 points ยท Posted at 02:41:06 on May 26, 2016 ยท (Permalink)
See, you know how I know that's a small number, because you can still point out physical things as analogies. The real big numbers you can barely do that with the number of operations involved, and the really big numbers it stops completely.
I am a bit confused by this. Are we doing one shuffle per second? Or one order? The number of random shuffles to have a 99% chance of getting all possibilities is a lot bigger than the number of possibilities.
And is the Pacific re-filling from the other oceans?
gp133 ยท 1 points ยท Posted at 06:50:43 on May 26, 2016 ยท (Permalink)
That is the most intricate way I have ever seen to explain how big a really big number is. I really enjoyed that!
greezeh ยท 1 points ยท Posted at 10:16:53 on May 26, 2016 ยท (Permalink)
I saw a different way of explaining this on Q.I. If you give a billion packs of cards to a billion different people on a billion different planets and get them to shuffle them at 15,000 per minute since the beginning of time. Then we'd only just be repeating shuffles. Something like that. I don't remember exactly but its a crazy thing to think about.
I don't know if this counts as a math fact, but it's my favorite math puzzle. I guess the fact would be the solution. Anyway, it would be the Konigsburg Bridge Problem.
It's an interesting mathematics puzzle that laid the foundation for graph theory. I remember going through it once in school for reasons that I can't quite remember now.
The problem from the outset is pretty simple. You have four landmasses with a series of seven bridges between them, pictured here. Now, what you need to do is find a path that will cross each bridge exactly once. Try it out for a minute and see how you do.
Now that you're back, you're probably telling me that it's impossible. Well, you're right. So now, the question is, why? Why can you not cross each of the bridges exactly once? I'll give you some hints if you need them, but try and figure it out.
I mean, you could also go up around the headwaters of your river system or take a ferry, steal a canoe or a number of other things that destroy the spirit of the question.
A portal gun would also work, as would stretching your hand out really far to reach the middle of a bridge, then doing the same from the other side chopping off your limbs one by one and tossing them across the bridges. If you're strong, you could bend one of the bridges so it points back at the land mass you just tried to leave.
[deleted] ยท 1 points ยท Posted at 13:47:33 on May 26, 2016 ยท (Permalink)
except its a real-life problem - e.g.quick delivery times for a postal service, where petrol consumption adds up when you're being inneficient. None of your engineering approximations over here. Its an application of Eulerian graphs as a part of decision or discrete maths, which has a lot of applications.
Discreet math? whispers "Psst. Two plus two is four."
Tavyr ยท 9 points ยท Posted at 15:09:02 on May 25, 2016 ยท (Permalink)
If anyone wants the technical graph theory definition of the theorem: "A connected, undirected graph has an Eulerian cycle if and only if every vertex has even degree."
In that it isn't a cycle I suppose, but I was taught that you'd describe the entire graph as eulerian/semi-eulerian if its possible to make a eulerian/semi-eulerian route. e.g this graph is semi-eulerian. Your wording made me confuse myself, so I've corrected the original.
Well, I figured out why it was impossible. But the rest of the solution was all a little above my problem solving ability.
[deleted] ยท 5 points ยท Posted at 16:15:24 on May 25, 2016 ยท (Permalink)
My favorite math puzzle/problem is this:
Two pastors, of two small villages, meet on a Sunday on the road between their villages. One tells the other: "There were so few people in church today, once again." The other says: "In my church too. Only 3 people were in church today! Let me give you a little quiz about the age of the three people who were in church. If you multiply their ages, you'll get 2450. But if you add their ages, you'll get the height of the church in your village!" The other pastor says he will try to figure it out, and they leave. On the next Sunday, they meet again at the same place. The one who tried to solve the problem says: "I tried and tried, but I can't seem to figure it out." The other says: "Sorry, you couldn't solve that, I forgot to give you one hint. The oldest of the 3 people is younger than our bishop." So then he could solve the puzzle.
Question: How old are the 3 people who were in church? How high is the second pastor's church? And, how old is the bishop?
I love this puzzle because at the first look it seems unsolvable, but if you think about it and find out, then it's actually pretty easy.
The best I could do was a range of ages for the bishop. Unless there's some minimum or maximum height for a church that I don't know about.
[deleted] ยท 6 points ยท Posted at 18:13:03 on May 25, 2016 ยท (Permalink)*
No minimum or maximum height. I'll type the solution out later!
Edit:
Solution: First, find out the possible ages for the 3 people. For that, it's easiest to split 2450 into its prime numbers: 2*5*5*7*7 = 2450 Combine them, and the possible ages are:
But now, the important part is, that the pastor couldn't solve the problem with this much info. He knows how high his church is, but it still wasn't possible for him to find the solution. And as there's only one sum which comes up twice, 64, that must be the height of his church, as these are the only options for which the puzzle is unsolvable for him. So, possible are 5+10+49=64, or 7+7+50=64. And, as he knew which of the two is the right answer after being told that the oldest (who is 49 or 50) is younger than the bishop, the bishop must therefore be 50, and the right answer must be 5, 10, and 49 years old.
Ah, of course, I forgot that while I have no idea a church can be, the other pastor is obviously able to check how high his own is even if he doesn't know it off hand.
I tried solving this and was totally stumped right of the bat. If the product of their ages is 2450 then the average age is 816. As a full disclosure, I am the worlds dumbest person when it comes to math so it's probably me. It's been years and years since I had to do any math. I had to look up the word 'product'.
[deleted] ยท 1 points ยท Posted at 20:55:09 on May 25, 2016 ยท (Permalink)
They can't be 816, because if you multiply 816*816*816, you get a way higher number than 2450. For the average (or rather, if all 3 were the same age), it would not have to be 2450/3, but rather the third root of 2450. That's about 13. And if you calculate 13*13*13 = 2197, so that's about right, and they could be all about 13 years old. But, easier solution to get to the actual possible ages, is by using prime numbers of 2450. Solution is in the other comment!
I also couldn't solve this problem by myself, when I heard it for the first time. :D I was sure it couldn't be solved, but I found it very interesting and clever after someone told me the answer.
I started thinking about what bridge (and what direction) to cross first and quickly found out the 3 surrounding masses all have 3 bridges entering, so if i enter on one, i have to exit on the second, leaving the third (and second entering) a dead end, which would be fine if my journey ended there, but i would need to go to the other landmass after. So the first move had to be entering the center mass. The second move again can not go onto any of the surrounding masses with 3 bridges, except the one i just came from (because it only has 2 unused bridges left) so i would have to go back to that one, and the third move was gonna be leaving it again over the last bridge, but that leads me to one of the masses from the beginning that i wouldn't be able to go onto because the number of bridges would always lead to one of them turning into a dead end before i can reach the last landmass.
jorellh ยท 2 points ยท Posted at 15:15:05 on May 25, 2016 ยท (Permalink)
Now that you're back, you're probably telling me that it's impossible. Well, you're right.
I didn't see this part, and spent half an hour on this
lazyl ยท 2 points ยท Posted at 20:22:30 on May 25, 2016 ยท (Permalink)
Not having looked at any of your hints this is my explanation.
Only the starting and ending landmasses (which could be the same) can be connected to an odd number of bridges. All other land masses must be connected to an even number of bridges. This is obvious when you consider that every time you enter a landmass it will be via a bridge you haven't used yet. Then you must leave by a second bridge which you also haven't used yet. This means those bridges must always come in pairs, i.e. there must be an even number. In this diagram all four landmasses have an odd number of bridges and so such a path is impossible.
Fuck me. I didn't read all of your post, so I didn't see the part where you said it's impossible. Spent a good 20 minutes trying everything thinking "THERE HAS TO BE A WAY".
So after trying this many many times, isn't the answer quite simple?
There is an odd number of bridges, and an even number of land.
So you would have to walk over one once more in order to evenly cross. Right?
[deleted] ยท 2 points ยท Posted at 15:55:54 on May 25, 2016 ยท (Permalink)
It doesn't have to do with even lands and odd bridges. Imagine 2 lands, and 7 bridges, and it works. Because you don't need to end where you started.
_NW_ ยท 1 points ยท Posted at 18:36:01 on May 25, 2016 ยท (Permalink)
Any location with an odd number of routes to it must either be a starting point or an ending point. One start point plus one end point means that you can have no more than two locations with an odd number of routes to it.
If you have two landmasses with an odd number of bridges, there will be a path but those two must be your starting and ending points. It's not possible to have only one landmass with an odd number of bridges leading to it. Each bridge has 2 endpoints, so the total number of bridge endpoints must be even no matter what your map looks like. If you try to make exactly 1 landmass have an odd number of bridge endpoints, there's no way the total number of bridge endpoints could end up being even.
[deleted] ยท 1 points ยท Posted at 16:27:46 on May 25, 2016 ยท (Permalink)
I did a presentation on this problem a couple months ago. It's a lot more fun to talk about than a lot of other math centered things
beeeel ยท 1 points ยท Posted at 16:57:44 on May 25, 2016 ยท (Permalink)
You're slightly wrong on the solution- it's possible to do it if 1 landmass has an odd number of bridges (eg: remove the left hand to bridges), and then one end of the path has to be on that landmass.
It's a nice problem though, I remember studying it in decision maths at school.
Now that you're back, you're probably telling me that it's impossible. Well, you're right.
I didn't get this far in your comment as I wanted to think about it first. Spent two hours thinking about it, graphing it, and I even wrote an algorithm to figure it out. I failed and felt really stupid. Then I went back to continue reading your comment to get to the line above...
Lol you know you're a nerd when you open a reddit thread about math trivia and you not only know the answer to the problem but also who first solved it.
Though to be fair if you had to guess which particular mathematician solved a given problem guessing Euler will be right more often than about anyone else.
I don't know why you're being down voted. That is part of the original problem. Although, the other people are right in which it is impossible to walk on every bridge without using a bridge twice.
Source: Just finished a semester of graph theory in college
If you took 1 cent and invested it at 5% interest, compounded annually, back in 0AD 1BC, it would now be worth 200 billion times the weight of the earth in gold.
It's not maths in the sense of a pure maths fact, but it's a fun fact and it's maths-related.
And for our calculations:
Earth weight: 5.972 ร 1024 kg
Price of gold: $39223.59 kg-1
=>Cost of a golden earth: $2.34 x 1029
Annual compound interest formula:
return = investment x (interest)years invested for
plug in the numbers:
return = $0.01 x 1.05 ^ 2016
= $5.22 x 1040
($5.22 x 1040 )/($2.34 x1029 ) = 222,822,878,846
Or about 200 billion.
The numbers were trimmed a bit for presentation so you might get some rounding error if you use those numbers exactly as presented
I perfer Terry Pratchett's (possibly Douglas Adam's) take on it which was if you take 1 cent and invested it at 5% interest and came back in 200 years or so the 1 cent would have been eaten up entirely in bank charges.
It is often hard to distinguish between Pratchett's and Adams' humour / insight into the human condition, because they were both so refreshingly weird, smart and funny.
(I nearly corrected that "were" then realised they're both past tense. Sad times)
Grant Naylor also did a bit in Red Dwarf where Lister left two pence in his account and after three million years in stasis he now owned most of the Earth.
But it was just an April Fools.
rusy ยท 15 points ยท Posted at 17:39:47 on May 25, 2016 ยท (Permalink)
To put this into more depressing terms, if you took 1 cent at birth, and invested it at 5%, by the time you retire at 65 you'd have 24 cents
Parey_ ยท 15 points ยท Posted at 15:05:59 on May 25, 2016 ยท (Permalink)
If I knew I was gonna get grilled on my calendars I'd have stayed at home.
Oh wait, I am at home, typing this in my underwear. Rock on, the internet.
Parey_ ยท 2 points ยท Posted at 15:18:52 on May 25, 2016 ยท (Permalink)
It did, because the calendar was made using imprecise data (I believe). To be fair, there was no precise count of days and years like we have now. So itโs completely understandable that errors piled up.
Not because of imprecise data, but because of qualitative (not quantitative) semantics. AD 1 was the first year of the common century, hence AD 1 (lit. "The first year of our Lord"). It's the same reason why years 2001โ2100 are the 21st Century and years 1001โ2000 were the 2nd Millennium.
AsterJ ยท 3 points ยท Posted at 18:44:20 on May 25, 2016 ยท (Permalink)*
It's because Christians didn't have a concept of zero at the time.
zeekar ยท 3 points ยท Posted at 18:46:05 on May 25, 2016 ยท (Permalink)
There was no year zero because Europeans didn't know about zero when they came up with the numbering system.
That said, it's perfectly reasonable to talk about the year "0 AD" - or "0 CE", at least, if using 0 with AD makes you uncomfortable. Astronomers use 0 and negative years CE instead of BCE. You just have to remember that 0 AD/CE is the same year as 1 BC[E], not an extra year that comes between it and +1.
fyi1183 ยท 1 points ยท Posted at 17:40:22 on May 25, 2016 ยท (Permalink)
And this is the flaw in all economic forecasts which assume unending exponential growth instead of the logistics function.
marsten ยท 3 points ยท Posted at 17:30:04 on May 25, 2016 ยท (Permalink)
A corollary is that it is mathematically impossible for any company's growth rate (revenue, profit, stock market valuation) to exceed the GWP (gross world product) growth rate of 2-3% on an indefinite basis.
ableman ยท 1 points ยท Posted at 18:58:03 on May 25, 2016 ยท (Permalink)
Even at a 2% growth rate, you'd end up with $1.5 quadrillion. That's more than total world assets right now.
This is actually a wonderful illustration that long-term growth on Planet Earth is definitely less than 5%.
If today's total world wealth is $250 trillion, and the total world wealth was $0.01 in 1 AD, that would identify a real interest rate of about 1.66%. Note that is also an overestimate, as the total world wealth in 1 AD was somewhat more than 1 cent, even in inflation-adjusted dollars.
This time traveler's weird trick can make you rich. Dr. Who hates him!
ableman ยท 1 points ยท Posted at 18:54:51 on May 25, 2016 ยท (Permalink)
It's more of a proof that no investment can possibly average 5% return for 2000 years.
[deleted] ยท 2 points ยท Posted at 23:42:44 on May 25, 2016 ยท (Permalink)
Similarly, I read something once like if we actually maintained exponential growth (2%) in food production from Roman times, the amount of bread we would produce fills the entire solar system.
Not in the slightest, this is just plugging numbers into a calculator.
I don't think any currency has been around that long so I don't even know how you would begin to do that. But the number is just so staggeringly large that I can't imagine any considerations like inflation can have a meaningful impact on it.
You could probably do it by starting in Denari and converting to pound sterling when it starts. Rome was the world so everyone would have been able to tie their local currency to Roman currency
If you take $1 and put it in a bank with 100% interest for a year, you get $2.
If you take $1, put it in a bank, take it out in six months, put it back in with the 100% interest (although because it's only six months you only put back $1.50), and then do that again, you get $2.25.
If you do that every four months for a year, you get $1.33 the first time, $1.79 the second, and $2.35 at the end.
What happens if you do that every millisecond of every day for a year? Every picosecond?
The answer is that as the number of times you compound approaches infinity, the total amount you get approaches e.
Good luck with paying off the bank charges you'll rack up which instantly outgrow any profit you make.
Zarco19 ยท 2 points ยท Posted at 04:43:38 on May 26, 2016 ยท (Permalink)
Yep. This is the definition of e we used in my high school classes, the limit as n->infinity of (1+1/n)n. You can use this to see how the formula for compounding interest (i.e. you have money in the bank whose interest is calculated n times per year) - Return = Investment x (1+interest rate/n)nt - turns into the formula for continuous compounding - Return = Investment x ert - as you compound more and more times per year.
zakky_b ยท 324 points ยท Posted at 14:11:28 on May 25, 2016 ยท (Permalink)
To find if a number is evenly divisible by 2: The last number is even.
To find if a number is evenly divisible by 3: add all the digits and if THAT number is divisible by 3, then the whole number is. (Ex. 744. 7+4+4=15. So 744 is evenly divisible by 3.)
To find if a number is evenly divisible by 4: As long as the last 2 digits in a number is divisible by 4, then the whole number will be. (Ex. 727483724 is divisible by 4 because the last 2 digits {24} is).
To find if a number is evenly divisible by 5: The last digit is 5 or 0 (that's an easy one).
To find if a number is evenly divisible by 6: If the number is divisible by both 2 AND 3, then it's evenly divisible by 6.
For eight, it's similar to 4. The last three digits must be a multiple of 8 (145373080, for example)
For nine, it's just like three except the digits should add to a multiple of nine.
jusjerm ยท 35 points ยท Posted at 16:59:15 on May 25, 2016 ยท (Permalink)
I like divisible by 11, if we want to keep going. Let's take a decently large number like 115973
Add up all the odd numbered digits (that is, the first, third, fifth... from the left in the string of numbers). 1+5+7 =13
Add up the even digits (second, fourth, etc). 1+9+3=13
Find the difference between both sums. 13-13= 0.
If the difference is 0 or a multiple of 11, then the original number is divisible by 11.
tommcdo ยท 17 points ยท Posted at 18:12:05 on May 25, 2016 ยท (Permalink)
0 is a multiple of 11 :)
jusjerm ยท 6 points ยท Posted at 18:25:11 on May 25, 2016 ยท (Permalink)
Yes, it is. However, some numbers (2841927, for instance) will leave you with a nonzero multiple of 11. I just meant to say that the difference between alternating digits won't always be zero to prove divisibility by eleven.
Initial reaction: "this person doesn't know what they're talking about. if this were true, then any two-digit number where the first digit is twice the size of the second digit would be divisible by seven, and that's just not true. look at it: 21, 42, 63... wait a second... 84... holy shit."
You can invent rules like this for any number*. For example:
Want to divide by 13?
Multiply the last digit by 9
Subtract that from the remaining digits
If the result is evenly divisible by 13, then the original number is as well.
Example:
13*455 = 5915
5 times 9 is 45.
591-45 = 546
Again:
6 times 9 is 54
54 - 54 = 0.
The reason this works is because 91 is a multiple of 13, just like 21 is a multiple of 7. In the algorithm you're subtracting large multiples of 7 or 13 and dividing by 10.
Want to invent your own? Take a number (preferably a prime), say 17, and find a multiple of that number that ends in a 1. For example 51 is 3 times 17, so we're going to use 5 and 1. The algorithm now is:
Multiply the last digit by 5
Subtract that from the remaining digits
If the result is evenly divisible by 17, then the original number is as well.
*: I should mention that the algorithm changes if for example you pick an even number and therefore can't find a multiple of it that ends in 1, but it's at most a cosmetic change, which is left for the reader ;)
Let's say the number is x and we break it up into the two parts we need, the first digit and all the other digits: 10b+a=x (a between 0 and 9, b any number, the multiply by 10 being there because we want b to be tens and greater)
10b+a=x
Take out the first digit and multiply by 2:
2a
Take that away from the remaining digits, b (which we divide by 10 to bring it to the units i.e. in the example above 180 becomes 18):
b-2a
Assuming the proof works, b-2a will be divisible by 7:
b-2a = 7y (for some y)
isolate b
b=7y+2a
multiply everything by 10
10b=70y+20a
Sub this back into the equation 10b+a=x
(70y+20a)+a=x
add the 20a and the a
70y+21a = x
Take out a factor of 7
7(10y+3a)=x
rwv ยท 3 points ยท Posted at 19:11:16 on May 25, 2016 ยท (Permalink)
105 => 10 - 10 = 0
This one makes my head hurt since 0 is indeed divisible by 7.
I wonder, when does a trick get so complicated that it becomes faster to just divide by seven (or whatever). Like 182/7=26 & 207+67=140+42.That's not really slower than 18-(2*2)=14 & 14/7=2.
I just think it's fun, and for me it's easier to do mentally than long division. It mostly comes in handy when I need to quickly rule out 7 as a factor without actually needing to know the quotient.
Explanation: If 10a+b is a multiple of 7, then so is 50a+5b (just five times it). Now, 50a+5b-(49a+7b)=a-2b, and subtracting multiples of 7 doesn't change divisibility by 7, so if 50a+5b is a multiple of 7 then so is a-2b.
Thus, if 10a+b is a multiple of 7, then so is a-2b. That's what this trick does.
To find if a number is evenly divisible by 4: As long as the last 2 digits in a number is divisible by 4, then the whole number will be. (Ex. 727483724 is divisible by 4 because the last 2 digits {24} is).
(My homework which is due to tomorrow, is to build a deterministic finite automaton to detect multiples of four digit-by-digit.) It's simply because 100 is divisible by four so also every multiple of 100 is aswell. And to make it even easier to check if something is evenly divisible by 4:
The very last digit must be even.
If the last digit is 2 or 6 the digit before it (the second-to-last digit) must be odd.
If the last digit it is 0, 4 or 8 the before it (the second-to-last digit) must be even.
[deleted] ยท 2 points ยท Posted at 02:19:12 on May 26, 2016 ยท (Permalink)
deterministic finite automaton
Ah, automata theory... surprisingly intuitive for the most part. It was a fun class (:
If the sum of the digits of a number is divisible by 9, the number is divisible by 9.
If the alternating sum of digits of a number is divisible by 11 the number is divisible by 11. 47817 => 4-7+8-1+7 = 11 so it's divisible by 11.
[deleted] ยท 2 points ยท Posted at 19:14:51 on May 25, 2016 ยท (Permalink)*
For funsies here's a breakdown of the 3's trick:
Evenly divisible by 3 (or 9)
Consider a number "x" where each digit is represented by a letter, with the one's place represented by "a", the ten's as "b", and so on. It can be represented like this (I'm gonna use a 4-digit number for example, but this can be extended to any number of digits):
Ta-daaa. I grouped the stuff that we know is divisible by 3 into the parens, so all that's left is the x (our original number). It follows that if our original number is divisible by 3, the whole left side of the equation is.
From there, it follows that if left side of the equation is divisible by 3, the right side (which is the sum of the digits of x) is also divisible by 3.
The left and right sides are equal so this logic also works going the other direction (if the sum of digits of x is divisible by 3, then x must be divisible by 3).
Although some other math facts IIT are more interesting, this is by far the most useful math fact posted thus far for the layman! If anyone is studying for SAT or even GRE these little math tips save you a lot of time.
If x is a factor of the base in which your numbers are expressed, then y is divisible by x when its last digit is a multiple of x. (applies to 2 and 5 in decimal)
If x has a multiple that is one less than the base, then y is divisible by x if the sum of its digits are. (applies to 3 and 9 in decimal)
If x has a multiple that is a power (p) of the base, then y is divisible by x if its last p digits are. (applies to 4 and 8 in decimal)
These rules can be combined to determine divisibility by multiples of their numbers. (e.g., the first two are used to test for multiples of six)
A number is divisible by 11 if the sum of the digits in the odd columns (ones, hundreds, ten thousands, etc) is equal to the sum of the digits in the even columns (tens, thousands, hundred thousands, etc)
You can continue to add the digits together until you get to a single digit divisible by 3. (e.g. 843795 -> 8 + 4 + 3 + 7 + 9 + 5 = 36 -> 3 + 6 = 9 -> 9 is divisible by 3)
And using same method, if your final number is 9, then the original number is divisible by 9.
I'm pretty sure that for 2x , for any number y where the last x digits are divisible by 2x , y is itself divisible by 2x .
At least, its true for any example I can think of.
awe778 ยท 1 points ยท Posted at 04:23:49 on May 26, 2016 ยท (Permalink)
To find if a number is evenly divisible by 3: add all the digits and if THAT number is divisible by 3, then the whole number is. (Ex. 744. 7+4+4=15. So 744 is evenly divisible by 3.)
And if that number is still too big, add the digits of that number and it will still retain its remainder if divided by 3.
[deleted] ยท 5 points ยท Posted at 20:45:43 on May 25, 2016 ยท (Permalink)
I remember being pretty excited on my 33 birthday. Next one I'm celebrating will be 25. After that its a short leap to 62, then a LONG wait to 72 and 43 (also known as 26).
I like math but have very few people show up to my birthday parties.
xereeto ยท 1 points ยท Posted at 02:31:19 on May 27, 2016 ยท (Permalink)
I remember thinking when I turned 16 that my birthday was a power of two, and then being slightly upset when I realized I only had two more of those left.
27 must be a magical year because sometime during your 27th year, you would reach 10,000 days old. That's a transition from 4 digits to 5 digits. You don't remember all the other ones.
1= 1 day old
10= 10 days old
100= 100 days old
1000 = almost 3 years old
10000 = 27 and a few months
100000 = long dead
If you are younger than 27, you can find out when your 10000th day birthday is by going into excel and typing in your birthday (day month year). Simply add 10000 to that number will give you the upcoming date.
xereeto ยท 1 points ยท Posted at 02:36:10 on May 27, 2016 ยท (Permalink)
This reminds me of Ryan McHenry, the "Ryan Gosling won't eat his cereal" guy. He was a friend of my cousin's, and he posted on Twitter about reaching his 10,000th day. Then he died of bone cancer shortly after :(
I wrote some code that does this (it's a little more generalized than the problem you're looking for, but be careful -- add too many input options and the runtime goes up an extraordinary amount); here's what the output looks like:
>>>seqpossibilities(printoutput=True)
Current testseq: 1+23-4+56+7+8+9=100
Current testseq: 12+3-4+5+67+8+9=100
Current testseq: 1+2+34-5+67-8+9=100
Current testseq: 1+2+3-4+5+6+78+9=100
Current testseq: 123-4-5-6-7+8-9=100
Current testseq: 123+45-67+8-9=100
Current testseq: 1+23-4+5+6+78-9=100
Current testseq: 12-3-4+5-6+7+89=100
Current testseq: 12+3+4+5-6-7+89=100
Current testseq: 123-45-67+89=100
Current testseq: 123+4-5+67-89=100
Here's the code:
def seqpossibilities(testseq=[1,2,3,4,5,6,7,8,9], targ=100,printoutput=False, possibilities=['+','-', '']):
N=len(testseq)
inputseq=[str(each) for each in testseq]
M = len(possibilities)
allopts = (M)**(N-1)
goodcount=0
for item in range(allopts):
testval=''
#attempt all possibilities, but only print the result if we get 100
for idx in range(N):
testval += inputseq[idx]
#see what the current testval would append
if idx != N-1:
#print ('item = ' + str(item) + ' for idx = ' + str(idx))
testval += possibilities[(item/M**(idx)) % M]
try:
if eval(testval)==targ:
if printoutput:
print "Current testseq: " + testval +"=" +str(eval(testval))
goodcount+=1
except:
#generated something that doesn't work. Move on
continue
return goodcount
I could, but would rather not -- that would take a lot of effort. That code was something I put together from one of those "you should be able to complete these five problems in less than an hour" interview tests, and eval was the obvious route.
What I would be more interested in would be optimizing the algorithm more to identify cases that don't need to be tested. Like in the default example, if it starts with 123456 as a single number then clearly there's no operation with 789 that could end up reaching 100, so I could prune off a lot of the chains involving concatenation of digits. Generalizing the cases that can be ignored is far from trivial, though.
n0rs ยท 1 points ยท Posted at 01:01:41 on May 27, 2016 ยท (Permalink)
Eval is the obvious route, yes. But writing either your own parser or evaluating the result based on a tree of your three operations (concatenation, addition, subtraction) is also an interesting problem.
Pruning would be interesting too, but yes, not trivial.
With three operations and little to worry about from order of operations, that it very doable. However, you may notice I have those as keyword params, so you can call it with other operations and other input lists. I've tested a few allowing for parentheses, multiplication, division, decimal points, mod arithmetic, and exponents, and writing that parser would be harder. Maybe I'll get to it eventually, but as noted, the pruning seems more interesting to me.
[deleted] ยท 6 points ยท Posted at 14:58:54 on May 25, 2016 ยท (Permalink)*
Now why do you do subtraction first instead of addition? Doesn't addition take a higher order of precedence than subtraction?
I.E PEMDAS?
I'm mainly referring to the first expression.
EDIT Huge apologies for my misinformation. I've always been taught PEMDAS(Well at least since I entered public school).
No, iirc addition and subtraction have the same precedence, same as how multiplication and division have the same precedence.
graaahh ยท 3 points ยท Posted at 17:26:14 on May 25, 2016 ยท (Permalink)
Yep, addition and subtraction have the same precedence if you treat subtraction like "adding a negative number", which is the correct way to do it. Otherwise, it can get a little messy. For example, I've seen beginner math students make the following mistake more than once: 9-8+2 = 9-10 = -1. But subtraction isn't really its own thing, it's just the opposite of adding a positive number. So in actuality, 9-8+2 = 9+(-8)+2 = 1+2 = 3.
This is a too common misconception. The order of operations should be thought of as PE(M/D)(A/S).
EDIT: Guys, don't downvote him (his comment is currently at -3). He didn't know something. He asked. What more can we ask for? While it may not be entirely true that "there's no such thing as a stupid question," this one wasn't stupid and if we suppress people questioning, that just leads to more widespread ignorance.
ananori ยท 3 points ยท Posted at 17:10:57 on May 25, 2016 ยท (Permalink)
All I wanna know is how such people have passed math exams up until high school graduation.
Suppose you encounter an equation saying 1 - 1 + 1=?. You would literally fail if you didn't know the correct order of operations.
Yeah, I don't get it either, but it's a failure of specific teachers, specific school systems, and specific institutes of higher ed. Some people are clearly being taught incorrectly. Ain't their fault!
Maybe I just have a mental roadblock and can't figure out how to do it incorrectly?
ananori ยท 1 points ยท Posted at 08:55:22 on May 26, 2016 ยท (Permalink)
1 - (1+1)
But I guess people misinterpreted the purpose of PEMDAS then. Changing the chronological order of performing operations without affecting the hierarchical is not wrong, although it's useless.
Well you added parentheses that were not in the equation
ananori ยท 1 points ยท Posted at 16:43:55 on May 26, 2016 ยท (Permalink)
Yes, illustrating the assumption that addition precedes subtraction... that's what order of operations means. It means you can put parentheses around expressions by the given order of operations without changing the outcome.
Bracket and Indeces (I think that's how it's spelt)
[deleted] ยท 2 points ยท Posted at 16:41:45 on May 25, 2016 ยท (Permalink)
Just looked it up. It's indices. I never realized that exponents had another name out there. Would you still use terms like "exponential growth" even though you don't say exponent?
Addition and subtraction have the same precedence so are completed in order from left to right. As much as i hate seeing them the Facebook "only 1 in 65.8 people will get this right" are good thought experiments for order of operations. Just don't look at the comments on them, 64.8 people are usually, actually wrong.
Kr1tya3 ยท 840 points ยท Posted at 11:46:15 on May 25, 2016 ยท (Permalink)
73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001
A lot of people love to hate that show because it's 'not true to geek culture', but it's probably way closer to geek culture than it is to waitress-at-a-cheesecake-factory culture.
source: have physics degree, work as engineer at a tech company, say shit like they do all the time.
People hate it because it makes fun of nerd culture as well as having humour that is not noteworthy. But I like it regardless.
Source: Have Maths degree, work as Implementation Analyst
karijay ยท 1 points ยท Posted at 18:20:02 on May 25, 2016 ยท (Permalink)
The humour is below the standard of acceptable (so slightly higher than 2 Broke Girls), but the relationships bewteen the characters are very well written.
[deleted] ยท 2 points ยท Posted at 21:48:49 on May 25, 2016 ยท (Permalink)
I hate the show because, like every other Chuck Lorre comedy, is devoid of humor.
It's on TV pretty often, without an HBO subscription in my area, but you do you man :)
[deleted] ยท 1 points ยท Posted at 17:40:49 on May 25, 2016 ยท (Permalink)
ARRR
bl1y ยท 0 points ยท Posted at 18:38:29 on May 25, 2016 ยท (Permalink)
Have you tried Silicon Valley? It's a much better show in my opinion for that kind of humor.
FTFY
dh363 ยท 1 points ยท Posted at 20:11:09 on May 25, 2016 ยท (Permalink)
But they're in academia, which is culturally FAR different from any other geeky job (for example, exactly 0 of my fellow PhD students were big gamers like the guys on the show). Their behavior is really not seen at all in academia.
bl1y ยท 1 points ยท Posted at 18:39:46 on May 25, 2016 ยท (Permalink)
I hate Big Bang Theory because it's lazy writing. Boobies upside down on a calculator bit? Every single 3rd grade boy has done that.
Itself and its mirror and 100 plus both numbers are all primes (73, 37, 137, 173)
If you take 73 and 100 more than its mirror, 37 (137) and multiply them together you get 10,001. Which leads to a calculator trick I learned when I was young: Take any four-digit number and multiply it by 73, then multiply the result by 137, your result is the four-digit number repeated twice.
There's more to this! They're both sexy primes, which means that they differ from another prime by 6. Even more, they're sexy prime triplets! For 73, that's (67, 73, 79), and for 37, that's (31, 37, 43).
derrman ยท 1 points ยท Posted at 15:31:37 on May 25, 2016 ยท (Permalink)
This reminds me of the way to remember how many books are in the Bible. There are 66 books, 39 of which are in the Old Testament. What is 3*9? The number of books in the New Testament, 27.
karlw1 ยท 1 points ยท Posted at 16:06:26 on May 25, 2016 ยท (Permalink)
That you can use your hands to do your nines times tables without doing any multiplication!
You just hold up 10 fingers
Counting from the left, fold down the finger with the number you want to multiply by 9.
The fingers on the left of the folded finger represent the number in the tens slot and the fingers on the right of the folded finger represent the number in the ones slot!
e.g. 9 * 6
You fold down your 6th finger.
there are 5 fingers on the left and 4 on the right.
9 * 6 = 54
Related to this, if you add up the digits in any multiple of nine, and repeat the process until you have a single digit, you will always end up at nine.
The relationship in the numbers with this is beautiful. It's the same relationship that makes this rule work for multiples of three (if the sum of the digits is a multiple of three, then the number itself is).
That all has to do with the fact that the number has a multiple that is one less than the base in which it's expressed. That of course means that if you express the number in hexadecimal, it won't work for multiples of nine, but ~will~ work for multiples of 3, 5 and 15. Similarly in base twelve, it will only work for multiples of 11.
When I realized how this worked, I was so thrilled that I had to write about it. Blogged it here if you're interested.
Plot twist for any number of fingers (x) you can do multiples of (x-1) so in your case multiples of 7.
With a small catch though, fingers to the right are still ones, but fingers to the left are no longer 10s place but (x) place, worth x. So 8 in your case.
For example
1 x 7, put down your finger to the left you have 0 - 7 or 7
You're a hero. You got people talking about Monty Hall, and Graham's number, and all sorts of other things, and you're keeping it real with finger counting tricks.
I'm a fan of the idea that there are different levels of infinity. For example, the set of integers and the set of real numbers are both infinite size; however, the set of real numbers is way more infinite than the set of integers. In fact the set of real numbers between 0 and 1 is way more infinite than the set of integers. Much of the theory around infinite sets was developed by a guy named Cantor. He was the perfect combination of insane and brilliant.
[deleted] ยท 3 points ยท Posted at 23:48:41 on May 25, 2016 ยท (Permalink)
There are actually infinite sizes of infinity, you can continually take power sets of an aleph-naught sized set and they're provably more infinite, because no isomorphism can exist between a set and its power set.
However it's unprovable if sets exist between these levels of infinity.
dozza ยท 1 points ยท Posted at 12:54:01 on May 26, 2016 ยท (Permalink)
Unprovable or unproved? If unprovable, that's really interesting, how come?
[deleted] ยท 1 points ยท Posted at 19:36:30 on May 26, 2016 ยท (Permalink)
I'm actually not sophisticated enough in math to say why, but it's proved that you cannot prove the existence of infinities between these sets.
I'd like to point out that there is a minority of mathematicians, called finitists, who hold that all of this is incoherent, idiotic bullshit, Cantor was a gigantic hack, and the rest of us merely fell for his seductive but superficial cleverness.
cool12y ยท 273 points ยท Posted at 13:17:21 on May 25, 2016 ยท (Permalink)
To those who didn't... Its actually a fact that if there are 23 people in the same room there's a 50percent chance that two of em have the same birthday
971365 ยท 114 points ยท Posted at 13:36:59 on May 25, 2016 ยท (Permalink)
Can you explain why a stuffed animal though?
edit: oh is it a joke? lol i thought it was some clever way to say they share a birthday
Since I didn't see anyone attempt this, I did some very rough brute force calculations with a small program, using US age demographics, and it hovered around 50% when there were around 202 people.
I have no idea if I made any glaring errors, so if anyone else wants to take a shot at it, please do. :)
innni ยท 3 points ยท Posted at 14:45:53 on May 25, 2016 ยท (Permalink)*
To solve this, we would have to have a set range of years.
This is the equation for 1 year, where n is the number of people.
1 - (364/365)n! = 0.5
For 10 years (assuming 2 leap years), the equation would be:
1 - (3651/3652)n! = 0.5
That fraction there is ((total days - 1) / total days)
Of course I can solve this to
n! = log(total days - 1/totaldays) (0.5)
Just correct this if I've done something wrong.
JTswift ยท 0 points ยท Posted at 14:55:40 on May 25, 2016 ยท (Permalink)
But there are going to be more and more people the more recent the year becomes. You'd need some data about population demographics if you want to answer the question accurately
JTswift ยท -4 points ยท Posted at 15:11:42 on May 25, 2016 ยท (Permalink)
Sigh. I didn't mean to use ONLY the year of the oldest person. Find the oldest person alive. That's the far end of your years to include.
So, if the oldest person was born in 1910, then you need to include everything from 1910 to now.
BDTexas ยท 3 points ยท Posted at 15:13:33 on May 25, 2016 ยท (Permalink)
I don't think that's what he was saying. He's saying he doesn't know the distribution of ages, which you need to know to answer this question.
But that doesn't fit with the problem. Births probably aren't evenly distributed among days/months either, but the problem assumes that they are. By the same logic you can assume that there's an even distribution of birth years too.
[deleted] ยท 1 points ยท Posted at 07:24:44 on May 26, 2016 ยท (Permalink)
It just depends on the question you're answering. The original question asks how many people you'd need to have a certain percentage chance of having two individuals with the same birth date (month and day) given a even distribution of births. Real birth data by month (for 2014) has an average of 12.375 births per month per 1,000 people, with a standard deviation of 0.81968 (source). That is a not insignificant deviation, yet the question states that it is acceptable to ignore it.
If you ask the same question of shared birth dates (month, day, and year) given an even distribution of births per year between (for example) 1910 and 2009, you still have a valid, and mathematically interesting question. Perhaps it does not have as much bearing on real life due to the larger deviation (mean 18.56825 births per 1,000 people, standard deviation 4.455987 (source), but that does not mean its a completely invalid question (and it is a much easier one to solve in order to get a rough estimate).
Edit: Here is the very sloppy excel spreadsheet I used for calculations, in case anyone is really interested enough to dig that deep.
I'm not sure about 50%, but for a 100% chance, the pigeon hole principle tells us that you need 367. That's the number of days in a year plus one and plus one again in case someone was born on Feb 29 of a leap year.
Edit: Just realized you said year too. I don't know how to do that.
JTswift ยท 4 points ยท Posted at 14:55:07 on May 25, 2016 ยท (Permalink)
I'm certainly no math expert, but I feel positive that the number is way higher than 367.
Two people might have August 8th as a birthday, but one may be born in 1990 and the other in 1972.
Wait, how the heck does that work? There's 365 days in a year and only 23 people. How does that end up working up to a coin toss of two people having the same birthday?
Because it's not the odds of a particular person (say, you) finding another with the same birthday. It's the odds of any 2 people out of the 23 sharing it.
So you've got your 22 chances to match up, the next guy has 21 (because he already compared with you), the guy after him has 20 (he's already compared with you and second dude) and so on.
You end up with 22+21+20...2+1 (works out to 253) possible pairings.
unless you're mean either February 29th is a day or birthdays aren't evenly distributed, would you care to elaborate?
[deleted] ยท 1 points ยท Posted at 20:00:11 on May 25, 2016 ยท (Permalink)*
The entire thing is modeled off of a n sample being truly randomly generated with conditions that are not naturally occurring.
People always cite this as a fun fact but ignores the actual implications of what it means. It is a model generated to test a variety of means in an idealistic scenario of statistical testing.
So we can use this fun fact in that context only. Can't just throw it out like it was here as that is untrue.
It was pointed out that without equal probability of each day of the year that the odds are probably higher. And that is very much likely. But that changes the claim, the mathematics, and the application is what is being cited.
Tldr: dont cite controlled assumption based statistical tests for real life application. Its simply wrong
[deleted] ยท -10 points ยท Posted at 14:28:15 on May 25, 2016 ยท (Permalink)
What you just said in itself is one such assumption
cool12y ยท 5 points ยท Posted at 13:17:21 on May 25, 2016 ยท (Permalink)
To those who didn't... Its actually a fact that if there are 23 people in the same room there's a 50percent chance that two of em have the same birthday
The probability that two people have the different birthdays is 364/365 = ~99.7%.
The probability that three people have different birthdays is (364/365) * (363/365) = ~99.2%.
The probability that 23 people have different birthdays is (364/365) * (363/365) * ... * (343/365) = ~49.3%
Since the probability of A is 1 - (the probability of not A), the probability of a birthday being shared in a group of 23 people = 100% - 49.3% = 50.7%.
Same day as in same day and month? Even if not, how the hell is there a 50% chance with 23 people and 30 days in a month?
lumeno ยท 1 points ยท Posted at 22:43:25 on May 25, 2016 ยท (Permalink)
Sorry, I don't understand this. Let's say that the probability that two people in a room of 23 have a birthday on the same day is X. Doesn't the probability you are trying to calculate also depend on the prior probability of stuffed animals being given to anyone as a birthday present? And so this could be arbitrarily low and you can't really say there's over 50% chance?
0vinq0 ยท 16 points ยท Posted at 18:14:45 on May 25, 2016 ยท (Permalink)
I like this one too, because after learning it, every time I had to consider an x Newton load, I imagined x apples stacked on top of each other on that point. Made problems a bit more entertaining.
He said "an apple weighs"... how did you translate that to "the apple's mass is" rather than "the apple's weight is"..?
Saying an apple weighs 100 grams is indeed technically incorrect because grams measure mass which is different from weight. But in common parlance you will normally hear grams referred to as a measure of weight, because most people don't understand the difference.
[deleted] ยท -7 points ยท Posted at 17:11:47 on May 25, 2016 ยท (Permalink)
At any point in time, somewhere on the Earth, there is a point such that the spot directly opposite it, on the other side of the planet, has precisely the same temperature and barometric pressure.
It's the Borsuk-Ulam theorem, which actually extends much further than the case I mentioned. The simpler case of maps from the circle to R is actually quite easy to see if you've seen the intermediate value theorem before.
Of course, my "physical example" is a bit simplified. It's assuming the earth is a sphere, and temperature and pressure are continuous. We can fix up that first part by considering a spherical shell in the atmosphere instead of necessarily the surface of the earth.
You don't actually care that it's not quite a sphere, because the surface of the Earth is homeomorphic to a sphere. The proof only cares about topology, not the ambient metric space, so we can redefine opposite to mean whatever we want it to mean. In this case, the obvious thing is put a line through your point on the surface and the center of the Earth and see where it pops out, but we could just as easily define opposite to mean something different two inches west (or any other arbitrary point relative to your initial point) (Edit: As pointed out by /u/rawling, this example isn't quite nice enough; see my reply to his comment for a better example), and the proof still works out.
I'd thought about that before and figured as much, but couldn't really make it precise so I was conservative about saying such things if I wasn't sure. :)
rawling ยท 1 points ยท Posted at 21:35:25 on May 25, 2016 ยท (Permalink)
but we could just as easily define opposite to mean two inches west
Okay, I lied very slightly. What you want is an open continuous bijection (basically, a nice function) from the surface of the Earth to the surface of the Earth; we'll call this function opp. Then for any continuous function f from the surface of the Earth to the real plane (we'll use the function evaluating temperature and air pressure), there exists a point x such that f(x) = f(opp(x)).
So in particular, two inches to the west isn't really as nice as we want; thanks for pointing that out. Two degrees west might be nicer, although that fixes the poles, so it's not really an interesting example. Maybe rotate two degrees west and then shift by rotating about an axis through the equator, and that's a better example, though complicated to explain.
vidango ยท 3 points ยท Posted at 15:00:37 on May 25, 2016 ยท (Permalink)
What? I call bluff
Philias ยท 17 points ยท Posted at 15:14:53 on May 25, 2016 ยท (Permalink)*
Nope.
Consider two points on opposite sides of the earth. Let t1 be the temperature of the first point and t2 be the temperature of the other.
Now consider dt=t1-t2. If dt is ever zero it means the temperature is the same at both points.
Assume that dt starts out positive (it works out the same if it starts out negative), now begin rotating point 1 and point 2 around the sphere, always keeping them opposite each other.
Now think about what happens when point 1 and point 2 have traded their original places. dt=t1-t2 will now be negative (if it started out positive).
So, dt went from positive to negative, always changing continuously. That means that at some point in between dt must have been zero. At that point the temperatures on the opposite sides were the same.
(Of course, this all assumes that temperature changes continuously. Ie. that there are no sudden jumps from one temperature to another. For example the temperature isn't 100 degrees at one pointment and right next to it the temperature is 0 degrees.)
I follow it up to this, but how can it account for two variables? I can see how there would be a point for barometric pressure and another, different point for temperature, but not a point where both match.
*Edit - I looked at the wiki and I think I grasp it mathematically, but not 100% intuitively.
*Edit2 - Holy balls I think I get it. Technically you could cut the earth into infinite circles. So start with the equator and find your two points, then rotate the equator an infinitely small amount and get your next points. Since temperature is continuous, the next point should be infinitely adjacent to the previous. Keep rotating and getting points until you've done a full 180, those points define a ring around the circle. Then do the same thing for pressure, sure enough those two rings have to cross and there are your points. Neat.
You don't have to do the same thing for pressure. Imagine you have your dt =0 ring for temperature. Then, for pressure, place your two points on the dt = 0 ring. Rotate your two points along the dt = 0 ring and at some point on this ring dp will be 0. Now you've found your point, because by definition dt=0 on the ring.
yeah but full disclosure: It's been a few years but I took a lot of math in college. calc 1-4, diff eq, linear algebra, algorithms, complex variables, intro to analysis (prob most relevant), discrete math, etc. I never took topology but this sort of proof seems like an extension of real analysis, and it's the same thinking that goes into a lot of proofs for theorems in complex variables.
That is fascinating. Could you help me understand it better? Around which axis do you rotate the equator? Around which circle do the points define a ring(ring=region bounded by two cricles)? Is dt=0 on every point in the ring or on a path bounded by the ring.
Also what happens if one of the two initial points with dt=0 is a local temperature maximum and the other one is a local minimum? Even when temperature is continuous there wouldn't be a pair of adjacent points with dt=0.
It's not precisely true as I have stated it, but for a continuous function from the 2-sphere to R2 , which is essentially how we think of temperature and pressure on everyday scales at the surface of the earth, it is true.
In AP Calc we learned about Gabriel's Horn, a geometric figure with finite volume but infinite surface area. So basically, you could fill it with paint but not paint the inside. Cool stuff
Ian666 ยท 19 points ยท Posted at 18:35:44 on May 25, 2016 ยท (Permalink)
If you can fill the inside with paint, isn't then the inside necessarily painted?
[deleted] ยท 5 points ยท Posted at 23:44:51 on May 25, 2016 ยท (Permalink)
Don't stress the physical analogy, it always embeds a contradiction. For one, you can't fill it with paint because then you would be sending paint an infinite distance in finite time.
It's crazy interesting. One of the uses is for stadiums and concert halls. You generate a close impulse sound and measure it at different locations. What you get is a signal convolved with the acoustics of the large room and then you can change how the speakers work so it nullifies any weird artifacts generated by the shape of the room.
Yep. Or you can do the opposite and make it sound like you're in any other room. I had to do this for a lab, where we were given a clap (impulse response) from concert halls or cathedrals and convolved it with someone speaking to make it sound like they were speaking in that concert hall / cathedral.
I wouldn't know where to start. I learned it in a signal theory class but it's not something I would recommend picking up as a hobby. Maybe Google/YouTube around for convolution, impulse response, inverse convolution and it'll get the ball rolling.
[deleted] ยท 1 points ยท Posted at 20:16:40 on May 25, 2016 ยท (Permalink)
What if you place it in a pool ful with paint?
z3ktorm ยท 5 points ยท Posted at 20:46:15 on May 25, 2016 ยท (Permalink)
It wont fit. It's infinitely long
[deleted] ยท 0 points ยท Posted at 21:01:08 on May 25, 2016 ยท (Permalink)
[deleted]
z3ktorm ยท 1 points ยท Posted at 21:05:04 on May 25, 2016 ยท (Permalink)
Well okey then. Then you would need an infinitely long pool
yo though there's no such thing as an "infinity number" (just an infinity, because infinity is never a number) and the different sizes of infinity apply to cardinalities of infinite sets, not limits like the the biggest size a pool could have
[deleted] ยท 1 points ยท Posted at 20:27:50 on May 25, 2016 ยท (Permalink)*
Not necessarily true. A sequence can increase by a number that approaches 0 and still diverge. For example, a Harmonic series which is the sum of 1/n starting from n=1 and going on to infinity. Even though 1/n approaches 0, the sum of the sequence still approaches infinity.
[deleted] ยท -2 points ยท Posted at 20:59:29 on May 25, 2016 ยท (Permalink)*
You can actually show that for any real number r there is some integer n such that if you add up the first n terms in the harmonic series you end up with a number bigger than r. This is what we mean by the series diverging.
The growth of the sum of the first n terms is logarithmic, the sum is greater than log(n+1) but less than log(n) + 1. Logarithmic growth is ridiculously slow, the example which is usually given is that the sum of the first 1043 terms is less than 100. Nevertheless there is some number of terms which will take you over a million, trillion etc.
The 4 colour theorem is a result of graph theory... and it's such a strange topic. The statement is easy enough for a 5 year old to understand but the proof required deep mathematical insight alongside heavy computational power. It's a subject where there doesn't seem to be any rhyme or reason to the results, no elegance. The 4 colour theorem is almost just a beautiful coincidence.
[deleted] ยท 3 points ยท Posted at 19:39:37 on May 25, 2016 ยท (Permalink)*
To be precisely, you can paint any planar graph with 4 colors (3 if there are no triangles). If you "translate" your map into a graph with vertices and edges you see that the pizza example is not planar. ;-)
Imagine I give you a map that is just a rectangle and it's divided into "countries" that are just vertical stripes. You could color the map black-white-black-white... so that each black stripe only ever touches white stripes. Sure, you COULD use 27 different colors, but you can make it so that no two countries of the same color touch by just using two colors.
But I could then draw another map where you'd have to have two countries of the same color touch if I only let you use 2 colors. Maybe this map requires you to use 3. Sure, you COULD use 27 colors, but this map requires you to use 3.
I could then come up with a harder map and require you to use 4 colors.
I cannot come up with a map that requires you to use 5. Sure, you could use 5, but you will never be required to use 5.
I think you have to already intuit 0.999... = 1 to intuit that 0.999...*10 = 9.999...
How do you figure? You just need to know that multiplying by 10 moves the decimal point to follow that step.
[deleted] ยท 1 points ยท Posted at 03:51:50 on May 26, 2016 ยท (Permalink)
Good point, I hadn't thought of it like that. I think I was taught this using the notation with a single digit of the repeating decimal and a line over it so addition made more sense like that.
Oh, I was taught that way too, and that's the notation I use (I'm a teacher). But of course, I don't know of any good ways to represent that on Reddit. I probably only recognized the proof immediately because I show it to people frequently.
maz-o ยท 1 points ยท Posted at 19:15:16 on May 25, 2016 ยท (Permalink)
or even simpler:
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...
3/3 = 1
0.999... = 1
Ddyer11 ยท 1 points ยท Posted at 00:55:30 on May 26, 2016 ยท (Permalink)
I've actually been thinking about this a good bit lately. The best way I've come to accept (dumb it down) it is to essentially look at it as 1.0000 repeating with a 1 at the end of the zeroes. If you accept that the zeroes are infinite, it's much easier to understand.
/u/rantforupdate was pointing out that 3! is 3 factorial, 3*2*1 so multiplying both sides by 3! actually ends up with you multiplying both sides by 6 and complicating the proof.
I really wasn't going through the math, but if you're unfamiliar with Terryology(actor Terrance Howard's math system) it very much worth a Google. The joke might make a bit more sense then.
I just meant that the original comment wasn't using any mistaken math and didn't want anyone misled. Though introducing people in this thread to terryology may be interesting...
I may or may not have created a new account called RealTerranceHoward and left that root 2 = 1. I was a little late to respond but I figure it would be worth it to those in on Terryology.
I forget the proof exactly but I think the most legitimate proof is the one using geometric series. Something along the lines of this: .99999 repeating is the same as .9 +.09 +.009 +.0009 ... which is a geometric series where first term a=.9 and ratio r = .1. using the geometric series sum, the series sum is equal to a/(1-r) = .9 / (1-.1) = .9 / .9 = 1. Correct me if anything is wrong but I think this is what it is
The problem with the "usual" proof is that there is a slight leap of faith when you start with x=0.9... and move to 10x=9.99... You indirectly use some kind of distributive property of multiplication over infinite sums, which does need to be justified properly.
I always understood the 'sum' of a mathematical series was the limit, as in the lowest number that would never be reached by that series, rather than the actual sum of all the values?
It is a limit, yes. But it's not quite right to think of it as something which can't be reached by the series. If that were true, what's 0 + 0 + 0 + 0 + ...?
[deleted] ยท 1 points ยท Posted at 19:06:15 on May 25, 2016 ยท (Permalink)
What does being a geometric series have to do with it? Your qualm doesn't seem to be specific to geometric series. In fact, you never even mentioned geometric series. You said:
I always understood the 'sum' of a mathematical series was the limit...
etc.
[deleted] ยท 1 points ยท Posted at 19:32:29 on May 25, 2016 ยท (Permalink)
You've raised no issue specific to geometric series. What does it matter what the original proof was? Your statement applies to infinite series in general. The fact that the initial proof was a geometric series is irrelevant.
But even if we were talking about geometric series specifically, what about this example:
0 + 0 + 0 + 0 + ...
Which you don't seem to have said anything about. Except the post immediately after it, which I honestly can't make heads or tails of.
[deleted] ยท 1 points ยท Posted at 19:38:33 on May 25, 2016 ยท (Permalink)
I think the primary issue is seeing a limit, and hence a series, as a "process." A series is not "reaching" anything. 0.9 + 0.09 + 0.009 + ... is equal to its sum as an infinite series, which is 1.
[deleted] ยท 1 points ยท Posted at 19:43:54 on May 25, 2016 ยท (Permalink)
It is absolutely equal to 1. By definition it is equal to 1. It is equal to the limit of its sequence of partial sums, {0.9, 0.99, 0.999, ... }, whose limit is unequivocally 1, again by definition.
[deleted] ยท 0 points ยท Posted at 19:56:33 on May 25, 2016 ยท (Permalink)
Ok so if it's equal to 1 tell me, when you've added the term that brings it to 1,
This is what I was talking about, thinking of the limit as a process. I think it confuses a lot of people. It would be best to stop imagining an infinite sum as a process, or thinking of a man adding up terms for the rest of forever. It's very confusing to think of that way. An infinite series is a limit of a sequence of partial sums. A limit is a number that satisfies the definition of a limit for the sequence.
[deleted] ยท 1 points ยท Posted at 20:14:19 on May 25, 2016 ยท (Permalink)
The limit is a number, the series is a process, why is that so hard for you to understand?
Because it's untrue. I'm not the one arguing with literally all mathematicians. There are numerous proofs that 0.999... = 1 that don't rely on series, how do you reconcile them with your belief that 0.9 + 0.99 + 0.999 + ... apparently does not equal 1?
That series is not a process. It is a representative for a number, and that number is 1.
That's not a proper series because it's common ratio is 0
That sounds like you've just thrown out a case as not proper because you don't like it. But fair enough, defining the common ratio for it is a little problematic.
[deleted] ยท 1 points ยท Posted at 20:26:03 on May 25, 2016 ยท (Permalink)*
Equality alone should tell you that. 1 + 3 = 4 is not representative of me putting two things together to get something different, the equals sign literally means "these two things are the same."
As for your not being convinced, what number falls between 0.999... and 1?
[deleted] ยท 1 points ยท Posted at 20:32:06 on May 25, 2016 ยท (Permalink)
It literally means that if you do the process of grouping 1 thing with 3 others you get a sum of 4 things.
"Adding up" is how we calculate things, and that is a process, but I think any algebraist would disagree with you that that's how we should interpret the mathematics itself, and I think empirically your rejection of well-proven mathematics is good reason to believe that that's not a helpful way to think of it.
That argument is useless as well. Its the same as saying no integer comes between 9 and 10 therefore 9 = 10.
No it's not, because the integers don't have the property that between any two distinct numbers there exists another number. The reals do have that property. It's easy to see, for instance, that (9 + 10)/2 is not an integer, but for any two distinct rational numbers, (9 + 10)/2 is a rational number which lies strictly between them. Not sure why you'd think you can just change number systems and expect all properties to carry over, but the fact that the reals have that property comes straight from the axioms for the construction of the real numbers. See Principles of Mathematical Analysis by Rudin if you don't believe me.
[deleted] ยท 1 points ยท Posted at 20:49:21 on May 25, 2016 ยท (Permalink)
What you're saying is that there ought to be some correct interpretation of numbers which means 1+3=/=4 which is frankly ridiculous.
That's is patently not what I am saying. In fact, what I just said is that 1 + 3 = 4 means that 1 + 3 and 4 are different representations of precisely the same object, which is quite the opposite of what you just said I implied.
Also we disagree on that being well proven. I hate to play the "my dad is a mathematician" card but both my parents hold maths based postgraduate degrees from prestigious universities and they disagree on whether 0.999...=1 so your insistence that I'm disagreeing with all mathematicians is just wrong.
If they were mathematicians I'd say that's frankly embarrassing for their respective universities, but what is "math-based?" I have spoken with many an electrical engineer, for example, who has had deep-seated misunderstandings of the structure of the real numbers. A math-based degree does not a mathematician make.
Also, I will admit that "all mathematicians" was a bit of hyperbole to begin with. There are some wacky mathematicians (see: N.J. Wildberger). But the vast, vast majority understand this. It's taught in introductory analysis classes.
I'm not going to disagree with Rudin's axioms, but I think your argument that they imply 0.99..=1 has the problem that if it were true there would be no such thing as any number at all as all numbers would blend into each other and be indistinguishable (I'm sorry if I didn't word that very well)
I don't see how that's the case. In fact, that doesn't follow from the axioms at all, but specifically I don't see your reasoning for it. All distinct real numbers have finite distances from each other. Arbitrarily small, yes, but finite.
[deleted] ยท 1 points ยท Posted at 21:17:01 on May 25, 2016 ยท (Permalink)
This is a bit of an awkward way to explain what I'm trying to say but if a number beginning with 0.9 can equal a number beginning with 1.0 something has gone wrong with the maths along the way.
I understand this. It's definitely not intuitive. In fact, I still find it a bit strange. This sort of thing causes some problems in places. For instance, proving that a line and a plane have the same cardinality. There is a common way to do this that involves taking points in the plane and interleaving the digits of their x and y coordinates together to get a single number that represents a point on the line (I was actually shown this in my general relativity class, and have found it other places since). The problem is, this isn't actually well-defined! The issue is that if you have a number like (0.500...,0.400...), trying to "interleave digits" to map it to a number like (0.540000...) can also be written as (0.4999...,0.3999...), which maps to (0.4399...) which is different from 0.54 no matter how you slice it. Luckily, there's a way to fix up this method into something that works, I just wanted to point out that even though the issue is settled, that doesn't mean it's not thorny. My general relativity professor was not ignorant of these sorts of issues, his research is closer to pure mathematics than physics despite being a physics professor, but even he didn't seem to notice the problem.
I feel a little bad that our discussion got somewhat heated, but hopefully it wasn't too bad. You definitely shouldn't take my word for it just because a lot of people believe it, but that should at least make you think. :)
If you want an introduction to this stuff that's gentler than Rudin (which is famously tough) take a look at something like Understanding Analysis by Abbott. I found it to be very gentle and clear. Rudin is far from gentle.
Good talking to you.
[deleted] ยท 2 points ยท Posted at 21:46:23 on May 25, 2016 ยท (Permalink)
I'll take responsibility for it getting heated, I have a terrible habit of getting frustrated when I can't understand something so I'm sorry for that:(
I have to take responsibility for part of it, but only because I have had so many discussions about this before. It starts feeling like arguing with one incredibly hard-headed person over the course of years...
It may also interest you to know that I am a convert! I didn't believe this either when I first saw it, but then I hadn't really taken a strong interest in math, and had taken no calculus at that point. That's my excuse and I'm sticking to it. :)
I'll definitely be reading that book and continuing to convince myself why I'm wrong. Once again thanks for taking your time to explain everything:)
The later chapters are calculus based, which it seems you might have had some exposure to if you know what a geometric series is, but the first few chapters can be read by pretty much anyone (given a certain amount of mathematical maturity). Good luck!
I think it depends on the type of series because different series have different behaviors. Geometric is very different from an alternate series for example
jusjerm ยท 8 points ยท Posted at 16:41:39 on May 25, 2016 ยท (Permalink)
I can only imagine how many "you can also explain it with 1/3.." comments this will force upon you by the end of the day"
Nibiria ยท 5 points ยท Posted at 17:32:10 on May 25, 2016 ยท (Permalink)
Is this only true because numerals are an imperfect representation for...well, numbers, I guess?
Kinda. It's a side effect of how decimal notation is defined. Any number whose decimal representation ends in a000... has a second decimal representation that ends in (a-1)999...
You don't need to. I like to think of .999... like an asymptotic curve, a line number that continually approaches a given curve 1 but does not meet equal it at any finite distance.
That sounds like the opposite of what I'm saying. You can continue counting off 9s until the end of time, but it isn't 1. You keep getting closer, but you never get there.
You don't continue counting until the end of time. If you stop counting at the end of time, you've left to count an infinite number of nines still. They are the same value. There is no counting, but in order for something to never quite reach another number, there has to be another step to counting it.
For example, if you stop for a moment during this "counting" and you realize that you aren't quite there, you can add another 9 and you have a number that is between your stopped number and one. The idea of .999.... Is that it represents the entirety of the infinity. You have an infinite number of nines. Think about as if you're taking a bite of a muffin, but each bite is half as small as the last. If your initial bite was only half of the muffin, will you ever complete your muffin? Get back to me with an answer.
converting a fraction like 1/3 to decimal as 0.333... is not precise.
Yes, it is. 1/3 is precisely equal to 0.333...
It's not precisely equal to 0.3 or 0.33 or 0.33333333333 or any other representation with a finite number of 3s. But the notation "0.333..." means that the 3s go on forever. And that is precisely equal to 1/3.
[deleted] ยท -4 points ยท Posted at 18:01:52 on May 25, 2016 ยท (Permalink)
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Filobel ยท 4 points ยท Posted at 18:15:07 on May 25, 2016 ยท (Permalink)
No it's a side effect of how the notation is defined. The nice thing about math is that 0.333... is perfectly precise because we know exactly what it means even though it's technically missing information. We know that it refers to 1/3 which is not missing information. Likewise, we know that 1.000... refers to 1 and 0.999... also refers to 1. It doesn't matter which way we choose to write it because our ultimate goal is to know which single object we're talking about, so it can't be a flaw in the number system or the notation because both representations do exactly what they're supposed to. They tell us that we're talking about 1.
And 0.999... = 1.000... in all numbers systems because that's how the notation is defined. You'll have to redefine your notation if you want 0.999... to be infinitesimally close to 1 in other number systems.
"1/3" and "0.333..." are two different representations of the same exact number. There is no number that is between them.
KSFT__ ยท 3 points ยท Posted at 17:46:45 on May 25, 2016 ยท (Permalink)
No, it's completely correct. The numbers are equal.
[deleted] ยท -6 points ยท Posted at 17:58:33 on May 25, 2016 ยท (Permalink)
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Rsaesha ยท 3 points ยท Posted at 18:14:15 on May 25, 2016 ยท (Permalink)
Saying 0.999... can't equal 1 because 0.999... is not 1 is a bit like saying 1/2 can't equal 0.5 because 1/2 is not 0.5. That is to say, just because two numbers look different doesn't mean their value is different.
0.999... and 1 are two different numerical representations of the value "1". 3/3 is another numerical representation of the value "1".
This is true for all bases. In base 3 (like your example), 0.222... is equal to 1.
[deleted] ยท -3 points ยท Posted at 18:32:30 on May 25, 2016 ยท (Permalink)
No it isn't. Decimal notation is the name in every number system. There are other number systems with infinitesimals but 0.999... is not how you would write 1-infinitesimal.
Filobel ยท 1 points ยท Posted at 18:14:47 on May 25, 2016 ยท (Permalink)
.9999 is not 1
0.9999 is not 1. 0.99 repeating is 1, that's the whole point of the proof. If you think it is false, then please prove that they are different numbers.
Another way to show that they are the same number is that any two numbers that are different has at least 1 number in between them. In fact, they have an infinite number of numbers between them. For instance. Between 1 and 2, there is 1.5. There is also 1.1, 1.123, 1.59178279345983474520897352, etc.
Now, please show me a number that is found between 0.9999 repeating and 1.
This is probably my least favourite mathematical fact. I get why it is true, I understand how it works mathematically with a ton of different proofs, but I still refuse to accept that, from a philosophical standpoint, .99 recurring is ever truly equal to 1
In one sense, that's probably because you have an almost correct intuition of what .999... is. We define infinitely recurring numbers as the limit of rational numbers. So .9999... is the number you get by finishing the sequence {.9,.99,.999,.9999,...}. The limit of this sequence is exactly 1. But in our real world, we don't have infinity, an at each step of this sequence, it's distinct from 1.
That said, let me state one somewhat philosophical problem with considering them as distinct numbers. There is a number between any two numbers, right? Well, what's the number between 1 and .9999999999.... ? It's impossible to write such a number down. In other words, these two numbers are infinitely close to each other (no space between them) but are different from each other. How can this be the case? It doesn't fit our understanding of the universe and how its order works.
I think a better way is to use the fact that the reals are dense. No matter how small your epsilon, you cannot find a find an interval that contains .999... and not 1. Thus they are the same.
Kahzgul ยท -1 points ยท Posted at 20:17:18 on May 25, 2016 ยท (Permalink)
This proof also disproves the "infinite points" problem. Namely the theory that nothing can actually move because in order to move from point A to point B you have to pass through an infinite number of points that lie between them, and it would take forever to traverse an infinite distance. Common sense shows this to obviously be false, but it takes the proof of 0.999...=1 to prove the claim is false. Namely, there are distances so small as to be literally indistinct from one another, and thus any two points, close enough together, are effectively the same point. Therefore stating that an infinite number of points exist between any two points A and B is a meaningless statement - in order to truly define distinct points, they must be far enough apart from one another to measure, and thus there cannot be an infinite number of them. It is therefore possible to traverse both a finite number of distinct points and an infinite number of indistinct ones.
Namely the theory that nothing can actually move because in order to move from point A to point B you have to pass through an infinite number of points that lie between them.
Is that about point's in the real world or in a Mathematical sense? The number of points is only an issue to begin with if you assume there is a lower limit in time/energy required to move from one point to the one next to it.
Therefore stating that an infinite number of points exist between any two points A and B is a meaningless statement - in order to truly define distinct points, they must be far enough apart from one another to measure, and thus there cannot be an infinite number of them.
This is only true if you cannot measure arbitrary small distances. Which probably holds in the real world since there are plank lengths and other Quantum stuff I'm not familiar with.
But in Math that is not true since the distance between points can be infinitely small. So we can measure any distance, no matter how small.
Between every two distinct points there ARE infinite many Points in Math. For one example:
Just imagine the distance between the points on a number line. No matter how big or small the distance between them if it's a real value we can measure it. (Actually also for complex ones but that gets complicated.)
So if we can measure it we know what half of it is. So we can also tell that and where the point exactly between the two is. Start again using the first point and the resulting middle point of that calculation and you can repeat the process getting another point. Then you can take that point to get another one and you can do this forever. And at each step you will have an exact number for where the Point lies. Resulting in a infinite series of points.
Kahzgul ยท -3 points ยท Posted at 22:42:40 on May 25, 2016 ยท (Permalink)*
Right, that's exactly the problem. And the proof that 0.999... = 1 solves it, because there exists some limit for the measurable distance between points such that 0.000...1 = 0. Evidencing that there is actually a limit to the number of distinct points between any two points.
To be short, it's because the notation doesn't really mean anything. There are multiple ways it can be interpreted so that it does make sense, such as what /u/VincentPepper did, or interpreting it as an infinitesimal, but the claim seemed to be that .0000...1 was a number that made sense in some self evident way, which isn't really the case.
That step is wrong unless you follow it with 1= 1. 0.99... is the same as 1. If you write 1 instead of 0.99.. which we can because we know the same it would be:
1+0.0..1 = 1 + 0.00..1
1 = 1 + 0.00...1
Which doesn't make sense. Because either 0.00..1 is distinct from zero in which case the transformation on the left side is wrong. Or it is zero in which case the one on the right side is while not wrong irritating because it's the same value as 1.
As it stands you treat it different on each side of the equation resulting in a wrong proof.
It helps to try and think about what 0.00...1 should actually be, as a value. I could think of two ways here.
0.00...1 = 1-0.999... = 0
Which would mean it's zero proving the above pointless.
Ok so let's define it as a infinite number of zeros followed by a one! Let's try this.
You can get an arbitrary number of zeros by rewriting it as 1/10n where n is the number of zeros. So let's just put infinity as n and be done.
So now we get 1/infinity. But what is 1/infinity? Short answer: It's once again zero.
For another approach: If you say there is a smallest mathematical defined length l that is different from zero you have to be able to define it.
So l = some formula.
But if you come to me and say "Hey l is the smallest thing!" I can always say: "But l/2 is smaller and also defined" Which is true and why there is no smallest number.
The infinite points "problem" is not wrong because there are not infinite many points. (There are). But because the absolute distance doesn't change no matter in how many parts you break it.
As the number of points increases the length between them decreases.
Break it in two parts each is half of it. Four parts each a quarter.
Until at infinit many distances the length becomes infinite small.
At which point the math becomes tricky, but you can show that even these infinite many distances which are infinitly small sum up to the same total distance that was between your two starting points.
epwnym ยท -4 points ยท Posted at 18:28:38 on May 25, 2016 ยท (Permalink)
It's impossible to write such a number down.
No it isn't. It's no more impossible than "writing down" an infinitely recurring set using an ellipsis. Just because the Real Number system doesn't have denotation for infinitesimal differences (I don't think) doesn't mean we couldn't invent one.
You can't just invent new real numbers by giving them notation. Whatever you invent is part of a different number system that extends the reals. It is not a real number.
And while we're at it, why don't you go ahead and define that notation? What exactly does it represent and how can you use it for other numbers?
Not really, since mathematicians have already considered a math along these lines. A number bigger than 0 but smaller than any other number is called infinitessimal and are used extensively when looking at the hyperreal numbers.
It's just decimal notation. They're both different ways of writing the same thing, but one of them is less annoying to write because we can just dump the zeroes and write 1.
This is actually true for every number that has a terminating decimal expansion. They all can be written as x.abcd000... or as x.abc(d-1)999...
Aww that other guy deleted his comment. I'm just going to reply to myself then.
It's a side effect of the notation that you're going to run into regardless of which base you pick. Changing the base just changes which numbers have two representations. If the denominator of a number is equal to a product of powers of its prime factors, then it has two representations in the base-n equivalent of decimal notation. So anything in base 10 with a denominator equal to 2a * 5b has two different decimal representations.
If it isn't equal to 1 then there must be a number in between 0.9 recurring and 1, as the set of real numbers is not discrete. Which means there must be some number 0.9...1. But there are infinite 9s, so this hypothetical 1 is never reached; the number is simply 0.9 recurring.
I completely agree with you in this instance. 0.999... = 1 is simply a result of a combination of the properties of the real number system and the notation we use for it. None of the 'proofs' (most of them make unstated assumptions in round about ways) do anything to show that infinitesimal numbers are impossible, which is what most people are really asking when they pose the question, as they are not and there are number system extensions where numbers less than any finite real number but greater than zero are possible.
The way I rationalize it in my head is that .999~ and 1 are not exactly the same number, as our intuition tells us. But they're so infinitely close together that there can be no meaningful or useful distinction between them. Our mathematics cannot differentiate between them, as shown in the proofs that you can find, but by definition they are not exactly the same number.
[deleted] ยท 2 points ยท Posted at 04:14:41 on May 26, 2016 ยท (Permalink)
They're both being represented in decimal numbers. It's not possible for two values to be represented by different numerals in the same format...that's by definition not how numbers work.
[deleted] ยท 3 points ยท Posted at 04:31:28 on May 26, 2016 ยท (Permalink)
It's okay for numbers to have different fraction representations. You think 4/2=6/3 right? It's the same thing with decimals. There's no reason why a number can't have two different decimal expansions.
[deleted] ยท 1 points ยท Posted at 04:21:19 on May 26, 2016 ยท (Permalink)
It's not possible for two values to be represented by different numerals in the same format
Proof?
that's by definition not how numbers work
Can you define the real numbers? Hint: if you don't know what Cauchy sequences or Dedekind cuts are, no you can't.
By the definition of decimal notation, that's exactly how numbers work. All numbers with terminating decimal expansions have a second representation. e.g. 0.5 = 0.4999...
This is a fact, and it's much more interesting to think about why it's true than to argue incorrectly that it isn't just because it doesn't match up with what you learned when you were 8 years old.
Well you're in luck because its not true. The issue with the proof is that he replaces .999... with x. You can't do that because x is fundamentally a different number than the .999... that was replaced with.
The issue with the proof is that he replaces .999... with x. You can't do that because x is fundamentally a different number than the .999... that was replaced with.
I was going to say there's a proof of this using an infinite series, but this works, too.
Dr-K-G ยท 5 points ยท Posted at 17:26:38 on May 25, 2016 ยท (Permalink)
If you'd really want to use the above proof rigourously you first need to prove that multiplying by 10 is the same thing as moving the decimal point one to the right which again requires using infinite series. Infinite series are unavoidable because that's how decimal representation is defined.
Zarco19 ยท 1 points ยท Posted at 04:54:39 on May 26, 2016 ยท (Permalink)
True, but for people who are really struggling with this, it's probably because they don't know a whole lot of math. These simple and loose arguments will probably work better than trying to talk about infinite series. At best, they probably don't get it and miss out on understanding it, and at worst they think you belong on r/iamverysmart.
There's also 1/3 + 1/3 + 1/3 = 1 and .3333... + .3333... + .3333... = .9999...
.3333... = 1/3
[deleted] ยท 7 points ยท Posted at 14:41:38 on May 25, 2016 ยท (Permalink)
always liked this one
[deleted] ยท 8 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
Same. Mainly because it is so hard for most people to accept, and watching their internal struggle to accept a fact that has been logically proven is amazing and insightful.
The reason it's "difficult to accept" is because I suspect that a lot of people who are curious about the answer aren't so much interested in say, what the limit of a sequence defined by lim[n from 1 to infinity] (sum of, for k from 1 to n: ( 9*10-k)) is. What they are interested in is whether or not infinitesimal numbers 'exist', and this why the solution to this other problem baffles them so much, it does nothing to show that they can't exist in itself or in what context this can be said to be true.
I am looking at this, but you got rid of x on one side but didn't get rid of it on the other. I am really confused by the work, but I am not really good at math either, so I can't dispute it.
Yes. Any number with a terminating decimal expansion (i.e. ends in 000...) has two different decimal representations. For example:
0.5 = 0.4999...
0.2483 = 0.2482999...
Remember that 0.5 = 0.5000... and we just chop off the 0's because it's clear what the number 0.5 represents. If we chop off the 9's from 0.4999..., we get 0.4 which is not the number we're trying to represent. That's why you only ever learn about one representation and why it seems to weird to find out that there's a second way to write the same number. It's just annoying to write it that way so we don't.
[deleted] ยท 1 points ยท Posted at 17:48:53 on May 25, 2016 ยท (Permalink)
10x = 9.999...
I lost you here. I was expecting to see:
10x = (10)0.999...
If you are trying to prove to me that 0.999... = 1, then you cannot say 10x = 9.999... in the same proof!
By the way I DO accept that 0.999... = 1, but I am not satisfied with the above proof.
if someone still doesn't believe this, ask them what the difference between 1 and 0.999...(reoccurring) is. Some will answer 0.000...(reoccurring)1 then point out that you will never reach the 1 because there are infinitly many zeroes before it.
meh100 ยท 1 points ยท Posted at 18:53:36 on May 25, 2016 ยท (Permalink)
That's not a proof. The step from x = .999... to 10x = 9.999... assumes that what 9.999... is is known. The same assumption is in that step as in the claim that .999... = 1.
0.999... is a real number because it's equal to 1. A number that's infinitesimally close to 1 is not a real number, and you wouldn't write it as 0.999... because that notation already means something, and that something just happens to be the same thing that 1.000... means.
I'm not convinced that .999... = 1.000...
If you imagine each decimal place as a step 90% of the remaining "distance" to 1, and you repeat that 90% step infinitely, you will never reach 1. Rounding to one makes a ton of sense for realistic applications of course, but I'm saying the actual value is more accurately ( 1 - an infinitely small number)
Thanks! It doesn't do 0.999...=1 (on purpose) but 0.999...=1 for the exact same reason that 0.4999...=0.5. There are actually two representations for every number that has a terminating decimal expansion.
This is just how things are defined. Real numbers and decimal notation both have rigorous definitions and you can't really disagree with a definition. You can only provide a different definition that you think is better, and that's a lot more difficult than you might think.
The cool thing about math is that a lot of the stuff you use is built on top of a lot of abstraction. The real numbers are a metric space which means that they're also a topological space, and we know a lot of things about both of those structures in general. That means that everything that we know about topological spaces and everything that we know about metric spaces automatically applies to the real numbers. Real numbers are also a field which means that we can apply all of the things that we know about fields in general to real numbers. Since they're a field, they can be used to build a vector space which means that we can USE real numbers to do all kinds of awesome stuff in linear algebra.
If you change the definition of the reals, then it's very possible that you will lose a lot of the properties that these other structures require. So it's totally okay to say that you can imagine a number that gets infinitely close to 1 but never touches it. It's just not a real number. It is a hyperreal number and a surreal number, but it still wouldn't be written as 0.999... You can write it as 1-ฮต where ฮต is your infinitesimal, just like you suggested at the end of your post.
If you imagine each decimal place as a step 90% of the remaining "distance" to 1, and you repeat that 90% step infinitely, you will never reach 1. Rounding to one makes a ton of sense for realistic applications of course, but I'm saying the actual value is more accurately ( 1 - an infinitely small number)
And so based on what I've said, this just isn't how decimal notation works. You're totally free to come up with your own notation, but when we say that 0.999...=1 we're using a very specific set of numbers and very specific notation, and people get really tripped up on it because they've been using those numbers and that notation forever without truly understanding what they mean. So my little app is just to show you how we construct a decimal. It's not my opinion, that's just how it works. And we don't have to round because we're doing math, not science. It is perfectly valid to talk about the end of an infinitely repeating process because we're not limited by reality and we can irrefutably prove that our result follows from our hypotheses.
conanap ยท 1 points ยท Posted at 19:47:55 on May 25, 2016 ยท (Permalink)
other than the 1/3 proof and this proof, also from geometric series:
0.99999999999.... = 0.9 + 0.09 + 0.009.... = 9/10 + 9/100 + 9/1000....
note ratio between each term is 1/10. 9/10 * 1/10 = 9/100, 9/100 * 1/10 = 9/1000....
then we have r = ratio, |r| = 1/10 < 1, so it converges to 9/10 / (1 - r) = 9/10 / (9/10) = 1
Is there any broader implications here? I mean... It breaks my brain a little but does this suggest that there is a finite quantity of numbers since there is a point where .999... = 1? Or that 1!=1 because 1=.999.... ?
Bit late here, but no. There are still infinitely many numbers between 0 and 1. For any given number .9...9 you can add another digit to the end and it won't be equal to 1. It's only at an infinite number of 9's that it becomes 1.
solos90 ยท 1 points ยท Posted at 23:55:44 on May 25, 2016 ยท (Permalink)
I know that 10 x .9999 = 9.999, but is there a proof that the "shift the decimal point to the right" is allowed to be used on infinitely repeating decimals?
He's not a bot, but is very angry. He just sent me this:
I went through your post history and you have a lot of comments that are literally the same.
Have a recycled answers? Yes I have. But I also spend about 6-8 hours a day on Reddit and have probably seen most answers in many threads. You said most of my top comments are copy and pasted....so let's examine my top 25 posts:
Yup got it from Reddit. But it is my actual favorite quote. I'm pretty sure I've posted that every single quote thread since I first saw it.
Mexican Cartels are scary as fuck and that was an original comment.
Completely original comment about me getting pissed at the Walking Dead.
The giraffe fact.....well I've posted this a million times. I am the original copy of that material I think.
I do torrent a lot of shit.
Geico caveman comment: I saw that on reddit before. But it was still a horrible show.
Original comment about some guys lab.
Subway one. Saw that on reddit.
Ted Cruz....I hate Ted Cruz. While not original, it is a running joke.
Comment about wife and dinner. I've made this joke a million times on reddit.
Comment about getting old. Completely original with an edit.
I live near Plymouth rock and it sucks. It's original although it has been said before on reddit.
would you rather question. It's a would you rather question. I'm sure it's been on reddit before.
Seen before on reddit but it's still funny.
My giraffe fact again which is also posted multiple other times by me I'm sure.
saw on reddit but someone asked me for it I think.
suicide hotline which isa complete copy and paste and I don't feel bad about that.
Don't know what this is from but it is original
It's about my wife.....sooo
this is a copy and paste......from my own story awhile ago.
common reddit answer but still true.
seen on reddit but certainly true.
just a true comment.
my favorite quote again
comment about my wife and dinner again.
So back the fuck off.
ijizz ยท 29 points ยท Posted at 15:44:10 on May 25, 2016 ยท (Permalink)
Well, at least his argument was relatively well substantiated as opposed to just blatant swearing.
Dude the Canadian cadet program does wonders for kids. Got it in 2013, I was 16 at the time. Haha I was just like "whoa that's cool" I actually had that password until this past year.
[deleted] ยท 49 points ยท Posted at 15:18:44 on May 25, 2016 ยท (Permalink)
I don't really think it is. Some made a false accusation to him and he responded in private to the person that did it.
He's just defending himself, jeez
akjax ยท 3 points ยท Posted at 23:28:45 on May 25, 2016 ยท (Permalink)
I love that about Reddit. It's like it's perfectly OK to accuse people you've never met of lying about their personal life or even not being real, but the second you try to defend yourself you're "sad", "over reacting" and "care too much about karma".
akjax ยท 1 points ยท Posted at 23:30:00 on May 25, 2016 ยท (Permalink)
Yeah, because calling out someone as not a real person isn't sad, but trying to defend yourself when someone says you aren't even real? Soooo pathetic. /s
Keep on posting (and reposting) as you feel the need, /u/gronkspike25, and please ignore complaints about reposting. When you (re)post good stuff, the reddit experience is improved for the vast majority of people who are mature enough to simply move on to the next comment, when they see something familiar.
I've been attacked really viciously a couple times for offerings of original material. One was a joke of my own invention, that I think is pretty funny, which I posted to /r/jokes with the hope and expectation that some redditors would enjoy it. One of the first three responses was someone's sarcastic "Oh you are so funny!" with a truly ghastly image -- like I was humorless but had a huge and distorted grandiouse self-image. I shuddered -- and deleted my joke. The memory is still painful.
I've allowed myself to be intimidated by that.
Don't let that happen to you.
In a spirit of kinship, I repost the relevant XKCD about the 10,000 who learn about well-known things for the first time every day in the US.
If a pizza has radius z and depth a, its volume is pi *z *z *a.
Today I'm one of the 10,000: that's a new one for me, and I am looking forward to sharing it with my son when it matches his math skills.
I'm a jokey guy. Sometimes my jokes kill. Often they don't. I'm OK with any response -- except for the asshole who feels obliged to share his opinion that "That's not funny.".
It requires no wit or intelligence to remark that something is not funny -- or that something has been posted before.
akjax ยท 1 points ยท Posted at 23:32:58 on May 25, 2016 ยท (Permalink)
Yep, it's like there's a select group of people who literally spend all their time on Reddit and they see literally every post and get seriously offended by any content that isn't 100% original.
I mean that post spartan accused gronk of copying is over a year old. There's plenty of people that didn't see that post and never will, so why make a big deal over it?
[deleted] ยท 2 points ยท Posted at 17:52:46 on May 25, 2016 ยท (Permalink)
He also just did it here too. But after taking a second look, I think you're right. Although the account does a lot coping and pasting of previous comments, there does seem to be human intervention too.
Do people actually care if it's a bot giving an answer that actually answers the question? Like...karma means absolutely nothing. I just don't get why people care about this.
That's a good question because many people don't even know that there are bots. This type of activity is indicative of a spambot. And spambots really do hurt reddit. They often copy top comments and are gilded for it. Most people prefer to guild (and connect with) people and not bots. If you're not familiar with them, the "What's the Point?" section on this page may help to explain. Also, there was a very good write up here.
I mean, it's not a huge deal...but when you spend your money to gild someone, you're trying to give them certain perks of the site that only gilded users get...so I can see why someone would feel defrauded out of their five bucks in that situation.
If you don't know you're gilding a bot, not a person, then your illusory connection is just as "real" as a connection to a "person," right, insofar as it's something that makes you feel good?
On the other hand maybe gilders often send followup PMs to the gildee asking how good gold feels, and maybe that's awkward when the replies are all "I don't know. Maybe your social security number would help me figure it all out."
[deleted] ยท 0 points ยท Posted at 15:09:18 on May 25, 2016 ยท (Permalink)
No, but reddit uses your karma and the age of your account to determine how much to "trust" a user, meaning the site would ignore more red flags from an established, high-karma account than from a brand new account.
Luwi00 ยท 7 points ยท Posted at 15:11:43 on May 25, 2016 ยท (Permalink)
I acutally dont care about the Karma, but I do care about bots reposting, because I want to talk to a human and not a piece of code.
[deleted] ยท 3 points ยท Posted at 16:56:34 on May 25, 2016 ยท (Permalink)
Do people actually care if it's a bot giving an answer that actually answers the question?
If it means actually new and interesting answers get less attention, yes? No one likes having to scroll past reposts to see the actual answers. Having reposts show up on occasion so people who missed them the first time can see them is one thing, but you don't need the same set of answers repeated every single time a question is asked.
Aside from the obvious (without OC there's no content so we need to encourage OC over reposts), there's also the fact that spambots are often later sold for astroturfing. Lots of subs involve talking about your experience with a business. Someone with no history is often scrutinized/less trusted than someone who's posted often/has high karma/has been gilded.
This is also done for political causes too like pro/anti Russia/Israel/Hillary.
[deleted] ยท 2 points ยท Posted at 16:55:26 on May 25, 2016 ยท (Permalink)
Karma does mean something, and post quality really means something. A good, recognized and under-the-radar spambot can be invaluable to a PR team trying to promote a product.
I'm relatively new to reddit and was oblivious to this until now. I guess I imagined that the reddit community wouldn't stand for such behavior. Then again, if one doesn't even realize the inauthentic nature, whose to blame. I hate feeling ignorant, but appreciate learning something to counter my lack of info.
TIL: metaspammers copy and paste comments all over reddit and sometimes get gilded for this regurgitation.
akjax ยท 2 points ยท Posted at 23:35:59 on May 25, 2016 ยท (Permalink)*
Also, sometimes, such as in this case, people accuse real people of being bots or whatever when they're actually totally wrong.
Since you're new to Reddit, know this. You will see comments you naturally believe, such as someone trying to get the word around that an account isn't real, or giving a seemingly through explanation of recent or political events. They seem like they know what they're talking about and they have so much evidence, when coupled with a clear and conscience (and often slightly humorous) writing style, it's easy to assume they're an expert.
Except so often it's total BS, or at least not as true as the person writing it thinks it is. Take literally everything you read on here with a grain of salt. Reddit loves to point fingers, but that doesn't mean it gets it right.
[deleted] ยท 1 points ยท Posted at 15:05:16 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท -3 points ยท Posted at 15:13:25 on May 25, 2016 ยท (Permalink)
I've said it last time and I'll say it again, how the fuck is this a maths fact at all, let alone an interesting one? I'm not trying to be a jerk here, but this is literally if i define an equation with letters in a word, the equation will spell that word. I mean, ok? If I define three variables u,c,k, I can define a function f(u,c,k). Is anyone impressed? Maybe it's a useful mneonic for some people to remember how to calculate a cylinder's volume, but that about it.
[deleted] ยท 1 points ยท Posted at 18:03:17 on May 25, 2016 ยท (Permalink)
I think he was trying to say rehkt in a funny way which is slang for wrecked meaning to watch someone win an argument so thoroughly that it appears to be painful to the other person.
Ehh.. not completely. They way he wrote it it'd be
((pi *z) *z) *a which wouldn't be correct.
[deleted] ยท 1 points ยท Posted at 18:08:49 on May 25, 2016 ยท (Permalink)
Yes it would. Associative Property of multiplication: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)
I've always thought this one was stupid because they're variables, you can call them anyway. All you're saying is that if you take pi, add two z's and then an a, you get pizza. Like no shit, that what spelling is.
Those who are amazed , you need not be.Pizza is just a cylinder albeit the one with small height. As volume of cylinder is Pi *radius2 *height. So it's just a bit clever presentation of same fact to make it sound cool.
It is unfortunate, though, that the convention would be to swap the letters for radius and depth, since the depth is along the z-axis in cylindrical coordinates, and because... radius has an 'a' in it? (I'm aware that radii are often labelled 'r' in physics, but for some reason 'a' seems to be the second choice when 'r' is taken)
The word "proves" in that saying means "tests", not "verifies".
So, it's not "The exception verifies the rule", it's "The exception tests the rule". The saying makes a lot more sense that way.
We don't use the word "proof" to mean "test" much anymore (except maybe in the phrase "proving grounds"), so the correct meaning of the sentence is lost.
Similarly, the phrase "The proof is in the pudding" is actually supposed to be "The proof of the pudding is in the tasting" (or eating). "Proof" in that sense also means "to test".
Kayyam ยท 4 points ยท Posted at 15:40:29 on May 25, 2016 ยท (Permalink)*
That's not what the expression means. The expression means the exact same thing as"the smoke proves the fire".
You can't have an exception without a rule. Therefore, if you're pointing to an exception, that means there is a rule.
The expression though was never meant to be accurate.
Is this true? I'd like to hear a story where math hasn't worked.
[deleted] ยท 6 points ยท Posted at 16:33:15 on May 25, 2016 ยท (Permalink)
Check out Russel's Paradox. Basically for a long time mathematicians weren't very careful when talking about sets and just used their intuition to assert basic facts. Then Russel comes along and gives something that sounds fairly innocent but turns out to be paradoxical. So math panics and cobbles together ZF, the set of axioms most math is based on now. (and then the axiom of choice comes along giving ZFC. Choice is really cool, look it up!).
Also there's Godel's completeness and incompleteness theorems, which basically tells us that as soon as a set of axioms is complex enough to be interesting, it is impossible to prove with the axioms that the axioms are consistent. That is, it's impossible to prove that the theory generated by the axioms is contradiction free.
This seems really interesting but the Wikipedia page looks incredibly uninviting. Can you give me a ELI5 of what the essence of this is and does that mean the axioms we hold today can be considered truth?
Also this "sets" math, completely goes over my head...what exactly do they mean by set? Perhaps once I gain an understanding of it, I can teach myself from there.
[deleted] ยท 4 points ยท Posted at 17:39:48 on May 25, 2016 ยท (Permalink)*
I think maybe I shouldn't have mentioned the completeness theorem, it's less related to the point I was trying to make than I thought, and honestly I don't know enough logic (the field of math that it concerns) to properly give an intuition for what it means.
One thing it definitely doesn't do is tell us that the axioms we use today can be considered absolutely true. Godel's incompleteness theorem means that we have no way of knowing that there isn't a contradiction hidden deep in ZF. Though something that's kindof fun is that if we assume ZF is consistent, then each of ZF plus the axiom of choice and ZF plus the negation of the axiom of choice are self consistent. We can't even know that Peano arithmetic is contradiction free. Peano arithmetic is defined by our axioms for the natural numbers. It says things like 0 is a natural number, each natural number has a next natural number (adding 1), a=a, if a=b then b=a, if a=b and b=c then a=c, etc. Basically it is possible, although extraordinarily unlikely, that our very concept of a number is contradictory
Sets, on the other hand, I can help with. A set is essentially a collection of objects. If something is contained in a set, we call it a member or element of that set. You can talk about the set of even numbers, the set of numbers divisible by 98, or the set of all giraffes if you want. You can even talk about sets of sets, eg the set of all sets of integers, which has as elements the set of all primes, the set of all integers greater than 9, the set of my favorite integers, and all the other literally uncountable (which has formal meaning) sets of integers. So at first glance it seems like the set of all sets that don't contain themselves is a valid set (that's Russel's paradox). Maybe you're concerned that the statement seems self referential, and that's exactly what you should be worried about. The problem with that set is determining whether or not it should be considered a member of itself. If it's not a member of itself, then it does not contain itself and is thus by definition a member of itself. That's clearly contradictory, so we consider the other option. If it's a member of itself, then by definition it's not a member of itself, another contradiction. The only conclusion is that this set is neither a member of itself nor is not a member of itself, which is problematic. The set thus must not exist in the first place. Mathematicians came up with ZF so that we can say precisely what sets are allowed and what we're allowed to do with them.
A while ago I wrote up a talk about the axiom of choice. It's pretty hastily put together, so it's by no means well written, but it starts off with a basic set theory intro and then talks about some really cool axiom of choice stuff, so maybe you'll find it interesting.
Axioms are like assumptions. We look for consequences of these assumptions rather than some inherent truth to the assumptions themselves (generally). For example, we know that 1+1=2 as a consequence of our definitions of 1, 2, addition, and equality (or a set of other concepts which leads to the same result), but it makes no sense to ask if our definitions of 1, 2, addition and equality are "true." Instead, we can ask if they are valid/consistent (yielding no contradictions) or strong enough (yielding meaningful results), etc.
Dr-K-G ยท 2 points ยท Posted at 17:34:25 on May 25, 2016 ยท (Permalink)
Sets are basically just collection of objects.
Godel's completeness theorem is a bit difficult to explain if you have no background in higher math at all. But "does that mean the axioms we hold today can be considered truth" is not what it means. The completeness theorem means that every statement that is true in every model of an axiomatic system is also provable with the axiomatic system. A model is just a thing in which all axioms are true.
[deleted] ยท 2 points ยท Posted at 17:59:10 on May 25, 2016 ยท (Permalink)
If I have a logical system that is complicated enough to be able to encode basic arithmetic then I have a way of creating meta statements for which it's not possible to decide whether the statement is true or not in the logical system that I started with. So if my system is contradiction free it will necessarily have statements that it cannot answer by itself. Repeat ad infinitum, giving the impossibility of any logical system that will be able to answer every possible question.
qazadex ยท 3 points ยท Posted at 15:18:20 on May 25, 2016 ยท (Permalink)
Well, we kind of hope it does. We don't know if ZFC (our basic axioms of mathematics) are consistent or not.
Dr-K-G ยท 1 points ยท Posted at 17:30:24 on May 25, 2016 ยท (Permalink)
Even if they aren't we can always find a new axiom system to work with.
[deleted] ยท 1 points ยท Posted at 16:14:06 on May 25, 2016 ยท (Permalink)
I'm still banking on peano arithmetic being inconsistent
Dr-K-G ยท 2 points ยท Posted at 17:37:14 on May 25, 2016 ยท (Permalink)
If Peano arithmetic is inconsistent then so is ZFC because you can prove that PA is consistent within ZFC.
[deleted] ยท 0 points ยท Posted at 19:42:57 on May 25, 2016 ยท (Permalink)
If Peano arithmetic is inconsistent, much more than ZFC goes down the drain. It'll be awesome. My mathematician friends all say they would cry.
dh363 ยท 1 points ยท Posted at 20:16:11 on May 25, 2016 ยท (Permalink)
It wouldn't be as bad as people think. There would suddenly be a lot more people working on getting foundations right but a lot of maths built on it would still be fine, and most likely easily reconstructive from whatever new axioms we come up with
Dr-K-G ยท 0 points ยท Posted at 20:05:35 on May 25, 2016 ยท (Permalink)
Well if PA is inconsistent then the natural numbers as we know them can't exist. That's also why realistically it is impossible that PA is inconsistent. We actually have a few consistency proves for PA in other axiomatic systems which we too expect to be consistent.
[deleted] ยท 6 points ยท Posted at 15:26:53 on May 25, 2016 ยท (Permalink)
Mathsematics
Salbee ยท 0 points ยท Posted at 20:16:49 on May 25, 2016 ยท (Permalink)
Mathematics is singular, which is why Americans use the word math. I don't know a good reason for why everyone else says maths, which is why it makes me cringe.
Don't be afraid to ask for an explanation. There are a lot of math brained people like myself floating around in here that I'm sure would gladly attempt to explain in some way.
anorex ยท 9 points ยท Posted at 18:43:44 on May 25, 2016 ยท (Permalink)
Not sure. Though, on further delving through this page, it looks like they're both correct, depending on what you are referring. Where I'm from (US), it was 55318008 for Boobless, but I see that 5318008 is for Boobies. Interesting.
Yeah that was the joke...cause he put a number that looked like boobies so I said he should show his working out but as if it was talking about going to the gym. Puns...puns everywhere
That isn't the reason though. You were basically right with your first comment, 0! = 1 because by convention, the result of multiplying 0 numbers is 1. It's the same reason that x0 = 1. It could have easily been 0, but I think that like you said, it makes recursive calculations easier.
Also, if you wanted to derive for example f(x) = 2x you'd derive it to f'(x) = 2x0 = 2*1 = 2. If x0 = 0, then f'(x) = 2x0 = 0, which is a strange derivative.
[deleted] ยท 2 points ยท Posted at 02:53:18 on May 26, 2016 ยท (Permalink)
Not entirely. Going from n! to (n-1)! is effectively the same as dividing n! by n. If n = 1 then (n-1)! = (1-1)! = 0! = 1!/1 = 1/1 = 1
Zarco19 ยท 1 points ยท Posted at 05:02:33 on May 26, 2016 ยท (Permalink)
It connects very well with algebra/group theory for the empty product to be 1, because 1 is the multiplicative identity, i.e. a x 1 = 1 x a = a for all a.
In algebra, I like to think of numbers more as something you "do" to another number by combining them within the group operation, rather than a "thing." The identity is the number that doesn't do anything. So, you can imagine doing as many identities as you want and not changing what you started with. As such, any number can really be thought of as some sort of process being done to the identity.
The identity is the baseline you get before you start multiplying by anything, so it's what you end with if you multiply by nothing at all.
Most times that you add 9 to a number, 1 is added to the tens digit and 1 is subtracted from the ones digit. Other times, one is added to the hundreds, nine is subtracted from the tens digit, and one is subtracted from the ones digit.
9 + 9 = 18
36 + 9 = 45
92 + 9 = 101
Of course, for numbers with more digits the process is more complex, but the idea is the same.
This is a consequence of our base-10 number system. In any number system, this trait is exhibited by multiples of the number 1 less than the base.
Very unrelated but accent historians believe the modern American accent is closer to the British accents of 300 years ago than the modern British accent
This factoid is attributed in large to the loss of rhoticity in most accents of England; to say the modern American accent is 'closer' is disingenuous and ill-informed.
hextree ยท 15 points ยท Posted at 15:12:28 on May 25, 2016 ยท (Permalink)
The entire debate is stupid, with elitists from both sides. English has many stupid rules, so it would be unreasonable to try to justify one way over the other. Math has been around for nearly a century longer, while Maths makes sense in the sense that mathematics is plural, though many other words such as the aforementioned economics contradict that, while some others support it. You people need to get over yourselves.
So far, all you have been doing is trying to argue an arbitrary linguistic point. Not even. All you have been doing is just attacking those without the same view as you. Sad, really.
Statistics = stat or stats?
Mathematics = math or maths?
I'm going to do some economics
I'm going to do an economic (doesn't make sense)
I'm going to do some mathematics
I'm going to do a mathematic (doesn't make sense)
I'm going to do some statistics
I'm going to do a statistic
There's a classic debate in the UK about how to pronounce the word scone
You can either pronounce it like cone as in s'cone' or like gone as in sc'one'
My point being there is more than one way at looking at things. Just food for thought
[deleted] ยท 7 points ยท Posted at 19:23:00 on May 25, 2016 ยท (Permalink)
The evolution of language is indeed a very interesting subject! I'm afraid I can't answer your question, however there's a very interesting series on the history of the English language called The Adventure of English which you may find fascinating!
Except that mathematics is a singular word, not plural. You don't have one mathematic and several mathematics. Its just a word that ends with an s. So your analogy doesn't really hold.
w675 ยท 6 points ยท Posted at 18:37:17 on May 25, 2016 ยท (Permalink)
Yeah, nice try.
Calling mathematics maths is implying that mathematics is plural, which is false. Mathematics is defined as thestudy of topics such as quantity, structure, space, and change.
The study. The singular study of those topics. Argument over.
I was trying to find this comment. This short question is so obviously not written by an American. Between favourite/favorite and maths/math. It stood out to me.
Maths makes sense because mathematics. But. Growing up hearing it only as let's study math. Here are some math problems. Etc. it just feels weird saying and hearing maths.
And forget about that crazy as U showing up everywhere.
mr_ewe ยท 3 points ยท Posted at 16:37:11 on May 25, 2016 ยท (Permalink)
I am proud to say I witnessed my watch strike 9:26:54am on march 14th 2015. I had been waiting for that single moment since I had learned about pi day six years earlier.
MrXian ยท 4 points ยท Posted at 18:14:36 on May 25, 2016 ยท (Permalink)
I had an alarm set on my watch and I got to explain it to my running mates.
[deleted] ยท 1 points ยท Posted at 22:04:06 on May 25, 2016 ยท (Permalink)
Well it's all arbitrarily based on some Roman jurors decree so...
In TouchMyDuck calendar (which is the world's first variable calendar) every day is Pi day.
You can estimate the number of zeros in front of a large factorial easily. For example, 100! has 24 zeros.
The number of zeros in front of a multiplicative expansion is equal to the number of 10's inside it. For example, say you have 3*5*10*10 = 1500, two zeros,
Now, 10 = 2*5 and when you fully expand q factorial there are a lot more 2's than 5's, so the number of 10's equals the number of 5's.
10! = 10*9*8*7*6*5*4*3*2*1
10! = 5*2*3*3*2*2*2*7*3*2*5*2*2*3*2*1
For 100! there are 20 fives (100/5 = 20), plus an additional five for each multiple of 25 (25, 50, 75, 100) so there are 20+4 = 24 zeros at the front of 100!
Another example: 52! has 10 fives plus one for 25 and one for 50 = 12 zeros
My dad was telling me about a programming competition he was in (back in the 80s) where this was the problem. His team ending up winning because they figured it out before anyone else. Really cool fact!
I have always enjoyed the birthday paradox. How many people does it take in a room to boost the probability over 50% that two people share a birthday in that room? Most people tend to guess much higher numbers, but the answer is just 23 people.
It's a great demonstration of how intuitively bad most people are at probability, which is relevant to so many areas of life. Lottery ticket, anyone?
Edit: in response to some comments, I agree it's probably better called "birthday problem," not "birthday paradox." But it is referred to by both names.
And with 367 people there is a 100% chance!!! Wow!!!
ExeusV ยท 1 points ยท Posted at 20:13:29 on May 25, 2016 ยท (Permalink)
It's a great demonstration of how intuitively bad most people are at probability, which is relevant to so many areas of life. Lottery ticket, anyone?
There's difference between lottery with e.g 49 numbers (6=win) and "ridiculous" fact like this bday problem.
JTswift ยท 1 points ยท Posted at 14:22:17 on May 25, 2016 ยท (Permalink)
I asked this to another person, but...
How many people do you need for that birthday to also include the same Year?
Multai ยท 2 points ยท Posted at 15:42:10 on May 25, 2016 ยท (Permalink)
Depends on what chance there is of having a certain birthyear. Are kids included? Are old people included? What 'limit' is there? We know the limit of birthdays is 365, but for age there is no real limit. (We all die, but at what point?)
The chance of n people sharing NO birthdays is (366-1)/365 * (366-2)/365 * (366-3)/365 * .... * (366-n)/365 * 100
Just subtract this from 100 to get the chance of at least 2 people sharing their birthday.
Note: Feel free to point it out if I'm wrong
Instead of days you could do years, assuming people can be anywhere from 0 to 80 years old (and assuming the odds are even for all ages) you could change 366 in the formula to 81 and 365 to 80. After you've calculated the chance of the year being the same just multiply that by the chance given by my other formula. Then it's just a case of finding what n gives you a chance of more than 50 percent.
I personally wouldn't know of a way to find this number without making a MASSIVE excel file that would do it for me, but there are probably ways.
Assuming there are 29,200 possible birthdays (most people born on actual February 29 are legally born on March 1). If we assume that the population pyramid is flat i.e a uniform distribution of all birthdays from 1936-05-26 to 2016-05-25. Then the chance of noone in a group of N people share a birthday and birthyear is 29,200!/((29,200-N)!*29,200N).
Since you specified Excel I decided to do it in Excel. Excel freaks out if you try and calculate 29,200! or PERMUT(29200, 70) so we'll do it the roundabout way.
In real life, groups are not uniformly random wrt birth year so you'll probably need less people. A school class is normally used in the example of the original birthday paradox so the chances are very high that you'll have overlap in birth year also.
You can still establish an upper bound. The less evenly distributed the birthdays, the fewer people you need on average. So assuming perfectly even distribution gives you the maximum average number of people.
Here is the distribution of birthdays through the year. If I remember right that's taken from the US bureau of statistics so it should be reasonably accurate.
Its not a paradox to math, but its a paradox to man. If you're being rigid, then the existence of a paradox invalidates the logic of the math, and therefore we resolve the paradox by changing the assumptions so that math can work and be logical. The abstract concepts of logic and math, do no permit paradox to exist within them. And so nothing which remains in math or logic may be a paradox.
The point is going around and telling people that things aren't really a paradox is completely goddamn pointless. By being pedantic about paradox you reach a point where paradox isn't actually a thing, and if its not a thing its not worth defending the use of the word. In defending you destroyed it, and thus you fall into a paradox.
It's not, it's mathematically air tight. Also, a couple of days ago the fact came up, and another person and myself both tested databases which included random people. You can see what we found here.
So, to prove this, lets work backwards a bit. Imagine, you have a whole bunch of people (lets say 100, but it doesn't matter as you can do this with any number of people).
You ask the first one what their birthday is. What's the chance it doesn't share a date with someone who's already been asked? 365/365, as no dates have been used. The second person is asked, and the chance of them not sharing a birthdate with someone already asked is 364/365. This is because 364 days of the year haven't been said yet. The third had 363/365, the fourth 362/365.
If you continue this out to n you get 365-(n-1)/365. You then multiply them all out to get the actual chance of no one sharing a birthday. This turns into (1/365)n * 365! / (365-n)!
The exclamation points are factorials which basically means 365 * 364 * 363 * ... * 2 * 1. By dividing by (365-n)! you end up with 365 * 364 * 363 * ... * (365 - n).
When you plug in 23 for n you end up with (1/365)23 * 365!/342! โ 0.492703. This means the chance, with 23 people, you have a 49.27% chance of two people in the group not sharing a birthday. Simply subtract from 100% to find the chance that two people will have a shared birthday (~50.73%).
Care to explain how it's total bullshit? The only problem there can be is birthdays aren't perfectly evenly distributed, but as far as I know they're even enough not to make a massive difference.
all i'm saying is its not math. its society. people fuck when power goes out.. spring is storm season. storms affect wide areas. people are born around 9 months later so on and so on. math is used to calculate the facts. the facts are not a math vs human "quirk" like (oh thats so counter intuitive)
All of those things have the effect of making it more likely for people to share birthdays.
The birthday paradox says that in a room of 23 randomly-selected people, there is a greater than 50% chance that at least two of them share a birthday. That is true regardless of how birthdays are distributed. The fact that birthdays aren't uniformly distributed just raises the probability even higher above 50%.
You seem to be saying that it's bullshit because birthdays come in "clumps" (e.g., people are more likely to have sex in the spring, etc). Is that what you were trying to get at?
If so, you're wrong. That makes the birthday paradox more true, not less.
when i first began computing this all out i was trying to say that people won't share a birthday. i'm always doing this. i put a decimal in the wrong place. always some mundane detail. (this is not a mundane detail... michael!
There is a difference between "several hundred pages dedicated to prove the validity of the expression 1+1=2" and "After several hundred pages it is proven that 1+1=2".
No, that's still not what the word 'dedicated' means. If the stuff before is used to establish stuff other than 1 + 1 = 2 (which it definitely is), then that stuff wasn't "dedicated" to the proof of 1 + 1 = 2 because that wasn't its sole purpose.
Ah, I didn't see the word dedicated in there. It's not usually in such claims, only that several hundred pages are required to prove the validity of the expression 1+1=2, which is in fact a true statement - there are several hundred pages of proofs used in building up the argument that culminates in the proof of 1+1=2.
Being even more pedantic (as one is wont to in this field) I should correct myself and say that my previous statement isn't correct in another way: even if there are some pages that do not present useful in the proof of 1+1=2, there still could be several hundred, albeit not consecutive, pages of mathematics leading up to the proof. As I'm already on this high horse of pedantry I should perhaps point out that my statement was a necessary condition, not a sufficient one, and therefore in such a pedantic view (as I have taken only in this paragraph) you objection to my (incorrect) claim is also false.
In my first year at university a lecturer spent 50 minutes trying to show what a number was. At the end she said "oh hang on that was wrong" - and never returned to it... now I've no idea what a number is
[deleted] ยท 23 points ยท Posted at 14:15:37 on May 25, 2016 ยท (Permalink)
If you're still wondering, I recommend Frege's "Foundations of Arithmetic". It's dated, but well-written and heavily influenced Russell (who wrote the aforementioned Principia Mathematica).
Frege and Russell independently came up with what is now known as the Frege-Russell definition of number, which can also be found in Russell's "The Principles of Mathematics" (1903). Russell did not read Frege in detail until he went looking for Frege's solution to what we now call Russell's Paradox (Russell simply called it "the Contradiction").
I do also recommend reading Frege's "Foundations". Russell's "Introduction to Mathematical Philosophy" (1919) is a good introduction as well, for those who do not wish to read Principia Mathematica itself.
It's really not as bad as some teachers can make it seem. Especially if leaving out the Irrational numbers is good enough for you.
The Natural numbers are sets containing some number of elements. Addition of two natural numbers is taking the disjoint union of the sets that those two numbers are. Throw in a bunch of extra rigor and some words on congruence classes to formalize it all, and you're ready for arithmetic.
For example, 2 is really the set containing two elements { 0, 1 }.
And so 1+1 = {0} U* {0} = {(0,0)} U {(0,1)} = {(0,0), (0,1)} = 2 as it contains two elements and so.
From here you build everything else:
Subtraction is the inverse of addition. You now have negative numbers (the Integers).
Multiplication is repeated addition.
Define fractions as the number pair (p,q) and expand the your earlier operations to have the rules you'd expect. We now have the Rational numbers.
Division is then just multiplication by a fraction.
So far, it's been easy, but now comes the most difficult part, the one big trick that actually gives you all the numbers:
Consider putting fractions on a number line and notice that there's always "space" between any two fractions you pick. Is that "space" a number? Not yet. You have to fill in the "spaces", by completing the the Rational numbers. You make every sequence of numbers that converges into a new number and give it a name. Lots of these sequences were already Rational numbers, but we just created some new numbers too.
For example:
2 = (2,2,2,2,2,2 ...) but also = (19/10, 199/100, 1999/1000 ... ) since the distance between elements of these sequences goes to 0.
0 = (0,0,0 ... ) but also = (1, 1/2, 1/4, 1/8 ... ) for the same reason
And a new number Pi = (3, 31/10, 314/100 ...) which, from its definition, can be shown not to be a Rational number. It's a newly created number, an Irrational number
Most people like to understand this with decimals, which is really the same thing, just with a different notation.
2 = 2.000... but also = 1.999...
Pi = 3.14159...
Once you have these sequences, you expand your operations to work with the sequences, show that this completion makes the number line "full" (there are no more numbers hiding somewhere), and BAM you have the Real numbers. From absolutely nothing other than logic, disjoint unions, and definitions (and taking the power set is hiding somewhere in there too).
You now have "numbers", the most fundamental tool in math, and are ready to build everything else in math.
Retbull ยท 1 points ยท Posted at 15:26:27 on May 25, 2016 ยท (Permalink)
A number is the thing between two different sets that is the same. So if I have 6 apples and 6 pears 6 is what is the same between them. This isn't really a proof so much as a fun way of thinking of it though.
Although I've never had "number" defined, I've been exposed to a few ways of building number systems.
Natural numbers can be built using Peano axoims and successor functions. Adding basic arithmetic properties can give you all other systems all the way up to rational numbers. This isn't too mind blowing to understand so I encourage anyone to go look at it if they are interested.
To build the real number system you can use Cantor sets or Dedekind cuts to define your numbers. This is a little more complex of a notion. Say you want to define the number "2". The idea of both methods is pretty much make two groups of numbers, one group being all the numbers smaller than 2 and the other being all the numbers greater than 2. Then you pretty much just say in fancy math terms that 2 is what is squished between those two groups. In a way we are defining 2 by what it isn't.
I'm not sure how you build the set of complex numbers from there, other than they are an extension of the reals in some form or way.
That's about all I know about building number systems personally. And there is the philosophical side of it as explained by a cool Numberphile video.
Reminds me of a story my math prof used to tell us, from back when he was a math student.
Apparently the lecturer is in the middle of a long-ish proof of something and says, "...and from this, it is obvious that-" and just stops and frowns for a bit. He walks out of the hall and the students awkwardly wait around for like 5 minutes. Then the lecturers strides back in and immediately starts up again, "Yes, it is obvious that..."
[deleted] ยท 1 points ยท Posted at 14:19:34 on May 25, 2016 ยท (Permalink)
If I remember my first year college maths right, numbers are sets. Yeah, I know...
Define 2:= the set of (the set of the empty set) and (the empty set) = { { {} } , {} } = { 0, 1} = {1} union with 1
Define (n+1):= n union with { n }
[deleted] ยท 6 points ยท Posted at 16:23:28 on May 25, 2016 ยท (Permalink)
Very misleading to say that.
They were developing set theory, which is "fundamental math" in the sense that all questions can be phrased in set theory language and all proofs can be derived from set theory's axioms.
What they showed was that set theory is capable of reproducing the integers, defining addition, and reproducing all of our familiar facts and intuitions about it. This is a boon because set theory makes use of fewer primitive notions than Peano arithmetic does.
ktkps ยท 2 points ยท Posted at 04:52:25 on May 26, 2016 ยท (Permalink)
That was far more about trying to create a good grounding for math, rather than actually proving that 1+1=2. Nobody even doubted that 1+1=2, and a rigorous proof is not needed other than to ensure the grounding is correct.
[deleted] ยท 1 points ยท Posted at 14:06:53 on May 25, 2016 ยท (Permalink)
Principia set out to prove all major mathematical theorems in something called symbolic logic. The idea was that this system would be better for mathematical proofs than English or any other verbal language because it had less ambiguity. It didn't really take hundreds of pages to prove that 1+1=2 so much as it took that long to establish the concept of numbers and arithmetic in order to prove that 1+1=2.
The interesting thing about the 1+1=2 proof is that they keep getting longer because we keep using weaker and weaker definitions of 1, thereby strengthening our entire system of mathematics by only needing to rely on weaker assumptions.
I'm not a mathematician, but my understanding is that the conclusion was that you can't fully prove a system like mathematics, you have to make some base assumptions. The proof for 1+1=2 is completely valid if you already have a definition for what "+" is. Bertrand wanted to provide proofs and definitions for everything in math, but found that such task was impossible.
You can probe it via the definition of addition. The only way you can't is if you prove the additive properties and numerical properties of addition are wrong. Which you can't.
It's not proving the validity its proving the concepts that go into math using 1+1=2. You could do this in one step. Subtract 1 from both sides and then u get 1=1 and by the reflexive ppty this is true.
I did. To use your proof, you need to already know that subtracting 1 from the 2 on the right side of the equation gives you 1, i.e. 2-1=1. This is unrelated to proving the concepts.
If you want a rigorous proof that 1+1=2 you need to do a lot more than that. For a start, it is much easier to prove 1+1=2 than it is to define subtraction.
Also, you started with 1+1=2 and deduced that 1=1, this is not valid. You could similarly say 1=0, multiple both sides by 0 to get 0=0, which is true, and so 1=0.
I said this in my comment that they weren't proving 1+1=2 they were just using it as a filler equation to prove the mathematical theorems we use everyday.
The pythagorean theorem and the equation of a circle are the exact same! A lot of people might see the two and notice they look almost exactly the same but at most it's just a small notice usually. Think about it like this a circle is all of the points that are the same distance from a central point and the pythagorean theorem gives you the length of the long line of a right triangle. Therefore if you find all possible lengths of the two other legs of the triangle for any given length of the long leg you've found all of the (x, y) coordinates of the circle! Also interestingly enough the absolute value function is also the exact same as the pythagorean theorem.
I'm about to get on a plane and literally copied and pasted this from my comment history but I'm sure if people wanna know someone will tell you about absolute value.
JaeD08 ยท 4 points ยท Posted at 17:24:56 on May 25, 2016 ยท (Permalink)
aka Trigonometry
Distance between two points on a plane also can be found from the Pythagorean theorem but that one's pretty obvious.
[deleted] ยท 2 points ยท Posted at 22:09:05 on May 25, 2016 ยท (Permalink)*
And this is how sinx and cosx are defined, a circle of radius 1, in which a triangle with its hypotenuse as the circle radius and it's horizontal base (centre circle to right-most edge) is cosx and while hypotenuse swings around the circle the changing vertical side of the triangle is sinx.
From Pythagoras we get the circle equation horizontal2 + vertical2 = 1 which in our case is sin2(x) + cos2(x) = 1 so that equation isn't some nice derived relation to make college easier, it's actually the first contact. All the other stuff you might think as more basic actually came by this or much later, like sinx = O/H.
[deleted] ยท 1 points ยท Posted at 17:26:12 on May 25, 2016 ยท (Permalink)
equation of a circle
care to elaborate OP, something doesn't add up here
pemboo ยท 2 points ยท Posted at 17:32:52 on May 25, 2016 ยท (Permalink)*
So in the cartesian plane (normal x-y graph) you can define a circle with the equation (x-a)2 + (y-b)2 = r2
Where (a,b) are the coordinates for the centre of the circle and r is the radius.
Take a circle around the origin and you get the equation x2 + y2 = r2
Edit: pressed save half way through, will continue this post
Pythagoras theorem says that for any right angled triangle, with the sides labelled a, b and c, c being the hypotenuse, then the sides satisfy the equation a2 + b2 = c2 which should look familiar.
Now this could be mere coincidence, but it's not.
It turns out that if you take any diameter of a circle and draw straight lines from the end points to the edge of the circle so that both these lines meet, it will form a right angled triangle with the diameter as the hypotenuse.
[deleted] ยท 1 points ยท Posted at 17:43:59 on May 25, 2016 ยท (Permalink)
i see. thank you
[deleted] ยท 1 points ยท Posted at 18:00:35 on May 25, 2016 ยท (Permalink)
It turns out that if you take any diameter of a circle and draw straight lines from the end points to the edge of the circle so that both these lines meet, it will form a right angled triangle with the diameter as the hypotenuse.
Lost you here :/ my visual imagination skills are shot right now
pemboo ยท 1 points ยท Posted at 18:11:29 on May 25, 2016 ยท (Permalink)*
Let me draw something with my phone since I'm sat in the pub, gimme 10
So the red line is an arbitrary diameter of the circle and the blue dot is an arbitrary point on the circle.
The two green straight lines going from the ends of the diameter to the blue point form a right angle labelled A.
This is true for ANY diameter you choose and ANY point on the circle.
Obviously, choosing your blue dot as the end of the diameter doesn't make a triangle so don't start!
[deleted] ยท 1 points ยท Posted at 18:33:07 on May 25, 2016 ยท (Permalink)
ooooooooooooooooooooooooh i get it!
pemboo ยท 1 points ยท Posted at 18:51:13 on May 25, 2016 ยท (Permalink)
It's pretty cool. If you leave c (the hypotenuse) constant and then draw EVERY right angled triangle that fits. (There's a lot, like infinity lots, uncountable infinity lots) you get a perfect circle with radius c/2.
well if you add in a z axis you could choose your bleu dot on the end of the diameter but further down the z axis. that would still make a right triangle just on a different plane
graaahh ยท 1 points ยท Posted at 17:45:01 on May 25, 2016 ยท (Permalink)
Absolute value's where you make stuff that's negative positive, because you don't care if it's negative or positive, you care about its distance from zero.
Take a dollar amount. Move your decimal one place to the left. You have just calculated 10%. Add half as much, and you have 15%. Double it instead, and you have 20%.
I know that seems painfully obvious and simple, but I'm always shocked by the number of adults that need a calculator to figure out their tip on a restaurant bill. It's not hard.
I can do the fractional multiplication in my head; 10%, 15%, 20%, 25% and then even integrate 12.5%, 17.5% and 22.5%. But I need my fingers and some scratch paper to add the tip and bill together.
Integrating means finding the area under a curve. The most basic integration is power rule where you add one to the power and divide by the new power. So ax becomes (ax+1)/x+1. There are others ways like u-sub, integration by parts, tabular method, partial fractions, improper integrals, and others. It's calculus.
Just saying, if you're using "a" as a constant and "x" as your dependent variable, your formula is wrong. Sounds like you kinda wanted to just run down the list of loosely related concepts from an intro calc class.
There is a really easy way to multiply by 11. You take the number you are multiplying, add its digits together, then insert that number between the two original numbers. It can get confusing when you have to carry numbers or you have more than two numbers.
Example 11*23 = take 23, comprised of 2 and 3 , add them together, you get 5 so the answer is 253.
11*34 = take 34, comprised of 3 and 4, add them to get 7, insert seven between original two digits, answer is 374.
Take a three digit number, 123 * 11. In this case you add the first two number to get the second, 1+2 = 3, then you add the last two numbers to get the third place, so 2+3 = 5, the first and last numbers remain the same. So 123*11 = 1353
This works for any number multiplied by 11 but gets complex when you have to carry a value forward because your addition resulted in a number 10 or over. Another three digit example, take 11 * 235. Add the first and second digit, 2+3 = 5, add the second and third digit, 3+5=8, insert the values you calculated between the original first and last digit. 11 * 235 = 2585
Take a three digit number, 123 * 11. In this case you add the first two number to get the second, 1+2 = 3, then you add the last two numbers to get the third place, so 2+3 = 5, the first and last numbers remain the same. So 123*11 = 1353
This works for any number multiplied by 11 but gets complex when you have to carry a value forward because your addition resulted in a number 10 or over. Another three digit example, take 11 * 235. Add the first and second digit, 2+3 = 5, add the second and third digit, 3+5=8, insert the values you calculated between the original first and last digit. 11 * 235 = 2585
jfree02 ยท 6 points ยท Posted at 18:04:57 on May 25, 2016 ยท (Permalink)
English: Voting theory fails.
Say we want to put an airport somewhere on the surface of the earth. We'll let some large number of people (at least 2) vote on its location. There is no voting scheme that has the following 3 properties:
1) If everyone wants the airport in place a, it gets put in place a
2) Everyone's vote has the same weight
3) Minor changes in a voter's preference for placement will not result in major changes in the outcome of the vote.
Math: For n > 1, there is no continuous map f: (S2)n \to Sn that
a) Is invariant under the action of S_n on (S2)n which permutes the factors
People who are coming in after /u/CannonLongshot edited his post and wondering why /u/kari_von_moor has upvotes, "no" is a counter example to the original phrasing of this post.
Apparently OP accidentally said it was the only word, and not that it was the only number, when written out, and "no" is a counter example, and not a refutation of the new claim.
As it stands, no one has a counter example to the new claim, that "forty" is a the only number written out whose letters are all in ascending alphabetical order.
Edit: But seriously, guys, couldn't any of you tell I was talking about numbers on a maths thread? I'm bad with words, I'm a mathematician, not a writer!
You're the worst kind of redditor. You made a mistake in your post, and when people correct you, you edit your post and then make fun of the people who corrected you. Shame on you.
I was planning on going through to all the posts I made replying to those people to make it clear that I messed up, I'm just at work and have random stretches of free time.
I'd be more inclined to agree with you if the "making fun of" wasn't possibly the most light-hearted banter I've seen on Reddit for a long while.
Also, I totally forgot that the score formatting existed on Reddit, I shall use it now! :)
[deleted] ยท -1 points ยท Posted at 14:07:37 on May 25, 2016 ยท (Permalink)*
Yeah, we're gonna win even if I have to go into the auditorium and personally jerk off every guy in the audience.
That's a lot of jerking.
And we only have ten minutes to present.
So So, we're fucked, aren't we?
Yeah, even if he's jerking two at a time, there are, what, 800 guys in that room? So that's 400 times whatever the mean jerk-time is.
The what?
Mean jerk-time. I mean, it doesn't matter, but, hypothetically, time is equal to 400 total jerks at a two-dick rate.
Unless Erlich jerks off four guys at a time, and then we can cut that in half.
How would he do four guys? He's got two hands, so that's two dicks at a time, right?
Look, you have two guys on either side with their dicks, tip to tip, so you're going full-length. Four, see?
Oh - From the middle out. That does make sense.
Like two Shake Weights?
Yeah, so what we're trying to do, hypothetically, is minimize time, which is 800 dudes, multiplied by mean-jerk time, divided by four dicks at a time.
Of course, Erlich would have to pre-sort guys by height, so that their dicks lined up.
Not by height, technically.
The measurement that we're looking for, really, is dick to floor.
Call that D2F.
Huh.
You know, if a guy's dick was long enough, it would be able to reach up or down to another guy with a different D2F. The longer the dick, the greater the D2F bridge, but I would still be able to jerk it off in one smooth motion I'd just have to jerk it on an angle.
So D2F sub-1 needs to equal D2F sub-2, and D2F sub-3 needs to equal D2F sub-4, where length L creates a complimentary shaft angle call that theta d. Now the orgasm threshold is a function of lambda sub from the time from the time he created the orgasm
Guys, does girth-similarity affect Erlich's ability to jerk different dicks simultaneously?
Shit.Yeah, I think it would.Of course, it does.Time to orgasm, or T2O, has to be the same for each matching pair of dicks otherwise I'm wasting a lot of great strokes on a guy that's already busted.
Unless you can hotswap dicks in and out.
So on a downstroke, you get a new one in.
So when you stroke up you're not wasting any energy.
Even so I think this is the most reliable metric for stamina.
kilkil ยท 15 points ยท Posted at 14:39:58 on May 25, 2016 ยท (Permalink)
I, um...I think you meant to post this somewhere else. It looks like you put a lot of...effort into it, so I figured I'd do you the courtesy of letting you know so you could post it where you intended.
I'm probably going to get the details wrong, but you can mathematically define the real numbers. The basic idea is that you define certain properties of a set, then you prove the real numbers have these properties, then you prove that all sets with these properties are identical up to isomorphism, then you artificially construct such a set (we used Dedekind cuts in the class I took), then viola you've defined the real numbers. Also I should note the first line in the Analysis textbook we used was "we will not attempt to define the word set" so...
pemboo ยท 4 points ยท Posted at 17:44:19 on May 25, 2016 ยท (Permalink)*
If you couldn't mathematically define the reals then we wouldn't use them, seems like a tautological statement.
Importantly, you must first construct the set of rationals before you get the reals, which in turn require the integers, which in turn require you define the wholes...
[deleted] ยท 4 points ยท Posted at 18:27:04 on May 25, 2016 ยท (Permalink)
Newton, Leibniz, Euler and I think even Gauss did not have a definition of real numbers as we do today.
dh363 ยท 1 points ยท Posted at 20:23:55 on May 25, 2016 ยท (Permalink)
I mean, today's real numbers are on firmer ground than even times after dedekind cuts were done, because our foundations for set theory are far stronger, and the natural numbers can be constructed from set theory. And the foundations of logic are far stronger, too. So in a way the foundations of all these number systems in general are actually much more solid than when the individual axiomatizations and contractions were first conceived.
You can define the sets before the reals using Peanio axioms and properties of arithmetic (i.e. groups and fields stuff). Once you have that that is when you can move to Dedekind cuts or Cantour sets to define your reals.
I think the mind blowing nature of this is more, before you learn it yourself, who the fuck thinks about defining a "number". Up to when you start learning about sets and such, your just using numbers and your understanding of them is not proved in any way, only built in a superficial way up to that point in school.
pemboo ยท 1 points ยท Posted at 18:20:34 on May 25, 2016 ยท (Permalink)*
Doesn't every class have that one prick who thinks he is smart by asking the teacher "but what is a number, they're not even real?"
I don't think it's mind blowing at all that we have rigorous definitions of our number systems.
I have never run into that personally. And at least for me it was mind blowing when we rigorously defined it for the first time. You can definitely disagree, there are plenty of valid feelings and perspectives on it. But it is mind blowing to some people at least.
Zarco19 ยท 1 points ยท Posted at 05:19:20 on May 26, 2016 ยท (Permalink)
I mean, there's the dick who is like "this is all made up, fuck this shit" and there's the dick who is like "how do we know this all works?" looks deeper into it, and then revolutionizes math or some shit
That's true, but to someone not familiar with analysis I think it would be pretty interesting that that is something you can do, and that it is necessary.
If your interested in that sort of stuff I would definitely suggest taking a class on Modern/Abstract Algebra or a similar topic. It covers groups and fields and the properties that go with them. Pretty much it helps show why those certain defined properties that seem to come out of nowhere work the way they do.
Helps explain the "real numbers work like this, now don't ask questions" thing that seems to happen early in higher math education.
You're completely right. I actually took Abstract Algebra before Analysis (although I took and then dropped Analysis I the semester before) and it made the beginning third much easier.
Is it shocking that we can define the real numbers mathematically? Why would we study the object in such detail if we couldn't define it? I don't mean to rain on your parade, but as a matter of fact it's fairly easy to define the real numbers by just assuming the least upper bound property or some other completeness property. We don't need to worry about any isomorphisms or some overly technical machinery.
Logic and set theory is an entirely different realm of study to real analysis, which is probably why your lecturer didn't dwell on the logical basis of the subject. Rest assured that with the right axioms the real numbers pop out very naturally.
Toph_er ยท 13 points ยท Posted at 16:58:51 on May 25, 2016 ยท (Permalink)
My favourite fact is that any number to the power of 0 is 1.
How can that be? Well, 162 * 162 = 164 right? Well with division you just subtract the powers. 162 / 162 = 160. When you look at any number like a fraction, e.g. 2/2, then 2/2 = 1 right? So that means 162 / 162 = 1, therefore 160 = 1 as well.
I think I finally got this whole abstraction thing that exists in math.
[deleted] ยท 1 points ยท Posted at 22:00:36 on May 25, 2016 ยท (Permalink)
Thanks for the work you put in to that. How would it include or adapt to meet 00, I never understood it
Lehona ยท 3 points ยท Posted at 23:32:52 on May 25, 2016 ยท (Permalink)
Well, you can't do 0n/0n, because that would obviously be dividing by zero, so it's usually undefined. Sometimes it gets defined as 1 because it makes calculation easier and doesn't mess with the results anyway.
[deleted] ยท 1 points ยท Posted at 21:58:51 on May 25, 2016 ยท (Permalink)
fireatx ยท 2 points ยท Posted at 09:58:08 on May 26, 2016 ยท (Permalink)
By his example...
02 / 02 = 00
we know 02 = 0, and division by 0 is undefined. therefore
02 / 02 is undefined
Toph_er ยท 1 points ยท Posted at 18:26:38 on May 27, 2016 ยท (Permalink)
Google Calculator also says its 1 for some reason XD, but I am pretty sure there is a lot of arguing over the fact of if it should be 1, 0 or undefined.
My understanding is that 'natural number' specifically refers to {1,2,3,...} while 'whole number' specifically refers to {0,1,2,3,...}.
Lehona ยท 1 points ยท Posted at 23:36:49 on May 25, 2016 ยท (Permalink)
Whole numbers means the same as integers and includes the natural numbers, their negative counterparts and 0.
[deleted] ยท 1 points ยท Posted at 22:36:31 on May 25, 2016 ยท (Permalink)
No. 0 is never specified as a natural number. It is a whole number.
[deleted] ยท 2 points ยท Posted at 00:01:09 on May 26, 2016 ยท (Permalink)
Really? My numerical semigroups text right here has zero as a natural number. Many places include 0 in the naturals.
[deleted] ยท 1 points ยท Posted at 05:28:23 on May 29, 2016 ยท (Permalink)
I might be wrong then. But if 0 is a natural number, whats the difference between Natural and Whole numbers?
[deleted] ยท 1 points ยท Posted at 05:30:09 on May 29, 2016 ยท (Permalink)
Nobody uses whole numbers. Never seen it used in any recent literature. People specify N union {0} usually if they don't believe the naturals contains zero.
K4mp3n ยท 1 points ยท Posted at 11:42:02 on May 29, 2016 ยท (Permalink)
At least in germany it would be all negative, 0 and all postive numbers {...;-2;-1;0;1;2;...}
[deleted] ยท 1 points ยท Posted at 16:36:52 on May 29, 2016 ยท (Permalink)
Those are integers.
K4mp3n ยท 2 points ยท Posted at 19:38:34 on May 29, 2016 ยท (Permalink)
A thank you, them it is the names that Digger in German that I got wrong.
[deleted] ยท 1 points ยท Posted at 00:00:28 on May 26, 2016 ยท (Permalink)
That's well-debated, many people include 0 in the naturals.
graaahh ยท 1 points ยท Posted at 17:39:53 on May 25, 2016 ยท (Permalink)
26 is the only integer number to lie between a square and a cube.
Edit: only known number (don't think it's been solidly proven) and by "lie between" I mean directly next to in terms of integers (25 is square, 27 is cube)
Edit 2: has been proven, I'm an idiot
TLDM ยท 5 points ยท Posted at 14:53:44 on May 25, 2016 ยท (Permalink)
I can think of lots of integers which lie between a square and a cube :P
It is not easy to approach a problem like this with elementary methods. In fact, Fermat probably had an incorrect proof of this fact.
The simplest proof I know of that y2 = x3 - 2 has only the solution (3,5) involves using unique factorization in the ring of numbers of the form a + bโ(-2), where a and b are integers.
I am not sure of the best method to approach y2 = x3 + 2, but a similar method may work, and in any case there are algorithms that have been used to identify all solutions.
Here is a good survey of the techniques used in solving these and similar equations.
jusjerm ยท 1 points ยท Posted at 16:42:57 on May 25, 2016 ยท (Permalink)
it can be proven by factoring y2=x3-2 over the ring Z[โ-2] to get (y+โ-2)(y-โ-2) = x3, then since Z[โ-2] is a unique factorization domain and a gcd domain, you can show (with a bit of work) that y+โ-2 must be a perfect cube in Z[โ-2], so y+โ-2 = (a+bโ-2)3 for some integers a,b. expanding shows that 3a2b-2b3 = 1, which has b=1 and a=ยฑ1 as the only integer solutions. this gives y=(ยฑ1+โ-2)3-โ-2=ยฑ5, which gives x=3, and so x3-1=y2+1=26 is the only solution
Edit: only known number (don't think it's been solidly proven)
It has been solidly proven. Equations of the form y2 = x3 + k (which are a type of elliptic curve) are called Mordell equations, and there are algorithmic methods for solving them, which have been applied at least for all k in [-10000,10000].
In fact, there are exactly two integers lying between a square and a cube: they are 26 and 0.
A reasonably accessible treatment of the methods used to solved these equations is found in these notes by Keith Conrad.
This theoreme is called Catalan's conjecture. You can read about it on wikipedia. The proof is actually quite complicated and it took people more than 150 years to come up with one.
When you are multiplying by 9, if you hold your two hands up and lower the digit you want to multiply by, it makes the number. For example, if you want to do 9 * 4. You face the palm of your hands, lower your ring finger. You have three to the left of the finger you put down and six to the right to make 36. 9 * 4 = 36. This works all the way from 9 * 1 to 9 * 10 Neat math fact / trick
I mean, it's cute, but how much easier do you find it than doing 10x-x? So 9*8 is 80-8 = 72 for example.
rakuanu ยท 5 points ยท Posted at 15:06:28 on May 25, 2016 ยท (Permalink)
Oh that's neat. The method I used growing up was (x-1)+y=9 where x is the number of times to multiply by 9 and y is the remainder that gives you 9. So 9*7 is 6+3 so 63!
[deleted] ยท 1 points ยท Posted at 23:57:32 on May 25, 2016 ยท (Permalink)
Depends because your phrasing is bad. Forever makes me think of a limit, in which case halving a value forever would get you zero. However, if you have the sequence An = 1/n, then while the limit of the sequence approaches 0, no term is equal to zero. It's also why infinity is not a number.
You can keep halving it for any amount of time, but not forever. 'Unbounded but finite time' is different to 'infinite time/forever', and it's a fairly important distinction to make.
I seriously stumbled upon this on my calculator last month. I know a lot about math, but this interbreasts me the most. Please... no one spoil why this works.
[deleted] ยท 216 points ยท Posted at 11:39:06 on May 25, 2016 ยท (Permalink)
They're missing the "number" two spaces before the 0 (8 for one digit, 98 for two digits, 998 for three digits, etc). This is caused by the 0 is actually 10 (or 100 or 1000, depending on how many digits are in each "number"), so it carries. The 9 becomes a 0, carrying 1 over to the 8, which becomes a 9. Since it doesn't carry over again after that point, the 7 is left unchanged, making it look like the 8 is skipped.
Also, if you multiply 12345679 by any multiple of 9 less than 100 (some number X), the result will be (X/9) repeating 9 times; e.g. 12345679 * 63 = 777,777,777
If you're interested in this type of thing, look up the Champernowne constant. My favorite approximation is 60499999499/490050000000. Both the numerator and denominator look innocuous, even a little "structured", but they approximate the constant out to almost 200 digits.
[deleted] ยท -2 points ยท Posted at 14:26:08 on May 25, 2016 ยท (Permalink)
It's because calculators can't memorize infinite decimals. They will round them up at a certain points and when you do the inverse product the last digits are missing
If you tie a string around a basket ball. And similarly you tie a string around the earth (assume both are perfect spheres). If you raise the string 1 foot off the surface of each. The amount of additional string you will need is the same.
Or does it not matter, as long as you're using the same units the whole time?
Yep! It's whatever unit you used for the distance between the earth and the string.
Tafkah ยท 11 points ยท Posted at 13:03:29 on May 25, 2016 ยท (Permalink)
There's a mathematical proof that every whole number is interesting. You can find an interesting fact about each whole number one by one. For example, 0 is the only number that can be multiplied by any other number without changing; 1 is the only number that is its own inverse; 2 is the only even prime number; 3 is the smallest odd prime number; 4 is the smallest square of a different number; etc. If you ever come to a number for which you can't find an interesting fact, that number is now the smallest whole number for which you couldn't find an interesting fact, which makes it interesting. Therefore all whole numbers are interesting.
If you ever come to a number for which you can't find an interesting fact, that number is now the smallest whole number for which you couldn't find an interesting fact, which makes it interesting. Therefore all whole numbers are interesting.
But if the next whole number is defined as the smallest uninteresting number, the previous whole number is no longer the smallest uninteresting number, making it uninteresting again
Tafkah ยท 2 points ยท Posted at 12:44:34 on May 26, 2016 ยท (Permalink)
I may have learned that from Art Benjamin. He was a professor at my college, and he taught a couple of my classes. But I probably heard it from Francis Su (professor at the same college, who may have heard it from prof. Benjamin). He started every class with a math fun fact, and this was the first one that popped into my head.
as a former accountant...
- when summing two sets of presumed identical values
- if the results are different
- take the difference
- sum the digits of the difference
- if the value is evenly divisible by 9
- then there is a transposition error somewhere in the number sets
it's old school, and really from my past life, how it really applies, if you are using a 10 key, with a tape, and you get a different value while confirming, if you compare the tapes, you will find a transpose error
It's not the most useful thing, but I was pretty proud of myself for figuring this one out (including why it works) while I was in the 5th grade.
For the numbers 17, 18, and 19, you can quickly figure out their square by multiplying the last digit by 4 to get the first to digits of the number, and then you can get the last digit by remembering what the last digit would be if you just took the square of the last digit.
So for 172:
4 x 7 = 28
7 x 7 = 49
Thus giving you 172 = 289
There is a more complicated formula that lets you apply this pattern to any number, but it looses it's beautiful simplicity.
In grade 9, I figured out the formula x2 + y2 +2xy =(x+y)2 and thought I was a genius. I got pretty pissed when I learned it the next year in Algebra 2.
In what sense? As a math major I spend 99% of my time proving various things from the most "obvious" like why does 1+1=2 work, to really complex shit for my level.
If your implying that math has to be built on at least some assumptions, then I argue that so does the universe and our existence. It's a huge more philosophical question at that point of what is a "truth" and how do we know it's true.
Edit: I realized that the original comment said there are some unsolvable problems and not that math itself is unprovable. Oppsy, my bad.
[deleted] ยท 2 points ยท Posted at 19:43:47 on May 25, 2016 ยท (Permalink)
I believe he is refering to gรถdels incompleteness theorem
Would make more sense. I always interpreted it as saying that there are inherent underlying assumptions in mathematics that are necessary for the proof of all things that follow. Everything from there is provable but it is proof based off a fundamental assumption.
[deleted] ยท 2 points ยท Posted at 20:03:02 on May 25, 2016 ยท (Permalink)
That kind of comment gives the wrong idea in a world where people already say that math has no point and comes out of people's asses. The fact that people need to make some assumptions is irrelevant. On a philosophical level everything makes assumptions and by that logic everything is unprovable or provable on potentially false terms. Which is not how we look at the world or science/math. Math is built on assumptions, but assumptions that are well thought out, necessary, and fit out intuitive understanding of numbers as human beings. So no one is making random unproven assumptions to prove whatever they want.
maz-o ยท 1 points ยท Posted at 19:26:09 on May 25, 2016 ยท (Permalink)
If I remember correctly there is a fancy ass proof in Principia Mathematica about it. I've never read it myself though so I'm just going to talk about what I know that makes it true.
There are two ways to look at it I think. One is a more formal proof way, the other is more to help understanding at a slightly more in depth level but really isn't a proof.
Basic arithmetic works because of the properties of groups. They are pretty simple rules that you can probably read and understand yourself, regardless of what level of math your at. They pretty much say, take a group of something (in our case a specific group of numbers) and define and operation on it (in our case addition) and a list of certain properties hold.
You can then use and play with those properties to show that 1+1=2 "works" in various situations. What people seem to not realize is that it doesn't always "work". Because of the way groups are defined, you could technically make your group to be anything you wanted, it doesn't even have to be made up of numbers. And you can define your new "addition" to work however you want. You can make 1 + 1 = fish if you want. The important thing is though, using the definition of groups you can show that it works for the numbers and operations as we are used to them (aka how you learn them normally in school).
This though really relies on the fact that you know the definition of this "addition" thing and "numbers". If you want to break it down into it's fundamental level you need to use successor functions and the peano axioms. These are just formal ways to define how we think about numbers, like "2 comes after 1".
With how it is defined (which you can see in more detail on the wiki if you like) we can just simply say:
2 = S(1) = S(1+0) = 1 + S(0) = 1 + 1
This right here is a more formal proof of why it works in the case of natural numbers. And you can prove it works with other groups of numbers (i.e. reals, integers, rationals, complex, etc).
TL:DR - We have a formal definition for the idea "2 comes after 1" that we can use to prove it along with this thing called "groups"
[deleted] ยท 1 points ยท Posted at 00:16:28 on May 26, 2016 ยท (Permalink)
You cannot prove there exist infinities of sizes between the repeated powersets of aleph-naught.
related to this: .999 repeating is the exact same number as 1, not just very very close.
pazur13 ยท 2 points ยท Posted at 14:04:03 on May 25, 2016 ยท (Permalink)
What's the reasoning behidn this? I always believed that if it's an infinite amount of nines, it's an infinitely little number (however little sense this description makes) away from 1.
[deleted] ยท 6 points ยท Posted at 14:16:44 on May 25, 2016 ยท (Permalink)
It behaves exactly the same way as 1 in every way. Therefore it is the same number as 1, just a different representation.
This is simple because you believe that .333 repeating equals 1/3 but it equals 1/3 for the same reason .999 =1. This proof just hides the real reasons because you already believe the part about 1/3. That said I have used this to convince people of this fact and think it works well enough for that purpose.
brwbck ยท 8 points ยท Posted at 16:42:54 on May 25, 2016 ยท (Permalink)*
Yes. Better way of doing it:
x = 0.999...
10*x = 9.999...
10*x - x = 9.999... - 0.999... = 9
9*x = 9
x = 1
EDIT: Also, if 0.999... is not equal to 1, then we should be able to construct a number that's halfway between them. Try finding me a number halfway between 0.999... and 1. How would you even write it?
This is what made me understand. The 1/3 = 0.333... was helpful but still didn't convince me.
[deleted] ยท 2 points ยท Posted at 19:56:20 on May 25, 2016 ยท (Permalink)*
The reason I didn't use this version was because people often argue that 10*0.999... /= 9.999..., which doesn't make any sense, because multiplication by the base (10 in this case) is just shifting all digits to the left by 1 place. But getting into number bases is another topic that might be confusing.
I like your argument regarding finding a number inbetween 0.999... and 1, as there exists, by definition, a real number between any two real numbers that aren't equal.
[deleted] ยท 2 points ยท Posted at 19:54:26 on May 25, 2016 ยท (Permalink)
I agree that it has its flaws, but I think it demonstrates the concept very well - especially for people who aren't very mathematically inclined.
1/3 is 0.3 recurring. 3*(1/3) is 1, or in decimal notation, 3*0.3 recurring is 0.9 recurring.
[deleted] ยท 1 points ยท Posted at 00:13:18 on May 26, 2016 ยท (Permalink)
There are quite a few reasons why.
For instance, I could say that, (.999...)x(.999...)=(.999...), and (.999...)x1=(.999...), which means (.999...) is acting as an identity and 1 is as well. There are trivial proofs that groups under a binary operation have a unique identity, thus 1=(.999...).
You could also note, that (.999...) and 1 are both rational numbers, 1/1 and 1/1. Assuming you don't buy the mapping between the rationals and the reals, you can cite the theorem about the density of the irrationals in the reals, which would show that there exist irrational numbers between any two rational numbers, as well, there exists rational numbers between any two irrational numbers. I'll assert as a claim that there exists no rational or irrational numbers between (.999...) and 1. Think on that for a while.
As well, if (.999...) did not equal 1 then [(.999...),1] would be a compact space. This would mean it's isomorphic to any other compact space. However, no mapping exists between [(.999...),1] and [0,1].
Really, what's going on is, you're saying there's an infinitely little number, but there isn't. Infinitely little means zero. If I give you (.999...), you have to be able to produce a number that I can add to it to get 1. If you give me any positive value 0.00...001, you've added past 1. Since no positive real number can be added to (.999...) to get 1, we can be sure (.999...)=1.
[deleted] ยท 1 points ยท Posted at 04:19:11 on May 26, 2016 ยท (Permalink)
it's an infinitely little number (however little sense this description makes)
That's the point. There is no such thing as "infinitely small" in the real numbers.
[deleted] ยท 1 points ยท Posted at 14:19:09 on May 25, 2016 ยท (Permalink)
Between every two numbers there is an infinite number of other numbers. Between 0.1 and 0.2 are 0.11, 0.12, 0.111, 0,198 and so on.
Between 0.888... and 0.9 is an infinite number of numbers. You can just add a 9 at the end of 0.888...: 0.89, 0.889, 0.8889 and so on.
Now we have 0.999... and 1. You can't add 9 at the end because the end is always a 9. Therefore there isn't a number between 0.999... and 1 which means it is the same number.
[deleted] ยท 4 points ยท Posted at 14:52:19 on May 25, 2016 ยท (Permalink)
They're not different numbers, just different representations of the same number. It's like saying that three thirds is the same as 1 - it's a different representation, but exactly the same. The 0.999...=1 is a less intuitive version of the same.
Just imagine it likewalls. The first number is a red wall, the second number is a blue wall. The numbers between it are free space.
1 = blue wall (---)
2 = red wall (---)
Between 1 and 2 are other numbers. The wall is something like --- --- It has free space between them. They are two walls.
1 = blue wall (---)
0.999... = red wall (---)
This looks more like ------ Both parts of the wall look different but they aren't seperated by free space. It's the same wall that looks different depending on where you look.
Does this make sense?
pemboo ยท 3 points ยท Posted at 17:47:46 on May 25, 2016 ยท (Permalink)
You're convoluting this beyond belief.
You can have two different ways of symbolically representing the same number
Multai ยท 2 points ยท Posted at 15:09:00 on May 25, 2016 ยท (Permalink)
ashep24 ยท 2 points ยท Posted at 15:36:52 on May 25, 2016 ยท (Permalink)
I had the hardest time believing this until I realized "why can't there be more than one decimal representation of the same number?" The answer is there is no reason. 0.999... and 1 are written ways of describing the same number.
cob59 ยท -3 points ยท Posted at 14:54:46 on May 25, 2016 ยท (Permalink)
x = 0.999... with 10x = 9.999...
Let's say x = 0.999, then 10x = 9.990
Therefore 9.990 - 0.999 = 8.991
Adding more nines to x:
9.999... - 0.999... = 8.99(...)991 โ 9
that 1 never shows up, because there will always be another 9 in both numbers. that's the point of periodic numbers.
the thing is, 0.999... is not exactly 1. for every 9 you hang at the end of the end the number tends to get closer and closer to 1. This is the correct way of saying it, I think.
cob59 ยท -1 points ยท Posted at 15:32:59 on May 25, 2016 ยท (Permalink)
that 1 never shows up, because there will always be another 9 in both numbers. that's the point of periodic numbers.
Even if the 1 "doesn't show up" (I don't know what this means mathematically), 9x value will still be 8.999..., not 9.
The formula you're giving is a limit. Calculating a limit towards +โ is not the same thing as solving for x=+โ, which is not allowed if the function/series is not defined for such a value.
You're right, it's a tautology. Tautologies have a purpose in math and logic. All tautological statements are necessarily true. If you can show that a statement is tautological, you then show that it is true. The thing you were responding to is just a way to help people see that 1 = 0.999...
cob59 ยท 1 points ยท Posted at 19:57:42 on May 25, 2016 ยท (Permalink)*
I explained here why the 2nd part of his demonstration is flawed (or at least why it didn't convince me)
You can't add a digit after an infinite number of 9s. There is no "after" the infinite number of 9s. 0.999...91 isn't a well-defined number. Also, 10 * 0.999... is not 9.999...0, it's just 9.999..., with the same (infinite) amount of 9s. See Hilbert's hotel.
cob59 ยท 0 points ยท Posted at 20:42:10 on May 25, 2016 ยท (Permalink)
Where did you get that 0.999...91 from? The result was 8.999...91.
If you think something from the Hilbert's Paradox disproves something I said, please tell me which part. Just don't throw some wikipedia article at my face.
... it doesn't actually matter. Neither 0.999...91 nor 8.999...91 is a well defined number. 0.999... * 10 = 9.999..., not 9.999...0. Shifting an infinite series of 9s does not leave a gap at the end. This is related to the example of Hilbert's hotel.
Duodecimal, the beautiful system that brings in the simplicity of conversion inherent in the metric system but still allows for your units places to represent the artistically valued relationships of halves, thirds, quarters and sixths without needing infinite-repeating decimal places.
More interestingly, when you break any of those 6-digit sequences in the middle and add, you get 999.
If you turn that upside down you get 666. 666 has three digits. In your example, you have shown three repetitions for each number. The third number begins with the digit 4, and the fourth number is shifted by three digits.
All these numbers arise from dividing by the magical number seven.
Take any whole number, add the digits up, and if the answer is divisible by 3, then so is the original number.
[deleted] ยท 6 points ยท Posted at 14:24:16 on May 25, 2016 ยท (Permalink)
It works for 9 as well. I.e. if the sum of the digits of a number is divisible by 9 then the original number is also divisible by 9.
Actually, I found that the trick works in any base system. So, in a base N system, you can find whether a number is divisible by N-1 by checking if the sum of its digits are divisible by N-1. The trick also works on any of N-1's divisors. In base 10's case, 3 is a divisor of 9.
E.g. 61 (base 8) has the sum of its digits 7 which means is divisible by 7. And it's true, 61(base 8) = 49(base 10).
You can also do this for 19, if you take of the last two digits, multiply them by four then add it to the other digits, if this divides by 19, then so does the number
wfaulk ยท 1 points ยท Posted at 14:49:26 on May 25, 2016 ยท (Permalink)
Which means that if that sum is still too big to easily determine its divisible-by-three-ness, you can just add the sum's digits.
Well, it is true that six was afraid of seven because seven is a registered six offender. What you didn't hear was what happened afterwards. Five had six with seven, who also eight nine.
Don't forget the other numbers: zero went to three, for five, but two also had three for five (2 + 3 = 5). Yet zero won. Still, two three's for five.
Numbers are cannibalistically perverted bastards, especially 5 and 7.
If you assume the impacts of time and money are not separable, then it makes sense to model them as an interaction term. The marginal impact of time on girls is affected by the amount of money you're spending. The marginal value of one extra day holding spending fixed at $100 is worth more in value to a girl than one extra day holding spending fixed at $10. Similarly the marginal impact of an extra dollar is greater the higher the time commitment. Formally:
pd=partial derviative
(pd)girls/(pd)time = 1*money
(pd)girls/(pd)money = 1*time
The original inspiration for the Cobb-Douglas production function was to solve this very issue where the original formula was:
Girls = P*Talpha*M1-alpha
where P is a penis size parameter and alpha is a preference parameter.
Sure but I think then the value of money would decrease exponentially in value.
For example,
If you were to find the limit of the value of money, then the difference in the happiness of the girl would not increase much between 10 million and 50 million since the difference in what you could do would not be that much different. Thus, even if the difference between 50 and 500 may be large it doesn't work for all values of n, where n is the increase in happiness achieved by spending certain amounts of money.
The answer to diminishing marginal returns is to make girls a concave function of money (and/or time), but you can still make money and time nonseperable while modelling either or both with diminishing returns.
Edit: it may not even matter much because 99% of the time a linear approximation of the marginal impact will work well enough. It also has the great benefit of supporting the original conclusion (that girls are evil) ๐
I think I have found a small mistake in your derivation. When you reach the statement "money is the root of all evil" it doesn't say which root, but you have assume the square (second) root. There are actually three possibilities, two of which you have not considered. Either money is the square root of evil, another nth root of evil, or multiple/all roots of evil. If it was a specific root they would have just said, "Money is the square root of all evil" or "Money is the tenth root of all evil" so the most likely case is "Money is the nth root of all evil for n in the natural numbers". Therefore, at step 4 you should have something like:
Girls = nโEvil
Where n is any natural number. From which it follows that:
I once showed this to a friend in class, then the teacher came around and looked at it. He said I had defined everything in such a way that it works and that I won't impress any girls with it. I had forgotten to tell him that this is based of proverbs. (which I had told my friend while I wrote it)
Knowledge = Power
Power = Work/Time
Time = Money
Knowledge = Work/Money
Therefore, as knowledge approaches zero, work done also approaches zero and money earned approaches infinity. This is called the Dilbert Principle, and it explains both why upper management tends to be the least intelligent part of the company, and why my knowledge is undefined.
In a similar vein:
Books = Knowledge
Knowledge = Power
Power = Energy
Energy = Matter
Matter = Mass
Therefore, all libraries are just genteel black holes that know how to read.
culb77 ยท 1 points ยท Posted at 15:51:22 on May 25, 2016 ยท (Permalink)
The Borsuk-Ulam theorem. It says that any function mapping an n-sphere to n-space has a set of antipodal points of the same value. So in the case of an ordinary sphere in our world (a 2-sphere), any function that maps a point on the surface to two variables will have points on opposite ends with the same values.
For example, take the Earth as a sphere. If you pick any two numerical values, for example, temperature and air pressure, there's always at least one set of points on opposite sides of the earth with the exact same value for both of them. You can say that about any two things about the Earth, as long as the function is continuous.
If you want to see if you can factor a three out of a number, add up the digits that make it up, and if they add up to a factor of three then you can factor a three out.
[deleted] ยท 1 points ยท Posted at 18:42:21 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 19:37:19 on May 25, 2016 ยท (Permalink)
The result is meaningless, since you can't sum an divergent series (the sum just keeps going up and up, tending to infinity, since that's the definition of a divergent series.) The people who made that sum were applying techniques used to sum convergent series.
No worries at all. A lot of these seemingly random facts are more like math parlor tricks or stuff that I didn't learn until a much higher level of math as a math major. So not stuff that most people would know unless they are pursuing a degree in math, which is very excessive by most standards.
[deleted] ยท 1 points ยท Posted at 00:17:11 on May 26, 2016 ยท (Permalink)
It has nothing to do with intelligence. People good at math simply care more and spend more time doing it.
[deleted] ยท 3 points ยท Posted at 17:03:42 on May 25, 2016 ยท (Permalink)
If the sum of a numbers digits is a multiple of 3 that number is divisible by 3.
If a number is even it is divisible by two, obviously.
4 is complicated, let's just say if you divide x by 2 and the result is even then the x number is divisible by 4. (Just something I thought on the fly, let me know if it doesn't work on any positive integer).
In a number If the digit in the units place is 5 or 0 then the number is divisible by 5.
If a number is even and divisible by 3 is divisible by 6
Don't know shit about 7.
If you divide x by 2 and the result is divisible by 4 then it's divisible by 8. (Same as 4).
Don't know shit about 9 either.
If a number has 0 in units place is divisible by 10
.999999999... (repeating) is exactly equal to the number 1, mathematically. It's not "close", it literally equals 1.
Simple way to visualize it is with a fraction. 1/3 is the number 1 divided exactly 3 times. Each 1/3 is exactly .3333... (repeating). .3333.... times 3 = .9999...
1/3 x 3 รท .999999...
1/3 x 3 = 1
D-Shap ยท 1 points ยท Posted at 23:45:27 on May 25, 2016 ยท (Permalink)
Not when working with nonstandard analysis and hyperreal numbers
MopsyWT ยท 3 points ยท Posted at 18:59:58 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers to infinity is -1/12.
The sum of all natural numbers, from one to infinity is -1/12. That's negative one twelfth. And it;s not just a math trick, apparently they use that identity in String Theory.
One night while trying to sleep I discovered that if you know the square of a number but not the square of the number before or after it you can find it easily.
Ex) 132=169 142=?
To find the square of 14 all you do is add the square root of the number you know and the number you want to know together.
13+14=27
Then add that sum to the square you already know.
27+169=196
142=196
This works for any two squares, if the roots are only 1 number away. You can also go back if you 142 and want to find 13, you just add 14 and 13 then subtract from 196.
To put it in a formula:
X(1)2=Y X(2)+1 or -12=Z
Add X1 and X2 together
Then use the same sign you did when adding or subtracting 1 to X
Sum of X1 and X2 added or subtracted to Y and that Equals Z
X(1)+X(2)+Y=Z
teyxen ยท 2 points ยท Posted at 20:33:34 on May 25, 2016 ยท (Permalink)
You can multiply by 9 very simply on your finger. Just bend the finger number that you're multiplying 9 by and you get the result. 2 x 9? Bend finger #2 and count 1 to the left and 8 to the right. 18.
To find the square of a number that ends with 5: Take the digits other than 5 as a single number and multiply it with the next consecutive number. Place 25 after the product and you have your square.
No pigeonhole theorem? Actually it's not that exciting but it's one of the only things I can remember from my math degree.
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
You're all nerds, and I'm super jealous. I suck at all things math. I want to be smart, too.
Zarco19 ยท 3 points ยท Posted at 05:42:55 on May 26, 2016 ยท (Permalink)
A fun one nobody has mentioned: Euler's Identity.
epi x i + 1 = 0
Where e is the natural base 2.718... , pi is the circle ratio 3.14... , and i is the imaginary unit sqrt(-1).
(i.e. epi x i = -1)
Written like this, though, it can be said to relate the 5 most important numbers in math. This is one of those facts that seems staggering when you first learn it. A number to an imaginary power? What could that even mean to multiply a number by itself an imaginary number of times? Yet, somehow, if that imaginary number is pi times i, we not only get an answer, but a negative answer, and one that is nicely equal to an integer.
But really, it's a core fact in complex analysis and can be understood in a pretty geometric way.
Basically, it stems from the fact that ei x theta = cos(theta) + i sin(theta). This identity says that to take an imaginary exponent, rather that move outward on the imaginary plane (like we might for ex), we instead move around in a circle, perpendicular to how we would otherwise. This kind of makes sense, since i represents rotating by 90 degrees on the complex plane.
A more detailed proof of this fact can be given by expanding the taylor series (basically an infinite polynomial that adds up to your function) of an exponential function with an imaginary argument. When you break the series into real and imaginary terms, you end up with the series for cosine and sine easily, since the signs of in are the same as the signs in the derivatives of sin and cosine. There's another easy proof starting with the polar definition of a complex number, taking a derivative, and solving the differential equation, and I've even seen some cool geometric proofs. The crux of them all is that if you want complex exponents to have consistent properties that align with real ones, they HAVE to equal cosine plus i sine. Anything else is incongruent with the properties of exponents.
Ultimately, though, this identity says that an imaginary exponent is a rotation in the complex plane. If we start at 1 and go pi around (half a circle), we end up opposite where we started, at -1. Similarly you can see that e0 = 1, epi/2 x i = i, e2pi x i = 1. You can even raise the middle one to the ith power to get that ii = e-pi/2.... a real number.
From this ability to relate complex exponents to complex numbers, we actually learn a lot about complex numbers as a whole, and it opens the door to redefining functions as properties in general. It's a cool fact that looks flashy, has interesting math to back it up, and is actually extremely important and useful.
The difference between successive squares increases by two as you go along.
For example, the difference between 1 (1 squared) and 4 (2 squared) is 3, while the difference between 4 (2 squared) and 9 (3 squared) is 5 (2 more than 3). This follows suit as the difference between 9 (3 squared) and 16 (4 squared) is 7 (2 more than 5). As far as I know, this continues endlessly
Makhiel ยท 1 points ยท Posted at 13:22:33 on May 26, 2016 ยท (Permalink)
The difference between n2 and (n+1)2 is 2n + 1, so yeah, if you raise n by 1 the difference raises by 2, larger number are not going to break it. :)
[deleted] ยท 7 points ยท Posted at 13:09:31 on May 25, 2016 ยท (Permalink)*
Hmm... You phrased the theorem wrong, it's "at least three people know each other, or at least three people don't know each other", which isn't that meaningful or interesting when you think about it. You could pretty much say "in a room with 6 people, all of them might know each other, or none of them, or any combination thereof".
I think it's actually more interesting in the graph theory context (if you're into that kind of thing), which is, "if you have 6 interconnected points and you colour each line one of two colours, there's is no way to avoid forming a triangle with one of the colours".
[deleted] ยท 1 points ยท Posted at 19:10:11 on May 25, 2016 ยท (Permalink)
I think this is why it's interesting though because you're right - it's a pretty uninteresting fact in itself and fairly obvious, but its the beginnings of a whole area of maths, namely Ramsey theory which is fascinating. For example you can prove the result that for any n and sufficiently large prime p there is a non-trivial solution to the Fermat equation modulo p using Ramsey theory.
graaahh ยท 1 points ยท Posted at 17:47:31 on May 25, 2016 ยท (Permalink)
I'm having trouble imagining how that could possibly not be the case. If three people know each other, then it works. And if no group of three people all know each other, then that means 4 or more don't.
[deleted] ยท 2 points ยท Posted at 19:32:19 on May 25, 2016 ยท (Permalink)
you're right, but the question becomes very non-obvious as soon as you ask the same for 4 people. I.e how many people do you need in a room such that at least 4 people know each other or at least 4 people don't know each other (it's 18 btw). Call this the 4th Ramsey number R(4,4). R(5,5) lies somewhere between 43 and 49 (currently unknown).
There's a really great proof using the probabilistic method due to Erdos which gives a lower bound on the Ramsey number for any R(k,k) for any k.
graaahh ยท 1 points ยท Posted at 19:55:05 on May 25, 2016 ยท (Permalink)
Oh, okay, that is pretty unintuitive when you take it higher than 3. Wasn't expecting that, very interesting!
I think it's actually more interesting in the graph theory context (if you're into that kind of thing), which is, "if you have 6 interconnected points and you colour each line one of two colours, there's is no way to avoid forming a triangle with one of the colours".
Where if you want to see if any number is a multiple of 3, you can add each individual number together, and if they come out to a multiple of 3, then the origional number does, as well.
For example, you can tell that 45243912 is a multiple of 3 because 4+5+2+4+3+9+1+2=30
Zywakem ยท 1 points ยท Posted at 14:03:24 on May 25, 2016 ยท (Permalink)
My favorite (and most used) math fact is that you can instantly tell if a number is divisible by 3 by adding the numerals until they are a single digit.
no actually those two are just different notations for the exact same value. There are infinite number of nines so you cannot name a single value between those two numbers.
You are confusing the map with the land. The land is the real numbers. The map is the decimal representations of them. There happen to be two decimal representations for the number 1. In fact there are two decimal representations for any real number which has a finite length decimal expansion: just reduce the last digit by 1 and add infinitely many 9s to the end. It is possible to show that these two decimal expansions represent exactly the same number.
1/9801, in decimal form, contains every number from 00 to 99...except for 98. So it looks like (0.0001020304...969799) and then it repeats. There's a Numberphile video about it, but I'm on mobile so I can't link it.
Take any number, write it out. Count the number of letters. Write that number out. Rinse, lather and repeat til you get to four.
Nistua1 ยท 1 points ยท Posted at 19:50:20 on May 25, 2016 ยท (Permalink)
That's because 4 is the only number, that has as many letters as it's value.
[deleted] ยท 1 points ยท Posted at 19:51:44 on May 25, 2016 ยท (Permalink)
The only values where this sequence terminates (by which I mean, it will loop back to the same value as before) are those in which the number of letters in a number equals the number itself. As far as I can see, this is only true for four.
A magic number is a number where all of the number's factors (excluding the number itself) add up to give that number. For example, 6 is a magic number because 3+2+1 = 6. 496 is also a magic number. This simply blew my mind when I was 10 and still does to this day now that I'm 20.
Never heard these called magic numbers, always called them perfect numbers. :). I liked them too. 6. 28, 496....
Similarly "weird numbers": the sum of all of their factors (including 1 but not the number itself) is larger than the number but no combination of its factors adds up to the number itself. 70 is the smallest, they get very big quickly.
This sort of stuff is sometimes called "recreational number theory"
I really like the repeating decimal of 1/998001. It goes .001002003004 and so on until 999 but skips over 998, and then it repeats starting at 001 again!
Mine is about probability. It's known by many as Godwin's Law.
According to Godwin's Law the longer an internet discussion goes on the closer the probability of a user mentioning Hitler or Nazis gets closer to one.
Minkar ยท 1 points ยท Posted at 21:36:36 on May 25, 2016 ยท (Permalink)
doesnt that also imply the probability of a user mentioning [insert topic] goes to one?
D-Shap ยท 1 points ยท Posted at 23:50:38 on May 25, 2016 ยท (Permalink)
Yes, and the fact that this law is often mentioned in reddit discussions also increases the chance of it occurring.
Ncurran ยท 2 points ยท Posted at 14:57:57 on May 25, 2016 ยท (Permalink)
That European people say maths and North American people say math.
dalisu ยท 2 points ยท Posted at 15:01:20 on May 25, 2016 ยท (Permalink)
6 is afraid of 7.
Minkar ยท 1 points ยท Posted at 21:36:57 on May 25, 2016 ยท (Permalink)
This is perhaps a small amount of hyperbole but I'd consider this theorem to be the bedrock upon which we understand our physical world. Considering the importance that symmetries end up having in our understanding of the physical world around us it might not be as much hyperbole as you'd think though...
That we have, and use, two different concepts of zero. When we count upwards we do not start at 0, but at 1. However, if we wanted to count down from 30, we would start from 30 rather than 29.
This makes the first unit of an upwards count a whole one, and the first unit of a downwards count empty, or null.
Holy it was more messed up than I thought. I had planned on changing it, but jesus it was fucked.
[deleted] ยท 2 points ยท Posted at 15:45:34 on May 25, 2016 ยท (Permalink)
I am obsessed with chaos. If I was going to go to grad school for math (which I considered but ultimately decided against), it would be to study chaotic dynamical systems. I love the butterfly effect (despite cringing at how it gets described/bastardized in pop culture).
Ar_Ciel ยท 2 points ยท Posted at 15:46:44 on May 25, 2016 ยท (Permalink)*
To help more quickly determine if a number is evenly divisible by 3, add all the digits in the number, then divide. For example, 9168 would be 9+1+6+8=24. 24/3=8, and 9168/3=3056
That's the only math fact I think I know, and it's not super useful.
soggie ยท 2 points ยท Posted at 15:52:00 on May 25, 2016 ยท (Permalink)
You can go one further. 24: 2+4=6.
JJean1 ยท 2 points ยท Posted at 15:54:38 on May 25, 2016 ยท (Permalink)*
That there are always at least two points on the Earth diametrically opposite each other (antipodal points) with the exact same temperature and barometric pressure. A good explanation can be found here.
culb77 ยท 2 points ยท Posted at 15:56:43 on May 25, 2016 ยท (Permalink)
If you were to receive $100 for every second since Christ was born, it still wouldn't cover 1/3 of the US national debt.
[deleted] ยท 2 points ยท Posted at 15:58:29 on May 25, 2016 ยท (Permalink)
Don't feel bad at all. A lot of the comments in here are either simple math "parlor tricks" that aren't really part of standard math education or higher level stuff that I only learned after taking classes as a math major. So most people will not know or ever encounter most of the stuff mentioned in the comments.
Indiana tried to pass a bill to change the value of pi to about 3.2. The only reason it didn't pass is because of the intervention of a mathematics professor that happened to be in legislature that day.
I was about to be flabbergasted but the I saw it happened in the 1800's, which makes a bit more sense. Still pretty ridiculous regardless but at least it wasn't something that happened with recent politicians thank god.
The sides of a pentagon, a hexagon, and a decagon, each inscribed in congruent circles, will form a right triangle, which is also half of a golden rectangle!
Start by choosing any three-digit number in which the first and last digits differ by at least twoโfor example, 753. Now, reverse this number to get 357. Subtract the smaller number from the larger: 753 โ 357 = 396. Finally, add this number to its reverse: 396 + 693. The sum you get is 1089.
Try it again, with a different number, say 421.
421 โ 124 = 297
297 + 792 = 1089
The answer is the same. In fact, no matter what three-digit number you start with, you always end up with 1089.
Consider the number 614. This is equal to 600 + 10 + 4. In fact, any three-digit number written โabcโ can be written 100a + 10b + c (note: โabcโ in this case is not a ร b ร c). So, letโs call our initial number โabc,โ where a, b and c are single digits. For convenienceโs sake, make a bigger than c.
The reverse of โabcโ is โcba,โ which can be expanded as 100c + 10b + a.
We are required to subtract โcbaโ from โabcโ to give an intermediary result. So โabcโ โ โcbaโ is
(100a + 10b + c) โ (100c + 10b + a)
The two b terms cancel each other out, leaving an intermediary result of
99a โ 99c, or99(a โ c)
At a basic level algebra doesnโt involve any special insight, but rather the application of certain rules. The aim is to apply these rules until the expression is as simple as possible.
The term 99(a โ c) is as neatly arranged as it can be.
Since the first and last digits in โabcโ differ by at least 2, then a โ c is either 2, 3, 4, 5, 6, 7 or 8.
So, 99(a โ c) is one of the following: 198, 297, 396, 495, 594, 693 or 792. Whatever three-figure number we started with, once we have subtracted it from its reverse, we have an intermediary result that is one of the above seven numbers.The final stage is to add this intermediary number to its reverse.
Letโs repeat what we did before and apply it to the intermediary number. Weโll call our intermediary number โdef,โ which is 100d + 10e + f. We want to add โdefโ to โfed,โ its reverse.
Looking closely at the list of possible intermediary numbers above, we see that the middle number, e, is always 9. And we also see that the first and third numbers always add up to 9, in other words d + f = 9.
So, โdefโ + โfedโ is
100d + 10e + f + 100f + 10e + d
Or
100(d + f) + 20e + d + f
Which is
(100 ร 9) + (20 ร 9) + 9
Or
900 + 180 + 9
Presto! The total is 1089, and the riddle is laid bare.
Hope you all enjoy as much as I did when I read it
A googolplex is such a large number that if a universe were to be measured as a googolplex meters in size, you would see repetition such that there would be exact copies of yourself throughout the universe. This is because there are only so many quantum states (a limited number of ways particles can arrange themselves) in that volume of space. Numberphile does a great explanation of this on their YouTube channel. So that would suggest every other option would have been exhausted before creating duplicates.
I thought about this a lot and it's actually terrifying if it holds truth. That means everything you can think of has happened in that universe once. You existing in a heavenly utopia, and the worst hell of nightmarish imagination. A kronenberg version of yourself. A constantly tortured version of yourself. You name it and the option had to be exhausted first before we can say with 100% certainty that duplicates are being created.
Edit: Minkar's question has made me realize my statement is a bit misleading as far as every other option needing to have been use first, but to say that duplication's begin to appear with 100% certainty, each quatum state would have to be used. Though duplication's could still happen before all options are used.
Minkar ยท 1 points ยท Posted at 21:45:57 on May 25, 2016 ยท (Permalink)
every other option would have been exhausted before creating duplicates
Why does every configuration state have to be used before a duplicate is used?
If my understanding of it is correct, you techniquely dont have to exhaust every option first for it to happen, it would actually probably be very unlikely that all options are used first without duplications. But if Im imagining duplicates being made, I assume for them to start happening with absolute certainy, everything else would have to have happened as well.
One that I find really interesting is that .99999999999... is exactly equal to 1. There are a bunch of different ways to prove this, but I found this one on my own when I was a kid.
If you divide any number by 9 you get zero with that number repeating in the decimal places. For example,
1/9 = 0.111...
2/9 = 0.222...
3/9 = 0.333...
...
On and on until you get to 9. Following this pattern you should get 9/9 = 0.999... but what do you actually end up with? Obviously 1 because a number divided by itself is 1.
It's not the most rigorous proof but as a kid I was amazed when I found it.
babaduv ยท 1 points ยท Posted at 07:44:23 on May 26, 2016 ยท (Permalink)
You can add up all the numbers from 1 to x by dividing x by 2 and then multiplying it by 1 plus X. (works best for even number X's but you can just add half of X rounded up to do odd numbers)
So for 1 to 500.
500 divided by 2 = 250
1 plus 500 = 501
250 x 501 = 125,250
doe28 ยท 1 points ยท Posted at 01:57:44 on May 26, 2016 ยท (Permalink)
I believe Gauss discovered this in elementary school when his teacher assigned busy work and had students add up the numbers 1 through 100. He saw that
1+100 = 101
2+99 = 101
.
.
.
50+51=101.
He realized that the total would be 50*101
Hence the formula for summing from 1 to n when n is even is (n/2)*(n+1)
When dealing with odd numbers, however, you would sum 1 to n-1 and add n.
For example, for n=5, we would sum 1 to 4 and add 5.
Using the formula for even sums to sum 1 to 4 and add 5, we get
(4/2)(5)+5=3*5=15.
Algebraically,
((n-1)/2)(n) +n = ((n+1)/2)(n).
So the equations for summing integers from 1 to n are:
Even n: (n/2)(n+1)
Odd n: ((n+1)/2)(n)
phuhcue ยท 2 points ยท Posted at 16:54:35 on May 25, 2016 ยท (Permalink)
There is an infinite amount of numbers between any two whole numbers.
Obelisp ยท 2 points ยท Posted at 17:15:21 on May 25, 2016 ยท (Permalink)
Why do people keep adding the "whole number" clarification? There's an infinite amount of numbers between any two non-equal numbers. The crazy part is that there's more irrational than rational numbers between any two numbers.
phuhcue ยท 2 points ยท Posted at 17:49:24 on May 25, 2016 ยท (Permalink)
Trying to make it simple. I am not a math guy and if I get too far away from what I understand I'll cease making sense. Thanks for expanding on this idea though.
In an interesting twist, the same is true with blood vessels.
taybul ยท 2 points ยท Posted at 17:00:56 on May 25, 2016 ยท (Permalink)
If you add all the digits of any number that's a multiple of 3, that number will also be a multiple of 3.
kane49 ยท 2 points ยท Posted at 17:01:26 on May 25, 2016 ยท (Permalink)
I only recently learned that a 0% Chance doesnt mean it can't happen, its just not very likely.
Phlum ยท 1 points ยท Posted at 17:09:24 on May 25, 2016 ยท (Permalink)
Can you explain, please?
kane49 ยท 2 points ยท Posted at 17:16:17 on May 25, 2016 ยท (Permalink)*
Oh thats easy.
Pick a number between 1 and infinity.
The chance of any number being picked is a clean 0%, you still picked one though
D-Shap ยท 1 points ยท Posted at 23:58:05 on May 25, 2016 ยท (Permalink)
Not always, when working with hyperreal numbers in nonstandard analysis, 1/infinity = infinitesimal, or .0000...1. When dividing by infinity, a nonreal number, you must use nonstandard analysis, which says that there is an infinitesimal chance that you will choose the right number.
Phlum ยท 0 points ยท Posted at 18:09:15 on May 25, 2016 ยท (Permalink)
Surely the chance is something like 0.000000000001%? Or is it the same principle that 0.9-recurring = 1?
kane49 ยท 1 points ยท Posted at 18:22:47 on May 25, 2016 ยท (Permalink)
Anything divided by infinity is 0, not a small number, just 0
Phlum ยท 1 points ยท Posted at 20:53:44 on May 25, 2016 ยท (Permalink)
I'm sure there's already been endless discussion to this effect, but even so...infinity isn't really a real number, so you can't divide by it, can you?
That doesn't seem right. It seems right to say the limit of 1/x as x approaches infinity is 0. And I don't know that a limit is the same thing as a final numerical answer.
I don't understand anything in this entire thread. I'm not even sure whether any/all of the submissions are jokes. I am scared.
Source:
Communications major
Kaylya ยท 2 points ยท Posted at 17:06:13 on May 25, 2016 ยท (Permalink)
Birthday Problem = It takes just 23 people to have 50% odds that 2 of them share a birthday. By 70 people, the odds are 99.9%.
Toph_er ยท 2 points ยท Posted at 17:11:55 on May 25, 2016 ยท (Permalink)
This is my second comment... But I really like math. Another cool thing is Binary, Octal and Hexadecimal forms of representing numbers. This is especially useful for computer science.
Each digit place in these systems (including decimal) have a reason why those are its places.
The number of digits available for the decimal system is 0-9, so ten different digits. We call this base ten.
For example, in decimal form the first digit is what most kids learn as the "ones place". That base is the 100 digit. As we know, 100 = 1 so the first digit is the ones digit. The second digit is our tens, therefore our digit is represented as 101. And so on.
In other forms this is the same idea. In Binary, there are two possible digits, 0, or 1. So, base 2. Which means that you ask yourself how many of that digit do I have? First digit is 20 (do I have a 1?) And the second digit is 21 (do I have a 2?) And 22 (do I have a 4).
Doboh ยท 2 points ยท Posted at 17:24:39 on May 25, 2016 ยท (Permalink)
It is mathematically impossible for giant or enlarged versions of normal creatures to exist, like in movies such as "honey I blew up the kids" and others. The reason is that it fucks up the ratio of units to square units to cubic units. So say you take a human and make him twice as tall, his height is doubled but his volume is 8 times bigger because volume is measured in cubic units and 23=8. So structurally humans and other creatures are designed to only support a certain size and changing one demensional aspects of a creature changes the 3 demensional aspects at a much faster rate. So we would collapse under our own weight. Also the organs are very precisely sized compared to our bodies and if we were enlarged they would not be efflient enough to sustain the body because of the same ratio imbalance.
I hope this makes sense, there are some great articles that explain it better than me.
Saw video now so I'm back. It's been years since I took calculus(this is algebra) but I don't get it, and by the time I do, I'll be stuck trying to explain it to someone else. Lol.
That they say "maths" in England and "math" in the US.
SQLDave ยท 2 points ยท Posted at 17:32:53 on May 25, 2016 ยท (Permalink)
Mine too! There's a series from the BBC Look Around You which spoofs those sciency shows from the 70s. One was called "Maths" and for the longest time I thought the pluralization was part of the joke. (Here it is, by the way)
That billion actually has 12 zeros, it's something like million1 is million, million2 is billion and million3 is trillion. It's supposed to be like this, then someone in America Fucked up and it caught on.
If you pick a 3 digit number (such as 123) and reverse it (now 321) and subtract the two, the two digits on the outside will always add up to 9, and the digit in the middle will always be 9. In this case, 321-123= 198
Another example:
450-54= 396
.........although I doesn't work with the same digit repeated 3 times. Obviously :)
The 23 paradox/the birthday paradox. If there are 23 randomly selected people in a room, there is a 50% chance that two of them share the same birthday.
Clearly you've never had soggy microwave pizza for breakfast.
[deleted] ยท 2 points ยท Posted at 18:20:37 on May 25, 2016 ยท (Permalink)*
You had the opportunity to eat stale cold pizza and you heated it up?
Heathen.
I once had a one night stand and had no idea where I was. Half naked I got dressed and made my way out of the bedroom to find the flat mate was reheating something, they didn't look at me and must have assumed I was whoever else lived there so they started talking at me.
I don't remember what they said as I'd just noticed the vomit on my trousers and missing shoes. I was too busy trying to work out if I would be happier if it was my own vomit or some strangers...
Finally I decided, definitely my own.
They popped something in the microwave and headed to the bathroom.
Immediately as I tried to work my way to the door a pang of hunger hit me.
By this point I had no dignity left so I popped the microwave open to find about 1/3 of a pizza some sort of meat feast. I tore the pizza in there in half and legged it out the door.
Whatever it was it was glorious and I believe helped me not have hangover gastritis/nausea. That was the one time I a pizza that had been at all reheated.
There you go, a story I've never told anyone else. Enjoy.
[deleted] ยท 2 points ยท Posted at 18:08:39 on May 25, 2016 ยท (Permalink)
.999... = 1
kazneus ยท 2 points ยท Posted at 18:11:46 on May 25, 2016 ยท (Permalink)
Probably going to get buried, but the coolest thing I've ever heard of in math (you dirty English and your extra s's) is Tarski's undefinability theorem which basically states:
(Given) any sufficiently strong formal system, [...] truth in the standard model of the system cannot be defined within the system
Anyways, it's a really powerful theorem - especially given it's connotations outside of math. That is to say it can be shown mathematically that no formalized system can formally contain it's own truth.
Another way to think of it is that it can be proven that no underlying truth cannot be completely proven by itself.
Which is just completely mind blowing if you ask me. I mean it holds for language itself.. you can't define all aspects of a language solely within the context of that language. Now it is entirely possible to prove those aspects of a language (or system of math) with a different language (or system of math). That is an acceptable consequence of the theorem.
I don't know... it just completely blows my mind. No formalized system of truths can completely contain a proof for all formal truths within that system.
This may be buried but one of my favorites is the contraction mapping theorem which implies that a map of the world placed on the ground will always have exactly one point which exactly aligns with the point of the world which it corresponds to.
To find the doubling time of any given population of people or animals, you just take the growth rate and divide it into 70.
So if the population of China grows 10% every year, you just divide 70 by 10, and you get 7. Then it will take 7 years for China's population to double. (That was all made up btw that's not the actual math on China's population. Thank god.)
I think any of the mathematical constants are just so interesting. Like, how the hell did someone figure out pi? Ridiculous.
EDIT: accidentally hit send while typing.
K4mp3n ยท 1 points ยท Posted at 21:18:14 on May 25, 2016 ยท (Permalink)
pi was found by Archimedes who constructed an 97tagon where all the sides had an equal length (I don't know the english words since I am not a native speaker)
mjd638 ยท 2 points ยท Posted at 18:23:15 on May 25, 2016 ยท (Permalink)
I don't know if there is a specific name on the theorum.
But, If you take a sinusoidal signal of frequency (f) and then add together every harmonic of that signal from 1 to infinity.
Then you get a square wave of the original frequency as the result.
Gibberish at first glance, but each fraction contains the same six digits, in the same order, in its repeating decimal form (142857), just starting with a different digit each time. How is that even possible?
If a polynomial(f(x)) of at most degree "n" has "n+1" zeros, then f(x)=0.
One can prove this just using Rolle's theorem, which states that between any two zeros of a function, there is a maximum or minimum(Exists c such that f'(c)=0, c is in [a,b])
Also, (p-1)! modulo p(the remainder function) is equal to -1 if and only if p is prime.(Wilson's theorem)
Finally, the sum of all natural numbers is equal to -1/12.
5w1m1n9 ยท 2 points ยท Posted at 18:32:36 on May 25, 2016 ยท (Permalink)
This is a little-known fact about parabolic motion and elliptical orbits.
Discounting air resistance, a thrown ball in a uniform gravitational field traces out a parabola. In geometry, a parabola is defined as the set of points which are the same distance from a particular point (the focus) and a particular line (the directrix). In this case, the directrix is horizontal because the parabola opens down. The directrix of the ball's path means something physically: the directrix represents the total energy of the ball (kinetic + gravitational potential). If at any point in its path, you redirected the ball straight upward with the same speed, it would just barely reach the directrix and then fall.
The same thing is true for planetary orbits in the 2-body problem. Discounting relativity and other planets, a planet orbits the system's center of gravity in an elliptical orbit. An ellipse is the set of points which are equidistant from a circle (I don't know a name for this, but let's call it the major circle) and a particular point inside the circle (the focus). In this case, the major circle is around the system's center of gravity. The major circle has the same significance as the directrix did: the major circle represents the total energy of the planet. If the planet's motion (and the sun's much smaller motion) were redirected exactly away from the center of mass of the system, the planet would have just enough energy to reach the major circle of its former orbit (and the sun would reach the major circle of its orbit).
Filobel ยท 2 points ยท Posted at 18:33:28 on May 25, 2016 ยท (Permalink)
I always liked the Braess' paradox, because I can bring it up whenever someone says "the solution to the traffic issues in Montreal is simple, just add more bridges!"
Basically, the paradox says that adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. In other words, adding roads can actually make the traffic worse (inversely, in some cases, you can actually improve traffic by removing roads).
Here's a theoretical example. Say 4000 people want to go from point S (start) to point E (end). There are two routes. One that goes through point A and one that goes through point B. The road that goes from S to A takes x/100 minutes to travel, where x is the number of people taking that road. The road from A to E takes 45 minutes regardless of how many people are taking it. The road from S to B also takes 45 minutes regardless, while the road from B to E takes y/100 minutes, where y is the number of people travelling that road. Basically:
S --- x/100 min ---> A --- 45 min ----> E
S --- 45 min ---> B --- x/100 min ----> E
(not sure if that's clear)
Both routes take the same total time, so we should reach an equilibrium where 2000 people take one route and 2000 people take the other. So it'll take people 2000/100 + 45 minutes = 65 minutes to go from S to E, regardless of the route they take.
Now add a road between A and B that takes a very short time to travel. Say a minute. Now, it makes no sense for any of the driver to take the direct route from S to B, because even in the worst case, where all drivers take S to A, it'll take them 4000/100 to reach A, then 1 minute to reach B from A, for a total of 41 minutes. That's shorter than 45 minutes. For the same reason, it makes no sense to take A to E. So the equilibrium is that everyone will take the route S -> A -> B -> E, which will take 81 minutes.
So adding a road between A and B adds 16 minutes travel time to everyone.
[deleted] ยท 2 points ยท Posted at 18:33:37 on May 25, 2016 ยท (Permalink)
I like that vector operations are the same in all coordinate systems, like curl, divergence, etc.
Math only really clicked for me once I realized most of my struggle was in coordinate transforms - not the concepts themselves.
ZPhox ยท 2 points ยท Posted at 18:37:35 on May 25, 2016 ยท (Permalink)
Any number that is not a decimal or fraction over 0, always equals 9 when multiplied by 9. (Add the numbers together at the end of the equations till you get a single digit)
There are many proofs for this, but here is the one I think best explains it. Between any two numbers, there are an infinite number of other numbers. For example, between 6.4 and 6.5, you have 6.41, 6.42, 6.421, and so on for an infinite number of numbers. But there are no numbers in between 0.9 repeating and 1. Therefore, according to the definition of a number, 0.9 repeating and 1 are the same number.
does anyone else find it rather mindblowing that we are a species that uses imaginary concepts like this to explain our universe, and it actually works?
stwhn ยท 2 points ยท Posted at 18:41:23 on May 25, 2016 ยท (Permalink)
The volume of a pizza with radius (z) and depth (a) equal to pi ร z ร z ร a
Pick any single digit number aside from 0. In this case I'll choose 5. Now create a number composed only of that digit with the digit count corresponding to number you chose which in this case would be:
55555 (a 5 digit number composed only of 5s)
Now square the number:
55555 x 55555 = 3,086,358,025
Now divide the answer by the single digit you chose, squared:
5x5 = 25 -> 3,086,358,025/25 = 123454321
As you can see we have a counting palindromic number that plateaus at the original digit and then counts back down. Works for any single digit number.
Examples:
(999999999x999999999) / 81 = 12345678987654321
(7777777x7777777) / 49 = 1234567654321
(4444x4444) / 16 = 1234321
Came up with this in pre-calculus and it has entertained me ever since.
If you multiply a 2 digit number by 11, you can add the ones and tens digit, put it in the middle of the tens and ones digit, and have the correct answer.
Examples:
10* 11: 1+0 = 1, so 110
63* 11: 6+3 = 9, so 693
If the sum of the 1s and 10s digits is a two digit number, just subtract 10 and add 1 to the tens digit:
It contains the three basic mathematical operations each once (addition, multiplication, exponentiation), as well as all 5 fundamental mathematical constants each once (0, 1, e, i, ฯ).
It is widely considered the most beautiful mathematical equation.
Pi is an infinitely long, random number. Meaning every combination of every number exists. So if you convert the numbers to ASCII text, your name, birthday, everything about you shows up at some point in the infinitely long list of numbers.
[deleted] ยท 2 points ยท Posted at 19:08:32 on May 25, 2016 ยท (Permalink)
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
gbs5009 ยท 2 points ยท Posted at 19:31:50 on May 25, 2016 ยท (Permalink)*
You can also check if any number is divisible by 11 by alternating adding or subtracting the digits, and seeing if the result is zero.
1 - 2 + 1 = 0, so 121 IS divisible by eleven
2 - 1 + 1 = 0, so 231 must be as well.
8 - 2 + 3 - 8 = 1, so 8,238 is NOT divisible by eleven.
When there are 23 people in a room, there is a 50% chance that two have the same birthday. Increasing to 70 people gets you to 99.9%. Here is more information on it.
This is from Bertrand Russell and his realization while advancing/developing set theory.
The setup:
You can have a set of sets, like "numbers" is a set of "even numbers" and "odd numbers", which are sets, too.
You can also have a set that includes itself, like "sets that have more than 10 items", might have 11 items, then it would be inside it's own set. This stuff is all very fundamental to set theory (I wouldn't understand it if it wasn't), and in turn, all of mathematics itself, since set theory was developed as a foundation for modern mathematics.
The problem happens when you try to create a set of all "sets that don't contain themself". You can't do it. A set of sets that don't contain themself is itself a set that doesn't contain itself, and thus is a member of itself. It is a paradox.
This paradox was later evidenced to claim that there is a fundamental problem in the logical makeup of conventional "true"/"false" mathematics, and contributed to the development of a different type of math that we now use every day (because it works) called fuzzy math.
It's true that Russell's paradox caused problems for naive set theory and that mathematicians had to come up with something else to deal with it, but the replacement wasn't fuzzy math and the paradox doesn't reveal any sort of fundamental problem in the logic of true/false mathematics. The replacement for naive set theory was Zermelo-Fraenkel set theory, which actually gives rigorous axioms for the behavior of sets and isn't vulnerable to Russell's paradox or similar problems. There is no way to define "the set of all sets that don't contain themselves" in ZF set theory. This theory, with the Axiom of Choice added in, provides an abstract basis for almost all modern mathematics. Fuzzy logic is a perfectly valid field of mathematics, but it's not like Boolean logic is invalid or has been replaced.
I only claimed that it contributed to the development of fuzzy math, not that fuzzy math in any way replaces boolean logic. That's not my territory to argue. It did force the development of the axiom of choice, though, which, I am not going to pretend that I understand fully. I just find the fact that the paradox was so elegant very pleasing, and I'm not really sure (though I would like to know) what the historical controversy was motivated by when ZF set theory was initially introduced.
The Axiom of Choice is an entirely unrelated issue to Russell's paradox. ZF without Choice doesn't fall victim to Russell's paradox either, and if it did adding in the Axiom of Choice wouldn't save it. The Axiom of Choice was suggested because it resolves many otherwise undecidable problems that many mathematicians feel should be decidable.
[deleted] ยท 2 points ยท Posted at 19:21:50 on May 25, 2016 ยท (Permalink)
First, the derivative calculates the slope of a tangent line, and integral calculates the area under the curve.
Secondly, velocity is the first derivative of position, because it is defined that way.
Lastly, calculus relates to physics so well, because it was invented by Isaac Newton to study physics.
If i is defined as โ-1, ii is a real number and is roughly equal to 0.208.
Proof: think of the complex coordinate plane, where each point is a number a+bi, a describes the horizontal coordinate, and b describes the vertical coordinate. Converting to polar coordinates, each point can be represented RรeiA where R is distance from the origin and A is the angle from the positive x-axis in radians.
In this case, eiฯ is the point on a circle of radius 1 (the unit circle) which is ฯ radians or 180ยฐ from the x-axis. It has a value of -1+0i, which is why eiฯ = -1.
What if we only go 90ยฐ from the x-axis? That point is on the y-axis, so it's equal to 0+1i. Also, 90ยฐ is ฯ/2 in radians, so eiฯ/2 = i.
If you raise both sides to the power of i, then ii = ei2รฯ/2 . But i2 is -1, so ii = e-ฯ/2.
Essentially, complex exponention is not always uniquely defined, since the complex logarithm is not uniquely valued (since e2ฯi=1, the map z -> exp(iz) is 2ฯ-periodic, so it has no continuous global inverse). On the other hand, we may define the logarithm on large regions of the complex plane -- the maximal regions looking like the hole plane minus a ray outward from 0. The "principal branch" is defined everywhere but for the negative reals, and gives the standard real-valued logarithm when applied to a positive real. But we could of course choose infinitely many other branches defined on the same region, by simply adding 2ฯi to everything.
Now if z=ii, then log(z) = i log(i), so that z = exp(iโขlog(i)). These operations are well-defined since the complex logarithm is a right inverse, or section, of the exponential map, though it is not a left inverse (that is, log(ew) does not in general equal w). But anyway, we obtain z = exp(iโขlog(i)). Solving for w=log(i) we have exp(w)=i, so if w=a+bi, then exp(w)=eaโข(cos(b)+i sin(b))=i, so that cos(b)=0, and since ea is positive for a real, we have sin(b)>0, so sin(b)=1. Hence a=0 and b=ฯ/2+2ฯn for any n.
Thus z=exp(ฯ(1/2+2n)) is a solution to z=ii for all integers n. The principal branch of the logarithm gives n=0, so that ii=exp(ฯ/2) ~= 0.203.
Yes, I think you're right. Another one with numbers is that 1 google raindrops would be able to fill the observable universe more than 100 trillion times.
cmnthom ยท 2 points ยท Posted at 19:57:48 on May 25, 2016 ยท (Permalink)
If you transpose numbers, the difference will always be divisible evenly by 9.
If you prove some function f(x) for x = 1, and you prove that given f(n) is true, f(n+1) must also be true, you prove it true for all positive integers.
When I first learned about inductive reasoning, it blew my mind. As a kid, I always thought "how do they know that's true for every number", but it's so simple.
Late to the party, but if you believe the Axiom of Choice...
Infinitely many mathematicians wake up blindfolded in a room. They are told that each mathematician is wearing a either a black or white hat. They will be given time to strategize while blindfolded (and have infinite memory, etc. etc.). Once their blindfolds are removed, they will be able to see every other mathematician's hat color, but they cannot communicate. Then, they must all simultaneously guess the color of their own hat. If infinitely many of the mathematicians guess incorrectly, they will all be executed; otherwise, they all survive.
There exists a strategy which guarantees that these mathematicians will survive.
The mathematicians apply the following equivalence relation on hattings: say two hattings are equivalent if they differ by only finitely many hats. Then, they may use the choice function from the Axiom of Choice to identify a representative for each equivalence class of hattings. So, when they can see each other, they have enough information (every hat but their own) to identify the representative for the equivalence class of hattings which includes their actual hatting. So, each person should guess their hat based on that representative hatting, which differs only finitely often from the actual hatting. Thus they survive to be kidnapped another day.
This thread is very old and likely dead but I noticed a number pattern at a very young age I'm still fond of. If you add every successive odd number you always get a perfect square.
Does anyone know if there's some kind of theorem or law for this or anything? It's pretty trivial observation so I know someone's seen it before, just didn't know if it was useful in any way.
One of my favourite facts is the birthday problem, which says that in a group of 23 people there is a c.51% chance that any two people share a birthday
Digital root, where you repeatedly add up a series of numerical digits until you get a single digit. For example, 2 + 4 + 5 + 7 + 8 = 26, then 2 + 6 = 8. So in this case, Digital Root = 8.
But it goes beyond that. If you laid out the numbers of base-10, 0-9, it'd show that 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45, then 4 + 5 = 9.
But if you were to go above base-10 into base-20, which would use a in place of the traditional number 10, b = 11, c = 12, converting them back into base 10 and getting the letters' digital roots then the digital root would, until j, would match with the traditional numerical cypher of the letters.
a = 10, 1 + 0 = 1.
b = 11, 1 + 1 = 2.
Also, the digital root of Supercalifragilisticexpialidocious is 1.
Translated from base-36 to base-10, supercalifragilisticexpialidocious = 65791925216734442002988169043447582627179158156970580. Adding the digits together, the sum is 244.
2 + 4 + 4 = 10, 1 + 0 = 1.
And for those who spotted the reference in the first sum... well done.
The birthday problem states that with just 23 people you have a 50% chance of at least two people sharing the same birthday.
With a real random sample of people however, the probability is higher because birthdays aren't uniformly random. C-sections are rarely scheduled for weekends or holidays.
I love that the sum of the sequence of all positive integers (I.e. Every positive whole number added together) is neither positive, nor is it an integer. It's -1/12.
0.999999999... is exactly equal to 1. Don't believe me? Let's say n = 0.999999999... Then 10*n = 9.99999999... But 9 + n also equals 9.999999999... Therefore 10n = 9 + n so 9n = 9 and n = 1.
9 is cool. Multiply nine by anything and take the outcome and ad the two numbers together and they always make nine. Example - 9x3=27, 2+7=9. 9x5=45, 4+5=9.
That is FACT, my friend, obvious TRUTH, and you can test it out your self with pen and paper, any number, pick any positive number that is REAL, and there you are. You think about that. You put that in your pipe and smoke it.
Don't listen to these "fractionists" or "calculars", you work it out for yourself using basic Pythagorean Principles, which are explained ONE TWO THREE in my Pythagorean Principles for Life, available for a love donation, or no donation at all, all you have to do is ask, My Friend, and the secrets of the Universe can be yours, don't listen to these other Charlatans, they pronounce "GOD particles" swarming around you, taking away your Free Will, do not listen to them, ORDER NOW my GUARANTEED MATHEMATICS based on Pythagoras, only $1 thin dollar postage paid. Step right up, all orders insured.
As an avid board gamer, non-transitive dice blow my mind. Basically it's pools of one or more dice that exhibit a kind of rock -paper-scissors behavior. Dice A beats dice B, dice B beats dice C, and C beats A. It's gets even weirder when you add more dice pools or 2 dice per pool. Here's a video that illustrates it better than I can explain
http://youtube.com/watch?v=zWUrwhaqq_c
if, say, we used 7 digits throughout our history instead of our 10 digits, our number line would go, '0,1,2,3,4,5,6,10,11,12,13,14,15,16,20...โ; becoming our 'base 10'.
fun fact: our weeks are in base 7. I guess Monday would be the 0.
lazyl ยท 2 points ยท Posted at 22:44:50 on May 25, 2016 ยท (Permalink)*
It's not a misnomer. It is correctly named 'base 10'. Your point is just that all base systems, when described using a number from their own base, would always be referred to as 'base 10'. Still an interesting observation though.
You're wrong, base 10 is correct. When you say "base x" the x is always said in base 10.
In your example, you said if we used base 7 throughout our history we would still say base 10, of course because then when we say "base x", the x would always be in base 7.
eg.
"base 2" (binary) signifies that there are 2 symbols in use, 0 and 1.
"base 8" (octal) signifies that there are 8 symbols in use, 0-7.
"base 10" (decimal) signifies that there are 10 symbols in use, 0 to 9.
"base 16" (hexadecimal) signifies that there are 16 symbols in use, 0-9 and A-F.
"10" in any base signifies that you've reached the extent of your available symbols and you're back to the first one (0), with an overflow count in the column to the left.
(And Excel has a setting that lets you start numbered days of the week with zero on either Monday or Sunday)
There is a curve called a cycloid in which no matter where you start a ball on this curve it will take the same amount of time to get to the end whether it starts 800 miles away or 5 inches. (while in a vacuum and friction is not a factor)
lazyl ยท 1 points ยท Posted at 22:39:57 on May 25, 2016 ยท (Permalink)
I assume you mean a ball accelerated only by gravity? Interesting.
That is correct. A mathematician (in the last 200-300 years? I don't remember anyway grandfather clocks were still a thing. The problem with them was that if you didn't start the pendulum at the right spot it wouldn't keep good time.
This mathematician designed a pendulum that followed a cycloid curve so it didn't matter where the pendulum was started. That said it was far too expensive to produce but interesting none the less.
I love epi*i+1=0 because it contains all the most important numbers, and after I took my first complex variables class, I was blown away by how this comes about, and how it should be written epi*i= -1
One and the square root of two have no common multiples. If you started counting numbers 1, 2, 3 and so on - and I started counting sqrt 2, 2 times sqrt 2, 3 times sqrt 2 and so on we would never say the same number.
I remember staying up at night thinking about it. There must be some way to rationalize sqrt 2. Sqrt 2 squared is two after all. But one sqrt 2 times isn't a multiple of one.
If you drew a line horizontally and a second line from the same point diagonally at 45 degrees, then marked out one inch intervals on both lines - there would NEVER be a point at which the intervals line up vertically. Never. Surely they would meet once in all the infinity numbers but they wont.
One learned from blackjack training years ago. If you have 3 consecutive numbers (ex. 6,7,8) you can always multiply the middle number by 3 to get the total (7x3=21 or 6+7+8= 21)
Unrelated gambling fun fact:
if you take the numbers on a roulette wheel 1-36 and add them (1+2+3...all the way to 36) the number you end up with is the mark of the beast 666. ๐น
The Banach-Tarski Theorem states that a sphere of any given size can be broken apart and rearranged in such away such that you obtain two spheres of equivalent size to the first.
Zaculus ยท 2 points ยท Posted at 23:00:23 on May 25, 2016 ยท (Permalink)
Definitely Benford's Law. It states that for many, commonly-occurring collections of numbers there is a 30% chance that the first digit is 1, a smaller chance that the first digit is 2...and the least likely chance that the first digit is 9.
This seems like it should't make sense. Intuition suggests that numbers are just as likely to start with 1 as with 8 or 9 or 5 or any other one-digit number. But they don't. This has been found to be true of a wide range of seemingly random numbers, such as randomly selected address numbers within a large city, populations of animal species, and most notably amounts from a collection of invoices. In fact, forensic accountants will look at a large group of invoice totals, and if far fewer or far more than 30% of them don't have 1 as the first digit, it's flagged as potential fraud.
It mathematical proof has to do with the size of the interval between the logarithm of numbers. But generally speaking, most numbers start with 1.
If you take any number, shuffle the digits and subtract the 2 numbers, the answer will always be a multiple of 9.
For example, i'll take the number of present upvotes, 4665. If I were to shuffle that number to say, 6456, then I would do 6456-4665=1791. And 1791 is a mulitple of 9.
In case you think the was just lucky, I'll take the number of present comments, 9778, make it 7897, do 9778-7897=1881. And 1881 is a multiple of 9.
The number of ways a deck of cards can be shuffled is 52!, which is 8 x 1067, so each time you shuffle a deck of cards, there is an overwhelming probability that they are in that particular order for the first time in history.
11 to any power gives you the coefficients for the corresponding exponential expansion. In layman's terms:
111= 11.
(X+y)1= x+y.
112= 121.
(X+y)2= x2+2xy+y2
113= 1331
(X+y)3= x3+3x2y+3xy2+y3
And so on and so forth. A bit of a higher lever nerd thing I discovered one day when I was bullshitting on my calculator instead of paying attention.
The element being moved is below average for its current set. Removing it will, by definition, raise the average of the remaining elements.
The element being moved is above the current average of the set it is entering. Adding it to the new set will, by definition, raise the average.
There are so many combinations possible in a deck of cards that every time you shuffle it you have most likely created a combination that has never been seen before and will never be seen again. 52! is a ridiculously big number.
kcg5 ยท 2 points ยท Posted at 00:01:31 on May 26, 2016 ยท (Permalink)
The number of combinations a deck of cards can be is called "52!" More combinations than stars in the sky. There is a good chance the deck you have at home is in an order never before seen on earth....
There are more attoseconds (10-18 s) in a second than there have been seconds since the universe began. An attosecond is the general timescale on which we can observe electron dynamics.
Heronda ยท 2 points ยท Posted at 00:58:50 on May 26, 2016 ยท (Permalink)
Universal objects are unique up to unique isomorphism. It makes it easy to see that certain constructions in mathematics are the "right" ones, and really the only way of doing it.
Sheldon: "The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
Zipf's law is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution. Zipf's law states that the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc. https://en.wikipedia.org/wiki/Zipf's_law
The sum of any two consecutive numbers is equal to the difference of their squares.
[deleted] ยท 2 points ยท Posted at 06:21:18 on May 26, 2016 ยท (Permalink)
Not really a fact, but my favorite graph is f(x)= ( x - x2 )x-1
pongze ยท 2 points ยท Posted at 08:10:34 on May 26, 2016 ยท (Permalink)*
Squared integers can be found by adding the relative odd number 1->3->5->7->9->11->...2n-1 Formula is actually something like: n2 = (n-1)2 + 2(n-1)+1 where n>0
0+1=12 , 1+3=22 , 4+5=32, 9+7=42
I figured this out back around Sophomore year of highschool and never told anybody. Once I learned about sequences it didn't really feel all that special.
The powers of 11 make up Pascal's triangle.
110 = 1
111 = 11
112 = 121
113 = 1331
And so on
[deleted] ยท 2 points ยท Posted at 05:17:31 on May 27, 2016 ยท (Permalink)
In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie of energy to heat up by one degree centigrade which is 1 per cent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it.
Whereas in the American system, the answer to "How much energy does it take to boil a room-temperature gallon of water?" is "Go screw yourself" because you can't directly relate any of those quantities.
A video by the Numberphile here.
I was first introduced to this number in the book "Things to make and do in the Fourth Dimension" by Matt Parker ( /u/standupmaths ). I would recommend this book to almost everybody on this subreddit.
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats.
You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.
He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
PS : I also like the fact that 0.99999... = 1 (but i'm not entirely sure it's correct; according to wikipedia it is but last time I checked I remember the article was less final about it)
EDIT : forgot to tell you that 1 + 2 + 3 + 4 + ... = -1/12
Except it isn't. Its not actually EQUAL to the sum, just related to it. Obviously 1+2+3+4... is divergent and thus tends to infinity. Numberphiles methods usually exploit a different use of the equals sign, meaning; "is assigned to", which in his case relates the value of a function to a series.
PS : I also like the fact that 0.99999... = 1 (but i'm not entirely sure it's correct; according to wikipedia it is but last time I checked I remember the article was less final about it)
That is 100% correct, just like saying 3/3=1 or 5*1/5=1. There's absolutely no question to it's finality. Unless we're discussing hyperreal numbers.
Ogurac ยท 1 points ยท Posted at 16:48:54 on May 25, 2016 ยท (Permalink)
The way it was taught to me in college was that this is the exact kind of situation where hyperreals diverge from the set of real numbers, i.e. .999...=1-h where h is the infinitesimal.
This is more of a physics fact, but the idea most people have of what particles are is wrong. They aren't tiny balls. Those are just graphs used to describe them to you in high school textbooks. They have no size at all. They're points. And so by extension their only real properties are mathematical / informational properties. Because all they are are "values" associated with a space. In a sense, the universe is made of math / information.
Because their size is zero. (fundamental particles that is). Size is an emergent property that comes from structure. Particles with no size can still be distances from eachother, and relate from that distance, and so size comes from relation, which becomes structure. It works similarly to how most people will learn in high school, except that particles aren't just very small, but have no size at all.
Their properties are informational, because "matter" as classically understood doesn't exist. Its an emergent property of relation. Fundamental particles don't have properties like size or shape or "texture." All those properties only exist for structure. The only properties fundamental particles have are informational ones. Since they aren't "solids" in the way that sience used to think existed before the early 1900s, their properties don't refer to anything solid, but to pure abstraction. The values are just data that exists in that location more or less.
From what you are writing it sounds like "the set of all informational properties" and "the set of all emergent properties" are distinct sets. Could you though be a bit more precise or maybe even give a definition for what an "informational property" is?
I can't really be precise because its not something science can directly measure. They can only describe it by analogy / how it works. Saying what it "is" is speculative philosophy in a way. How it works is what I described already. The only properties particles have are specific "values" that say how it relates to things. Its not itself a solid, because its sizeless. Particles are just a special case of what energy is doing. And energy isn't a thing either. Just an abstraction of potential and value. So it makes more sense to describe it as data than anything else. But we can't really know what that "means" directly.
The difference between fundamental particles themselves, and emergent structure is that things like texture can only be properties of things with shape or size. But particles have neither. But their relations add up to it by being in different places.
Like look at a chemical model. Obviously you know that the sticks don't refer to literal material things. They're just structural relations that say what's happening. The point is that the balls are more or less the same way. They're basically locations that provide the ability to generate the relations between them. At the end of it all you have a bigger shape. The shape can interact in ways with even bigger shapes, etc. And that's where structure comes from.
It is. The "value" can be measured, but not what it actually "is" doing so to speak. The measurement is indirect, rather than direct like with macro scale things. The key word there was directly, not measure. There's a limit on our ability to fully understand the "nature" of things. Because beyond a certain point we can only really understand them in terms of effects.
Have a hard time to understand what "directly" would mean in this context and why it is an important distinction.
Isn't it just enough that we design a model with a certain amount of parameters that to great accuracy describes phenomena in nature? Then whenever we experimentally find something that our model cannot currently explain, we try to expand the model or make corrections to it and then see if the new model is in agreement with experimental results?
That's enough if all you're trying to do is get results that you can interact with. But it doesn't always tell you what's happening. Take quantum indeterminism and decoherence for example. The reason we don't really know what's happening is because all we know is that the particle should be in multiple places at once, but when we check its only in one. If you decide to stop there you don't need to know what causes this, since it doesn't change what you're likely to measure in the immediate sense.
But there's multiple theories about the fundamental nature of what's going on. Does reality just "delete" the data of its extra locations and reset it when that happens? Or the more bizarre many worlds theory where the collapse simply never happens, but there's split worlds where many different versions of us observed different results? Or maybe indeterminism doesn't exist in the first place, and how the particle moves is deterministic, but impossible for us to know, since its evolution is related to all other particles in the universe in a way that is impossible to predict in the small scale? These are things that experiments as of yet are something we have no way of using to find the answer to. Since all of those theories will look the same to us when we check. This is an example of our inability to directly understand the nature of what's going on. Its one of the many times that that's the case when interacting with quantum things. we can measure the effects, but something underlies the effects that we can't really directly see.
But just describing how something works / its effects doesn't always tell you its nature. At the point where you're describing fundamental interactions, you can only really describe them informationally. Information has a definition in physics, but its not clear if these mathematical properties of particles are themselves identical with what we call information or not. Or what the difference would even be.
Something that's probably more intuitive to understand is imagine we were in the matrix. We could do science and discover how things act, but from inside the system we'd be fundamentally unable to understand some aspects of the nature of the world. Its "real" nature would be a code on a computer. But that's something that to us is fundamentally un-seeable. We can only see what the code generates in relation. This is an apt comparison, since "code" is similar to the mathematical properties of particles. We know what it looks like its -doing- from our perspective. But we're not able to see it directly in any kind of way that lets us confirm absolutely its nature entirely. There's a surprisingly larger amount of times this is the case than one would think when on the quantum level. Making it the type of thing that the ore one knows about the more they realize how much we don't know about.
skordge ยท 2 points ยท Posted at 10:47:49 on May 26, 2016 ยท (Permalink)
eiฯ + 1 = 0
A specific case of Euler's formula (x = ฯ). Look how beautiful it is! It's got a zero, a one, the square root of -1, Euler's constant and pi very neatly packed!
If you add an infinite series in a different order, you can get a completely different answer, or no answer at all (I.e. Trails off to infinity). Good old Riemann.
No it doesnt, it looks like a piece of paper at a weird angle
-d0ubt ยท 2 points ยท Posted at 15:20:52 on May 25, 2016 ยท (Permalink)
If there radius of a pizza is said to be 'z' and the height of the pizza is said to be 'a', Then (assuming the pizza is a perfect cylinder) the equation of the pizza can be defined as Pizz*a.
MHG73 ยท 3 points ยท Posted at 15:25:11 on May 25, 2016 ยท (Permalink)
The number 73 is the 21st prime number. It's opposite, 37, is the 12th prime number.
It's mind blowing at first but the proof is deceptively simple in the end which is also part of how mind blowing it is. Just throw some numbers in Euler's formula and boom, magic.
That actually isn't too crazy difficult either though definitely not something you'd touch on as a Sophomore in high school. Though would probably lead down more "rabbit hole" well how do you prove this stuff.
The only new thing you would probably need to know is what a power series it. Which is just a special way to express some equation as a sum of an infinite number for fractions. You can see some examples here. From there it's just simple math.
eix = 1 + ix + (ix2 / 2!) + (ix3 / 3!)...
= 1 + ix - (x2 / 2!) - (ix3 / 3!) + ...
Sort out the terms from here into the power series for sin(x) and cos(x)
And there you go, just some simple algebra and some knowledge of a few special equations. Why power series work is something I've never learned myself so I don't feel comfortable explaining it. But you use them every now and then after learning them to prove a few things.
No worries! A lot of this is stuff that I never even thought about until I'd started doing higher level classes as a math major. Most of it is not stuff that people would regularly just know.
the fact that there are an infinite amount of prime numbers is very simple and can be proved in 1 sentence. every even number greater than 2 being the sum of 2 primes is an open problem that has been unsolved for hundreds of years.
lanemik ยท 2 points ยท Posted at 16:44:15 on May 25, 2016 ยท (Permalink)
The cardinality of a set S is strictly less than the cardinality of the power set of S. This seems intuitive for sets with a finite number of elements because the power set of S is the set of all subsets of S. So if S = {0,1,2}, then the power set of S is P(S) = {{}, {0}, {1}, {2}, {0,1}, {0,2}, {1,2}, {0,1,2}}. Note that |S| = 3 and |P(S)| = 23 = 8.
What isn't obvious, but what is true, is that even if S has an infinite number of elements, P(S) has more elements. If S is the set of all Natural Numbers, an infinite set, then the power set has yet more elements in it. The consequence is that there are different sizes of infinity!
mainly due to the fact to be considered prime it can only have factors of itself and 1. all even numbers have 2 for a factor. since 2's only factors are 1 and 2 it makes it a prime number
For the same reason .999...9 = 1, Throwing an infinitely sharp dart at the real number line could NEVER result in said dart hitting a whole number. The probability of doing so is exactly 0.
You just have to ignore the fact that you have an infinitely sharp dart.
Even better, it will never hit a rational number either; that is, any number that can be represented as a fraction. This is because for each rational number, there are an infinite number of irrational reals.
But the best part is despite all of this, there is always a rational number between two irrationals (so numbers "alternate" between rational and irrational)
Similarly (and even better I think), is that if you separate the numbers into algebraic vs. transcendental, the probability of hitting an algebraic number is also 0.
I would say the number pi is the most interesting thing. It is infinite and contains every combination of numbers possible. Everyones birthdate, telephone number, social security number, or anything appears in it at some point. There used to be a website where you could look them up at.
If you began shuffling a deck of 52 playing cards in a new, random order every second since the beginning of the universe over 13 billion years ago, you would be nowhere near finished. The Universe is about 1018 seconds old. And there are over 8x1067 ways to rearrange a deck of cards.
0! (Zero factorial) = 1. It seems wierd because not only is it a mind bender, but also the notation 0!=1 looks like it could be the logical operator != (does not equal). So it looks like it's saying 0 does not equal 1.
The ratio of the total length of ANY river and the total source length (point a to b) = Pi
The total length of ANY river (the distance you would travel as you sailed down it) and the straight line distance from begining to end. (as the crows fly, etc) = Pi
Might be true if we don't think mathematically. The way water flow doesn't allow most rivers to be straight AFAIK. They will normally develop the back and forth pattern.
rmfei ยท 3 points ยท Posted at 23:50:25 on May 25, 2016 ยท (Permalink)
The shape of a river depends on lots and lots of factors, and it changes over time as the banks are eroded by the flowing water. It's very hard to believe that this relationship would always be even approximately correct.
[deleted] ยท 2 points ยท Posted at 21:44:30 on May 25, 2016 ยท (Permalink)
You would be correct sir :) Posted solely for the purpose of allowing @jager1966 to verify. Erosion alters bends in the river sometimes significantly and thus sinuosity will be altered so no river would stay the same. While it sounded reasonable, the data collected thus far shows that even the average is not Pi....
"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14, which is close to the value of the number pi... The ratio of pi is most commonly found for rivers flowing across very gently sloping planes, such as those found in Brazil or the Siberian tundra."
[deleted] ยท 2 points ยท Posted at 15:07:58 on May 25, 2016 ยท (Permalink)
If you took the probability of Neil Patrick Harris having sex with Honey Boo Boo's mom, and divide that by the number of atoms in the universe, you still have more fucks than I give about college basketball.
A faster way to multiply by Nine is to put both your hands in front of you. Now, say you want to multiply 3 by 9. from left to right, count to your third finger. Put that one down. The finger you put down now creates a border between the tens and ones. The tens will be on the left, while the ones will be on the right. You have 2 fingers on the left, and 7 on the right. Hence the answer is 27.
Unfortunately, this only works up to 9x10... Unless you have more fingers.
There's a method for testing divisibility by any prime number.
Take any prime number and mulitply it by whatever single digit number you need to make the ones place a 9. Add 1 and divide by 10.
The resulting number is what you can multiply the last digit of a number and add it to the rest of the digits. If the resulting number is divisible by your prime, then the whole original number is. If you're not sure, you can always do the trick over and over again.
For 13
Multiply 13 * 3 to get 39. 39 + 1 = 40. 40/10 = 4.
So take 169, 132 , 169 so 9 * 4 = 36. 36 +16 = 52
52 is 13 * 4, but if you still weren't sure try it again
52, take 2 * 4, get 8. 8 + 5 = 13. 13 is definitely a multiple of 13, so 169 is a multiple of 13 as well.
The largest number to ever be used constructively in math is called graham's number. To find the number, arrow notation is used, where an arrow represent putting a number to a power. Call g1= 3333, now repeat this where g2 has a g1 amount of arrows! Now repeat this until you reach g64. https://www.youtube.com/watch?v=XTeJ64KD5cg
wanmoar ยท 1 points ยท Posted at 14:27:24 on May 25, 2016 ยท (Permalink)
the sum of the digits for any number obtained after multiplication by 9, is 9
for example.
9 * 7 = 63 = 6+3 = 9
9 * 65468 = 589212 = 5+8+9+2+1+2 = 27 = 2+7 = 9
[deleted] ยท 1 points ยท Posted at 14:29:08 on May 25, 2016 ยท (Permalink)
mkicon ยท 1 points ยท Posted at 14:35:53 on May 25, 2016 ยท (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
iamnos ยท 1 points ยท Posted at 14:35:59 on May 25, 2016 ยท (Permalink)
Late to the party, but...
To determine if any number is divisible by 3, add up the individual numbers and see if the result is divisible by 3.
ie: Is 1584 divisible by 3?
1+5+8+4 = 18. 18 is divisible by 3 so, 1584 is.
It scales as well. In the above example, if you weren't sure if 18 was divisible by 3, you could do 1+8=9 and 9 is divisible by 3, so both 18 and 1584 are.
That was very useful in middle and high school. I was all over divisibility rules.
Works for 9, summing the digits works for 9
2 and 5 are easy, last digit is divisible by 2 or 5 respectively
11: add the first digit subtract the second add the third, etc. is the result divisible by 11?
Example: 25795: 2 - 5 + 7 - 9 + 5 = 0
11*0=11 so yes 25795 is divisible by 11
Take a square, divide into thirds length and width wise. You now have 9 squares. Punch out the middle square. Repeat the process with the remaining 8 squares ad infinitum. The resulting shape has an infinite perimeter but exactly 0 area.
Realize that any decision or question you need answered in your life, math will provide your answer, just finding the correct formula is your path to success.
A mathematical expression that, at first glance makes absolutely no sense. An irrational number raised to the power of another irrational number times an imaginary number equals an even, negative number.
Additionally, you can't raise a number to a power and get a negative number. the closest you can theoretically get is zero.
Yet, this is a mathematically accurate formula. Plug it into any scientific calculator.
In my high school calculus class, I was told that a mathematician had it inscribed on his grave because it was so absurd. Not sure if that's true, though.
Finchyy ยท 1 points ยท Posted at 14:39:42 on May 25, 2016 ยท (Permalink)
The digital roots of a sequence of square numbers are palindromic.
36 is the sum of the first three cube numbers and the product of the first three square numbers. Also, it's the 8th triangular number and the 6th square number, being the smallest number other than 1 that's both, and it's the only one that's both who's square root is also triangular (again, excluding 1). It's 13-gonal. It's semiperfect because 6, 12, and 18 all divide into it, and when summed give 36. It's the sum of twin primes (17 and 19).
The fact that I just finished my last exam of this year.
Until August that is where I will have to resit them.
cthulu0 ยท 1 points ยท Posted at 14:44:38 on May 25, 2016 ยท (Permalink)
Because there ~11million people in New York City, and the average human has way less than 11 millions hairs on his head, there are at least 2 people in NYC with the EXACT same number of hairs on their heads.
This is the pigeon hole principle.
_Eerie ยท 1 points ยท Posted at 16:20:07 on May 25, 2016 ยท (Permalink)
Can you prove this theory?
cthulu0 ยท 1 points ยท Posted at 19:56:20 on May 25, 2016 ยท (Permalink)
The pigeonhole principle is an established long ago proven mathematical theorem. It is also intuitive to understand. It states that if you have N holes and more than N pigeons which you are trying to put in the holes, then at least one hole will have 2 pigeons in it.
i'm a big fan of the classic:
multiply any number by 9 and the sum of all the digits in the answer always equals 9 (when you keep adding the digits to the point of having only 1 digit obviously). even works with decimals.
eg. 113.9486 x 9 = 1025.5374 -> add that shit up and get 27 -> 2+7=9
The harmonic series (1/1 + 1/2 + 1/3 + 1/4...) diverges (reaches infinity). The harmonic series missing any integer converges. Like, if you take out all the numbers with a 9 in them it never gets higher than 23. It doesn't have to be 9- as long as something is missing, it won't reach infinity.
If you want to know the square of a number, say 13, simply take the sqaure of the previous number, which is in this case 144 and add the number and the previous number to the square of the previous number, which means 12 + 13 + 144 = 169 = the square of 13
number 6174.)
1 - Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
2 - Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3 - Subtract the smaller number from the bigger number.
4 - Go back to step 2.
The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations.
tck91 ยท 1 points ยท Posted at 14:49:04 on May 25, 2016 ยท (Permalink)
I LIVE FOR OBSCURE MATH FACTS.
8 x 12 = 102 - 22 = 96
That is: any two numbers multiplied equals the midpoint number squared minus (the distance between the higher/lower number and the midpoint) squared.
[deleted] ยท 1 points ยท Posted at 14:51:57 on May 25, 2016 ยท (Permalink)
If you multiply eleven times another two digit number and to get the answer you can put the two digits at the front and end, then the middle digit will be the sum of both numbes(requires rounding after a certain point.)
Multiplying by 9 can give you a factor that sums to 9. For example 9X9=81 8+1=9, 9X17=153 1+5+3=9, 9X11=99 9+9=18 1+8=9. Always helped me know if I multiplied by 9 correctly
Put simply: if you have more pigeons than pigeonholes then at least one of the pigeonholes contains more than one pigeon.
The simple formulation might seem like it is too obvious to be useful, but it can be generalised into forms that are useful for solving problems involving probabilities and infinite sets.
Pythagoras (known most notably for the pythagorean thereom) believed beans were evil and this led to is death.
He thought beans pulled evil up from hell. An angry group of folks who disagreed with his work were after him one day and it was between them and a field of beans. He chose death.
Take any 4 digit number, with at least one digit different than the others. (eg 3324) Arrange the digits in descending order (4332), and ascending order (2334), Find the difference (4332-2334 = 1998).
Now repeat the process with 1998, eventually you will end up with:
6174
Start with an integer. Then, create a new integer that has the same number of digits as the original but is composed of nines. Divide the original by the new number, and you'll get a decimal number that is the first integer repeated indefinitely.
Assume that we have two variables a and b, and that: a = b
Multiply both sides by a to get: a2 = ab
Subtract b2 from both sides to get: a2 - b2 = ab - b2
This is the tricky part: Factor the left side (using FOIL from algebra) to get (a + b)(a - b) and factor out b from the right side to get b(a - b). If you're not sure how FOIL or factoring works, don't worryโyou can check that this all works by multiplying everything out to see that it matches. The end result is that our equation has become: (a + b)(a - b) = b(a - b)
Since (a - b) appears on both sides, we can cancel it to get: a + b = b
Since a = b (that's the assumption we started with), we can substitute b in for a to get: b + b = b
Combining the two terms on the left gives us: 2b = b
Since b appears on both sides, we can divide through by b to get: 2 = 1
The proof based around Graham's number is so interesting. It is so incredibly large that if your mind tried to comprehend it, you would die of a brain overload. It is bigger than googolplexgoogolplex. If you learn up on the actual application of this number, you will be astounded at how unnecessarily big this number is for the app.
cucufag ยท 1 points ยท Posted at 15:03:15 on May 25, 2016 ยท (Permalink)
Infinity is fun to talk about, and even though I've discussed this topic plenty of times, I still sometimes have a hard time grasping the concept. Most people struggle when they first learn about it as well.
Not a fact but a fun proof. It will sometimes take a while for a person to catch the problem with this proof of 1=0
x = y.
Then x2 = xy.
Subtract the same thing from both sides:
x2 - y2 = xy - y2.
Dividing by (x-y), obtain
x + y = y.
Since x = y, we see that
2 y = y.
Thus 2 = 1, since we started with y nonzero.
Subtracting 1 from both sides,
1 = 0.
The size of the set of all negative integers is equal to the set of all integers. That is, there are as many negative whole numbers as negative and positive integers. You can prove this by creating a bijective function (a one to one function) between the two sets.
The Golden Ratio (ฮฆ) can be derived from the Fibonacci sequence (1, 1, 2, 3, 5, 8...) by alternatively adding and subtracting the ratio of subsequent values in the sequence:
Let F(n) = 1, the first number in the sequence.
[F(n+1) / F(n)] - [F(n+2) / F(n+1)] + [F(n+3) / F(n+2)] ... -> ฮฆ for odd values of n and -> 0 for even values of n.
vulp ยท 1 points ยท Posted at 15:06:26 on May 25, 2016 ยท (Permalink)
Everything applies to everything else. When I learn combinatorics, I use stuff from analysis to solve problems. In representations, I needed combinatorics. And analysis used pieces of both. And everything is kind of multiple ways of looking at one problem at higher levels and that's sort cool.
Take voting theory - there are equivalent explanations both geometrically and abstract algebraically, and that's super cool!
Tivia ยท 1 points ยท Posted at 15:07:25 on May 25, 2016 ยท (Permalink)
That no matter what common core claims, 2 + 2 = 4 and be damned at how you arrived at the answer.
Joeg332 ยท 1 points ยท Posted at 15:07:55 on May 25, 2016 ยท (Permalink)
There are different sizes of infinity some are larger than others
If you add up every number from 1 to infinity, the answer is -1/12. This is not a trick or play on words, and nobody knows why it works. The proof is relativity simple to understand too.
On Earth, Affix a cord/rope between two points, no matter how taught you pull that cord/rope, it will never be a straight line/plane, there will always be a sag.
More of a physics example, but the math behind it is pretty cool.
ย As you pull tighter the sag gets less, but it's a function of 1/force, so to get zero sag you need infinite force.
.999999 forever (.9 repeating I don't know how to type that symbol) equals 1.
Not approximately 1, but exactly equals 1.
Best example I have to explain it is: 1/3 equals .3 repeating (most everyone understands and agrees with this). 1/3 plus 1/3 therefore equals .6 repeating. And 1/3 plus 1/3 plus 1/3 equals .9 repeating which also equals 3/3. Boom 3/3 equals 1 equals .9 repeating.
fbb755 ยท 1 points ยท Posted at 15:11:43 on May 25, 2016 ยท (Permalink)
The Pigeonhole Principle allows us to say with certainty things such as "There are at least two people in the city of New York who share the same number of hairs on their head" and "In a packed Carnegie Hall performance, there will be two people who have the same first and last initials."
These sound counterintuitive, but the Pigeonhole Principle is very simple, and seems obvious once you hear the explanation.
Is there any reason for this? Me and a friend were trying to figure out why 1/3+1/3+1/3=1 but if you take the decimals of each (0.333...+0.333...+0.333...) it would never reach 1 because they are all repeating infinitely.
"If 0.999... represented a real number, which real number would it represent?"
You find that the only answer that makes sense is that 0.999... = 1.
In the real numbers there is no such thing as an infinitesimal difference, and so 1 - 0.999... = 0.000... = 0 thus they represent the same number along with many other factors.
Lots of people are assuming that 0.333... = 1/3 but if you can truly convince yourself that they are equal then along the way you should have convinced yourself that 0.999... = 1.
Katur ยท 1 points ยท Posted at 15:12:03 on May 25, 2016 ยท (Permalink)*
You can see multiple of 9 on your hands.
So for example 9 x 7. That would be your right index finger(7, from left to right) and you'd have 6 fingers to the left (including your left hand) and 3 to the right making the answer 63.
(2 times every number less than the number summed) + the number.
5x5 = 1+1+2+2+3+3+4+4+5 = 25
And you can use this to get. The square of a number is the square of the number less than it, plus the number less than it plus the number.
5x5 = (4x4) +4+5 = 16 + 4 + 5 = 25
So if you know
25x25 = 625
Then
26x26 = 625 + 25 + 26 = 676
Then
29x29 = (30x30) - 30 - 29 = 900 - 30 - 29 = 841
Helps a lot with weird squares near easy squares.
Sometime during JHS or HS I figured this out. I'm sure I'm not the first one to do it, but I've never ran across it something they teach people in school. Made test on squares easier.
Simple facts: The sum of the first N odd numbers equals N-squared
The sum of any three consecutive integers is always a multiple of 3
The sum of three consecutive integers, where the middle integer is a multiple of 3, is always a multiple of 9 (duh!)
Not a fact but I have a sneaking suspicion that a new universe is created every time someone divides by zero... like a tiny big bang happens inside your calculator that is dramatically smaller than a quark. Billions of years from now your calculator will be teaming with life... unaware of how tiny they are and unaware that other life forms are relatively close to them in proximity...
Are we inside a calculator right now? O___O
Tavyr ยท 1 points ยท Posted at 15:16:35 on May 25, 2016 ยท (Permalink)
In the game Set, when the properties of each card are expressed as a vector of integers mod 3, a "set" is formed when sum of the vectors on three cards is the zero vector.
Dereg5 ยท 1 points ยท Posted at 15:16:38 on May 25, 2016 ยท (Permalink)
111,111,111ร111,111,111= 12,345,678,987,654,321
devonha ยท 1 points ยท Posted at 15:16:53 on May 25, 2016 ยท (Permalink)
The Four Color Theorem.
You can fill in any map (and have no adjacent bodies with the same color) with only four colors.
If you start at 0 and every odd number, +1, 3 5 7 9 11
You get a perfect square every time
gagsy92 ยท 1 points ยท Posted at 15:17:38 on May 25, 2016 ยท (Permalink)
Pretty simple one but to find out if a number is divisible by 3, just add all the digits together until you're left with a single digit, if that digit is divisible by 3, the original number is.
Example A: 2,375,274 = 2+3+7+5+2+7+4 = 30 = 3+0 = 3 = Divisible by 3.
Example B: 2,654,984 = 2+6+5+4+9+8+4 = 38 = 3+8 = 11 = 1+1 = 2 = Not divisible by 3.
If you take some building blocks and make a flat square out of them, some squares can be disassembled into two smaller squares using every block. A well known example of this is that a 5x5 square can be disassembled into a 3x3 and a 4x4 square. This is obvious because 32 + 42 = 52 . It can be relatively easily shown that there are infinitely many different squares with that property.
However, if you were to try the same with cubes you would not succeed, since no cube can be disassembled into two smaller cubes using every building block. This is a consequence of one of the most famous theorems called Fermat's Last Theorem. It states that the equation an + bn = cn , where a, b, c and n are positive integers, has no solution for n > 2. The theorem was conjectured in the 1600s by Pierre de Fermat but not proven until 1994 by Andrew Wiles.
cnk93 ยท 1 points ยท Posted at 15:20:16 on May 25, 2016 ยท (Permalink)*
That everything we know can be broken down into numbers and measured. That these numbers can justify peoples entire existence. They make or break how things work. Can be repeated and replicated by anyone who wants to try.
The fact that you can tell right away whether someone is from America or GB by whether they say math or maths. On the odd occasion it might be a jabroni that goes to Princeton saying "maths".
[deleted] ยท 1 points ยท Posted at 15:28:27 on May 25, 2016 ยท (Permalink)
Riemann's Rearrangement Theorem: You can rearrange the terms of certain infinite series to get any number you want.
It's more detailed, but I'm not going to really about those details.
I've always liked that if you lose a bet, but then offer a another bet that is double the previous one, and repeat this until you finally win, you will walk away with a net gain.
I bet and lost $1, putting my overall at -$1.
Then I bet $2 and lose, putting me at -$3.
Then $4, putting me at -$7, etc until I finally win a bit and leave with $1.
The only downside is this assumes you have an infinite amount of money to bet with!
I get irrationally upset when I see "Math" referred to as "Maths". Its not called "Histories" is called "History". Its not called "Englishes" its called "English". Its not called "Sciences" its called "Science".
Take both your hands, not the palm side but the other side, like as if your looking at them, and from left to right you can easily do your 9 times table. So from the left if you put down your pinkie, you've got 9 fingers left meaning 1 times 9 equals 9. Then lift your pinkie back up and put down your wedding ring finger (also from the left), you will have your pinkie representing 1 and apart from your wedding finger which is down you will have 8 fingers left to the right i.e 2 times equals 18 and so on. :)
SiVGiV ยท 1 points ยท Posted at 15:55:41 on May 25, 2016 ยท (Permalink)
cboski ยท 1 points ยท Posted at 15:32:15 on May 25, 2016 ยท (Permalink)
The conversion factor between kilometers and miles is approximately the same as the factor affecting the Fibronacci's sequence. So when you have 1 1 2 3 5 8... 2 miles = 3 Km, 3 mi = 4.8 Km and 5 mi = 8 Km
SiVGiV ยท 1 points ยท Posted at 15:56:42 on May 25, 2016 ยท (Permalink)
This one's useful
no_en ยท 1 points ยท Posted at 15:32:16 on May 25, 2016 ยท (Permalink)
You can always determine if a number X is divisible by three by adding up the digits in the number X. If the sum of those digits is divisible by three, then X is divisible by three.
In a graph or any sort of diagram where lines are connected to each other with dots AKA vertices. If those vertices all have even degrees meaning they have an even number of lines connecting to other vertices than there exista an eulerian cycle where basically you can start at any vertice go through every possible line (edge) connecting the vertices ONCE and still go back to the original
It's possible to count to 242 on one hand and 59048 on 2 hands if you use trinary.
Example:
Closed fist=0
First knuckle of thumb=1
Thumb extended=2
First Knuckle of Index=3
Index extended=6
Each knuckle is the next power of three and each full extension is the previous power of three*2.
queazan ยท 1 points ยท Posted at 15:33:10 on May 25, 2016 ยท (Permalink)
That the coefficients of binomial expansion as demonstrated by Pascal's triangle also perfectly dictate the probabilities of head/tail counts when flipping coins so long as you don't eliminate overcount. Interpret by summing up each row of pascal's triangle and treating each digit in a row as a single event's probability out of the sum. So:
When flipping a one-sided coin, every flip will always give you 1, out of 1 possible outcome.
When flipping a single two sided coin, there is a 1 in 2 probability of one head, and 1 in 2 probability of one tail.
When flipping two double-sided coins, there is a 1 in 4 possibility of two heads, 2 in 4 possibility of one head and one tail, 1 in 4 possibility of two tails.
And for 3 double-sided coins, 1 in 8 chance of three tails, 3 in 8 chance of one head two tails, 3 in 8 chance of two head one tail, and 1 in 8 chance of all tails.
Or:
1
11
121
1331
It's trivial, but it absolutely enchants me that a simple observation about binomial expansion applies to binary probabilities. I believe (though I haven't tried to prove) that similar would hold for trinomial expansion and probabilities where each element has three outcomes, as the expansions really are just enumerating all possible outcomes of a given n-ary equation, I think, which is basically the same thing as simple probabilities.
[deleted] ยท 1 points ยท Posted at 16:52:42 on May 25, 2016 ยท (Permalink)
that's probably why it's called a binomial probablity. I thought about that fact and it was plenty clear to me that it's not a coincidence and there is plenty reaspn why.
queazan ยท 1 points ยท Posted at 18:13:40 on May 25, 2016 ยท (Permalink)
That's basically what I was getting at when I said that expansions are just enumerating all possible outcomes, and why I'm moderately sure it'll apply to trinomial and upwards expansions. I've just learned over time that when it comes to math, I should never assume that I know what the hell I'm doing :P
And I know it's not "coincidence", but I still find it enchanting. It's one of the wonderful things about math - that you can prove one thing many different ways, and each of those ways interrelate and shine a little more light on some phenomena underneath the thing you're looking at. I just feel that this is a wonderfully clear example of it.
[deleted] ยท 1 points ยท Posted at 18:28:32 on May 25, 2016 ยท (Permalink)
when it comes to math, I should never assume that I know what the hell I'm doing :P
haha we can totally agree on that. I think I'm just less enchanted by that example. I thought for a bit, huh, and then it makes sense to me. The thing that really strike me was all the construct they used in Real Analysis and further down some Banach space stuff. It's just so fascinating but difficult to wrap my head around at the same time.
I took Statistical Inference the same semester as Functional Analysis. That's probably one of the reasons that I found statistics way easier. A binomial distribution, after all, is still quite straightforward, compared to an infinite dimensional Hilbert space or something like that.
queazan ยท 1 points ยท Posted at 18:37:02 on May 25, 2016 ยท (Permalink)
That's completely fair. It's a very subjective thing, I think. I mean, in general I love any example where one particular mathematical concept or idea ties directly in to another one. And I don't have the statistical background that you have - I did mostly calc and discrete mathematics.
I think, too, for me it's more impactful because it was something I worked out on the side of something else. A few of my coworkers had invented some silly betting game, where they flipped a set number of coins and tried to guess whether more would be heads or tails. That got me thinking about probability, and working out the statistics of their game...which in turn lead me to realizing the correlation between binomial expansion and binomial probabilities.
So maybe a big chunk of it for me is that "I came up with it myself" (which, I mean, I know I didn't come up with it first but you know what I mean) - it was that sort of "bolt out of the blue" that made me go "oh shit, bitchez, these maths are totally insane".
Note: I did not actually say that to my coworkers, but I really wish I had.
[deleted] ยท 1 points ยท Posted at 19:09:17 on May 25, 2016 ยท (Permalink)
haha. THAT IS REALLY NEAT. You know if you were born 500 years early it would be queazan distribution instead of Bernoulli distribution! What is neat, is that modern statistics/probability theory is indeed founded on gambling, either throwing a coin, or a die.
I can see where that comes from :) I think it really takes a genius to actually found things. It's really easy to understand, nowadays, why it is a Bernoulli distribution. But whoever comes up with it themselves are genius, imo.
Take any number and add the digits up, then subtract that number from the original. It will always be divisible by 9.
Ex: 23,045
2+3+0+4+5=14
23,045-14=23,031
23,031/9=2,559
[deleted] ยท 1 points ยท Posted at 16:51:35 on May 25, 2016 ยท (Permalink)
it is fascinating until you think about the proof. suppose the number is two digit. 10x+y. what you did is basically (X+y)-(10x+y) = -9x. of course it's divisible by 9.
Doing the best at each step doesn't guarantee the best at the end.
Simple example: Suppose we have coins of value 1,10,25 and we want to get a value with as few coins as possible. If you always take the largest possible value, called greedy, you may fail. Say you want 31, if you are greedy you get 25,1,1,1,1,1,1 but the optimal is 10,10,10,1.
In fact, is very rare that a greedy algorithm produces the actual optimal.
[deleted] ยท 1 points ยท Posted at 15:35:19 on May 25, 2016 ยท (Permalink)
It is proven that peano arithmetic=>1+1=2, or ZFC=>1+1=2. What do you mean by proven? Of course it has to start from axioms, you can't prove anything without axioms. For a start, you need axioms to define 1,2,+ and =.
[deleted] ยท 2 points ยท Posted at 16:49:01 on May 25, 2016 ยท (Permalink)
I remember that argument from college in Real Analysis. that was when I realized that I can never be a mathematician. I can learn but I'm not that smart to come up with something like that lol
That if you have a series of all positive integers ascending (1+2+3+4+5+6+7+8+9...) and you need to do algebra on it you can just replace the series with -1/12.
Gabriel's horn. Otherwise known as the infinite paint can. With infinite surface area but finite volume. It can't hold enough paint to paint the outside of its own paint container!
Gabriel's horn!
Edit: Format and spell
[deleted] ยท 1 points ยท Posted at 16:46:49 on May 25, 2016 ยท (Permalink)
is it a similar idea to Cantor's set where it is not countable but the length of the set is 0?
I'll have to dig into Cantors set. I haven't head of it before. The idea is that essentially a molecule of paint will get stuck near the the narrow end of the funnel. But the surface area continues on to infinity but there is no more volume that can squeeze past the circumference of a molecule in the funnel.
[deleted] ยท 2 points ยท Posted at 19:06:27 on May 25, 2016 ยท (Permalink)
ah I see. Interesting. Cantor set has a similar idea on 1d I think, where you can have infinite amount of numbers, but the length of the set itself is 0 because it is nowhere dense or something. https://en.wikipedia.org/wiki/Cantor_set
Isn't this only true if you assume winds operate in two dimensions? If winds move other than parallel to the surface, you can have winds everywhere, I would have thought.
I never understood why, perhaps an expert can ELI5, but if 1/3 + 1/3 + 1/3 = 1 and 1/3 = .3333(repeating) then why does .3333 + .3333 + .3333 = .9999 (repeating), and not 1.
I understand they're infinitely close, but they aren't equal which upsets me.
[deleted] ยท 1 points ยท Posted at 15:46:05 on May 25, 2016 ยท (Permalink)
They are not infinitely close, they happen to be the same number! We sometimes are blown out by that, but there's no rule that says that a number has an unique way of writing it down (for example, it's crystal clear that 1/2 = 0.5).
About 0.9999... (with an infinite trail of 9's) being the same than 1, what you said is just one of the multiple proofs of it. There are many ways of proving it, my personal favourite being that if two numbers are different, there's always a different number in the middle (for example, as 0.5372 is different than 0.5373 we can find a number in the middle, such as (0.5372+0.5373)/2). As there is no number between 0.999... and 1, we can conclude that they are the same number.
canalis ยท 1 points ยท Posted at 15:48:06 on May 25, 2016 ยท (Permalink)
No ELI5, but 1/3 is not actually equal to 0.33333333... The difference is just infinitely small and thus does not matter mathematically.
So 3 x 0.3333333333... Is infinitely close to 1 but never actually 1, kinda like an asymptote that gets ever closer to 1
They are equal, and you just described one of the proofs. They're "infinitely close" meaning that the difference between them is smaller than any real number, so the difference between them is zero.
I wish I could find the exact quote, it was something along the lines of: "Nothing is more equal than a set of parallels" which was how the equals sign was conceived. I remember it was from a book call "against the gods" I read about 10 years ago
144 is the 12th Fibonnaci number, it is also 12 squared, it is also the only square Fibonnaci number.
moomsy ยท 1 points ยท Posted at 15:40:27 on May 25, 2016 ยท (Permalink)
I guess just the fact that infinity is everywhere if you look for it. Any space between two integers/points can be cut in half an infinite amount of times. The existence of asymptotes is probably the coolest thing I can think of.
As you may have guessed, it keeps going:
9 + 10 + 11 + 12 = 13 + 14 + 15
Et cetera
Expressed generally, for any natural number n:
(n2) + (n2+1) + (n2+2) + ... + (n2+n) = (n2+n+1) + (n2+n+2) + ... + (n2 + 2*n)
Once you express it in the general form like this, you can prove it with induction. I had a lot of fun with this when I first saw the original statement of two equations. Nerd-sniped me for a good hour playing with it.
Probably a bit late to the party, but I love how you can use the Fibonacci sequence to convert miles to km and vice versa.
Here's how:
The Fibonacci sequence goes as known like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Take two consecutive numbers, let's say 5 and 8. There's actually 5 miles in 8 kilometers.
This happens because the ratio between two consecutive numbers in the sequence closes up on the golden ratio, which is 1,618. Coincidentally, there are 1,609 km in a mile, so there you go!
If you drop a stone on the ground, it must first fall half way.
To continue to the ground, it must first fall half way again.
Repeat.
Does the stone ever mathematically hit the ground?
Zeno's paradox. All motion is impossible, in order to go from point A to point B you have to go halfway (point C). In order to go from point A to point C, you must go halfway (point D), this can be duplicated infinite times therefore, theoretically you will never make it from point A to point B.
But obviously we all can make it from point A to point B, but it's a fun.
The fact that 0.999999(repeating) is equal to 1. Due to limits and infinity and all that. This can be demonstrated intuitively by thinking about the fractions 1/3 and 2/3. They are 0.3333(repeating) and 0.6666(repeating). So then 3/3 should be equal to 0.9999(repeating) if you multiply, say, 1/3 times 3. And also equal to 1.
knowing that you can never really prove that a square is a square. try to look up mathematical and philosophical proofs that a square has right angles and is equal on both sides, most proofs will reach a point where you have to assume that an infinity it would withstand but we don't get to that infinity we just say that assuming we get there it will be square. When i learned that you can never really say a square is a square my mind was blown
Any integer modulo 10 will give you the last digit of this integer
(Meaning: if you divide an integer with 10 the remaining number will always be it's last digit).
This might sound really simple and obvious but I don't think many people realize it.
It can have many applications, especially in Computer Science and various algorithms. For example, if you add two integers of any size the last digit of that sum will be the last digit of the sum of the two numbers modulo, etc.
When choosing colours for different regions on a map, you only need four different colours to ensure that no two adjacent regions have the same colour!
If you add up all the positive intergers, i.e 1+2+3+4...etc. to infinity, you get -1/12 as the sum. This still blows my mind. Proof: https://www.youtube.com/watch?v=w-I6XTVZXww
A sum diverges if it keeps getting bigger and bigger, and is not bounded. The sum in question if clearly not bounded, since if it was bounded by x then just let N be any integer larger than x, and then 1+2+...+N>x. It can be proven that divergent series don't converge.
What converge means is that the sum keeps getting closer to some value. This sum actually just gets further and further away from -1/12, so it certainly doesn't converge to it.
Did you watch the video? It looks like this is an accepted answer for the sum of all positive integers, and its used effectively in physics calculations. Infinity doesn't always give intuitive answers.
I've seen the video before, it's wrong because you cannot manipulate infinite series like that.
In some contexts it makes sense to assign 1+2+3+... the value -1/12, but the sum absolutely does not equal -1/12 under the normal definitions of sum and converge.
It is not an accepted answer. This isn't a time when infinity is unintuitive.
BTW, I'm not arguing, I'm genuinely curious if you had more information. I found this video because I subscribe to numberphile and thought it was cool.
He explains it fairly well I think. The key idea is that (as the video sort of shows) IF 1+2+3+... had a value, THEN that value would be -1/12. For there we pretend that it converges and see what we can do with it.
As for the applications to physics, in some calculations someone ended up with the result 1+2+3+..., but this would have made no sense since they know the answer to their problem could not be infinity. They plugged in the value of -1/12 and suddenly it all works. I don't think it is fully understood why it works, but physics is more concerned with making things work than knowing why.
Well, Mr. Potty Mouth, I merely find it amusing that in the American colonies they think of "Math" as a singular subject whereas in other places it's often rendered as if it were a plural. What an odd conclusion you jump to, thinking that I must not realize that Yankees are not the entirety of Reddit. Carry on with your VCR pornography, oh confident one.
Well I'll give you the benefit of the doubt as per your intentions with your original comment, but the way you wrote it certainly suggested a passive aggressive tone. You can bet that I'll continue with my VCR pornos.
Ibarfd ยท 1 points ยท Posted at 15:49:36 on May 25, 2016 ยท (Permalink)
That pie r squared even though pies are round.
[deleted] ยท 1 points ยท Posted at 15:49:39 on May 25, 2016 ยท (Permalink)
If you add the single digits of any number together and then subtract it from the original number you will always get a multiple of 9.
Ex: 23
2+3=5 23-5=18
Its great for simple magic tricks that give people the feeling that they have some control.
Borsuk-Ulam: Given a continuous function f from the sphere to the plane, there exist points x and -x on the sphere such that f(x) = f(-x).
Example in plain English: There are two points exactly opposite of each other on the Earth with the same temperature and air pressure.
The fun thing about this is that the proof doesn't use what you might expect (ie, calculus); it uses topology and group theory, which are about space and number systems and are in some sense about as far from calculus as you can get in the realm of math.
[deleted] ยท 1 points ยท Posted at 15:50:24 on May 25, 2016 ยท (Permalink)
The pattern of seeds in sunflowers, as well as many other plant life follows the Fibonacci sequence
Erch ยท 1 points ยท Posted at 15:57:15 on May 25, 2016 ยท (Permalink)
The "steel ball run" series of Jojo's bizarre adventure used the Fibonacci sequence as a mechanic for super powers. Shit was cray.
[deleted] ยท 1 points ยท Posted at 16:22:33 on May 25, 2016 ยท (Permalink)
I'm not into anime but interesting. I'll have to look it up
Erch ยท 1 points ยท Posted at 18:04:27 on May 25, 2016 ยท (Permalink)
Well, that series is only in the manga so far. The anime is catching up pretty quickly though (25 years worth of comics being turning into television takes a while). To sum it up though: the two protagonists have the ability to throw objects -mostly steel balls-, at the "golden ratio"... somehow. This somehow grants them the ability to do all kinds of things. Yeah... Jojo's bizarre adventure is pretty weird.
Really elementary level one, here. If you spread all of your fingers out, you have the basic times table for the number 9. What's 4*9? Pull down your fourth finger from the left and count the remaining fingers on the left and right side to get the tens and ones value respectively. Kid me hated nine multiplication until I was taught this.
lazyant ยท 1 points ยท Posted at 15:50:51 on May 25, 2016 ยท (Permalink)
A 2-dimensional being could prove that 3 dimensions exist, some theorem in my topology class.
The probablity of a random number containing a 3 (this can be substituted for any number 1-9) that is less than 10x is equal to (10x - 9x )/ 10x which approaches one as x increases.
[deleted] ยท 1 points ยท Posted at 15:52:32 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers 1+2+3+4....=-1/12
That's a sum from positive 1 to positive infinity mind you.
Did you actually read even the intro to that article? It clearly states the series diverges, and can be assigned the value -1/12.
[deleted] ยท 1 points ยท Posted at 16:37:30 on May 25, 2016 ยท (Permalink)
Yes, and I'm very proud of you having read words too.
Doesn't strike you as even a bit interesting that the sum of all positive integers, up to infinity, can be assigned a value at all, and that it's a negative one, and a fraction at that? And this is done using standard methods used for solving many traditional mathematical series, and that the result is also used in other high level mathematics and physics problems? Or do you just want to sound like you have a big peepee on the internet?
In some sense the series can be assigned any value you want. Giving it this value is interesting for other reasons, as are the physical applications. However it is still very false under convensional definitions.
And the standard emthods used are used wrongly, they only apply to covnergent series.
[deleted] ยท 1 points ยท Posted at 15:52:43 on May 25, 2016 ยท (Permalink)
.999999 = 1
x=.999999
10x= 9.99999
then subtract the first equation from the second aaand just like magic...
epi*i+1=0. Math is strange since all these "special" numbers e, pi, sqrt -1, 1, and 0 can all be related by a relatively simple equation!
eXLoV3 ยท 1 points ยท Posted at 15:53:33 on May 25, 2016 ยท (Permalink)*
I hope i'm not late to the party, but the graphic for the ecuation (ex - e-x )/2 looks like a neckless and the ecuation is called the neckless ecuation. I find it cute.
I hope this is on-topic can somebody help me with this? this always has me scratching my head.
if you stand in front of a wall and move halfway towards the wall from where you are standing, and do it an infinite amount of times, you will never reach the wall.
can somebody explain this like I'm five?
[deleted] ยท 1 points ยท Posted at 16:28:21 on May 25, 2016 ยท (Permalink)
think of it as distance left. the first time you move, you have half distance left. the second time, you still have half of half. each time you move, there is some distance left not covered. no matter how many times you move, the distance not covered is still there, therefore, you can grt infinitely close, but never really reach it.
thank you for this. I kind of get that I guess were still has me scratching my head is the fact that you will never reach it. at some point you will be down to a space smaller than an atom and I guess it brings to mind how small a space can be cut in half yet never get there!
Thanks
Vpie649 ยท 1 points ยท Posted at 15:54:03 on May 25, 2016 ยท (Permalink)
Benford's law says that naturally occurring leading numbers are more likely to be small (i.e. 1 is more common than 2 is more common than 3...)
Things like electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants all follow this rule and it's not fully understood why.
Benford's law is regularly used to detect fraud by large financial institutions and has been in used as evidence in criminal cases.
I'm late to this, but there is a geometric shape that exists (Gabriel's Horn) that has a finite volume but an infinite surface area. In other words, you could fill with paint, but never paint it.
teh_g ยท 1 points ยท Posted at 15:54:33 on May 25, 2016 ยท (Permalink)
Infinities are funny. They make weird things happen.
For example:
There are as many even numbers as there are counting numbers (1, 2, 3, etc.). There are also as many multiples of three as there are counting numbers. There are also as many multiples of one hundred as there are counting numbers.
This actually applies to multiples of any integer except zero. (Integers are the positive and negative counting numbers, and zero.) Multiples of googol? There are as many of those as there are counting numbers. Multiples of Graham's Number? Same thing. We can do this because we never run out of multiples of a given a nonzero integer.
Speaking of integers, there are as many of those as counting numbers. We can go further. You know rational numbers? Numbers that can be represented by fractions? Turns out there are as many of those as there are counting numbers. What about the rational numbers between 0 and 1? There are an infinite number of those, right? Yep, and there are as many of those as there are counting numbers.
All these sets (multiples of a given integer, the integers themselves, rationals, rationals within an interval) are called "countably infinite" because they are the same size as the set of counting numbers. You can do this trick with any countably-infinite set.
Let's try going one step further. Let's take the real numbers, which are the rational numbers and the irrationals. (Irrationals are numbers that can't be represented by fractions, like pi or e or the golden ratio.) Are there as many of those as there are counting numbers? No. There are actually more of them. It turns out that the set of real numbers is bigger than the set of counting numbers. This set is uncountably infinite. You could say that "its infinity is bigger than the infinity of the counting numbers."
But this means that there are more than one kinds of infinity, right? And since there are more than one, we can talk about how many there are, right? Yes, and this brings me to the fact I actually wanted to share.
There are so many infinities that there there is no infinity large enough to describe it.
[deleted] ยท 1 points ยท Posted at 15:55:18 on May 25, 2016 ยท (Permalink)
The way you can shuffle a pack of cards (52!) is huge. From http://czep.net/weblog/52cards.html and much more fun to tell at parties than just the 'when you shuffle a pack it has never been in that order ever':
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time youโve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits havenโt even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still wonโt do it. There are still more than 5.385e67 seconds remaining. Youโre just about a third of the way done.
And you thought Sunday afternoons were boring
To pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands. If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when youโve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When youโve levelled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds. You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt.
There is a type of number called trancendental number.
e and ฯ are trancendentals. The funny thing about trancendentals is that:
a) They are the only type of numbers that are truly infinite (so infinite and uncountable). So the reason the real line has infinite amounts of numbers in it (uncountably) is because of those little fuckers, that are absurdly difficult to detect.
b) We know relatively little about them. Proving a number is trancedental is absurdly difficult. Only recently it was proven that ex is one of those, but e + ฯ may or may not be!
There are as many real numbers in the interval [0, 1] as there are on the rest of the entire (infinite) number line. This works for any interval you choose.
capilot ยท 1 points ยท Posted at 15:59:31 on May 25, 2016 ยท (Permalink)
eiฯ = -1
Tenth grade, thought I knew a lot of math (champion of the math team). Heard this tidbit, went to my math teacher. He goes "Really?", does some math I couldn't begin to follow, and then says "Huh, I'll be damned, it is."
That's when I realized I wasn't nearly as smart as I thought I was.
In topography, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
Gabriel's horn is a mathematical Construct with infinite Surface area and finite volume . Suppose you want to paint the inside of the horn, all You'd need is a finite Volume of paint to fill it to full and coat the sides . But since the Surface area is infinity , You just painted an infinite Surface with a finite amount of paint '
Ioseb ยท 1 points ยท Posted at 16:01:44 on May 25, 2016 ยท (Permalink)
It's maybe already been posted. But based on quantum mechanics and black holes and stuff, if you'd walk a googolplex meters straight out from where you are and into space, chances are you'd eventually stumble upon an exact copy of yourself. Mathematically speaking of course.
ZbaconZ ยท 1 points ยท Posted at 16:01:48 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers starting at 1 = -1/12
I've always like Kaprekar's constant. Rearrange any 4 digit number, not starting with zero, into descending order minus ascending order. Get the sum and rearrange them again. And you will always eventually reach 6174.
52! is the number of combinations that a deck of 52 cards can be shuffled into. 52! is such an enormous number that humans can't comprehend its size. It is estimated that if there were a billion stars with a billion planets each with 1 million people in each planet shuffling a deck of cards 1,000 times per second, orders of cards would just now start repeating if they have been shuffling since the time the first deck of cards was created.
Multiply 9 by any non-zero integer.
If there is more than one digit, add these digits to each other, repeating until reduced to one digit.
The result will be 9.
Law of Nines: Take any random list of numbers, from 2 numbers to ....however many. Calculate the sum of the individual numbers and take it away from the original number. The answer will always be a multiple of 9. Add all the numbers of the answer and they will also be a multiple of 9, etc.
379372649 = 3+7+9+3+7+2+6+4+9 = 50
379372649-50 = 379372599 = 9 x 42152511
3+7+9+3+7+2+5+9+9 = 54
5+4=9
It stems from the structure of base 10. If we counted in base 9, it would be called the Law of Eights :D
That there are an equal amount of numbers between 1 and 2 as ther are numbers between 1 and 3.
For everyone that thinks this is obviously bullshit, real numbers are weird. Cardinality, how you measure how large a set is, is also very weird when dealing with infinites. It has a very intutive interpretation: Two sets have an equal amount of numbers if you can somehow pair them up, one by one, so that you use all numbers in both sets. But the conclusions you reach are weird.
Since the sequence of numbers in Pi's decimals is chaotic and infinite you can pick whatever number you want with how many digit you want and you'll find it somewhere in the decimals of Pi
tommasz ยท 1 points ยท Posted at 16:09:49 on May 25, 2016 ยท (Permalink)
Many of the good ones have already been mentioned but one rather basic thing I haven't seen in this thread yet:
To find out whether a number is divisible by 9 just calculate the sum of the digits and see whether that is divisible by 9. Also works for 3. For 11 you have to calculate an alternating sum of the digits like 6809 would be 9-0+8-6=11 which is divisible by 11 and so is 6809.
I used to have a teacher who's license tag read: SQRT-1
People would say "what does squirt one mean?"
Square Root of Negative 1! The Imaginary Number he would say.
A neat and helpful little math trick for everyday life.
If you get paid hourly, and want to know how much you make per year, you take your hourly wage and multiply it by 2, and add 3 zeros.
Therefore if you make $20 / hr, you roughly make $40k per year (if you work 40 hours a week)
cnwilks ยท 1 points ยท Posted at 16:11:11 on May 25, 2016 ยท (Permalink)
I'm not sure that this fits, but I've always enjoyed the puzzle of the three businessmen who show up to a hotel, and there's only one room left. The room rate is $30, and each of them put in $10 a piece.
After they get to their room, the desk clerk realized that the room rate was only $25, so he sends $5 to the room with the bellhop. He gives them the $5, and they give him a $2 tip, and pocket $1 each.
That means that each of them paid $9 for their share of them room, which adds up to $27, and when you add the $2 tip back in, it amounts to $29. Where did the other dollar go?
h-jay ยท 1 points ยท Posted at 16:11:58 on May 25, 2016 ยท (Permalink)*
The positional representation of any rational number is non-unique.
All integers have two representations in any base. E.g. 1=0.(9)=0.99999... in base 10, or 1=0.(1)=0.11111... in base 2.
All rationals have at least one base where their positional representation is non-unique. E.g. for one third, 0.1=0.0(2)=0.02222... in base 3.
This is important because there are silly arguments about whether 0.9999... "really" is 1. Such arguments are usually drawn out, not-to-the-point and often incorrect unless one first explicitly acknowledges the non-uniqueness of positional representation in such cases. The reasoning should be, then, whether 0.(9) can express any number other than 1, while still maintaining the semantics of the positional representation. The answer is: no.
The sum of n odd numbers, starting from 1, is n2. 1+3+5+7+9=25, which is 52.
eceuiuc ยท 1 points ยท Posted at 16:14:10 on May 25, 2016 ยท (Permalink)
Given an alphabet A of size k, it is possible to construct a sequence that contains all possible subsequences of length n in A exactly once. These sequences are known as De Bruijn sequences and are always of length kn.
There's so much of everything in that equation: 0 is defined, e looks like a grand wizard using I and Pi to get 0. Though it's in polar format, it can be rearranged in rectangular trig format.
Stare at that equation long enough, you start to realize that math with real numbers (or what we just call numbers). May be a very very small part of what is really out there.
If you draw lines on paper which are two matchstick lengths apart, there is exactly pi chance a matchstick you drop onto the paper will lie across that line. This is know as Buffon's Needle if you wish to Google it.
One millimiter of water occupies one cubic centimeter, weighs one gram, requires one calorie to heat up one degree centigrade, which is one percent of the difference between its freezing point and its boiling point.
Read it on a reddit post once...
Galt42 ยท 1 points ยท Posted at 16:14:54 on May 25, 2016 ยท (Permalink)
Euler's identity:
ei*ฯ + 1 = 0
It's insane because the 3 constants have nothing to do with one another, and it uses every level of mathematical operations through exponents.
[deleted] ยท 1 points ยท Posted at 16:15:05 on May 25, 2016 ยท (Permalink)
Solve any of the problems listed there and you receive one million dollars as well as a Field's Medal which is the mathematics equivalent to the Nobel prize.
One of the problems, the Poincarรฉ conjecture, was solved earlier in the century by a Russian mathematician who refused to accept the money or the prize.
Generally speaking the problems are all incredibly difficult to solve. People have devoted their entire life to just one small part of each of these problems and made little progress.
Here is a video explaining the Riemann Hypothesis, one of the millennium prize problems. Even if you do not have a math background this video is quite easy to understand, as it was made so that pretty much anyone can watch it: https://www.youtube.com/watch?v=d6c6uIyieoo
That the moon is almost exactly 400 times smaller than the sun, but the sun is 400 times further away, making them seem almost exactly the same size in the sky. Such a random coincidence, though I know not strictly a maths fact.
It's true.
The proof is as complex as it is rigorous, and requires learning a bit of new math, but this could change the entire future of the world. It would blow Pythagoras' mind if he could see it.
You know the Pythagorean theorem: the square of the length of the long side of a right triangle is equal to the sum of the squares of the lengths of the other two sides. It turns out this works for arbitrary dimensional objects. If you have a k-dimensional parallelogram in n-dimensional space, the square of the k-volume of that parallelogram is equal to the sum of the squares of the k-volumes of the projections of that parallelogram into all of the k-dimensional planes in the n-dimensional space.
robogo ยท 1 points ยท Posted at 16:19:35 on May 25, 2016 ยท (Permalink)
The Fibonacci Sequence (1 1 2 3 5 8 ...) can be used to roughly and easily convert between miles and kilometers and vice versa.
3 mi is about 5 km, 5 mi is about 8 km, and so on. A bit down the line we see adjacent terms 196418 and 317811. Well, 196418 miles is 316104.13 km, a percent error of only 0.54%. Sure it's not accurate enough for science, but for most applications it's close enough.
I'm not a big fan of math, but I have to admit that the Fibonacci number sequence is amazing. The fact that it pops up all over in nature, like in flowers and snail shells is so fascinating.
uzi ยท 1 points ยท Posted at 16:20:21 on May 25, 2016 ยท (Permalink)
Checking if a number is divisible by the first twelve numbers:
1: Easy, everything is divisible by 1
2: Is it odd or even? Even you say? Then it is.
3: Add up the digits... if they're divisible by 3, then you're good. For example: 726 is because 7+2+6 = 15 which is because 1+5 = 6.
4: Are the last two digits divisible by 4? So 34508 is because 28 is divisible by 4.
5: Does the number end in 0 or 5?
6: Combine the rules for 2 and 3.
7: Ok, I lied. Can't do this one easily that I know of.
8: Trickier version of the 4 rule... check if the last two digits are divisible by 4, then if the hundreds digit is odd or even.
9: Similar to the 3 rule. Do the digits add up to something divisible by 9?
10: Does the number end in 0?
11: This work up until a point, but do the alternating digits equal each other when added up? 3795 is because 3+9 = 12 and 7+5 = 12.
12: Combine the rules for 3 and 4.
BONUS: I didn't say anyone mention the investor favorite Rule of 72 ... if you want to know how long it'll take to double your money when growing a consistent percentage, divide 72 by it. So if you're getting 15% a year, then it'll take 72/15 or roughly 5 years. Getting 8%? Then it'll be more like 9 years.
Its not necessarily a fact, more of a mind bender and it has a special name, but I've forgot it. It goes something like this:
A man has a bag of potatoes weighing 100kg. These potatoes are 99% water. He goes home and dries them out, so that they are now 98% water. He reweighs them, how much do they weigh now?
That makes sense. 99% of the weight of the potatoes is water. So the potatoes are 1kg potato and 99kg water. In order for the potatoes to be 98% water, they would need to be 1kg potatoes and 49kg water.
The theory of higher dimensions such as 4D and 5D can actually be simply explained by adding perspective lines in a 2D representation. I'm on a phone so I can't hyperlink images.
Say for example I have a 2D drawing of a box and to make it 3D, the vertices of the corners of two boxes need to be connected to make a simple cube. To make the cube 4D, another cube can be placed inside it with all of the two sets of corners connected by another set of lines, making the well known hyper cube or tesseract of the Avengers. It can be converted to 5D with a heck lot more lines and so on.
Pretty interesting to apply it as a possible link to parallel universes like pages of a book if multiple 3 dimensional planes formally existed.
[deleted] ยท 1 points ยท Posted at 16:24:16 on May 25, 2016 ยท (Permalink)
This is kind of unrelated, but whenever I try to make a text post on any sub-thread it says "that sub Reddit only allows text posts" but my post is only text.
F0sh ยท 1 points ยท Posted at 16:24:27 on May 25, 2016 ยท (Permalink)
That there are different sizes of infinity. A very clever madman named Georg Cantor proved it using a method called diagonalisation. There's a proof on Wikipedia and I wrote an explanation about it a while ago too.
It's a pretty simple argument but it's quite astounding because people tend to think of infinity as being bigger than anything - so how could there be something even bigger? Well, countable infinity is only bigger than all the finite stuff - that's the key :)
This is a number that is so big that to fully write it out, using 1 atom in the universe for each number in the sequence. You would run out of atoms in the Universe before you finished writing it down.
The fact that there are different sizes of infinity. This is my favorite mathematical argument from real analysis. You'd think that infinity is simply infinity, because it is freaking infinite, but no!
Let's say we have the integers: {1,2,3... n, such that n goes to infinity}. Now let's say we only consider the even number (i.e. 2, 4, 6...) one would think there might be "half" as many even numbers as there are integers, but no there are still an infinite number of even numbers and in fact we can write the even numbers as {2, 4... 2*n}, there is an even number that corresponds to every integer n. These sets have the same cardinality, the same size (countably infinite).
You can cary this out for any multiples of integers (3n, 4n... and eventually n*n or n2) there is still a 1 to 1 correspondence, there is an integer corresponding to every square. We can take this further to n3, n4, etc all having a 1 to 1 correspondence with the integers. These are all countably infinite sets!
Now this is where things get tricky. If you think of n as a set of countably infinite things, the 2n is two of those sets, 3n is 3, n2 is a countably infinite number of countably infinite sets kind of like an infinite square like:
1 2 3 4 ... n -> infinite times
2 4 6 8 ... 2*n->
3 6 9 12 ... 3*n
...
...
1 4 9 16 ... n2
Bare with me now. Then n3 is like a giant cube, a countably infinite number of a countably infinite number of countably infinite sets. Yet it still has the same cardinality of just one countably infinite set. Now take this to the extreme, what about ninfinity ? That would be a countably infinite number of a countably infinite number ....of a countably infinite number of countably infinite sets. This my friends is what we call uncountably infinite and is the cardinality of the Real numbers.
I apologize if that makes no sense, I did my best trying to explain this in words on Reddit. The point is there are different sizes of infinity, and that is freaking crazy.
If a piece of paper is .1 mm thick, folding it 50 times makes it 250 times thicker, and you get 112 million km (80 million miles), or .75 AU (the distance from the earth to the sun).
My 3rd grade teacher was wrong, I DO have a calculator in my pocket wherever I go.
rdogg4 ยท 1 points ยท Posted at 16:30:23 on May 25, 2016 ยท (Permalink)
"Benford's law, also called the first-digit law, is a phenomenological law about the frequency distribution of leading digits in many (but not all) real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.[1] For example, in sets which obey the law, the number 1 appears as the most significant digit about 30% of the time, while 9 appears as the most significant digit less than 5% of the time. By contrast, if the digits were distributed uniformly, they would each occur about 11.1% of the time.[2] Benford's law also makes (different) predictions about the distribution of second digits, third digits, digit combinations, and so on."
Birthday Problem It only takes 23 people in a room to have >50% chance of two people sharing a birthday.
Brouwer Fixed Point Theorem If you take a map of the USA to any point in the country, there will always be a point on the map that represents that exact point in the country.
Four Color Theorem No matter how a map is drawn, with just 4 colors, you will always be able to color each region such that it is not the same color as any region it touches.
0.999... = 1 Since there is no number between 0.999... and 1, they are actually the same number! (By 0.999..., I mean a number with 9's repeating infinitely; e.g., the limit of 0.9, 0.99, 0.999, ....)
The difference between the square of consecutive numbers is the same as the sum of those consecutive numbers.
Example: The square of 30 is 900. The square of 29 is 841. 30+29=59, which is 900-841. It's a quick and relatively easy way to find the square of large numbers without a calculator, assuming they're near to an easily-calcuable square.
smep ยท 1 points ยท Posted at 16:31:27 on May 25, 2016 ยท (Permalink)
e raised to the pi*i minus one is equal to 0.
epi*i-1=0
Uthak ยท 1 points ยท Posted at 16:31:34 on May 25, 2016 ยท (Permalink)
If you pay attention and take good notes in class, its not fucking hard.
Valveq0 ยท 1 points ยท Posted at 16:31:54 on May 25, 2016 ยท (Permalink)
My favorite fact about Math is propably that, despite everything is thought up and defined by Humans, it applies to everything we do and everything we do can be calculated.
saello ยท 1 points ยท Posted at 16:33:36 on May 25, 2016 ยท (Permalink)
I always found the fact that every multiple of 9 the answer will add to 9 to be pretty cool. For example 3x9 = 27 and 2+7 = 9. This holds true on a larger scale 458 627x9 = 4 127 643 and 4+1+2+7+6+4+3 = 27 and then 2+7 = 9. Try it out with any random number multiplied by 9 and eventually the answer will add to 9.
My favourite math fact is that since I've graduated high school I haven't had to use pythagorean theorem nearly as often as the teacher implied I would.... I do however need to learn how to do taxes..
It's probably not as interesting as the others here, but I really loved finding out that in calculus you find the instantaneous rate of change for a function by basically faking a distance equation from beginner's algebra. It's just rise over run and you pretend there's a run instead of a zero.
You can mathrmatically show that there will be always be at least two spots on earth with the exact same temparature and pressure whicb are perfectly opposite of eachother:
Let's say you had a globe with the temperatures at every point on it marked. and now let's say the tempeatur at the north pole was -10ยฐ while it was -40 at the south pole. Now you had a copy of the globe but instead of having the temperature on it it had the temperature differnce between the point you are looking at and the point on the opposite side of the earth. So the north pole would have -10- (-40)=+30 and the south pole would have -30. Now consider that temperature is a continous function. That means that whichever way you take on you second globe from one pole to the other you will pass a point where the function is zero.
So we have established that there is some kind of "ring" around the earth where the difference between the temperature on opposing sides of the globe is zero. There are infinitly many of these points.
Now we do the same for atmospheric pressure. We get a second ring. Each point of these rings (by way of their construction) has another point of the respective ring on exactly the other side of the globe. If you put two rings with this property on a sphere like our globe they will always have at least two intersecting points. These points will be on the exact opposite side of the globe.
So there will always be a pair of points with exactly the same pressure and temperature that are on the exact opposite side from eachother.
Benford's law, which basically says that in many naturally occurring lists of numbers, around 30% of the numbers start with a 1 and less than 5% of them starts with a 9. For example the Fibonacci numbers.
If there are 23 people in a room, there is a 50% chance that two of those people will have the same birthday. It's called the birthday problem and by the time there are 50 people in the room, there is a 97% chance that two people share a birthday.
In fact, I have been tempted to think these equations which I produced are actually quantum models but I haven't been able to prove it. For example, the 2 fits into any physics equation that has a two in it and there are numerous occurrences of a 2 -- such as when something is squared or rooted, like the speed of light. The other thing is that there is particle wave duality -- perhaps this equation models the co-existence of a particle and a wave which are mathematical symmetric of each other? The other thing is the components 3 and 4 represent space and time, which is really physics-y. And other stuff too!
[deleted] ยท 1 points ยท Posted at 16:37:39 on May 25, 2016 ยท (Permalink)
Figures don't lie but liars figure.
[deleted] ยท 1 points ยท Posted at 16:37:45 on May 25, 2016 ยท (Permalink)
The probability of randomly selecting a rational number from the set of all real numbers bounded by two points is zero, even though there are infinitely many rational numbers within that set.
If you add up the mass of quantum vacuum fluctuations (packed in a holographic interference pattern, totally space filling - colloquially known as the flower of life) that fit in the sphere of the proton, you yield 1055 grams.
Basically, this thing messes with your mind because we're so used to the size of finite numbers (i.e., if you were counting, you could eventually count up to this number) that when we try to deal with the size of infinity it messes with our thinking because our finite number thinking "breaks" in multiple cases.
Monte Carlo integration. If your calculus teacher asks you how to go about integrating something and you don't have a clue, just yell "Monte Carlo Integration!"
Kilieks ยท 1 points ยท Posted at 16:41:06 on May 25, 2016 ยท (Permalink)
The fact that they call it "maths" in the UK and "math" in the US. Definitely one of my favorite Britishisms; right up there with "boot" for "trunk" in a car.
If you get 1% better at something every day (compared to the previous day), by the end of the year, you'll be thirty-eight times as good as you were on the first day! :D
There are as many even or odd integers as integers themselves because if n represents all integers, then 2n represents all even integers, and 2n-1 represents all odd integers. The relation of f (n) = 2n or f (n) = 2n -1 is bijective. So the sets are of equal size.
My favorite is that there is no solution we know of yet tonthe traveling salesman problem and if that problem ever gets figured out all the cryptography and other math problems in P=NP will go from thousands of years to crack to days or hours.
Compound interest, or the exponential function. Non mathematicians (and even some mathematicians) overlook this in every day life.
For an example, practically every government and central bank in the world aims to create inflation of 2% a year as a matter of policy. They usually run a little higher, on average.
Now calculate what this will do to the value of your money, or the price of anything you buy, over the course of your lifetime. Or over 10, 20 or 50 years.
This crops up all the time in ways we don't think of.
For example 11 x 54 = 594. You add the digits that are being multiplied to 11. In this case 5+4=9. Insert the resulting sum between the original numbers. With larger numbers it gets more complicated.
11 x 56 = 616. You must "carry" the additional number to the first digit.
11 x 125 = 1375: take the first and last numbers, those will stay the same. Then start adding. 1+2=3. 2+5=7. Add these, in order, with the first and last numbers. 1,375.
In math-eese: The result of the recursive summing of digits is path independent.
In English: If I have a number and I add its digits together, and add those digits together, until I have a single digit, the order in which I add the digits does not matter. In fact, I do not have to finish summing the whole number before I add them together. If you don't get what I'm on about heres an example: http://i.imgur.com/nNUSqqj.png
There's a whole bunch of other cool stuff about that, such as the digit 9 does not have any result on the output number unless the number is 9. Ie: 1,999,999 --> 1. Same goes for any combination of numbers that add up to 9. This fact only applies in base 10.
The resulting number for any non zero positive integer is additionally given by n mod 9, but if the result of that is zero, then the actual result is 9. The general rule is n mod base of n - 1, but a zero result results in the base minus one.
EDIT: forgot two words.
[deleted] ยท 1 points ยท Posted at 16:49:39 on May 25, 2016 ยท (Permalink)
The sum of all odd numbers up to any 2N+1 where N is an integer results in a perfect square.
[deleted] ยท 1 points ยท Posted at 16:52:52 on May 25, 2016 ยท (Permalink)
That there probably is no function that returns all primes, or that e or Pi are irrational. Mathematics is the science of pure logic, there is nothing more universally true than it.... and still - it's a pure chaotos and an unordered mess!!!
Both 0.99999999___ and 1.000___00001 are equivalent to the number 1. This is because the number 1 is the only real number that is unprovable to exist.
Zeptic ยท 1 points ยท Posted at 16:54:03 on May 25, 2016 ยท (Permalink)
Math is just a concept of numbers thought up by humans. They don't actually mean anything to people who don't understand their significance. Say for example 8 x 2 = 16, that would be completely useless to a child, but to someone who understands it, it actually means something.
If you ride a bike around a circular track, starting from a standstill and coming to a stop at the point you started, no matter how fast you go and how you vary your speed during the bike ride (no going backwards though), there will always be two spots directly opposite each other on the circle where your speed was the same. (the speed needs to vary Continuously though. Instantly accelerating to the speed of light or whatever is cheating.)
[deleted] ยท 1 points ยท Posted at 16:55:55 on May 25, 2016 ยท (Permalink)
Fermat's last conjecture
[deleted] ยท 1 points ยท Posted at 16:56:19 on May 25, 2016 ยท (Permalink)
Fave fact: Americans think "maths" is incorrect shorthand for mathematics
Take ANY three digit number, repeat it so it is a 6 digit number. For example 123123. That number will always be divisible by 13. The result is always divisible by 11. And that result is always divisible by 7 and you get back to your original three digit number.
My dad always told my brother and I this story to see if we had an answer.
3 guys are stranded but then find a hotel in a blizzard, the manager charges them $10 each for their room, total being $30. Bellhop takes them up to their room, when he comes back down the manager says he feels bad for the guys and takes $5 off and tells the bellhop to give it back to the guys. On his way up to the room, he figues he can't split $5 equally for the 3 guys, so he keeps $2 and gives each one back $1. So if each man is given back $1, they essentially paid $9 each, so $9ร3 is $27 and the bellhop kept $2, what happened to the last dollar?
Not a mathematician, but I like cross canceling, eg 140/100% = x/34%. I find that I've used that formula in daily life more than anything else. Math was my favorite subject, though I sucked at it. =/
Sitk042 ยท 1 points ยท Posted at 17:00:00 on May 25, 2016 ยท (Permalink)
For Any number divisible by 9, if you add up its digits, their total will be a number divisible by 9. 3 * 9 = 27, 2 + 7 = 9; 42 * 9 = 378, 3 + 7 + 8 = 18...
[deleted] ยท 1 points ยท Posted at 17:00:15 on May 25, 2016 ยท (Permalink)*
2x +2x =2x+1 works
But
3x +3x =3x+1 does not work
But
3x +3x +3x =3x+1 does work
And so on
4x +4x +4x +4x =4x+1
Edit: Added some spaces so it looked correct
Edit no 2: math was wrong, now isn't.
There is a theorem called the fixed point theorem which states that:
If g is a continuous function g(x) in [a,b] for all x in [a,b], then g has a fixed point in [a,b].
Here is a basic example:
g(x)=x2 -2 in [-2,0] has a fixed point at x=-1 because g(-1)=(-1)2 -2=1-2=(-1)
Boring but how about a cool application. The function (projection) that sends spherical coordinates in space to a 2d image (map) is continuous (I hope...). This is why it's possible to read a "You are here" sign at the mall or airport and you actually are. Seems obvious but this is why.
I was playing around with squares when we first learned them in elementary, brought that to the teacher and she showed that to the class, claiming she had never seen that before. Don't know how truthful she was about that though.
If you start with the number 41, and add increments of 2*n, the series you produce: 41, 43, 47, 53, 61, 71, etc. is one of the longest running series of primes!
Feel a bit late, but there are more real numbers between 0-1 then there are integers. The set of integers between -infinity and +infinity is smaller than the set of real numbers between 0 and 1. And while on infinity, the sum of all positive integers is a negative fraction.
Apofis ยท 1 points ยท Posted at 17:08:35 on May 25, 2016 ยท (Permalink)*
There are no general solutions in radicals for polynomial equations of degree more than 4. Polynomials are one of the most fundamental things in mathematics and computing in general, because computers can evaluate them simply. However, finding all roots analytically can be difficult for polynomials of high degree. Luckily we have efficient and stable numerical algorithm for finding all roots of polynomials. Its name is "QR iteration", and it is an algorithm for finding all eigenvalues of a matrix, but can be used to find roots of polynomials as well.
Conisder the set of all boring numbers. Define it however you like. Within that set there must be a smallest number, which is officially the smallest boring number. That makes it interesting, so we must remove it from
the set. Now consider the rest of that set, there is now a new smallest number of the set. Repeat ad infinitum and we can conlude that there are no boring numbers and hence ALL NUMBERS ARE INTERESTING.
YAY Maths! FML
[deleted] ยท 1 points ยท Posted at 17:09:23 on May 25, 2016 ยท (Permalink)
Happy Numbers - take the digits of any number, square all of them and add them together - repeat until the sum of the squares of the digits equals 1, or the system loops endlessly in a cycle which does not include 1 (thus meaning the number is a sad number) - absolutely 0 mathematical use (it's part of maths known as "recreational mathematics"), but it's a pretty interesting way to pass time if you have nothing else to do (and like maths)
By using analytic continuation of the Riemann Zeta function, you can prove that the sum of all the natural numbers (1+2+3+4+.....) is equal to -(1/12). It is a very important result that is famous in analysis and has physical significance in quantum field theory and string theory.
I understand that this is supposed to be a joke, but its way too painful to see this stuff brainfuck a bunch of people.
e: Alternatively, if this is a scenario where you are subscribed to this idea, as some are, something being mathematically correct while factually incorrect simply proves the faults within our own system.
Syfawx ยท 1 points ยท Posted at 17:36:34 on May 25, 2016 ยท (Permalink)
Firstly, it is, and i think i made it pretty clear by adding an ellipsis instead of the dot on top of the number to show it is recurring. An ellipsis is commonly used instead of a dot anyway. 10 x 0.99... is 9.99...
This isn't supposed to be a joke - it's an actual mathematical phenomenon. Look it up for yourself before writing so passively agressive.
I am familiar with it. I understand the logic of it(Not having seen someone use an ellipsis to show repeating, i've always seen it with the line above(which obviously is not something that we have immediate access to at a keyboard, thats my own bad) I assumed it was strictly .99). Currently considered a phenomenon by many, yes, But plugging something into a system that is clearly not built to handle it and deciding that it is fact is ridiculous to me. Based on how we handle numbers, yes this can be argued to be "accurate" or "correct", but the real fact is that we clearly have just reached a limit of our own system or understanding.
Syfawx ยท 1 points ยท Posted at 17:48:25 on May 25, 2016 ยท (Permalink)
But that's exactly why its my favourite maths fact - because it is so clearly ridiculous is our minds but logic tells us differently and it shows a flaw in our numbering system.
I can agree with that. I mean, it certainly is interesting that we have managed to break our own number system. Fantastic really. People all too much just assume things like this are perfect because that is what they grew up with, but something like this can hopefully help show people that the system simply isn't complete. What i don't care for is that it is always presented as something that is "proving" something that isn't true when the majority of people do not understand that proving something mathematically is not the same as proving it factually, and because that isn't usually mentioned as it is brought up in the context of fucking with peoples head(which is usually fun to me), they accept it because "the system works"
1) There are different sizes of infinity
2) .9999999999999 (repeating) equals 1
[deleted] ยท 1 points ยท Posted at 17:09:57 on May 25, 2016 ยท (Permalink)
0.9999... = 1
[deleted] ยท 1 points ยท Posted at 17:10:22 on May 25, 2016 ยท (Permalink)
If you were to write out the longest, most complex mathematical equation on a single chalkboard with an unlimited amount of chalk, you would be wasting your time.
Let's play a game. It's not very fun, but it goes like this:
I have 2 coins. I will flip both coins (both at once each time) without you seeing until I get at least one heads.
I have the coins in front of me, one covered by each hand.
I reveal a heads (if they are both heads I pick randomly).
So you now have a revealed heads, and a hand covering the other coin.
What is the probability that the other coin is heads?
It's not 1/2. It's 1/3.
Jaarl ยท 1 points ยท Posted at 17:11:04 on May 25, 2016 ยท (Permalink)
Im not sure if this is common knowledge, but I cant find any info on it... if you have a number where all the digits add up to 9 ex. 400302 (4+0+0+3+0+2=9) then it is divisable by 9
This is not precisely true. The series diverges. However, there is a way to assign -1/12 to that sequence of numbers that is consistent with some useful mathematical operations.
The potato paradox. More about how we conceptualize numbers than being a neat math fact:
Fred brings home 100 lbs of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then lets them dehydrate overnight so that they consist of 98 percent water the next day. What is their new weight?
The notion that it's "impossible to say" is kind of a misconception about the way infinity works. Like people want to assume reality has some hard limit where eventually there will just stop being another 9, because it's easier to comprehend things that way, but it's not the case. In truth, we know how much infinity is, and that answer is... well, infinity.
[deleted] ยท 1 points ยท Posted at 17:11:50 on May 25, 2016 ยท (Permalink)
If you take the length of a river (as the crow flies) from its source to its mouth and multiply by pi, you get an almost exact measurement of its total length including the meanders.
efurnit ยท 1 points ยท Posted at 17:12:08 on May 25, 2016 ยท (Permalink)
given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n โ 1)-dimensional hyperplane.
VMorkva ยท 1 points ยท Posted at 17:13:52 on May 25, 2016 ยท (Permalink)
[deleted] ยท 1 points ยท Posted at 17:14:50 on May 25, 2016 ยท (Permalink)
a simple one - that you can do your nine times tables on your hands by raising them in front of you fingers splayed out and lower the digit you are multiplying by 9. Any fingers to the left are in the 10's and to the right are in the 1's. Works up to 9x10 obviously.
Simply put, if there are 9 holes and 10 pigeons, then at least one hole has more than one pigeon.
lurgi ยท 1 points ยท Posted at 17:19:15 on May 25, 2016 ยท (Permalink)
Between any pair of distinct rational numbers there is an irrational number. Between any pair of distinct irrational numbers there is a rational number. Yet there are more irrational numbers than rational numbers.
The number 9 both exists and doesn't - if you add up the sum of any whole number, the digital root (sum of all the single digit numbers) will be the same with or without the 9's.
The number four. Square root = 2. Cut it in half? 2. It's an even number, which for some reason I associate with good (odds are evil!). You can square it a bunch and those numbers are sweet as well. And 2+2=4. Everyone always comes back to it as a known fact. I just really love 4. Also I associate it with the color green, my favorite color.
[deleted] ยท 1 points ยท Posted at 17:23:14 on May 25, 2016 ยท (Permalink)
0.9 repeating = 1.
This gets a lot of people. One way to explain it is that 0.9 repeating is just another way of saying the same thing, like speaking a different language. Another way to explain it is that 0.3 repeating is 1/3, and if you add up the infinite 3s, they all become 9s but that's just like 1/3 + 1/3 +1/3. Some people still have a hard time dealing with it.
I prefer to think about in more abstract terms, but they might not be helpful to other people. Basically for two real numbers to be distinct, there must exist numbers between them. A single point can't have any distance, so its just the basic truth that to establish any distance between real numbers, which is to say, make them different, we need to be able to form a collection of intervening values.
Since one cannot imagine or create any number between 0.999999... and 1 there can be no distance between them, and thus they are the same. Its a conceptual argument, but its clean to me.
Simple but interesting. You can see if any number is divisible by 3 if the digits added up are divisible by three.
ex: 2,894 //
2+8+9+4=23//
2+3=5 not divisible by 3.
8,634,270//
8+6+3+4+2+7=30//
3+0=3 divisible by 3.
If you're not sure what the next perfect square is and know the previous two perfect squares, you can figure out the next one(s) by taking the difference between the previous two perfect squares. From the difference, add the next odd number to the previous perfect square.
Ex: What's the next perfect square after 169? Well 169-144=25. The next odd number is 27. 27+169 = 196, which is a perfect square of 14. What's next? 196+29= 225, which is a perfect square of 15. And so on...
I'm sure this is an actual theory somewhere, but I figured it out after reading in Steve Jobs that they used adding sequential odd number to make rounded edges instead of doing square roots: 1+3=4, 1+3+5=9, 1+3+5+7=16...
The coin flipping problem I solved with some of my friends at University - If I flip a coin forever, what are the odds I get one more head than tails; and what is the average number of flips?
It's my favorite because it's incredibly unintuitive. The odds you will get one more heads than tails is 100%; if you flip forever, you will eventually get one more head that tails.
However, the average number of flips is infinite. So yes, you will definitely get one more heads than tails... But on average it will take you an infinite amount of time :) it is so weird I love it.
The set of all numbers is the same size as the set of all odd (or even) numbers โ they're both infinite. One would think that the set of all numbers would be double the size of the set of only odd (or even) numbers, but all you have to do is imagine linking each number in each set together with an imaginary line. Like this:
1, 2, 3, 4, 5...
1, 3, 5, 7, 9...
No matter how high the list of all numbers gets, there will always be another odd (or even) number to "match" it with.
dyfx ยท 1 points ยท Posted at 17:27:10 on May 25, 2016 ยท (Permalink)
Imagine that you send a message of zeros and ones and every number has a 10% chance of being flipped, you can make the message redundant in such a way that the original message can be recovered with virtual certainty AND that message is only twice as long as the original. Shannon's Noisy Channel Theorem.
Derivatives and integrals? They don't have to be integers.
You can take one half of a derivative. You can take 3.14159... (a special constant like Pi, or e) of a derivative. You can take cos(theta) (A function!) of a derivative.
It's called Fractional Calculus and it dates back to 1695 and it will blow your freaking mind.
They also coined an operator that does both integration and differentials. Somewhat understandably called "differintegration."
What would be the use of taking a partial derivative? I just finished a college calculus, so I understand what I might want a regular derivative for, but in what situation would a fractional derivative be wanted?
Since .9999 is equal to 1, doesn't that mean .9999 does not exist, because it is a different number?
Er, no? .999... is just another way to represent the number 1 with our decimal system. It's like saying that the number 4/2 doesn't exist because it's equal to 2.
bobroxs ยท 1 points ยท Posted at 20:24:24 on May 25, 2016 ยท (Permalink)
Ok. That makes more sense. Sorry!
Cmac253 ยท 1 points ยท Posted at 17:28:28 on May 25, 2016 ยท (Permalink)
Fibonacci Sequence shows up in nature
[deleted] ยท 1 points ยท Posted at 17:29:20 on May 25, 2016 ยท (Permalink)
When we talk of "squares" in algebra, it means the same thing as an actual geometric square. A common example of this is the Pythagorean Theorem: a2 + b2 = c2,that is the exact same thing as this. When ancient mathematicians squared things or took a square root, they literally were dealing with actual squares that they drew down. Ever wonder why (a+b)2 = a2 + 2ab + b2 ? Well, here you go. In fact, most of your algebra problems from high school can be drawn as pictures. Here is how medieval mathematicians solved x2 + 10x = 39.
I don't know if this is actually true, but I once read that every possible combination of numbers is contained within the decimals of Pi. Any mathematicians care to weigh in on that?
Pi is irrational, so it does not repeat or terminate. This means that somewhere in there, every sequence of numbers is contained somewhere (and an infinite number of times, in fact)
Any power of Phi (the 'golden ratio', ~1.618) can be expressed as A(phi)+B, where A and B are not only integers, but consecutive members of the Fibonacci sequence.
On a related note, as you get deeper into the Fibonacci sequence, the ratio of ( F(n) / F(n-1) ) very quickly approaches Phi.
EDIT: For clarification, the first fact happens because Phi has a pretty unique property such that
(phi)+1 = (phi)^2
and
(phi)-1 = (phi)^-1
bubadmt ยท 1 points ยท Posted at 17:34:25 on May 25, 2016 ยท (Permalink)
Some infinities are different, or even larger than others. I.e. an infinity series of numbers from 1-2 and all between 2-3. They are both infinite, yet the first series is different and smaller.
Despite what certain celebrities believe, 1x1 does not, in fact, equal 2. Why? Well, you have one group of one, and you multiply that by one, you get... One.
mzoltek ยท 1 points ยท Posted at 17:36:09 on May 25, 2016 ยท (Permalink)
That you people call it "maths." How many of them are there?
Ldeezy ยท 1 points ยท Posted at 17:38:26 on May 25, 2016 ยท (Permalink)
That 1 = .9999... repeating
Algebraic proof:
Let n = .999.... So 10n = 9.9999...
Subtract the first equation for n from the second
9n = 9 (repeating decimals subtract out)
Divide both sides by 9, we now get n = 1
[deleted] ยท 1 points ยท Posted at 17:38:32 on May 25, 2016 ยท (Permalink)
Mom showed me this. As an adult it doesn't do much, may have been useful as a kid... But do a column of 0-9, then after each of those do a column of 9-0... And you get the multiples of 9.
0 9
1 8
2 7
3 6
Etc.
I know this one is a simple explanation and all, and not a miracle, but still could be useful.
Bonus fact- The other one I found odd in elementary- if you add up the digits of a number, and that number is divisible by 3... The whole number will be divisible by 3.
For example- 5,622,810- the numbers add up to 24. So since 24 is divisible by 3, 3 will go into it evenly.
If not, it's not divisible by 3.
Dafuq up wit dat
[deleted] ยท 1 points ยท Posted at 17:39:11 on May 25, 2016 ยท (Permalink)
I don't know what you call this but if you swap between adding and subtracting this formula 1/(n+1) . And n starts at 0 and continue forever. You end up with 1 - 1/2 + 1/3 - 1/4 + 1/5 ... - 1/n+1. It ends up with ฯ/4.
june 7 1967 israel killed many Americans but killed more on 9/11 and succeeded in pulling us into endless wars in the middle east now what does America get for being an ally? that is right nothing.
Dr-K-G ยท 1 points ยท Posted at 17:39:59 on May 25, 2016 ยท (Permalink)*
We don't know wether pipipipi is an integer or not.
Edit: A few more of my favorite unsolved problems:
We don't know if e+pi or e*pi is rational but we know that at least one of them has to be irrational
Can every even number greater than 2 be expressed as a sum of two primes?
A perfect number is a positive integer that is equal the sum of its proper positive divisors, for example 6 = 1+2+3 or 28 = 1+2+4+7+14. Unsolved problems: Are there odd perfect numbers? Are there infinitely many perfect numbers?
Are there infintely many twin primes? That is primes that are exactly two apart, for example (3, 5), (5, 7), (11, 13) and (17, 19).
[deleted] ยท 1 points ยท Posted at 17:40:24 on May 25, 2016 ยท (Permalink)
One million seconds is eleven and a half days.
One billion seconds is almost 32 years.
Not really a "maths fact". Or my favourite.
roshoka ยท 1 points ยท Posted at 17:41:10 on May 25, 2016 ยท (Permalink)
If there are 6 people in a room, you can be completely certain, without knowing a thing about any of them, that at least 3 of them know each other or at least 3 of them are strangers.
"You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large. But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.โ
[deleted] ยท 1 points ยท Posted at 17:45:59 on May 25, 2016 ยท (Permalink)
That consecutive lottery numbers are just as probable as any other sequence.
Frogole ยท 1 points ยท Posted at 17:47:03 on May 25, 2016 ยท (Permalink)
I feel so sick , Go on you Gods and save humanity :)
Kakshoo ยท 1 points ยท Posted at 17:47:35 on May 25, 2016 ยท (Permalink)
(Posted already so this must be my second favourite right?)
When you tighten a rope that covers the whole equator in length(approximately 40,000km), and then lengthen the rope by 6 meters and tighten it again, so that the rope hangs in the air at an equal height the whole way, that height will be approximately 1 meter.
That you get the frequency spectrum of a function by multiplying it with ei*o ther_stuff and integrating it.
Kasoo ยท 1 points ยท Posted at 17:51:22 on May 25, 2016 ยท (Permalink)
If you take a point called Z in the complex plane and let Z1 be Z squared plus C, and let Z2 be Z1 squared plus C, and let Z3 be Z2 squared plus C, and so on.
If the series of Z's always stays close to Z and never trends away; that point is in the Mandelbrot Set !
No, if the sequence starting with Z=0 stays bounded then C belongs to the Mandelbrot set. You're mixing up the Mandelbrot set with the filled Julia set for f(z)=z2+c (also a fractal that often looks quite cool)
Kasoo ยท 1 points ยท Posted at 18:11:28 on May 25, 2016 ยท (Permalink)
Jonathan Coulton lied to me!
msa001 ยท 1 points ยท Posted at 17:51:26 on May 25, 2016 ยท (Permalink)
You can easily find the Nth prime number by jus <jd on dmkwke,
[deleted] ยท 1 points ยท Posted at 17:51:29 on May 25, 2016 ยท (Permalink)
Could you possibly explain to me how the Fibonacci sequence can be applied to many different areas of life? For example, I've heard of it somehow applying to music theory, but it's never been explained in a way I could understand...
Goodstein's Theorem. Easily one of the weirdest theorems I know, and it at first seems very counterintuitive.
In layman's terms:
When we representing a number in a base (say 99 = 10200 in base 3) we are implicitly representing it as a sum of powers of the base, for instance
99 = 1โข34 + 0โข33 + 2โข32 + 0โข31 + 0โข30
= 34 + 2โข32.
A Goodstein sequence is defined as follows:
Start with any positive number n in any base b_0 > 1, and write out the base b_0 representation for n as a series as above. But don't just do that: every time you see a number greater than to b_0 in one of the exponents, also write that as a power series in b_0, and so on until all the numbers written down are at most b_0. So in our case (n_0 = 99, b_0 = 3) we have
99 = 33+1 + 2โข32.
This is called the hyper-base b_0 representation of n.
So starting with n, we write it in hyper-base b_0. Now comes the cool part: every time you see b_0 in the expansion of n, replace that with b+1. Note that "usually" this will dramatically increase the value represented. After doing this, subtract 1 to obtain a new number n_1, and if n_1 is positive, rewrite the number in hyper-base b_1 = b+1.
So in our example, we have
n_1 = 44+1 + 2โข42 - 1 = 1055
= 44+1 + 42 + 3โข4 + 3
in hyper-base b_1 = 4. We now just repeat this process. For instance, we have
n_2 = 55+1 + 52 + 3โข5 + 2 = 15688,
n_3 = 66+1 + 62 + 3โข6 + 1 = 279991,
et cetera. As you can see, these numbers increase quickly.
On the other hand, Goodstein's theorem states that no matter what our initial base is -- you could start with 1,000,000 in base 2, of you like -- the sequence will eventually terminate, i.e. n_k will equal zero for some finite k.
Somehow, once these numbers get big enough, their structure is exhausted, and they stop increasing, so we then simply subtract 1 until we reach 0.
On the other hand, the time it takes for the sequence to terminate is generally enormous. Indeed, the function giving the number of steps to terminate starting with n_0 in base 2 increases at a very rapid pace. For instance, if we start by writing n_0 = 4 in base b_0 = 2, the sequence takes 3โข2402653211 - 2 steps to reach 0, while if n_0 = 12, the number of steps needed is more than Graham's number.
But the real punchline is that while this theorem is true (according to standard set theory), it cannot be proven using the standard axioms of arithmetic. In a sense, the function described in the above paragraph grows too quickly for first order arithmetic to prove that it is finite for all n (note that it n price the function is finite for each n, by simply writing out the whole sequence, but this is quite different from proving the statement for all n simultaneously.)
One day I wanted to know what number times 666 would equal 121212. I found that same number did some other weird things
666ร182=121212
555ร182=101010
444ร182=80808
33ร182=6006
xxx182=2x2x2x
xx182=2x02x
I don't know what's up with 182, but it fascinates me.
bjsy92 ยท 1 points ยท Posted at 17:54:32 on May 25, 2016 ยท (Permalink)
It's more of a logical fact, but the fact that Commutativity is not universal which implies that the "frame of reference" impacts the logical axioms that rules it.
I know this thread is mainly for geniuses/brainiacs, but there's something my 5th grade Math teacher told me that has stuck in my mind forever: if you add up all the digits in a number, and the result is divisible by 3, then the whole number is divisible by 3.
103 = 1+0+3 = 4, so 103 is not divisible by 3.
105 = 1+0+5 = 6, so 105 can be divided by 3.
I know it's silly, but me being completely biased towards humanities makes me even prouder of the fact that at least I got this from elementary school mathematics :)
Budalla ยท 1 points ยท Posted at 18:00:14 on May 25, 2016 ยท (Permalink)
If you get 20 random people there's about a 50% chance of at least 2 of them sharing a birthday. The maths is easy if you calculate the chance of none of them sharing
Melba69 ยท 1 points ยท Posted at 18:00:20 on May 25, 2016 ยท (Permalink)
etc. and for a sequence of N ones, this is true in every base of N+1 or more, e.g. if the 1st example is in hexadecimal, its decimal equivalent is 17x17=289.
Take any arbitrary number with more than 1 digit, call it xyz. Add the digits to one another (x+y+z) =s. Subtract that number from the original (xyz)-s =abc. Then add those digits, a+b+c = T. That number, T, is always evenly divisible by 9. Example: 573. Add it up 5+7+3=15. Subtract from the original 573-15=558. Add those digits, 5+5+8=18. The sum is divisible y 9! /2=2. It works! Now, please tell me why this works.
onzie9 ยท 1 points ยท Posted at 18:01:59 on May 25, 2016 ยท (Permalink)
Take every integer, square it, and invert it. Add them all together. The answer is pi2/6. That is, 1/1+1/4+1/9+1/16+1/25+...=pi2/6.
I'm no fan of pi, but that is a decently cool place for it to show up. The two proofs I know of this fact are both found here. Euler's version is not rigorous (or, rather, it was not rigorous when he came up with it), but the Fourier transform method was solid from the start.
If you lay a map of a country down on the ground in that country there will always be one point on the map that lies exactly on its actual location in the real world. This is guaranteed in any country other than South Africa and Italy or any other I am forgetting which completely surrounds another nation.
142857 multiplied by any whole number 1,2,3,... will give you digits that are either a permutation of 142857 or digits that can be summed to create 142857. As the numbers get higher and higher this becomes more difficult but at numbers < 20 or so it's pretty clear.
MrMoe18 ยท 1 points ยท Posted at 18:04:25 on May 25, 2016 ยท (Permalink)
That to average guess salary real quick when someone says they make $12 an hour all you have to do is double that number and add three zeros assuming they work 40 hours a week. $12 dollars would equal to aboutish $24,000 a year before taxes and stuff. Its pretty easy and comes in handy a lot more then i thought.
If you take a calculator and type the top row of numbers backwards for example 987 and then subtract the top row of numbers but in the opposite direction for example 789, you get 198.
Now take the second row 654 and do the same, subtract the opposite, 456 you get 198.
Guess what for 321 minus 123? 198. Pretty simple but quite interesting too.
My favorite math fact, as an American, is that the English call it "Maths." Adorable. Also, since I am American, that is the extent of my mathematical knowledge.
Gabriel's Horn is a mathematical object which has a finite volume, but an infinite surface area. Mind blowing really.
daweber ยท 1 points ยท Posted at 18:08:50 on May 25, 2016 ยท (Permalink)
You can quickly find out what (9x1to9) are by putting your hands up in front of you palms towards you and putting the finger down that you are trying to multiply 9 by. For example 9x8=72 you put down your eighth finger and count the fingers before and get 7 and the fingers after and you get 2. The seven is in the tenths place and the two is in the ones place so it makes 72.
If anyone doesn't understand pm me and I'll try to explain it better or I'll send pictures
The fact that if you were to wrap a cord around the Earth (assuming it's perfectly spherical), and then you added one metre of cord, it would be able to be lifed about 16cm uniformly (or, in other words, the Earth woul have to have a radius 16cm larger for it to be wrapped tightly). The best pat is that this doesn't depend on the radius of the sphere, so it also holds true for, say, a basketball.
Sleyck ยท 1 points ยท Posted at 18:09:27 on May 25, 2016 ยท (Permalink)
0.9999999999999.... = 1
Because periodic numbers are written dividing them in 9 so 0.9 periodic would be 9/9 and that is = 1
qp0n ยท 1 points ยท Posted at 18:10:55 on May 25, 2016 ยท (Permalink)
"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14"
TLDR; Pi is eerily found in the chaos of nature.
[deleted] ยท 1 points ยท Posted at 18:10:56 on May 25, 2016 ยท (Permalink)
Probably won't be seen but I've always liked the concept of perfect numbers and if my programming is ever branched out of web development I'd love to find ways to discover more perfect numbers, if possible, but I bet people try already and it's hard as hell.
In between each number, from 1-9 there are infinite numbers.
It's a paradox of sorts. For instance, in between 3.1 and 3.2 is pi and so far... infinite.
[deleted] ยท 1 points ยท Posted at 18:11:42 on May 25, 2016 ยท (Permalink)
There is an infinite amount of numbers between 0 and 1.
This infinity is so great that it's impossible to even begin counting it since you could never find where to start, since there could be an infinite amount of zeros before the first real digit. (Ex. 0.0000...1).
Omvasu ยท 1 points ยท Posted at 18:12:11 on May 25, 2016 ยท (Permalink)
0.99999โฆโฆ=1
and the war began.
lite67 ยท 1 points ยท Posted at 18:12:19 on May 25, 2016 ยท (Permalink)
That there cannot be an infinite series of non-zero finite intervals regressing into the past.
TGentG ยท 1 points ยท Posted at 18:16:04 on May 25, 2016 ยท (Permalink)
Picked this one up in discrete math, the sum of all positive integers (IE 1 + 2 + 3 + 4 .... and so on) is equal to -1/12. Here's a numberphile which explains it.
a bit cliche, but it takes some mathematical maturity to understand its importance
youngrb ยท 1 points ยท Posted at 18:17:28 on May 25, 2016 ยท (Permalink)
I have been outside more than 10,000 times.
60 years - 8 years (supervised) * 365 days * 12 times outside per day = over a quarter million times. I have ten friends. If they are all roughly the same age, that is 2.5 million visits outside. No one has been hit by a meteor.
There are more numbers between 0 and 1 than there are rational numbers overall.
SmLnine ยท 1 points ยท Posted at 18:19:47 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + ... = - 1/12
Obviously the sum will keep increasing forever. But you can assign a finite value to it, and that value happens to be -1/12. If you're feeling skeptical:
This is not just some kind of mathematical trick, it has been applied to scientific problems in quantum field theory and string theory.
There are two completely independent ways to assign a value to the sequence above: zeta function regularization and Ramanujan summation. They give the same result.
If you graph y=ln(x) on 1/4 inch graph paper, with a scale of 1 integer every inch, if the paper stretched for one million miles, the graph of ln(x) would only be 24.9 inches above the x-axis!
Ln(x) is the wimpiest function ever! Yes, it is unbounded, so the y-axis technically approaches infinity, but to do so, the paper would literally stretch beyond the limits of the universe!
All prime numbers are multiples of six plus or minus one. And the Fibonacci sequence forms a repeating pattern of 24 numbers in base (or modulo) twelve. Ok, so that's two facts. But they are related facts.
this is more of a tip for elementary kids. all single digit multiples of 9 equal 9 when added together.
9 x 1 = 9
9 x 2 = 18 | 1+8 =9
9 x 3 = 27 | 2+7 =9
9 x 4 = 36 | 3+6 =9
and so on
In any base system, take base 10 for example, the first number in the base system will appear a gazillion times more than the last number in the base system in any valid statistics you take. It's how they know you faked an experiment or your experiment was flawed.
I figured this out in first grade for multiplying by 9.
If you take 9 x 5, the answer is 45. Two ways to figure this out, both the numbers (Excluding when multiplying by 11 or factors of 11), results in the numbers equaling 9 if added together.
Another cool trick is 9 x 4 = 36, take the 4, multiply it by 10 and then subtract 4 to get 36. This works for any single digit number such as 9 x 9 = 81, take 90 - 9 = 81.
9 x 8, 80 - 8 = 72
9 x 7, 70 - 7 = 63
9 x 6, 60 - 6 = 54
9 x 5 , 50 - 5 = 45
9 x 4 , 40 - 4 = 36
9 x 3, 30 - 3 = 27
9 x 2, 20 - 2 = 18
I was really good at multiplication in first grade.
Edit: I tried to explain this in front of my class and another girl did it the same way and we were both the "smart" ones so Im not sure if other people use this or not for multiplication.
There's fermat's last theorem which is either a tragic tale of lost mathematics that took 358 years to rediscover, or it's the most effective example of trolling in the history of mankind.
[deleted] ยท 2 points ยท Posted at 19:40:07 on May 25, 2016 ยท (Permalink)
I have evidence showing that Fermat had the proof but I'm on mobile and can't post it right now
This is rather simple, but always puts it in perspective for me: $1,000,000,000(1 billion) is simply 1,000 million. When thinking about $ it seems absurd!
I always found it odd that sequentially adding odd numbers together happens to match the values of the perfect square number set.
The number set of perfect squares f(n) = n2, (0,1,4,9,16,25,36,49...) is equal to the sequential sum of the odd number set f(n) = 2n-1 (1,3,5,7,9,11) starting at 0.
0+1=1, 1+3=4, 4+5=9, 9+7=16, 16+9=25, 25+11=36.
There was a girl who was 69 lbs. She thought she was 222 fat. Drove down 51st. Went to see doctor X, took the 8 pill and became 55378008. This is when you would turn the calculator upside down and it would read boobless... Or something like that.
There are more than 11,000 species of moths in the U.S. alone.
Moths make great mimics, presenting themselves as wasps, tarantulas, even praying mantis. Some moths even mimic bird droppings to make themselves appear less palatable.
Moths are important pollinators, day or night.
Some moths are born without mouths and never eat. Their sole purpose is to mate and lay eggs. Speaking of mating, males can smell a female from more than 7 miles away.
If you divide 1 by 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 (that's 999 quattuordecillion btw), the Fibonacci sequence neatly pops out.
2 + 2 = 4. It's (obviously) simple math, but it's fact. It's special to me because I've spent much of my life drowning in variables and non-constants, it took 30 years to realize that the stability I craved was that fact, and math, as fact, is in variable. It took me 30 years to realize that no matter how much I fight it, numbers are my favorite.
For base ten the entire multiplication table can be easily memorized with two number sequences.
01234567890
03692581470
Take the number you want and find the list with it closer to the beginning or end then read every number in sequence skipping the same number that you had to skip from 0 to reach it. Each time the number you are looking at decreases you add 1 to the 10s place.
Lets take 8
8 is -1 away from 0 in this list.
01234567890
So remove every other number
024680
Count backwards
0 8 6 4 2 0
Increase 10s place every time the number decreases.
00 08 16 24 32 40
crahs8 ยท 1 points ยท Posted at 18:29:57 on May 25, 2016 ยท (Permalink)
I have only ever needed to use Pi once in my life, and that was to calculate to price difference, per square inch, of a large circular pizza vs a rectangular party pizza. The first was over twice as expensive BTW.
And I believe that that one-time calculation likely means that I used pi one more time, on average, than the average american.
TL/DR - You can use the value of pi to calculate the value of pie.
[deleted] ยท 1 points ยท Posted at 18:30:59 on May 25, 2016 ยท (Permalink)
The finger multiplications for 9 is my favorite... Hold up both of your hands facing you... Think of a number 1-10 to multiply by 9. So say 3. Now starting from the left most finger of your left hand (thumb). Count down to the right 3 fingers... (Middle finger) then put your middle finger down. To the left of your middle finger there are 2 raised fingers... To the right of you middle finger there are 7 including the ones on your right hand... So you have the answer 27. Works for every number 1-10
[deleted] ยท 1 points ยท Posted at 18:31:21 on May 25, 2016 ยท (Permalink)
ii is a real number (if one takes the principal value of the arg function)
Sheldon: "The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
gnuchu ยท 1 points ยท Posted at 18:32:16 on May 25, 2016 ยท (Permalink)
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ยท ยท ยท is a divergent series. The nth partial sum of the series is the triangular number [snip]
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
You can, however, use certain summation methods to provide a value; these are special sums, however. The normal sum is divergent and does not have a value.
The sum of digits of multiples of 9 reduce to 9 (in Base 10 systems like ours). Take 9*43 = 387. 3+8+7 = 18, 1+8 = 9. This same practice works with any multiple of 3, because 3*3 = 9. Example: 3*614 = 1842, 1+8+4+2 = 15, 1+5 = 6, which is a multiple of 3.
The interesting fact is that this expands into any base system. If you're in a Base N number system, the sum of the digits of any multiple of N-1 will add up to a multiple of N-1, eventually reducing down to N-1. In addition, the factors of N-1 hold the same property that the sum of multiples will add up to a multiple.
Take Octal, base 8. The multiples of 7 have this property, but no other single digit number does. 14 in base 8 is 016, 21 is 025, 35 is 052, and etc.
Look at Hex, base 16. The multiples of 15 (0xF) do this, but so do multiples of 3 and 5. 100000 in hex is 0x186A0. 1+8+6+A+0 = 0x19, 1+9 = A, which is 10, which is a multiple of 5.
This has always been a favourite of mine: There are as many odd numbers in the universe, as there are odd and even numbers added together. It's a different way to describe infinity.
One milliliter of water is one cubic centimeter, which weighs one gram, which takes one joule to heat one degree Celsius which is one percent of the amount of energy to heat one gram of water from freezing to boiling.
(I think I've probably forgotten or messed up something. Sorry)
Perhaps my favorite is the Alabama Paradox, in 1880 they were figuring out how many congressional districts each state would have. If there were 299 representatives Alabama would get 8 spots. But if there were 300 representatives Alabama would get ONLY 7 spots.
So going to more representatives would mean Alabama would have LESS Spots.
jwor024 ยท 1 points ยท Posted at 18:42:03 on May 25, 2016 ยท (Permalink)
10 = 1
[deleted] ยท 1 points ยท Posted at 18:42:23 on May 25, 2016 ยท (Permalink)*
An infinite amount of time passes every second, so our thinking of either infinity or time are wrong.
If infinite implies something goes forever, that also implies it NEVER stops.
1=1 and 1 second = 1 second
Between every second that passes, all other variations of that second (.1 second, .11 second, .111 second, etc) happen infinitely before the next second. However, we KNOW the next second comes, we can measure it with a simple stopwatch. Infinite doesn't make any sense to me.
Not sure if this is a fact, but if an equation in the form az3 + bz2 + cz + d has two complex roots and one real root, the third root can be found easily by equating -b/a to the real sum of the two known roots and the unknown root.
Example: Suppose we are given the equation z3 - 4z2 + z + 26, and that one root is 3+2i (Hence 3-2i is implied to be a root as well).
So -b/a would be -(-4)/1= 4, therefore 4= (3+2i) + (3-2i) + x (Where x is the third root).
Hence the complex parts cancel out and rearranging the real parts to obtain x we get x= -2, which is the third root.
I remember using this in my exams, much quicker method than long division
I'm a little late for this thread, but my personal favorite is that anything multiplied by 5 is always half the number * 10. (Ex. 5 * 6 = 6 / 2 = 3 * 10 = 30) The opposite is also true when dividing, a number divided by 5 is always double / 10.
Anything that points out that as things approach infinity our ability to understand them intuitively dissolves. For instance 1+2+3+4+5+6+7... equals = -1/12
Basically, in certain situations how you go about choosing a random value affects the probability distribution of what that value might be, even if you don't change the pool from which the value is chosen. This would seem at odds without understanding because random implies that each value has an equal likelihood of being chose, so if you were selecting a random value from 1 - 100 each value would have a 1% chance of being chosen, but in some instances this breaks down.
Take for instance a factory that assembles cubes randomly with dimensions 0 - 1 unit, so at most they would be 1x1x1 cubes and at least 0x0x0 cubes (nothing).
A consequence of this method of production is that you should expect something with a volume of 1/8 or less to occur about 1/8 times because volumes are even distributed between 0 and 1.
However, side lengths are also evenly distributed between 0 and 1 and you would expect a side length of 1/2 or less to occur half the time, but this is the same as expecting a cube of volume 1/8 to occur half the time (because volume = side length squared).
The result is that we have what are apparently different probabilities of manufacturing the same set of cubes. The explanation for why this is the case is pretty tricky, and I honestly don't have a solid enough grasp on it that I can explain it to other people without working it out as I say it.
When multiplying a two digit number by eleven, you add the digits and put it in between the two values to find the answer.
It should look like this: xy X 11=x(x+y)y
Ex: 10x11=110
1(1+0)0= 110
13x11=143
1(1+3)3=143
52x11=572
5(5+2)2=572
It gets wonky when the middle digit is over ten, but still works. You just carry the one.
99x11=1089
9(9+9)9=9(18)9= (9+1)89=1089
66x11=726
6(6+6)6=6(12)6=(6+1)26=726
Virus64 ยท 1 points ยท Posted at 18:51:28 on May 25, 2016 ยท (Permalink)
One thousand is the first number in sequence to have the letter "a" in it.
That 99.9% of the time you won't have to use algebraic equations to pay $2.00 for candy at a store.
pemboo ยท 1 points ยท Posted at 18:54:00 on May 25, 2016 ยท (Permalink)
Would anyone be interested in a small series of videos outlining some of these facts with explanations and proofs? Obviously not the ones that have been done to death (ei.pi = -1)
If you multiply a number by the same number (number squared) it will always equal 1 more than the number before it and after it multiplied.
reki ยท 1 points ยท Posted at 18:57:57 on May 25, 2016 ยท (Permalink)
Bunch of interesting ones I heard from my friends. Not all of these are rigorously true, so mathematicians please excuse me if I'm butchering terms or simplifying things a bit.
1) Using bipolar coordinates, you can find the 4-volume of a 4-sphere. In fact, you can easily extend this for every even number, and you notice the constant factor of pi required increases by 1. Being a little more clever, you can actually write a formula that finds the N-volume of an N-sphere, for both odd and even N. You'll find that it ends up having a factor of piN/2 in there somewhere...the fact that you don't end up using half-powers of pi in odd-numbered dimension spheres results from the next fun fact.
2) Using the Gamma function to extend the factorial system, you find that the gamma function (and hence "factorial") of 1/2 is the square root of pi. Indeed, you find a factor of (N/2) factorial in the N-volume of an N-sphere equation as well, this cancels out nicely with the factor of a 1/2 pi you get from the other part of the equation for odd-numbered dimensions.
3) There are multiple kinds of infinities. There's countable and uncountable ones: the rationals are countable, the reals are not. More interestingly, general math assumes that the reals are of the class of the simplest uncountable infinities: aleph-1. The countable infinity is labelled aleph-0. There's an axiom we kind of just assume that there is no grade of infinity beyond aleph-0 and aleph-1, and using this system, you can generate an infinite number of sizes of infinities, labelled aleph-0, aleph-1, aleph-2, etc. But wait! That series is of itself, countable. What size of infinity is used to describe all of the set of possible infinities? Turns out, it can't be in that countable series describing sizes of infinities, because you run into contradictions. It's a whole another type of uncountable infinity.
4) While we think of the "mean" as an average of a collection of numbers, it has a mathematical definition that's formulated as an integral, making it applicable to continuous probability distributions. By messing with your probability distribution to undermine this integral definition, you can create a probability distribution that doesn't have a mean or variance (or any higher moments either): the Cauchy distribution.
5) A classic thought experiment: is it possible to hang a painting by strongs on 2 nails, such that removing either nail causes the painting to fall? How about for N nails, assuming a massless, frictionless string? The answer: yes! By creating a real-world analogue of a commutator, such as aba-1b-1, you can create such a system. It's not very practical though.
6) There are certain famous mathematical problems that have yet to be solved, such as the Riemann Hypothesis. Nobody knows if it's true or not, and we might not for some time. What we DO know, however, is that either it is true, or it's negation is true: the law of excluded middle. There are some subtleties that make this different than saying it's either true or false, but that's an issue of semantics. People have shown proofs and theorems for statements by first assuming the Riemann hypothesis is true, and using the consequences to prove the results; then, they turn around and assume the Riemann hypothesis is false and use the same consequences to prove the exact same result. Regardless of whether the Riemann hypothesis itself is true or false (or even undecidable), these theorems hold!
[deleted] ยท 1 points ยท Posted at 18:58:06 on May 25, 2016 ยท (Permalink)
I should not have got on this thread stoned.
20mcgug ยท 1 points ยท Posted at 19:52:08 on May 25, 2016 ยท (Permalink)
3 friends split a motel room for $10 each. The manager tells them the next morning they were having holiday special and the new teller last night was unaware, then gives them 5 singles. The friends take $1 each and give $2 to the breakfast cook. Now they paid $9 each and the cook got $2, where the hell did the other $1 go?
DeltaF1 ยท 1 points ยท Posted at 19:00:04 on May 25, 2016 ยท (Permalink)
If the digits in a number can be added up to reach a number divisible by 3, then the original number is divisible by 3.
For example: 8,965,271,586:
8 + 9 =17 +6 =23 +5 =28 + 2 =30 + 7 =37 + 1 =38 + 5 =43 + 8 =51 + 6 =57. If you can't easily identify 57 as divisible by 3, you can reduce again 5+7 =12. (you should be able to identify 12 as divisible by 3, but if not, then reduce once more.... 1+2=3)
[deleted] ยท 1 points ยท Posted at 19:04:27 on May 25, 2016 ยท (Permalink)
if p and q are primes, then (p/q)(q/p)=(-1)[p-1]*[q-1] *1/4, where (p/q) and (q/p) mean "p is a square mod q" and "q is a square mod p", which each have value 1 if its true, or -1 if its not.
I love that if you want to know whether a huge number is divisible by 3, just add up each digit. If that sum is divisible by 3, then the original number is also divisible by 3.
Example: Is 168354 divisible by 3? Yes, because 1+6+8+3+5+4=27, which is also divisible by 3. 168354/3 = 56118
If the individual digits of a large number add up to a number that is divisible by three, that number as a whole is divisible by three.
Example: 105: 1+0+5=6, six is divisible by three, therefore 105 is divisible by three.
[deleted] ยท 1 points ยท Posted at 19:06:09 on May 25, 2016 ยท (Permalink)
Leonard Euler made so many discoveries that a lot of his theorems are named after the first person after him to discover them.
gforret ยท 1 points ยท Posted at 19:07:28 on May 25, 2016 ยท (Permalink)
The fact that maths comes from mathematics which comes from the Greek mathฤmatikรก which means "all things mathematical". The รก at the end of mathฤmatikรก means it is plural. The way we use now refer to mathematics isn't really plural so when we shorten it, we should actually drop the s and it should become just "math".
I have no proof for it, but if you add up all the digits in a number and that number is divisible by 3 then the entire number is divisible by 3.
Example: 6783245 -> 6+7+8+3+2+4+6 = 36 which is divisible by 3. Therefore, 6783245 is also divisible by 3.
Ja89015 ยท 1 points ยท Posted at 19:09:38 on May 25, 2016 ยท (Permalink)
Not a mathematician here, just something that blows my mind. Pi works for calculating both the circumference and area of a circle. I get it that all circles are proportional and the ratio between the radius and circumference will always be the same no matter the size. And I understand that there's a direct relationship between the radius and area that is constant regardless of the size of the circle too. What blows my mind is Pi works for both and there isn't one constant for circumference and another for calculating the area.
Super easy one. If you are trying to find a percentage of a number the opposite is true. For example if you are trying to find 2% of 50 it is the same number as 50% of 2. Super basic. I really didn't even think about it until a friend told me the other day.
Dolly Parton gained 69 pounds. She said that was 2-2-2 much. She wanted to lose 51 pounds, so the doctor said take these 8 pills every day and it will leave you...
6922251x8=boobless
It's used to find the expected value of functions of a random variable when you don't explicitly know the function but know the distribution of the random variable.
Kolego ยท 1 points ยท Posted at 19:15:21 on May 25, 2016 ยท (Permalink)
I thought this would be the first thing people would mention, but I can't find it, so here it is: 1+2+3+4+5+ . . . = -1/12
Mad, huh! There's a great explanation here: https://www.youtube.com/watch?v=w-I6XTVZXww
EDIT: Spelling
You only need 23 people in the same room to have a 50% chance of 2 of them having the same birthday. It seems really counterintuitive, and it's very tempting to say it should be 365/2... but the key to it is that any 2 can have the same birthday.
I find stats which make extremely rare things near-certain similarly interesting. I listened to a podcast recently where a nurse was accused of poisonings because multiple patients had unexpectedly died of respiratory arrest on his watch in the span of a few months, and under nobody else's. Statisticians determined the odds of it happening were in the 1/100,000 range, but by taking into account the number of ER nurses in England and the number of arbitrary 3-month periods (I.e.: December-February, January-March, etc. For every nurse), there had been plenty more than 100,000 possible time periods during which this could've occurred. The nurse ended up being acquitted on appeal, I believe.
NGC660 ยท 1 points ยท Posted at 19:16:40 on May 25, 2016 ยท (Permalink)
I really like Mandelbrot's set. I like that in the initial set every part is the same but smaller, but the more you zoom in it creates some awesome wild fractals. https://youtu.be/PD2XgQOyCCk
It states that there are rather simple formal systems where some truths cannot be proven, but they still remain true. It actually was discovered while looking for exactly opposite result.
This has far-reaching consequences such as that you can't write a finite virus scanner that would run in finite time or be finite in size (this is better stated as halting problem).
Or that a human can't provably simply grasp some truths unless humans are somehow magic (because no steps lead towards such truth.
Jimp0 ยท 1 points ยท Posted at 19:16:55 on May 25, 2016 ยท (Permalink)
When doing mental multiplication, just break the numbers down into simple problems.
So 13x741=
10x700 = 7000
3x700 = 2100
10x40 = 400
3x40 = 120
13x1 = 13
Add em all together and u get 9633 which is 13x741. All you have to remember is your current total and the next step to take, so the answer goes 7000, 9100, 9500, 9620, 9633.
smbell ยท 1 points ยท Posted at 19:20:02 on May 25, 2016 ยท (Permalink)
.99999... = 1
Not that .9999... is close to 1 but they are actually equal.
This goes along with my other favorite fact, there is no smallest number greater than zero.
I'd elaborate but I'm on my phone.
iexpi ยท 1 points ยท Posted at 19:20:19 on May 25, 2016 ยท (Permalink)
ii = e-pi/2, which is approximately .2
[deleted] ยท 1 points ยท Posted at 19:21:21 on May 25, 2016 ยท (Permalink)
if you have a table on an infinite plane an a ball drops at a random place, the probability for it to hit the table is 0, but it still has a chance to happen
Late to the party because the number of the bus that I took to visit my sick friend was the smallest number expressible as the sum of two cubes two different ways and I was trying to remember which four cubes.
The arithmetic mean of the sum of measurements with any distribution converges towards the normal distribution as the number of measurements increases towards infinity.
Urcinza ยท 1 points ยท Posted at 19:26:51 on May 25, 2016 ยท (Permalink)
There are as many numbers between 0 and 1 as between 1 and infinity. Because a pair of "a and 1/a" one is beween 0 and 1 and one is between 1 and infinity.
Moreso physics, but whatever. Any moving object is moving back and forth in a wave-like motion. This is only noticeable on the atomic level, since the more massive an object is the smaller the wavelength is. So for example a car rolling down the street is till moving back and forth even though it appears to be moving straight
Rule of 72
To calculate the time it will take to double your investments, divide 72 by the annual rate of interest.
Eg. at 8% pa, your money will double in (72/8=) 9 years
The Four-Color Theorem: basically says that any map you draw, of any number of countries1, can always be colored with four colors, so that countries sharing a border2 have different colors.
(countries are assumed not to overlap, consist of multiple pieces, or contain other countries inside of them)
(where the border has length greater than zero, not just meeting at a point)
Proved only after enormous effort over many years, and all known proofs use large computations.
20mcgug ยท 1 points ยท Posted at 19:45:00 on May 25, 2016 ยท (Permalink)
If the sum of the digits of any number equals 9, then the number is divisible by 9. Example: 7,092 = 7+0+9+2 = 18 = 1+8 = 9, so 7,092 is divisible by 9. It doesn't even matter what order the numbers are in. 7,029; 9,072; 2,970; etc. are all divisible by 9.
Same works for 3 if the the sum is 3, 6 or 9. But fuck 3's.
colski ยท 1 points ยท Posted at 19:35:07 on May 25, 2016 ยท (Permalink)
ii = -0.208...
aperks ยท 1 points ยท Posted at 19:35:32 on May 25, 2016 ยท (Permalink)
ITT: So many people butthurt over the spelling of math vs maths.
TazStun ยท 1 points ยท Posted at 19:35:40 on May 25, 2016 ยท (Permalink)
The book Principia Mathematica proves 1+1=2. It only takes about several hundred pages.
People see the "s" at the end of Mathematics and think it's plural.
"Maths" is the incorrect way to spell/pronounce the shortened version of Mathematics. This is because "Mathematics" isn't plural, so you need to make it agree with a singular verb, not a plural one.
You don't say "Mathematics are amazing.", you say "Mathematics is amazing."
That numbers up to 999 where the 1st & 3rd number add up to the middle number are always divisible by 11, and not only that give you the answer of by how many
For example
484 = 4+4 = 8
and 11 goes into 484 44 times...
198 = 1+8 = 9
and 11 goes into 198 18 times....
451 = 4+1 = 5
and 11 goes into 451 41 times....
So if I say to you what is 36 times 11, you can show off by being a smart arse and say (3+6 =9, therefore the answers is..) 396
If you put a grain of rice on a square of a chessboard and doubled the amount you put on each succeeding square, by the end if you laid all the grains of rice you had end to end they would reach Alpha Centauri and back. 25 trillion miles there and 25 trillion back.
To check to see if a number is dividable by 3 (w/o remainder), add all of the digits and if the result number is dividable by 3, then the number itself is dividable by 3.
Ex: 123456789/3? 1+2+3+4+5+6+7+8+9=45, 45/3=15, therefore 123456789 can be divided by 3 without a remainder (the asnwer is 41152263)
This is also true of the sum of the big number so in your example 1+2+3+4+5+6+7+8+9= 45
45/3?
4+5=9
9 is divisible by 3 without remainder
Dalroc ยท 1 points ยท Posted at 19:39:38 on May 25, 2016 ยท (Permalink)
If we square a string of ones of length n, where 0<n<10, we get a number that goes from one up to n and then back down to one. It's easier to show some examples:
12 = 1
112 = 121
1112 = 12321
111112 = 123454321
11111112 = 1234567654321
1111111112 = 12345678987654321
The Fibonacci sequence, 1,1,2,3,5,8,13... is well known and has been mentioned several times in this thread already. What most people don't know though, is that any string of numbers where you add the last two together to get the next one will approach the golden ratio, phi, 1.618, when you divide a number by the one before it. It is not unique for the Fibonacci sequence.
Even if we start with, oh I don't know, let's say 3 and 761, the first 10 numbers we get are:
Someone will probably call me out for inaccuracies, BUT anyway: If there's a disease that only infects 1 in every 1 million people, and you get a test that is 99% accurate that confirms you have the disease, there's only a .01% chance you actually have the disease. I probably described it a little wrong, but it's the False-Positive Paradox.
sibbo11 ยท 1 points ยท Posted at 19:40:53 on May 25, 2016 ยท (Permalink)
If you take 0.5, halve it, and add it again and repeat, you will never reach 1.
E.g. 0.5 + 0.25 + 0.125 + 0.0625 .... you will never get 1.
The fact that some infinity's are larger than other infinity's.
That shit blew my mind when it was first explained. Cause it sounds like childish nonsense when it's first said in the above way. When it's explained it makes total sense
(for anyone confused: there are an infinite number of decimal point numbers between 1.0 and 2.0, but there is a larger set of infinite decimal point numbers between 1.0 and 3.0)
Complex numbers are also vectors. They're the 'missing link' between geometry and number theory - that's what makes them so useful. As a physicist it took way too long to realise that connection and every physicist I've told since had their minds blown.
Assuming sufficient randomness properties for the digits of pi, the Prime Number Theorem implies that with probability 1, infinitely many starting substrings of the decimal expansion of ฯ are prime (since the harmonic series diverges). So the existence of a single such string really isn't surprising at all.
Krisoz ยท 1 points ยท Posted at 19:44:35 on May 25, 2016 ยท (Permalink)
if you add a series of numbers twice and come up with a different answer (as check figure) and the difference between the answers is divisible by nine you have swapped two digits....
ie
27+16+15+21+19=98
27+16+51+21+19=134
134-98=36....36/9=4
as i recall this works for any number of digits or numbers
as a young pencil-pusher in the olden days i used this at least once.
i dont know why this works, i just put numbers in boxes on forms.
If only one number has switched digits (15 and 51 in your example), then the numbers can be represented as 10a+b and 10b+a. Say 10a+b>10b+a, thus a>b. The difference is then (10a+b)-(10b+a)=(10a-a)+(b-10b)=9a-9b, which is divisible by 9 and still greater than 0 because a>b
Voley ยท 1 points ยท Posted at 19:45:26 on May 25, 2016 ยท (Permalink)
We get the Maclaurin expansions of cos(x) and sin(x)
eix = cos(x) +i*sin(x)
Subtistite pi=x
ei*pi = cos(pi) + i*sin(pi)
cos(pi)=-1, and sin(pi)=0 so:
ei*pi = -1
or
ei*pi +1 = 0
Vega3gx ยท 1 points ยท Posted at 05:10:56 on May 26, 2016 ยท (Permalink)
I understand the Maclaurin expansion. The issue is that providing that to someone who doesn't already know it is like giving someone the equation to solve a word problem without explaining why. Let's be honest. Taylor & Maclaurin is a Calc II topic, and most Calc II students already know this formula.
If you want to know if a three numbered figure is divisible by three, you can add the three numbers individually and see if the result is evenly divisible by three.
So it isn't hard to believe that between every two rational numbers there is an irrational number (in fact infinitely many). And in terms of the cardinality of the sets, there are way more irrational numbers than rational ones.
But, and this is the part that still messes with me, between every two irrational numbers there's a rational number, too! In fact, infinitely many!
You can take any number over three digits (such as 56823) and add each digit together (= 24) and if the number you get can be divided by three, so can the original number. So 24 can be divided by 3 and 56823 / 3 is in fact 18941.
Yes it's applied to physics but without calculus we wouldn't be able to take derivatives to find them in the first place so I guess you could say it's a multi-topic fact
See I thought you just meant easy math, it didn't dawn on me to do that, thanks!
Aeleas ยท 1 points ยท Posted at 20:15:24 on May 25, 2016 ยท (Permalink)
9 * 11 = 99
9 + 9 != 9
What may be the case is that the sum of the digits of 9x is
9 * (1 + (x mod 10))
Lovehat ยท 1 points ยท Posted at 20:02:41 on May 25, 2016 ยท (Permalink)
8
[deleted] ยท 1 points ยท Posted at 20:04:45 on May 25, 2016 ยท (Permalink)
Take any two numbers two apart from each other like 6 and 8 and multiply them, 48. Then take the number in between, 7, and square it, 49. Following this pattern the number in between will always be one more than the two numbers two part multiplied.
We use a lot of big numbers in astronomy, and I find that millions/billions just get muddled together as "big number" in a lot of talks. This is the best comparison I've seen to communicate the immense different in scale in a way that people intuitively understand:
1 hundred seconds = just under 2 minutes
1 thousand seconds = just over 15 minutes
1 million seconds = just over 11 days
1 billion seconds = just over 31 years
Saying "it's the difference between 11 days and 31 years" does a better job to communicate the difference in scale than simply "it's a thousand times bigger".
[deleted] ยท 1 points ยท Posted at 20:09:24 on May 25, 2016 ยท (Permalink)
DearKC ยท 1 points ยท Posted at 20:10:49 on May 25, 2016 ยท (Permalink)
I wrote my senior thesis on the distribution on non-standard dice, as seen here
What I loved about this project was the patterns of average roll. The paper explains how the average of 1d6 is 3.5, 2d6 is 7, 3d6 is 10.5, etc. This also applies to 1d4=2.5, 2d4=5, etc and all of the other regular polyhedral dice. I don't know if I'd go so far as to say favorite, per se but I did greatly enjoy this and got to present it an AMA conference at Willamette University a few years back.
rezdm ยท 1 points ยท Posted at 20:11:48 on May 25, 2016 ยท (Permalink)
Say you have a rope tied around the Earth's equator such that it makes a circle touching the ground. How much additional rope would it take for that rope to float 1m off the ground?
You'd think a lot right?
The answer is only 6.3m.
So the circumference of the Earth is C = 2piR. You're adding 1m to the radius, so it becomes:
C' = 2pi(R+1) = 2piR + 2pi = C + 2pi
So given any circle, whether it's a cookie or the Earth, would take roughly 6.3m extra rope to increase the radius by 1m.
rezdm ยท 1 points ยท Posted at 20:12:49 on May 25, 2016 ยท (Permalink)
There are as many natural numbers (0, 1, 2, 3, ...) as there are integers (natural numbers and their negatives). There are as many natural numbers as there are rational numbers (a/b where a,b are integers and b != 0). However, there are more real numbers (numbers that can be expressed with decimals) in any interval than there are natural numbers.
I'm way late to this party, but, starting at 1, each square of a whole number is the just the previous square added to the next odd number.
1x1=1 (+3)
2x2=4 (+5)
3x3=9 (+7)
4x4=16 (+9)
Etc..
Sorry for explaining and formatting what is in my head like an idiot.
[deleted] ยท 1 points ยท Posted at 20:21:29 on May 25, 2016 ยท (Permalink)
there's a simple proof for it on numberphile YouTube channel. If you add all positive integers the sum is actually a negative fraction instead of infinity. It has applications in quantum mechanics.
All unique Pythagorean triples have a difference of an odd number squared between the hypotenuse and the even side. And in fact there are an infinite amount of unique Pythagorean triples for EACH odd square difference.
Poxx ยท 1 points ยท Posted at 20:22:28 on May 25, 2016 ยท (Permalink)
You can color the individual regions (countries, states, counties, etc...) of any map with only 4 colors and never have two of the same colored regions touch each other.
HaruAnt ยท 1 points ยท Posted at 20:33:43 on May 25, 2016 ยท (Permalink)
A single domino can fall and knock over a dominoe 50% larger than itself. If you continuously stack dominoes 50% larger than the previous in a line, by the 23rd dominoe the height will be the same as the Eiffel tower, by the 31st mount everest, and by the 57th the moon. And they would all be knocked over by tipping the first original dominoe.
haha, fair enough. OK, so 57.10113597 dominoes to get to the moon...as long as it is exactly 384,000,000m away. Also, assuming the moon is exactly 3474km in diameter, using 58 dominoes we would overshoot the other side of the moon by 165959.5km.
The coolest park is knowing that tipping the first initial 50.8mm domino would still knock over that huge 58th domino.....theoretically.
I know I know. But I'm bored at work and wanted to work it out. I actually just took it out of a book I'm reading and didn't check to make sure it was right. At least now I know I'm not spreading a lie haha.
lubbi ยท 1 points ยท Posted at 20:42:55 on May 25, 2016 ยท (Permalink)
When two halves is gone, there's nothin' left. And you're right, it's a little ole worm, who wasn't there. Two nothin's is nothin'. That's mathematics, son! You can argue with me, but you can't argue with figures! Two half nothin's is a whole nothin'!
There is ALWAYS an answer, even when the answer is a range, indefinite number, etc. There is always an answer. Also, you can easily ace most multiple-choice algebra tests by plugging the provided answers into the equation - the answer should be equivalent on both sides of the equation. TMYK...
The one that blows my mind still is this:
If you were to assign a letter value (1=a, 2=b... 26=z) to every number in Pi (or any other irrational number), somewhere in that number is ever single word you have ever spoken, in order. It contains every book ever written and that ever will be written.
I'm fascinated by how the decimal versions of 7ths (1/7, 2/7 ... 6/7) all consist of the same looping 6-digit sequence of numbers (142857), the only difference being the start point in the loop:
The birthday paradox!
In a room of 23 people it's 50% chance that two people share the same birthday (day and month, not year unless of course everybody in the room is born the same year, like a school class)
With 70 people the probability is 99.9%
I also like the fact that there are more possible ways to shuffle a deck of cards than seconds it has been since the big bang
There are an infinite amount numbers between 1 and 2 (1.3, 1.5387, etc) but there are also an infinite amount of numbers between 1 and 5. The difference between one and five is greater, even though both differences are infinite.
[deleted] ยท 1 points ยท Posted at 20:55:01 on May 25, 2016 ยท (Permalink)
1x1=2 Howard method
nmagod ยท 1 points ยท Posted at 20:55:43 on May 25, 2016 ยท (Permalink)
Any fraction (Say 14/37) multiplied by the denominator (37) equals the numerator (14)
I never had a single decent mathematics class in my life and this is the kind of thing I figured out on my own
More of a physical property. But Im endlessly fascinated by the fact that when firing photons one after another from 2 sources, they make the same pattern that should only mathematically happen if they were being sent all at once as a wave. Entanglement has so many weird implications, since the light is entangled beyond time does that mean that light exists out of time? When a photon is released does it instantaneously reach is destination from its perspective?
Interesting fact: the number of megabytes of an email message grows with the rank of the perceived importance of the role of its sender, while remaining inversely proportional to the importance of its content.
Oh god, childhood C-average-in-math me is having a fucking nightmare scrolling through this thread.
alio84 ยท 1 points ยท Posted at 20:59:08 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+....r = -1/12
Usted11 ยท 1 points ยท Posted at 20:59:09 on May 25, 2016 ยท (Permalink)
Weird thing I found out being bored in class is if you square a number 22 is 4 you can find the square of 3 by adding the number you squared and the number you are trying to find the answer of to the answer.
[deleted] ยท 1 points ยท Posted at 20:59:11 on May 25, 2016 ยท (Permalink)
(10 * 9 * 8 * 7 * 6)/(5+4+3+2+1) = 2016
halsar ยท 1 points ยท Posted at 20:59:50 on May 25, 2016 ยท (Permalink)
1+1=3
[deleted] ยท 1 points ยท Posted at 21:02:35 on May 25, 2016 ยท (Permalink)
There exists a function (or more properly, a distribution), called the Fermi-Dirac function, for which the following holds:
f(x) = โ where x=0 (the function value is infinity, in case it doesn't show up)
f(x) = 0 where xโ 0
What's more interesting, is when you take the integral over this function from negative infinity to infinity, the result equals 1.
Mathemathically speaking I've yet to come across a use case for it, but it is used quite a lot in physics, especially in Quantum physics and Electricity & Magnetism.
h_west ยท 1 points ยท Posted at 21:03:13 on May 25, 2016 ยท (Permalink)
Using degrees, sin(666) = cos(666)= - phi / 2 where phi =( sqrt(5)-1)/2 is the golden mean. This is exact!
you can only do these steps if it converges, which it doesnt.
nulloid ยท 1 points ยท Posted at 21:04:37 on May 25, 2016 ยท (Permalink)
If you have an infinite series of 1, 2, 3, .. and you try to add them together, with a few clever math tricks, you get -1/12. This result is actually used in some physic problems. See this wiki page
gwot ยท 1 points ยท Posted at 22:44:19 on May 25, 2016 ยท (Permalink)
Its a bit of a maths card trick with an infinite series see wiki here
But IIRC you basicaly re-express the series as an alternating series: 1-2 + 3 -4 + .... and with a bit of algebra you get to -3x = 1/4, (if x was the original series), so x = -1/12
The fact that literally no maths above basic addition, subtraction, multiplication, and division are necessary in the average adult's life from day to day.
xHarryR ยท 1 points ยท Posted at 21:07:29 on May 25, 2016 ยท (Permalink)
Finally someone else who says this! haha
the_0wl ยท 1 points ยท Posted at 21:07:00 on May 25, 2016 ยท (Permalink)
Take arbitrary points A,B,C,D and connect them to form a Quadrilateral. Draw a square on the outside of each side. Connect the middles of the squares on opposing sides. Both line segments you get this way are the same length and perpendicular to each other.
Illustration
It's less a maths fact and more about physics, but the explanation is mathsy. If the well-known theory is correct about their being an infinite number of universes, this does not mean that any possibility you can come up with exists in one, despite what people think, because infinity doesn't necessarily work that way.
Basically it can be explained there being an infinite amount of numbers between 0 and 1, 0.1, 0.01, 0.001, you see where I'm going here.
ITT: "If you do the math, this math fact makes perfect sense and isn't that cool"
I didn't come here for things that make sense, I came here to be amazed god damn it!
zaqwsx3 ยท 1 points ยท Posted at 21:09:30 on May 25, 2016 ยท (Permalink)
I like the fact that:
1 x 1=1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111=1234321
[deleted] ยท 1 points ยท Posted at 21:09:35 on May 25, 2016 ยท (Permalink)
The Chinese were the first ones to develop the Pythagorean Theorem. Since western ideas were first to be taken into account; Pythagoras was selected for the name of the equation. The Chinese history is largely fragmented due to the different dynasties and wars. Pascal's triangle is also to have been in place centuries before Pascal.
Assuming that the other person is constantly and randomly roaming around, it's theoretically better to constantly wander around if you wanted to look for them, as compared to standing still in the same spot.
If you want to add a series of numbers together that are in a row you multiply the last number by the next higher number and divide by 2. So 1+2+3+4+5 = (5*6)/2 = 15. Go as high as you dare!
lozzero ยท 1 points ยท Posted at 21:13:03 on May 25, 2016 ยท (Permalink)*
It's trivial, but kids love it, and if it gets them in the mood to start a lesson, who can judge?
If you take any large number and repeatedly add the digits until you get a single digit (e.g. 456; 4+5+6=15; 1+5=6), if you end up with 3, 6, or 9, the original number is divisible by 3.
Another fun one is for multiplying by 9. Put your hands out in front of you, palm down. Put down your ring finger on your left hand (the second along from the left). You'll have 1 finger to the left and 8 fingers to the right. 9x2=18. Put down your pointer on your left hand (fourth along) and you have 3 to the left and 6 to the right. 9x4=36.
It is also really funny to watch a bunch of kids (or drunk adults) put their hands in front of their face and count their fingers.
You can use different kinds of math for different things, such as calculating what kind of bird you're looking at, calculating the best flavor to add to a meal, or even calculating the size of something!
This has either been said or will get buried, but, one of the most useful calculations I frequently do is convert pounds to kilograms. Here's the secret: add 10% and double it (same as multiplying by 2.2).
I also have a really simple estimation for Celsius/Fahrenheit that's close within a 1/10th of a degree if anyone is interested.
The number 82000 in base 10 is equal to 10100000001010000 in base 2, 11011111001 in base 3, 110001100 in base 4, and 10111000 in base 5. It is the smallest integer bigger than 1 whose expressions in bases 2, 3, 4, and 5 all consist entirely of zeros and ones.
Easy trick for multiplying a number by 11 write the number on the far right add that number to the number directly to its left. Then add that second number to the one to its left and so on until the last number which you simply write down. Any double digits as answers when adding the tens spot gets carried.
So it is something like this:
2837702 ร 11=
Not exactly a maths fact, more like a... numbers fact. Youtube uses a base 64 number system for their video id's (that string you see at the end of a youtube url, consisting of characters A-Z, a-z, 0-9, -, and _). And with just 11 such characters, which is what youtube uses, it has enough url's for every person on the planet to upload a new video every minute... for 18,000 years.
The difference between the squares of two consecutive numbers is the sum of those numbers.
For example: 3 squared is 9, and 4 squared is 16. 16-9=7, and 3+4=7
I learned two from high school, both involving squares.
When squaring numbers ending in a 5, take any digits to the left of it, multiply that number by (that number+1), and tack a "25" on the end of it as two digits. Ex. 852 = (8 * 9=72), and add "25" at the end = 7225. 1252 = (12 * 13=156), and add "25" at the end = 15625.
For squaring numbers consisting of only ones (i.e. 11, 111, 1111, etc...), the answer is a sequential number of digits (starting at 1) equalling the number of ones being squared, and then tacking on digits that descend back to the number 1. 111 has three ones, so the answer is 12321, 11112 is 1234321.
For all "odd" number magic squares, one solution is just simply placing the middle number of the series and then adding/subtracting the next number in sequence in a diagonal direction (wrap around and end) and move up/down one square when you run out of room.
This method works for all odd squares. There is one for even numbers too but I don't remember what the sequence is.
In a number sequence there is only one known number in existence that sits between the square of a number and the cube of another number; i.e 1,2,3,4,5,6,7... Can you guess what the number is?
[deleted] ยท 1 points ยท Posted at 21:34:31 on May 25, 2016 ยท (Permalink)
The fact that without it we would never have got off planet earth, not would we have any complex technology
I 'find it sufficiently counterintuitive that [I] question or reject it.' lol. I'm an engineering student though so it doesn't really effect me. Great fact either way
nthai ยท 1 points ยท Posted at 21:38:43 on May 25, 2016 ยท (Permalink)
We know that e and pi are irrational. But we don't know if e+pi or e*pi is rational or not. But we do know that if one of them were rational the other would have to be irrational.
Here's a few: multiply 11 x a 2 digit number very quickly. Note x y in the example below is not x times y but a two digit number where digit 1 is x and digit 2 is y. X and y can be equal here no problem.
11 (x y) = x, (x+y), y as the 3 digits. If x+y is a double digit number, add 1 to x, to keep the 2nd digit of the sum of the two numbers in the middle. It's hard to write out as a formula so I'll give some examples.
11 x 45 = 495
11 x 47 = 517
11 x 74 = 814
11 x 36 = 396
The area of a circle with a circle cut out of the middle is equal to the area of a circle whose diameter is a chord on the outer circle and tangent to the inner circle.
Example
Area of black disc is the same as the blue circle.
haigins ยท 1 points ยท Posted at 21:45:50 on May 25, 2016 ยท (Permalink)
Let x be represented as follows: x = x1x2x3x4x5... where xi is the ith digit of x.
Ex. if x = 45 then x1 = 4 and x2 = 5
If x is divisible by 11 then x1 - x2 + x3 - x4 + x5 + ... = 0
if x is divisible by 9 then so is x1 + x2 + x3 + x4 + x5 + ...
no matter how long the number, if you add up all of the numbers in it and it is divisible by 3, then the number is divisible by 3.
Example 720 7+2+0=9 9 is divisible by 3 which means 720 is divisible by three.
It works really well for using maths to prove statements. For instance, if someone says "Knowledge is the key to success"... I'll come back with "and knowledge is power... therefore, power is the key to success... life solved with math"
Another one "time is money, and money is the root of all evil, therefore time is the root of all evil"
I think I am the only one who finds it funny, but I still enjoy it.
NSFWdw ยท 1 points ยท Posted at 21:48:33 on May 25, 2016 ยท (Permalink)
IF you give a topologist a mug of coffee and a donut, they won't know which to drink and which to eat.
A number is divisible by 3 if and only if the sum of its digits is also divisible by 3. (This result is best proven by induction.)
The same result holds for the number 9.
Each integer power of 11, ie. 11โฟ for some integer n, has 1 as its last digit.
Somewhat similarly, the last digits of powers of 9 alternate between 9 and 1.
Lastly, if two positive integers end in the same digit, all their powers will end in the same digit too. And unlike all the above results, this result is true for any base number.
I wash them with sanitiser that kills 99.99%, or 99,990,000 of them.
I now have 1,000 bacteria on my hands.
...... which are resistant to that level of exposure antibacterial agent in the sanitiser and quickly multiply again. A few more rounds of this is how you get bacteria that are strongly resistant to antibiotics.
It's extremely easy to prove there are an infinite number of primes, taking note of the fact that the first prime, and only the first, is actually even (2).
Suppose the number of primes was finite. Now multiply all these primes and add 1. Done.
You know this number can't be divided by any of the primes you had before because it was made up of all of them, but now it's larger by 1, which is smaller than any prime and no matter by what prime you divided that's what you'll be left with.
Note that the number you get will likely be much much larger than the largest prime in your finite list. It's not a given that it actually will be prime since between the largest prime on your finite list and the monster you created will be many many numbers that could be prime and might divide your monster.
All the proof shows is that if there ever was a 'last' prime, it's impossible that no primes come after that, because if none of numbers afterwards were prime, your unholy monster would have to be one.
These types of numbers are called Quaternions. They are related to the simple complex/imaginary numbers you learn about in school and were the predecessors to vectors.
while multiplying a number with 10n , just add n zeroes to the number after it
5 * 100 = 500
6*10000 = 60000 etc
buggy65 ยท 1 points ยท Posted at 21:53:02 on May 25, 2016 ยท (Permalink)
For some reason I always loved the Birthday Problem. At a party (or classroom) with 23 people in the room? There's a greater than 50% chance that 2 of them share a birthday.
buggy65 ยท 1 points ยท Posted at 03:36:05 on May 26, 2016 ยท (Permalink)
There's a really good wikipedia article on it. It's NOT the probability of someone matching your birthday, its that somewhere in the room two people will match. Basically it's easier to think about it in reverse, how many people can you stick in a room without someone sharing a birthday? The probability that one person alone in a room doesn't match another person is 365/365 (1 of course), the probability 2 people in a room don't match is 364/365, 3 people not matching is 363/365, ... , the 23rd person not matching is 343/365 ways. So all together in one room is (365 x 364 x 363 x ... x 343)/(36523 ) = 0.49, a 49 percent chance of NOT matching! Another simpler way to think about the problem is how many dice can you roll before ANY two of them match? 6/6 x 5/6 x 4/6 = 0.55 chance not matching with only 3 die, with 4 die we drop to 0.27 chance of two not matching!
colbymg ยท 1 points ยท Posted at 21:53:59 on May 25, 2016 ยท (Permalink)*
The equation:
1/2 < floor( mod( floor(y/17) * 2^ (-17 * floor(x) - mod(floor(y),17)) ,2) )
for 0<=y<=106 and k<=x<=k+17
where k is some giant number with about 600 digits.
depending on the value for k, you can literally have it display anything you want in that 17x106 area as pixel art. A series of smiley faces, your name, etc. The 'Everything' Formula
cstreak ยท 1 points ยท Posted at 21:54:13 on May 25, 2016 ยท (Permalink)
lazyl ยท 1 points ยท Posted at 22:59:28 on May 25, 2016 ยท (Permalink)
By definition.
D-Shap ยท 1 points ยท Posted at 21:54:23 on May 25, 2016 ยท (Permalink)
E2(pi)i (e as in 2.718281828... i as in root of -1)= 1
It combines four different realms of math, whole numbers, circles, irrational numbers, imaginary numbers) into one simple beautiful equation.
fam1ne ยท 1 points ยท Posted at 21:56:57 on May 25, 2016 ยท (Permalink)
When multiplying by 9 the product when added equals 9. I had figured out this trick way back when I had learned multiplication to "cheat" and know multiples of 9 when tested. For instance 9x15=135 1+3+5=9. It never really came in handy other than learning multiplication when I was in grade school but always found it odd
This may be incredibly late to the party, and potentially already mentioned, but my favorite fact in math is that there are just as many numbers between 1 and 2, or any neighboring numbers for that matter, as there are numbers period.
For example, if you were to attempt to list every possible decimal point between 1 and 2, it would go on indefinitely.
"If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told it's two, and that cannot be."
26 is the only number that is inbetween a cube (33) and a square (52)
JM8289 ยท 1 points ยท Posted at 22:17:06 on May 25, 2016 ยท (Permalink)
Not sure how true this fact is but i heard every time you shuffle a deck of cards, the chance that the order of the cards has even once been replicated is incredibly small.
The number is so small, that it's perfectly safe to say "it's never happened before in the history of humanity and will never happen again" (assuming the deck was shuffled well).
There are 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 different possible combinations for the order of a deck of cards.
yuoopwe ยท 1 points ยท Posted at 22:22:15 on May 25, 2016 ยท (Permalink)
2+2 DOES NOT = 5
Dazz316 ยท 1 points ยท Posted at 22:22:55 on May 25, 2016 ยท (Permalink)
What's that fact that if you have three cards you have 1/3 of choosing the correct one. But if you choose wrong, take that card away and choose between the remaining two you still have 1/3 chance of choosing the right card or something.
Your playing a game with a friend and and they put 3 cards down, 2 black and 1 red and they know the position of each and you have to find the red. You choose one of the cards (not flipping it over) then your friend flips one of the black cards over and give you the option to choose again, the odds of the red being under the one you chose previously is 1/3rd while the odds of it being under the other remaining one is 2/3rds.
Dazz316 ยท 1 points ยท Posted at 22:47:04 on May 25, 2016 ยท (Permalink)
Right this is the thing I don't understand, how does the old decision affect the new one? I Rkinda get it but the new decision involves 2 cards. The previously chosen card has been ejected and is now non exisitant in the new decision.
No. Here is a video of a person doing it 100 times and showing 71% of the time switching won, 29% of the time staying won (which is close to 66% and 33%).
Dazz316 ยท 1 points ยท Posted at 23:28:57 on May 25, 2016 ยท (Permalink)
Well it doesn't actually show us though. But I've looked up others and seems you're right.
Say we have 3 cards, 2 black 1 red and you want the red:
First say you choose a card, then look at it then the two other cards. You expect to get the red 1/3rd of the time.
Second, say you choose a card and I flip over a black card and then you look at your card. Nothing has changed from the first time except the order the cards have been flipped over. You still expect to get the red 1/3rd of the time.
Third, say you choose a card, I flip over a black card then hand the other card over to someone else. As before, you're expecting to get the red card 1/3rd of the time, so clearly the other person has to get the red card 2/3rds of the time.
Dazz316 ยท 1 points ยท Posted at 23:46:00 on May 25, 2016 ยท (Permalink)
Yes but that's to say these happens each time. So we have outcoms 1 2 and 3 here.
How does it have to land 1,2&3 1,3&2 etc. Why not 1,1 then 3? or 32 then 1? There's again a 1 inn 3 of any of these happening each time. Chances are higher not getting all three than getting all 3.
ravenQ ยท 1 points ยท Posted at 22:23:33 on May 25, 2016 ยท (Permalink)
e{i \pi} + 1 = 0
I got ton, but this one blows my mind.
Spiv5 ยท 1 points ยท Posted at 22:24:03 on May 25, 2016 ยท (Permalink)
I think that the mobus loop is pretty cool, if thats a maths trick
Might seem like a boring fact but it means if you know 25 squared is 625, then you know 26 squared is 625+25+26 = 676. Can make for some easy mental math sometimes. I just like it cuz I thought it was like a magical math thing i invented when i was in school.
The classic birthday paradox. If you have a room with 50 people in it, two of you have the same birthday.
What helped me grok it is that it's the number of pairs in the room, and pairs aren't consumed on use. So person #1 compared with #2 through #50. Then person #2 compared with #3 through #50. And for every birthday that someone has, no one else can have it or you have two people with the same birthday, so just by having 50 people you have 316 possibilities, and 1,225.
It's a classic, but I didn't see it listed here yet. But it's not even probability, but more of a graph theory problem.
I dont know how mathy this really is, but the discussion of the Monty Hall problem in this thread reminds me of The Island of the Blue-Eyed People. I have to reeeally stretch my mind to make sense of that one.
I like that 7 is the first (whole) number that doesn't evenly divide into 360 (the number of degrees in a circle). The second number to do that is 11. They both are non-terminating and repeating values, 0.01944444444~4 and 0.03055555555~5 respectively.
But if you add 7 and 11 together, they equal 18, which is 1/20th of 360, and does divide evenly into it. (0.05)
I secretly suspect that mathemagicians, geometers and numerologists have raved about this fact since the dark ages.
If you could fill the horn with paint (which you should be able to because it's a known finite volume) and the paint could soak through to the other side, you could paint an infinitely long surface with a finite amount of paint.
I know, i know, not really but its still pretty cool.
you actually cannot fill the horn completely with paint because at one point the diameter of paint atoms will be wider than the diameter of the horn creating a block and leaving an infinite length of horn unfilled. A horn is even a bad example because that needs a medium to travel through. A medium which at one point will be too think to enter the narrower parts of the horn.
To me, every single math fact is fucking amazing. Think about it. 1 + 1 = 2 is true here, there, and anywhere in the universe. The value of pi is the same in any place, in any language, in any representation. Using maths, we've effectively created a universal language. If we want to talk to aliens, we can communicate to them by using math facts.
You can easily square two digit numbers as long as the last one is a 5.
You always take 5ร5 and put it to the end. Then multiply the first digit with itself +1. Then just write them next to each other.
x52 = x ร (x+1) and 25
Example: 652 = 6ร7 and 5ร5
6ร7 = 42 5ร5 = 25
This means: 652 = 4225
I remember my first math tutor told me that the sum of any number, however large, adds up to a number divisible by 3, then so is the entire number. Example, 123,456,789. 1+2+3+4+5+6+7+8+9=45. Because 45 is divisible by 3, so is 123,456,789
if you have 20 books on a bookshelf, the number of ways you could arrange those books is 2,432,902,008,176,640,000. For reference of how big that number is, there are 100,000,000,000 stars in the milky way.
My favorite is that any natural number {1, 2, 3, ...} can be written as the sum of four perfect squares. For example, 15 = 9 + 4 + 1 + 1, 24 = 16 + 4 + 4 + 0, etc.
The proof I'm most familiar with uses properties of convex bodies in 4 dimensional space and their interactions with lattices -- basically studying objects in a different area of math results in this beautiful piece of number theory in a wonderful, unexpected way. Also you need at least 4 squares to write every natural number in this way; for example, there's no way to write 15 as the sum of just three squares.
It's insane that two irrational numbers and an imaginary number end up as such a simple number. It's called Euler's identity if you want to look up videos on why it works.
[deleted] ยท 1 points ยท Posted at 23:02:20 on May 25, 2016 ยท (Permalink)
You can multiply 25 by any number easily. Take the number you're multiplying and divide it by 4. Then add 2 zeros to the number. If you have "1" remainder, then add 25, "2" remainder then 50 and "3" remainder then 75.
Here's an example:
25 x 66 = 66/4 = 16 with a 2 remainder. 1600+50=1650
Probably too late to the party but I like the fact because it it practical.
If you have a wobbling table on a static surface (uneven floor without steps) then there is a position of the table within a rotation of 90 degrees such that the table no longer wobbles.
Fibonacci sequence and its occurrence in nature. I barely learned about it this year because the Fibonacci sequence is one of the topics our outreach group attempts to teach kids in elementary schools. Now I constantly find myself picking up pinecones, brussel sprout stalks, and flowers to count the number of spirals; without fail, the number always falls within the sequence. Sure wish I learned about it earlier!
I heard this once on some TV show about the morning announcer team, at some chool that had Warthogs as a mascot. They had a trivia competition one episode, and this fact kind ajust stuck with me.
If you multiply any number full of ones (eg. 1111) up to nine ones with another number of ones, you will receive a palindrome with the highest number in the palindrome, being the lowest number of ones you used in one of your numbers.
Fourier law stating that any periodic function under the Dirilicht conditions can be constructed using a sum of sinusoidals of varying frequency, wavelength and amplitude. This means you can take sine waves to sum up to make. Square wave. Furthermore every aperiodic function can also be estimated using these methods. Doing this allows one to observe any waveform as a function of frequency which is very interesting. This idea has some remarkable applications ranging from thermodynamics, image processing, sound, signals, communications, etc.
An irrational number raised to an irrational power can yield a rational result.
We know that โ2โ2 has to be either rational or irrational. If itโs rational then our task is done. If itโs irrational, then ( โ2โ2 )โ2 = 2 proves the statement.
Not really a math fact, but indicial notation is awesome. It allows you to present long and tedious matrix calculations in a very compact and simple form.
[deleted] ยท 1 points ยท Posted at 23:30:02 on May 25, 2016 ยท (Permalink)
The infinite monkey theorem does not state that you are guaranteed to get any string of text. It states you have a probability of 1 of getting any string of text.
You also have a probability of 1 that if you select a real number at random that it's irrational. Claiming the infinite monkey theorem means you're guaranteed the works of Shakespeare is like saying rational numbers don't exist (inside the reals).
Constellations, the form of the 7 sisters, IP network reconfiguration protocols and dating algorithms are all tied together with the same basic math in graph theory.
fantumn ยท 1 points ยท Posted at 23:34:43 on May 25, 2016 ยท (Permalink)
The gap between perfect squares increases by 2 each time and is always odd.
Ants are really good at counting. They can work out how far they've walked by counting the steps they've taken, they can work out what job they need to do by counting how many ants are doing each job, and they can work out the size of an area by walking around randomly and counting how many times they're in the same place, which they use to check the quality of potential nest areas.
I don't know much about mathematics, but I love the Gaussian integral. I love the fact that the total area under the curve of e-x2 is root(pi). I've taken enough calculus to know what that means philosophically, but I've never tried to actually go about solving it.
thezim ยท 1 points ยท Posted at 00:02:48 on May 26, 2016 ยท (Permalink)
In a room of just 23 people thereโs a 50-50 chance of two people having the same birthday. In a room of 75 thereโs a 99.9% chance of two people matching.
A little less than 1ft is approximately the distance that light travels in a nanosecond. I think it's the best way that I've found to wrap my head around the scale of 1 billion.
The actual distance is 0.914...ft
[deleted] ยท 1 points ยท Posted at 00:23:40 on May 26, 2016 ยท (Permalink)
Right now, it would have to be the central limit theorem. The sum of n independent and identically distributed random variables becomes normal as n tends toward infinity. This is not only remarkable in and of itself, but also is important for many practical reasons.
[deleted] ยท 1 points ยท Posted at 04:14:32 on May 26, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 04:44:35 on May 26, 2016 ยท (Permalink)
Fair enough. However, this is Ask Reddit, and not my probability final. These details are not so important to statisticians, since all useful random variables have well-defined variance. As for how the sum is normalized, obviously I'm talking about the sample mean. I'm not sure how you could suggest this is only "vaguely" right, but OK.
rboy31 ยท 1 points ยท Posted at 00:25:27 on May 26, 2016 ยท (Permalink)
.9 recurring = 1
[deleted] ยท 1 points ยท Posted at 00:34:51 on May 26, 2016 ยท (Permalink)
A great and fun mathematical fact is this: The "size" (or cardinality) of the set of rational numbers is equal to that of the set of integers. And the cardinality of the power set of the natural numbers (that is, the set of all subsets of the natural numbers) is equal to that of the real numbers. Amazing.
If you take every number in the Fibonacci sequence and devide it by the number before it, the higher you go, the closer you will get to Phi.
ElGoorf ยท 1 points ยท Posted at 00:40:36 on May 26, 2016 ยท (Permalink)
ITT: Grammar Nazis but no math[s]
JPfreak ยท 1 points ยท Posted at 00:43:17 on May 26, 2016 ยท (Permalink)
If you multiply 11 by a two digit number, you take the two digits, add them and place the sum in the middle and that's the answer. Eg 11x23 =253 (2+3=5) If the digits add to a two digit number, you just add a 1 to the front of the final sum. Eg 11x29 = 319 because 2+9 is 11, so it will be 2119 if you don't carry the one, but when you do it's 319. It's a bit hard to explain when typing on mobile but I think it's a cool trick worth sharing.
Not exactly a fact, but the popcorn function is a really cool looking function that's defined as: f(x) = 1 if x = 0, 0 if x is irrational, 1/b if x is rational and x=a/b in lowest terms. The graph of the function from x = 0 to 1 looks like popping popcorn!
10 = 7+3. "Every even number can be expressed as the sum of two primes" is not the same as "every way of expressing an even number as a sum of two numbers implies the two numbers are prime."
Stolen from the last time a similar thread came up:
The Collatz Conjecture is an unproven theory which states that with any given number, that number can be reduced to 1 through two steps: if the starting number is even, divide by two. If odd, multiply by 3 and add 1. After repeating these steps enough times, any number will reduce to 1. For example, let's start at 10. 10 is even, so we divide by 2 and get 5. 5 is odd, so we multiply by 3 and add 1 to get 16. 16 divided by 2 is 8, then 4, then 2, and finally, 1. This theorem has been proven for every number up to 1060
[deleted] ยท 1 points ยท Posted at 01:29:09 on May 26, 2016 ยท (Permalink)
I have one, although I am terrible at math and everyone probably knows this one, but multiplying 9 by any of the digits 1-9 will give you a 2 digit number that adds up to make 9.
Sterling's Approximation (wiki here). It basically says that in the limit as N increases to infinity,
N*ln(N) - N -> ln(N!)
Edit: Formula. Forgot ln(N!) instead of just N!.
It basically makes the field of statistical mechanics possible as the approximation is treated as exact due to N generally being on the order of >6.022x1026.
Okay you smarty pants. Please explain the "mother nature" factoid. Like I know that some shells are mathematically correct. What is this and how does this work?
Think of all possible numbers between 0 and 1. The number is infinite, yes? Now think of all possible numbers between 1 and 2. This is also infinite, yes? But NONE of the numbers that appeared between 0 and 1 will EVER appear between 1 and 2, despite there being an infinite number of each. MIND BLOWN!
Even when we take something like the ordinals or the surreals, where ฯ is well-defined, it's not the largest member of the class. For that matter, taking ฯฯฯฯฯ... until it reaches a fixed point isn't the largest member of the class, because you still have the successor operator to rely on.
What890 ยท 1 points ยท Posted at 01:48:43 on May 26, 2016 ยท (Permalink)
I can't remember what it's called but when you measure 3' from a corner one way, then 4' in the other direction, and when you measure between the ends of those lines it should equal 5' to assure the corner is square. Sorry I'm a math idiot but I've used this when I've built shit
*Correct, the limit of 1 - ((x-1)/x)x as x approaches infinity is 1 - (1/e)
If I remember correctly you end up using the "sandwich" method for that proof, and it was a good one.
Fact: British and Australians say Maths, Americans (US) and Canadians say Math, but only Americans (US) spell Favorite, all you others add the "u".
[deleted] ยท 1 points ยท Posted at 06:24:08 on May 26, 2016 ยท (Permalink)
Probably the present value of an annuity certain formula. It's a great way to forecast how much your money will accumulate to of you invest it properly. The formula is accumulated value = (annual payment amount)(((1 + interest rate)number of payments-1)/ interest rate) For example, if you are 24 years old and make a 5000 investment at 8% on your 25th, 26th ... to 65th birthday, you will have $1.4 million dollars at age 65.
In Pascal's Triangle, on the Nth row, the first row being the 0th row, if N is prime, then all of the numbers on that row (excluding the external 1's) are multiples of said prime number.
Multiply 9 by any number (except 0) and the sum of the digits which make up that number will eventually give you 9.
E.g. 9 * 9 = 81, 8 + 1 = 9; 9 * 56 = 504, 5 + 0 + 4 = 9; 9 * 213 = 1917, 1 + 9 + 1 + 7 = 18, 1 + 8 = 9. Ouala!
This is a pretty simple one I worked out at school. Everything multiplied by 9 equals a number that when added together, equals 9 or a multiple of 9. Then add that answer and it will equal 9.
More of a history math fact, but when Pythagoras and his people found out there was such a thing as irrational numbers, they had people keep it a secret because it went against how they explained the cosmos. The first guy who spilled the beans? Yeah, he was sailed out to sea and then thrown overboard. The first martyr of mathematics. From "God created the Integers".
[deleted] ยท 1 points ยท Posted at 12:30:36 on May 26, 2016 ยท (Permalink)
This is more geometrical: The length of one side of a triangle is always smaller than the summation of the lengths of the other two sides. I've used this pretty simple and basic rule countless times on navigation (such as finding shortcuts).
0.(9), the repeating decimal with all 9's to the right of the decimal point (forever), is equal to 1. There are lots and lots of good reasons for this, but to some people it "looks wrong" and it's fun to listen to them try to explain why.
DDekker ยท 1 points ยท Posted at 22:33:58 on May 26, 2016 ยท (Permalink)
Dont know why but I love the fact that square root 2 is irrational
To invert a digit's order of numbers in a multiplication table, you have to subtract 5, multiply by 10 and then add 0.5 to the digit.
Example:
1. 6*4=24
((6-5)*10+0.5)*4=10.5*4=42
2. 7*2=14
((7-5)*10+0.5)*2=20.5*4=41
Jacobak ยท 1 points ยท Posted at 19:04:51 on May 30, 2016 ยท (Permalink)
I'm so late BUT 18 is the only number who's digits add to be half of itself. Like, DAMN 18!
There is only one smooth structure (up to diffeomorphism) on Euclidean space when the dimension is anything but 4, but when the dimension is 4 there are uncountable many distinct smooth structures which form a continuum.
Man, I just like singing that quadratic formula song we learned in math class. That's like the only thing I can remember because of that song - it is forever stuck in my head.
[deleted] ยท 1 points ยท Posted at 14:49:19 on May 25, 2016 ยท (Permalink)
Girls require time and money : Girls = timemoney.
time is money: Time = money
therefore: Girls = moneymoney = (money)2
Money is the root of all evil: Money = โEvil
Therefore: Girls = (โEvil)2
Girls = Evil. QED
[deleted] ยท 1 points ยท Posted at 15:15:01 on May 25, 2016 ยท (Permalink)
the Fibonacci spiral. it's fucking crazy, a sequence of numbers that make a spiral that is commonly found in nature and shit. it goes like: 0 1 2 3 5 8 13 21 34 55 by adding the previous number to the current one. shits crazy bro
gaggzi ยท 1 points ยท Posted at 14:53:34 on May 25, 2016 ยท (Permalink)
Gabriel's Horn : Spin the function 1/x around the x-axis, and make it infinitely long.
You would be able to fill the horn with a finite volume of paint. But it would require an infinite amount of paint to cover the surface area. Hence, you can fill it, but not paint it.
_Eerie ยท 1 points ยท Posted at 16:24:16 on May 25, 2016 ยท (Permalink)
I can't imagine how does it look like. Well, it is a horn. But how is it infinitely long but has volume?
This one is incredibly lame, but it blew my mind when I was about 8 or so. I'm not sure how true it actually is, mind you.
0.99999999... = 1
By the logic that 0.333333... = 1/3, 0.66666666... = 2/3, and thus 3/3 would follow the trend being 0.9999999... however 3/3 reduced is one.
I'm going to get down-voted to hell for this, but any way you look at it bernie Sanders has lost the election to Clinton. She leads by 3 million more votes, over 250 pledged delegates (excluding supers), has won the majority of states and virtually all large states. Has won the majority of open primaries and has a more geographically diverse win. Even if you account for the caucuses, and give Bernie extra votes becuse of "closed" primaries, she would very likely still be leading at this point.
DaJanzk ยท 1 points ยท Posted at 14:59:31 on May 25, 2016 ยท (Permalink)
.9 repeating to infinity actually does equal 1.
ok so let n = .9 (w/vinculum)
assume 10n = 9.9 (w/vinculum)
subtract n from the 10n side (.9 with vinculum from the 9.9 side)
now you have 9n = 9
divide both by 9.
that gives you n = 1
since n also equals .9 repeating forever, 1=.99999999999999999999...
rysto89 ยท 1 points ยท Posted at 15:08:23 on May 25, 2016 ยท (Permalink)*
You can graph a 3-D cone with a curved profile that has a volume that converges to a real number, but has a surface area that diverges to infinity.
In other words, you can fill this cone but never paint it. I think this concept is explained in Cal III
EDIT: mixed up SA and volume. Apparently this is called Gabriel's Horn. Thanks to narcolepticasian
I could be wrong so don't quote me on it, but didn't you get that backwards? It sounds like you're talking about Gabriel's horn, which has infinite surface area but finite volume. You get it by having 1 over x to a power that is greater than 1 (it might be equal to 1 also but I feel like that's not right) and then rotating that graph over the x axis. It's in Calc 2 and also something that really interested me.
It's also the same for fractal patterns. They repeat a continuously smaller pattern ad infinitum, this having infinite perimeter but a finite area. In a 3D fractal, this results in a finite volume but infinite surface area. Theoretically it would be impossible to paint, yet could actually be the size of a pine cone in volume.
Obviously, it's a moot point in real world because there is a hard limit of lowest size (atoms building said pattern), and thus there will be a point at which we can say the fractal pattern had ended and can work out the perimeter.
acc7x3 ยท 1 points ยท Posted at 15:09:34 on May 25, 2016 ยท (Permalink)
That using base 12 you can count to 144 using both hands.
Phalanx on hand 1 represents each number, Phalanx on hand 2 represents each 12. Using your thumbs as place holders.
"You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I'll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame!"
โ Scott Smith, Ph.D. University of Florida
Obviously once you get to row 6 (1 5 10 10 5 1), this doesn't map directly to the actual number. But if you start from the rightmost digit (treating it as the ones place) and work your way to the left, the property still holds:
You know they say all men are created equal. But you look at me and you look at Samoa Joe and you can see that statement is not true. See, normally if you go one on one with another wrestler, you got a 50-50 chance of winning. But I'm a genetic freak and I'm not normal. So you got a 25 per cent - at best - to beat me. And then you add Kurt Angle to the mix, your chances of winning drastically go down. You see, the three way at Sacrifice you got a 33 and 1/3 chance of winning. But I, I got a 66 and 2/3 chance of winning cause Kurt Angle knows he can't beat me and he's not even gonna try. So Samoa Joe, you take your 33 and 1/3 chance, minus my 25 per cent chance and you got an 8 and 1/3 chance of winning at Sacrifice. But then you take my 75 per cent chance of winning if it goes one on one and then add the 66 and 2/3 per cent chance, I got a 141 and 2/3 chance of winning at Sacrifice. See Joe, the numbers don't lie and they spell disaster for you at Sacrifice.
You can add zero, subtract zero, and multiply by zero. But if you divide by zero the unholy demons of academia will rip your atoms apart and step in your potato salad and then the universe will implode.
This is my fave fact too! The sum of all positive integers from 1 to infinity equals -1/12.
It's not too hard to understand when it's broken down; it's a play on math theorems. It manipulates a couple different number series to come to the -1/12 conclusion. So interesting doe. Maths, man. Maths.
[deleted] ยท 1 points ยท Posted at 16:16:09 on May 25, 2016 ยท (Permalink)
That 50% of all statistics are made up on the spot.
That there are 10 types of people. Those that understand Bianary and those that dont.
za419 ยท 1 points ยท Posted at 16:17:28 on May 25, 2016 ยท (Permalink)
And those who weren't expecting a base 3 joke
[deleted] ยท 2 points ยท Posted at 17:00:20 on May 25, 2016 ยท (Permalink)
Get a single and run for home. that... that was a nerd joke too! ha! BOOM!
[deleted] ยท 1 points ยท Posted at 12:30:22 on May 26, 2016 ยท (Permalink)
For example, from 0 to infinity is a smaller infinity than from negative infinity to positive infinity. There are other types that are bigger than that too.
0.9999... (.9 repeating) is equal to EXACTLY 1.
It's not "almost 1."
It doesn't "approach 1." It doesn't approach anything! It IS 1.
I wasted hours arguing with an idiot on Facebook about this.
My favorite maths fact: "Math" is bizarrely called "maths" in some ancient back-woodsy parts of the world that never would have invented jazz if it jumped up and bit them in the ass.
The Monty Hall Problem is one of my favorites... but probably only because I got it, while at least half of my Prob & Stat class didn't. It took me a bit to grasp it, to be honest, but once i got it, it was like, duh!
SQLDave ยท 1 points ยท Posted at 17:34:54 on May 25, 2016 ยท (Permalink)
What let me finally "get" it and what I use to explain it to people (mostly successfully) is to change the problem from 3 doors to 100. The key then is that Monty doesn't open ONE door, he opens ALL BUT ONE door (which in a 3-door game is the same thing). Suddenly they realize that the prize almost HAS to be behind the door Monty did not open.
Folding a standard piece of paper 20 times will make it taller then Mt. Everest. Fold it 42 times to get to the moon and 103 times to be as tall as the universe.
G3POh ยท 1 points ยท Posted at 18:31:48 on May 25, 2016 ยท (Permalink)
Don't know if this applies but i was amazed when i heard that story about a rich man offering a poor man a job at whatever salary he desired.
So the poor man asked for a penny the first day of work and for the rich man to double that everyday for a month, comes out a millionaire or something like that at the end of the month.
The fact that there are as many even numbers as whole numbers is really interesting. Because there are both an infinite number of even number and an infinite number of whole number, there are just as many even numbers as whole.
infinity/2 = infinity
[deleted] ยท 1 points ยท Posted at 20:02:49 on May 25, 2016 ยท (Permalink)
That Pi, as an infinite non-repeating number, contains somewhere within it (encoded somewhere in it in ASCII or another format of your choosing), the unbroken narrative of your life.
Everything that happens to you, everyone you meet, everything you achieve or fail to do, is right there.
There's no reason to believe that. Infinite non-repeating numbers don't necessarily contain every possible string of numbers possible.
For example:
0.123456789112233445566778899111222333444555666777888999 etc. is an infinite, non-repeating number that will never have 13 in it, or any string of numbers exept for xx or x(x+1)
Pi is finite. The decimal expansion of pi is infinite. And no, this does not mean that the decimal expansion of pi contains every finite string of decimal digits. This is conjectured to be true, but has not been proven.
Edit: Actually, that guys math seems a little sketchy to me. I don't think you can just append something on to the end of a divergent set the way he does when trying to disprove 'the trick'.
Based on math. The series 1+2+3+4+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
Ok, that's what I figured. It's just your made up interpretation of what certain words mean. Neither math, or a fact. Just semantics.
[deleted] ยท 1 points ยท Posted at 14:28:58 on May 26, 2016 ยท (Permalink)
Just stating round-off happens everywhere and there is no way to get exact integers. Or to be 100% confident in them.
Not an "interpretation" its a fact.
This is why we have a standard for everything, even constant have uncertainty.
The semantics are important and not to be glossed over.
[deleted] ยท 1 points ยท Posted at 00:41:30 on May 26, 2016 ยท (Permalink)
Let's say you have three doors to choose. One of them has a car behind it.
If you choose a door, and then told the car is not behind one of the remaining two doors you should change your answer 66% of the time I think.
So for example left right and middle door. I pick the left door, and then I'm told the car is not behind the middle door, there is a 66% chance I should change my answer to the right door.
this is to a greater degree a measurements certainty, however in the event that there is a 1 in x possibility of something occurrence, in x endeavors, for substantial numbers more than 50 or thereabouts, the probability of it incident is around 63%
1-(1-1/x)x
For instance, if there's a 1 in 10,000 shot of getting hit by a meteor in the event that you go outside, on the off chance that you go outside 10,000 times, you have a 63% possibility of getting hit with a meteor sooner or later. In the event that there's a 1 in a million shot of winning the lottery and you purchase a million (arbitrary) lottery tickets, you have a 63% possibility of winning.
Alter: for the lottery illustration, the watchword is arbitrary - no doubt in the event that you deliberately purchase each conceivable mix then it's 100%. In the event that you purchase one ticket in a million distinct lotteries, or a million haphazardly produced tickets for any one in a million lottery, then it's 63%.
Because it's a mass noun. Mathematics is a singular thing. Linguistics agree that it is a mass noun. There are not multiple mathematics. There is one mathematics and there is one algebra and one geometry and one calculus. There are descriptors of each but each is singular.
Alright, so back to the first argument, you're stupid.
I'll explain why : linguists don't dictate how language works, they merely study it. People do. Language is primarily a way of communication, and we strive to optimize it all the time, be it by simplifying it or by organizing it. There are two branches, descriptivists and prescriptivists. The first ones think that if a majority uses a certain word to describe something, then that is the meaning of the word. The second ones believe in choosing a meaning and sticking by it. The only problem is that language evolves all the time, favouring the first branch.
And really dude ? A whole country is wrong and you're right ? You can't be this deluded
Back to my original argument there is an entire field dedicated to the study and research of language and it's evolution and they are calling you retarded.
NeilZod ยท 18 points ยท Posted at 20:12:38 on May 25, 2016 ยท (Permalink)
Here's the thing: since at least the end of WWII, the US has been sending all sorts of things to the UK to try to get them to speak like Americans; things like movies, TV shows, and even Ruby Wax. During that time, the Brits have responded by continuing to speak like Brits while they retaliated by exporting Piers Morgan. You might even say the Brits are responding as if they invented the language.
So where do the linguists fit in? They'll happily record what the Brits are doing with their English and what the Americans are doing with their English. Those linguists are diligently working to identify the rules that everyone is following, and they're interested in whether we are following different rules.
So how does that help us here? Linguists know that Brits shorten mathematics to maths while Americans shorten it to math. Linguists would likely advise you to write math in American English and maths in British English. You may well ask what advice linguists would give to people writing on the Internet. I suspect that they won't tell you what to do - instead, they will wait to see what all of us decide on and then try to figure out why we did it that way.
But you really should never expect a linguist to deride someone for using their native English.
Wait do you guys call it mathematic? Because maths is an abbreviation of mathematics, hence the 's'. Unless I'm misunderstanding your point completely (quite possible).
Lunnes ยท 0 points ยท Posted at 15:28:50 on May 27, 2016 ยท (Permalink)
It's always funny how Americans try to criticize foreigners because of a grammatical mistake, yet most of them can only speak English. Try speaking four languages and see if you don't make small mistakes sometimes.
No, it is not true. The series 1+2+3+... diverges. There are other ways of associating values to infinite series, and a few of these ways associate the value -1/12 with the series 1+2+3+... But this does not mean that 1+2+3+...=-1/12.
You almost qualified it completely, but no the sum of all positive integers is trivially divergent. The Ramanujan sum of those integers has that value.
Not really, the sum is divergent to infinity. It's fairly easy to prove so. Also it is a (relatively trivial) theorem in analysis that a series of nonnegative terms must (if it converges at all) converge to a nonnegative number.
This leads to an interesting question: Which maths brain do you trust more, Ramanujan and bunches of other mathematicians, or the author of this article? Personally, I'm inclined to side with Ramanujan et al.
No sane mathematician claims that the sum of all natural numbers is -1/12. In some situations it makes sense to assign it that value, but under the normal definition of infinite sum it is obviously not equal to -1/12. It isn't difficult to prove this.
This is what you get when you go outside the "normal" realm of Mathematics and accept something that we deem impossible by regular standards, similarly to how we accepted that i2 = -1 and continued from there to get a whole bunch of useful complex stuff.
It's not. The sum diverges to infinity, as one would expect. Using zeta functions you can replace the sum with -1/12 but in most contexts it doesn't make any sense
The sum is -1/12. You need not use zeta functions. Using basic algebra and substitution you can show that. Watch the video I linked or go through the wiki article.
A simpler proof is that 1 + 2 + 4 + 8 + ... = -1.
S = 1 + 2 + 4 + 8 + ...
2S = 2 + 4 + 8 + ...
1 + 2S = 1 + 2 + 4 + 8 + ... = S
1 + S = 0
S = -1
QED
Everything in that proof is mathematically legal
Edit: I'm not saying if you add up all positive numbers you'll get -1/12. I'm saying you can prove that the sum is equal to -1/12.
You didn't remove numbers you changed the order and scale. When you multiplied by two you screwed it up. But that's not really the point. You can't do addition as you normally would with infinity.
You can in a series, just not every series. Convergent series have a finite value. Divergent series tend towards infinity and you can't just multiply infinities. You should go to the askamathematician subreddit for a detailed answer.
[deleted] ยท 0 points ยท Posted at 20:51:38 on May 25, 2016 ยท (Permalink)*
There is no inconsistency. Multiplication is defined on real numbers, and in general series are NOT real numbers, they are just series. In the case of convergent series then they can been seen as real numbers, which allows us to multiply and add them. But divergent series cannot been seen as real numbers, so you cannot multiply or add them.
... in general series are NOT real numbers, they are just series
But all multiplication can be defined as a series.
...divergent series cannot be seen as real numbers, so you cannot multiply or add them.
We do multiplication on numbers that aren't real... That's the only reason you're typing this message to me (AC electricity.) Unless you're telling me you can add real numbers and get a category of non-real numbers. That seems super sketchy as well.
We do multiplication on things that aren't real numbers. In the case of complex numbers we are lucky that multiplication works out fine. In fact it is nearly identical to how it works on the real numbers.
However in the case of series it is much harder to suitably define multiplication and addition in a consistent way, and to show what rules it follows. Using only addition and multiplication of real numbers, how do you define multiplication and addition of series?
What I'm asking is, given to series A=sum of a_i and B=sum of b_i, what is A+B? If c is some real number, what is cA? You could also ask what AB is, but you never multiplied two series together in your proof so it isn't needed.
I'm not sure why the sum of two series is unclear. Is it supposed to be something other than the sums of the individual series? Sums are defined as term by term addition, and addition is associative, so you can combine the series term by term, assuming they cross the same space (1 to 10 and 1 to 10 and not 1 to 10 and 2 to 5.)
As for scalar multiplication on a series, that's very well defined by distribution. A * (B + C) = A * B + A * C, (at least in my experience) no matter what space you're in.
Well if A is a series, which I assume you know what a series is, then A is some sum of a1 + a2 + a3 + ... + an. B is similarly defined. Therefore if C = A + B and A and B cross the same space, then C = a1 + a2 + ... + an + b1 + b2 + ... + bn, and since addition is associative, C = a1 + b1 + a2 + b2 + ... + an + bn. If they don't cross the same space then there will be an extra series at the end containing the difference (again, term by term.)
I apologize, but I feel like I'm talking to a middle schooler, having to explain what a series is...
You never said infinite series. You just said series.
Likewise, I can still say the same thing. Just add a "+ ..." to the end and everything still makes sense. Call it a proof by induction and the fact that addition is still associative.
Let me say this again slowly, because apparently you don't get it.
A == a1 + a2 + a3 + ...
B == b1 + b2 + b3 + ...
C = A + B = a1 + (A - a1) + b1 + (B - b1)
C = (a1 + b1) + (A - a1) + (B - b1)
Can you take it from there? As for the apparent inability to multiply series by a scalar, are you saying that two times the sum of reciprocal squares is not necessarily two times the square of pi divided by 6? Because it is. Because that's how math works. 2(a + b + c + ...) = 2a + 2b + 2c + ... though I'd love to see anyone try to dispute that statement and say it's not allowed for some reason.
You haven't defined anything there. Saying C=(a1+b)+(A-a1)+(B-b1) relies on knowing what series A-a1 is, and then know what (A-a1)+(B-b1) is. But the latter is summing series. You can't define the sum of 2 series as a different sum of 2 series, it's circular. Can you state clearly what the nth term of the series corresponding to A+B is?
As for scalar multiplication, that happens to be as easy as you have said. Adding series is also easy but I'm wanting you to explain it so I don't put words into your mouth. Normally the sum of two series (sum of an from n=0 to infinity)+(sum of bn from n=0 to infinity) is given by sum of (an+bn) from n=0 to infinity, i.e. you jsut add the corresponding terms together. I have been asking if this is what you mean and you haven't answered.
If I have to tell you that a is a number and b is a number then I think we're done here. If you can't even make basic connections that the presence of an addition sign between two symbols when we're discussing infinite summation implies strongly enough that you can believe my symbols represent numbers (real, imaginary, purple, whatever you want to call it) then I have no business trying to discuss anything further with you.
I belive your symbols represent infinite series, which are absolutely NOT real or complex numbers (they aren't even a field).
I get paid to teach this stuff to undergrads, and am published in this field (more specifically functional analysis). DO not patronise me, I know this area far better than you. It is you who has completely failed to explain what you mean. I kept asking you are yes or no question which you refused to answer.
I feel like I should just give up and stop repeating myself. Do you know the difference between A and an in the examples? A is the series, and an is an element in the series. That's how I came to the definition that A is the sum of terms a1, a2, a3, ..., all the way to an. You're welcome to say the little "a" is a series all its own, which is technically true, as it's a series of one element or an infinite series that sums up to some value an. We know of plenty of series with finite value that you could manipulate (with multiplication, oohh) to be any of the summing terms aboce. Here is one example, and I know I'm being sloppy and not rigorous, but it's about all I can handle after having to teach an undergrad teacher who doesn't even know that he hasn't been asking yes or no questions
Anyway, take the sum of reciprocal squares. We know it adds up to a sixth the square of pi. If you double the sum of the series, you get a third the square of pi, right? That's been proven by smarter people than I. Well what is multiplication? Multiplication by definition is adding something to itself. So what do you get when you add (1 + 1/4 + 1/9 + ...) + (1 + 1/4 + 1/9 + ...)? Looks to me like one third of the square of pi. But wait, I'm not allowed to put ellipses in the middle of an equation because reasons! Even though these are well defined sequences with a given pattern, it isn't allowed because it looks weird. Ok, then rearrange term by term (as I've explained, we can do this because a + b + c + d = a + c + b + d. It's the basis of addition.) So we get 1 + 1 + 1/4 + 1/4 + 1/9 + 1/9 + ... and hey! We only have one ellipse at the end. Even though that ellipse represents twice as many digits, it's still infinite, so we haven't changed anything or truncated anything or obfuscated anything. I just made it look prettier for you. And the sum is still a third the square of pi.
Also, throwing around your professorship only makes it a little sad that I'm having to explain this stuff to you. Don't ever tell someone "believe me because I have a degree in this stuff and teach it to 18-21 year olds for a living." It's logically useless and senseless to do, not to mention a little arrogant.
Unless you're saying that the individual terms a1 to an are each their own infinite series and you're asserting that I can't add them because it's senseless to add infinite series therefore my A, which I defined as literally the most generally defined series imaginable (the sum of some numbers) is undefined or circularly defined. So that'd be pretty funny.
I have never said that the little a's are series, they have always been the terms in the series. I have used capitals to refer to series in all my posts.
I'll ask again because you seem to be refusing to answer. This is a very simple yes or no question. I think I know your answer but I don't want to put words into your mouth.
Is the series corresponding to A+B the series sum of (an+bn) from n=0 to infinity, where A is the sum of an from n=0 to infinity, and B is the sum of bn from n=0 to infinity? YES OR NO?
are you sure about that? he had no intention of actually telling me why I was wrong. He was just trolling me so he could post it here later.
[deleted] ยท 3 points ยท Posted at 21:41:35 on May 26, 2016 ยท (Permalink)
No, I don't believe that's what he was doing. He was hoping that you would see what's wrong. Sometimes the best way to teach is to guide someone to understanding that what they thought was correct was not. Now this is not always the best way as it doesn't work with everyone. He could have done a better job, yeah. But this is the Internet, and those kind of discussions often work best in real life, face to face.
No. I know your math was wrong, so I know somewhere you were going to make a mistake. I think I know where your mistake is as well, you assume that the left shift operator applied to series with initial term 0 is equal to the identity operator, which is proveably false.
rjem ยท 2 points ยท Posted at 23:24:00 on May 25, 2016 ยท (Permalink)
So that goes back to the "you can't do these normal things that our entire number system is based on in these specific circumstances because we don't like the results" that other people explained.
The number systems we usually work with don't include infinite values at all. If you do want to include infinities (which is sometimes very useful) then you have to change the rules slightly to avoid contradictions.
And infinite series aren't actually numbers, they are infinitely long lists of numbers. You have to do some work to make sure that a series is nicely-behaved before you can start manipulating it in the way you were doing. For example, the series
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...
actually does converge to a finite value, but if you simply reorder the terms to, say,
1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + ...
(taking the first two positive terms, then the first negative term, then the next two positive terms, then the next negative term, and so on) then it converges to a completely different finite value. You could try coding it up if you don't believe me.
2*n is a value even when n is infinite. In that case it just so happens to be n.
So infinity = 0? Or does infinity break the rule that x - x = 0, for any x? One way or another, we have to change the ordinary rules of arithmetic if we treat infinity as a number.
I didn't treat infinity as a number. I treated the series as a number. You said the series is infinite. You also can't say the series is equal to infinity, which means your substituting my "S" for your "infinity" doesn't hold as a valid substitution. It's a circular argument. If S is infinite then you can't add or subtract it. Well yeah. You can say the limit is infinite, but I'm not concerned with the limit. And you can say the only way we can look at infinite series is by looking at the limit. And I can ask "why?" and you'd say "because it's been the only way to approximate all of these other series." and I would say "but you know that's not mathematically rigorous."
I didn't define S as a partial sum or a limit. S is the sum. And it looks to me like a number. That number is -1. Show me the step that is not allowed.
You said you would talk about the mistakes then flat out didn't talk about any mistakes lol.
Right. The sum of a series is the limit of the partial sums of the series. That limit does not exist. Go ask on /r/math about this. We'll be sure to tell you exactly why it doesn't work.
I still don't see where the math falls apart. You're basically saying "hey you can't do that. Why not? Because it's wrong. Well why's it wrong? Because it is. You just can't do that."
I'm not saying that if you add up all non-negative powers of 2 beginning with 20 that you'll get -1. I'm saying that the sum of the series 1 + 2 + 4 + 8 + ... is equal to -1. Similar to how there is no real reason for 0.999... to be equal to 1. It is so because we say it is so. It's useful for us to define it that way, therefore it is. You aren't saying that if you add enough nines you'll get to 1. You're just saying that the existence of an infinite number of 9s means the value is 1.Likewise, adding positive numbers will not get you a negative number, but we aren't explicitly breaking any rules, and it is useful for us to do so, therefore it is.
If your method works, then you can replace the first part with S = 1 + 2 + 3 + ... = -1 and it would give you the same result.
So if my method worked, I could assume my conclusion? If I started out by stating that the sum of natural numbers were -1 then it wouldn't make sense to say that it's anything later in the proof because you already asserted that it's -1.
This is the reason you can't just assign values to divergent series so otherwise you would be able to prove that any divergent series would equal -1 using your proof. Using similar proofs you would be able to say that any divergent series is equal to any number you want, which would be blatantly false (since you would be able to get things like 1 = 2, which is a contradiction).
The math falls apart because you assume S is a number, it isn't. That sum is divergent. Ramanujan sums assign finite values to divergent sums but they aren't true sums.
PazDak ยท -7 points ยท Posted at 14:49:05 on May 25, 2016 ยท (Permalink)
That it is Math. I know Math comes form Mathematics, but can you think of a another word where you when shortening it you still carry the s?
It isn't used in a plural sense in our language. Think of this do you say Maths is fun or Maths are fun? Every person I have seen has used the is version which is singular and not plural so the (s) makes even less sense.
I have a British wife and we have fought about this several times and I will defend to the death that it is Math over Maths.
mtiyl ยท 2 points ยท Posted at 22:11:50 on May 25, 2016 ยท (Permalink)
can you think of a another word where you when shortening it you still carry the s
Statistics? As in the academic field, not the plural of "statistic".
I'm struggling to think of similar words that are routinely shorted anyway. I think "economics" is sometimes shortened to "econ" in the US, but I have never heard this in the UK.
Tuviah ยท 3 points ยท Posted at 15:26:35 on May 25, 2016 ยท (Permalink)
But we also say that "mathematics" is fun, rather than mathematics are fun. We do so because "mathematics" is a mass noun which is generally only used in its singular form.
There is some evidence that in the early 1800s a contracted version of the word (math's) was used in publications, and this may have diverged between the US and UK later in the century when the UK dropped the apostrophe leaving "maths" and the US abbreviated it to just "math", though I'm not aware of an exact etymology for either variant.
There are a number of good response to this question found by googling math vs maths, if you're interested in learning more, but in short both are likely as valid as each other.
That it makes you sound like a fool when you say "maths", because there is no "s" after the "th" in "mathematics", and anyways the word is an uncountable noun (and so no plural form).
No rounding involved. This is an example of what we call a limit in maths. When we write 0.9999999... this is shorthand for 0.9 + 0.09 + 0.009 + 0.0009 etc so we're actually summing up:
9 * 10-n
For n = 1 to infinity. It is possible to show that this sum is 1.
This is completely rigorous and not at all controversial maths (every mathematics undergraduate student will be taught how to prove this, generally in their first year).
Note that this is actually a general property of the decimal number system. Any number which has a decimal expansion with a finite number of non-zero terms in it actually has two decimal expansions. To get the second one you just subtract 1 from the last digit and then append an infinite series of 9s.
Remember not to get the "map" confused with the "land", here the land is the real number system and the map is the decimal expansions. Some real numbers have multiple decimal expansions, this isn't a fault with the decimal system but its something we should be aware of.
TatchM ยท 2 points ยท Posted at 22:19:11 on May 25, 2016 ยท (Permalink)
As a side note, do you know of any sources dealing with non-natural numbered bases? Or perhaps an explanation on why such cannot exist?
You certainly can write things out in non natural numbered bases. I don't know of any good sources (my work is very much not in this area) I'm afraid but the wiki page has some interesting stuff.
There is also an extensive page on using the golden ratio as a base since that system has some quite nice properties (largely because ฯ2 = ฯ+1).
TatchM ยท 1 points ยท Posted at 22:43:37 on May 25, 2016 ยท (Permalink)
Thanks for the leads!
TatchM ยท -2 points ยท Posted at 22:15:14 on May 25, 2016 ยท (Permalink)
Not going to lie, your explanation was pretty bad. You probably should have looked up the limit proof before referencing it.
Luckily, the examples provided on Wikipedia are much better.
Well, not the most interesting aspect of math I learned from this thread. Still interesting enough though.
I didn't go into depth about the proof because either a reader already understands limits, in which case they don't need the proof or they don't know about limits, in which case I can't really explain any of the proof in a reddit comment in a way I'd find satisfactory.
I'd basically have to start from the axioms of the real numbers, define what a limit means from that, have a bunch of explanation about what it and then give the proof using the definitions I'd given. Thats a couple of lectures worth of material in an undergrad course.
I could have given one of the more handwavey explanations, or maybe go into depth using one of the explicit constructions of the reals (Cauchy sequences, Dedekind cuts etc) I guess.
TatchM ยท 2 points ยท Posted at 22:38:34 on May 25, 2016 ยท (Permalink)
or maybe go into depth using one of the explicit constructions of the reals (Cauchy sequences, Dedekind cuts etc) I guess.
That would be nice!
And I understand it can be difficult to explain things briefly. Linking to a proper proof or explanation would have been a good way as well.
Sorry if I came across as salty (as /u/rrussell1 pointed out), I did not mean to be such. It was just that your partial explanation was confusing, and I felt a more in-depth explanation would have been better.
In any case, I found a few good leads on non-natural numbered radix systems. But if you have any good sources related to them, I'm still open to suggestions.
he pretty much is out of the race, but if you want to be strict, there is still a mathematical chance for him to win... soooo, your wrong.
for example if he win 100% of the remaining delegates. it wont happen, but the pure math allows it.
CaptZ ยท 0 points ยท Posted at 18:25:56 on May 25, 2016 ยท (Permalink)
Not too mention that when HRC is indicted and drops out of the race, Bernie is in. That is why he staying in the race, Just as HRC did against Obama, stating that he might die while running for POTUS giving her an in to win. What goes around comes around.
xibfeii ยท -2 points ยท Posted at 16:51:19 on May 25, 2016 ยท (Permalink)
The fact that we can do more than just give up when we try to add up infinite numbers, and when we do we get
Eย = mcย 2. So basic and simple, yet so fascinating. Thinking of mass and energy as the same thing really opens our eyes and made us better at understanding the universe around us.
[deleted] ยท 13 points ยท Posted at 11:36:32 on May 25, 2016 ยท (Permalink)
Not at all. Physics is mathematics. Issac Newton invented calculus in order to solve physics problems. You clearly are just too ignorant to this subject.
[deleted] ยท 3 points ยท Posted at 12:34:11 on May 25, 2016 ยท (Permalink)
Chill dude. I never said I was superior. All I meant was math and physics literally go hand in hand. And a physics equation is a mathematical equation. No need to get butthurt over someone else's opinion.
Dd_8630 ยท 2 points ยท Posted at 14:04:45 on May 25, 2016 ยท (Permalink)
Eย = mcย 2. So basic and simple, yet so fascinating. Thinking of mass and energy as the same thing really opens our eyes and made us better at understanding the universe around us.
It's also only a corner case of the more complete and much more interesting equation: Eยฒ = mยฒcโด + pยฒcยฒ.
ktkps ยท 3 points ยท Posted at 11:39:11 on May 25, 2016 ยท (Permalink)
No... no they don't. That statement only defines addition and, by extension, multiplication and exponents. There's no subtraction or division. There's also no trig.
If the statement 'defines addition and by extension multiplication' then subtraction and division are also covered by extension. If 1+1=2 then 2-1=1. The inverse of multiplication is division. If multiplication is covered by extension then so is division.
Once division is covered then so is the concept of irrational numbers since once you can divide, some asshole will try to divide 5 into 3 parts.
The relationship between sine, cosine and tangent is multiplicative so trig is covered by extension.
The concept of zero isn't covered by 1+1 even by extension.
Dd_8630 ยท 1 points ยท Posted at 14:02:48 on May 25, 2016 ยท (Permalink)
The relationship between sine, cosine and tangent is multiplicative so trig is covered by extension.
No it's not, you need to define angles, circles, and triangles, before you can then define trig. This all does not come solely from 1+1=2.
If 1+1โ 2 then 2 one degree angles will not create a 2 degree angle.
If 1+1โ 2 then the angles that make up a triangle will not add up to 180.
Trig requires 1+1=2 to be true.
Dd_8630 ยท 1 points ยท Posted at 16:58:40 on May 25, 2016 ยท (Permalink)
Trig requires 1+1=2 to be true.
Of course, but trig doesn't come from 1+1=2. We can't say "1+1=2, therefore sinยฒ + cosยฒ = 1". The definitions of sine and cosine need to be made before we can bring trig into the picture, and those definitions aren't derived from arithmetic.
[deleted] ยท 1 points ยท Posted at 16:19:37 on May 25, 2016 ยท (Permalink)
So if 1+1โ 2 then some of those postulates are incorrect; the partition postulate comes to mind. Those postulates are dependent on 1 plus 1 equaling 2. The other postulates, the ones that are true regardless any hypothetical sum resulting from adding one and one are independent of the equation and irrelevant to this discussion.
I have no idea what you are tlaking about but you are totally wrong. None of the standard axioms in mathematics rely on 1+1=2, instead 1+1=2 is a consequence of some of them.
Try proving the axiom of choice from 1+1=2 (hint, it's impossible).
There's actually a book, Principia Mathematica, that lays out the foundation of mathematics, including formally defining arithmetic, number theory, and several other logical systems. Famously, it take hundreds of pages of postulates, definitions, and theorems until it is finally possible to prove 1+1=2
Burdiac ยท 0 points ยท Posted at 14:15:15 on May 25, 2016 ยท (Permalink)*
100% of Canadian hockey players give it 110% every game.
Markual ยท 0 points ยท Posted at 17:10:48 on May 25, 2016 ยท (Permalink)
When u turn an 8 sideways it's an infinity sign.
[deleted] ยท 0 points ยท Posted at 17:28:32 on May 25, 2016 ยท (Permalink)
1 + 1 = 2 ;)
I really like the fact that once something in math is proven, it will remain the same for all the time. The sentence of Pythagoras was true thousand years ago and will be true in thousand years.
[deleted] ยท 0 points ยท Posted at 22:09:27 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 0 points ยท Posted at 22:09:27 on May 25, 2016 ยท (Permalink)
A negative boy couldn't decide whether or not he wanted to go to a rad party, but he decided to be square and miss out on four awesome chicks...and it was all over by 2 am.
solve for x, using the reinterpretted...quadratic equation!
People in Britain and America have been using it for at least 180 years. Apparently at some point you guys decided to drop the s. For what its worth we also dropped the apostrophe but in British English maths is absolutely standard (no one here ever says math unless they're trying to do an American accent).
Ah. I've lived throughout the US and never heard maths in person, only on reddit. Seems it's just the Brits using their crazy jibber jabber. Should've known. Thanks for teaching me something today!
Rikon ยท 0 points ยท Posted at 22:39:21 on May 25, 2016 ยท (Permalink)
Every time you divide 1 by 3, you lose 0.1, as 3 times 3 is 9 and not 10
wilts ยท 1 points ยท Posted at 15:20:20 on June 2, 2016 ยท (Permalink)
If you spent your entire life calculating the digits of pi by hand you would die.
[deleted] ยท 0 points ยท Posted at 22:46:13 on May 25, 2016 ยท (Permalink)
The number of Astronomical Unitsโthe distance between the earth and the sunโin a light year is roughly the same as the number of inches in a mile.
There are 63,072 light years in an AU. There are 63,360 inches in a mile. Close enough, and a neat coincidence.
If I build a model of the solar system where the sun is a speck of sand and the earth is a (much smaller speck of sand) an inch away, then the nearest star would be a couple of grains of sand a few feet apart 4.3 miles away. From there, we can visualize the stars as being anything from sand grains to pebbles to a few boulders, several miles apart. It's a great way to get a sense of perspective on astronomical distances.
Sephrik ยท 2 points ยท Posted at 23:34:10 on May 25, 2016 ยท (Permalink)
You've got it backwards. There are 63240 au in a light year
Nine, nine, nine. Fantastic number nine. Perfectly consistent, it works out every time. Nine, nine, nine, that crazy number nine. Times any number you can find, it all comes back to nine.
2 x 9 = 18. 1 + 8 = 9
3 x 9 = 27. 2 + 7 = 9
4 x 9 = 36. 3 + 6 = 9
5 x 9 = 45. 4 + 5 = 9
6 x 9 = 54. 5 + 4 = 9
7 x 9 = 63. 6 + 3 = 9
8 x 9 = 72. 7 + 2 = 9
9 x 9 = 81. 8 + 1 = 9
9 x 10 is 90. Just drop the zero sign.
9 x 11 is 99. 9 + 9 = 18. 1 + 8 = 9.
Times any number you can find, it all comes back to nine.
It's impossible to tune a piano because the harmonic series split into 12 even fractions don't fit into eachother perfectly when dealing with 3rds 4ths and 5ths. You can tune it pretty close though
2 out of every 5 league of legends players have autism
[deleted] ยท 0 points ยท Posted at 00:37:54 on May 26, 2016 ยท (Permalink)
Maths? Math?
Faiyez ยท 0 points ยท Posted at 00:39:45 on May 26, 2016 ยท (Permalink)
This might be dumb, but the fact that integer square roots are infinite, given the limited amount of integer square roots that you'll find in any sequence of integers.
Toover ยท 0 points ยท Posted at 02:34:14 on May 26, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
Godel proved, using Mathematics, that given any theory, it will never be complete, that is to say it will never be able to prove everything. By design, a theory always require axioms, and those axioms tend to lock down a part of the mathematical truth you can consider.
In short: there is no "single truth" whatsoever, and this was proven mathematically.
[deleted] ยท 0 points ยท Posted at 03:56:15 on May 26, 2016 ยท (Permalink)
i always liked the old 'cross multiply and divide' trick you can use to solve a variable. not to mention the Pythagorean theorem. made me feel so smart when i was in school lol
its my favorit fact.
Say x = 100, so the odds of not winning 100 times in a row are (99/100)100
The compliment of that is simply 1 - (99/100)100 = 0.63397
Godel's Incompleteness Theorems which prove that a complete system cannot exist. It is more of a metamathematical fact but still some of the most important and misunderstood results in mathematical history.
So you have ex = โซ ex right?
Rearrange to get ex - โซ ex = 0. Nothing strange there.
Now factor out the โซ: (1 - โซ)ex = 0. Huh? Bear with me...
Now write ex = 0 * 1 /(1 - โซ). Ok...
Expand the geometric series of 1/(1-x): ex = 0 * (1 + โซ + โซโซ + โซโซโซ + ...)
Take the 0 inside the integral: ex = 0 + โซ 0 + โซโซ 0 + โซโซโซ 0 + ...
Let's ignore integration constants for simplicty, so โซ 0 = 1, โซโซ0 = โซ1 = x, โซโซโซ0 = โซโซ1 = โซx = โซx2/2 and so.
This gives ex = 1 + x + x2/2 + x3/3! + ...
The regular power series for ex.
[deleted] ยท -7 points ยท Posted at 17:01:14 on May 25, 2016 ยท (Permalink)
Whoa there fellow American. Not good to assume our way of saying math is the correct way. The term "maths" is the proper British English way to refer to mathematics.
Math sounds singular and maths sounds plural, They both correctly refer to Mathematics.
[.com] was originally administered by the United States Department of Defense, but is today operated by Verisign, and remains under ultimate jurisdiction of U.S. law.
if you could fold a piece of paper in half 27 times, i would eat a lot more tacos.
CFftVoN ยท -2 points ยท Posted at 15:39:04 on May 25, 2016 ยท (Permalink)*
The sum of all natural numbers (S = 1+2+3+4+5+...) has a finite sum and it happens to be -1/12.
It requires some series manipulation and many people aren't satisfied with one step of the process but it works and has been used in string theory and other strange branches of physics. This only works if you properly go out to infinity. If you stop short, you obviously just get a really large number.
you can only do these steps if your sequence converges, which it doesnt.
you can assign a number to the series and that is used in stringtheory but it is not the normal sum.
CFftVoN ยท -1 points ยท Posted at 15:50:39 on May 25, 2016 ยท (Permalink)
Yeah, that's the step of the process some people don't like. Still my favorite maths fact though so I feel I have adhered to thread requirements even though it's controversial.
[deleted] ยท 2 points ยท Posted at 16:43:33 on May 25, 2016 ยท (Permalink)
it's not even a fact, how can it be your favorite fact.
this is similar to saying my favorite fact is all Americans are overweight gun lovers.
well the math fact is not that the series converges(it doesnt) but rather that you can sensibly assign a finite value to it(-1/12) which has use in real physics.
what you basically do when you assign -1/12 to the series is that you say that you made a mistake earlier when you wrote 1+2+3... and actually meant zeta(-1) which equals -1/12
See my comment here for a proof that if that sum equals any real number x (including -1/12) then 1 = 0. Since 1 does not equal zero we can conclude that that sum does not equal any real number.
See my answer here. Setting this sum equal to any real number x allows you to derive 1=0 which is a contradiction.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
That wasn't my point. The fact is that we call it maths in Australia. I also think throughout Asia it is the same. Whatever came first is of zero relevance to my post, if you say math where I am people will look at you like you are an eejit. :)
[deleted] ยท -7 points ยท Posted at 14:34:26 on May 25, 2016 ยท (Permalink)
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Umbrall ยท 5 points ยท Posted at 15:00:16 on May 25, 2016 ยท (Permalink)
They have the same number of numbers. We can map each number in (0,1) and (0,2) by simply doubling or halving, so every element pairs up.
Also for what it's worth the vast majority have decimal expansions that don't terminate or repeat, ala pi sqrt(2) etc
[deleted] ยท -3 points ยท Posted at 14:09:24 on May 25, 2016 ยท (Permalink)
Suppose 1+2+...=-1/12. Then, by the definition of a limit, with epsilon=1/12, there exists a natural number N such that whenever n is larger than N we have
1+2+...+n<1/12
however this last equality is false for n>0, a contradiction, so it does not converge to -1/12.
This is not true. He proved that under some methods of assigning values to divergent infinite series, the divergent series 1+2+3+4+... is assigned the value -1/12. This is not the same thing as saying that the sum of the positive integers is -1/12. The series 1+2+3+4+... obviously diverges.
bmullan ยท 1 points ยท Posted at 16:14:29 on May 25, 2016 ยท (Permalink)
I think its also very cool that he was so poor he worked out all of his spectacular theorems using a piece of slate rock & chalk because he couldn't afford paper. At his death he left behind only 6 notebooks with mathematical theorems so complex that they are still trying to figure some of them out today 100 yrs later.
He has been called the equal of Albert Einstein in pure mathematics but had no real formal education.
eIImcxc ยท -5 points ยท Posted at 17:38:42 on May 25, 2016 ยท (Permalink)
1+2+3+4+...= - 0.5
This have been proven in a physic experiment too which only worked when this mathematic fact has been applied.
This formula proves the limit of our imagination for me.
[deleted] ยท -4 points ยท Posted at 19:53:03 on May 25, 2016 ยท (Permalink)
No, that series is divergent and the sum does not exists. You can assign it a value with certain summation methods (Ramanujan and Zeta regularization puts it at -1/12). But that doesn't change the fact that it's divergent.
[deleted] ยท -4 points ยท Posted at 22:05:05 on May 25, 2016 ยท (Permalink)
This was literally posted two days ago. Also learn to spell
You're right about that first part, sorry, I always get those mixed up. You're only half right about the second part. Yes, the series does diverge, but it is also equal to -1/12
Yes, the series does diverge, but it is also equal to -1/12
Those statements directly contradict each other.
There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
See my answer here. Setting that sum equal to any real number gives a contradiction. If that sum converges to a real number (including -1/12) then 1 = 0.
We're so weird. I mean it's normal for us but we do so many things our own way that the rest of the world does uniformly. It's not even like what we do is better it's just different.
[deleted] ยท -1 points ยท Posted at 14:39:31 on May 25, 2016 ยท (Permalink)
Capitalism can be expressed with one differential equation: d$/dt = k$ (change in money is directly proportional to the amount of money you have)
[deleted] ยท -1 points ยท Posted at 15:02:39 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 22:05:54 on May 25, 2016 ยท (Permalink)
You're being somewhat unfairly downvoted, as there are ways to manipulate the sequence in order to argue that it sums to -1/12. These are called summation methods. There are lots of them, so it's misleading to say that any one answer is the "right" answer. You may get a different answer from a given infinite divergent series sum depending on the method you go with.
You cannot prove that the sum of that series is -1/12 because that series diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 0 points ยท Posted at 03:24:40 on May 26, 2016 ยท (Permalink)
It is correct to say that zeta(-1)=-1/12. It is correct to say that the Ramanujan summation of the function f(x)=x on the positive integers is -1/12. It is not correct to say that the sum of the natural numbers is -1/12. The series 1+2+3+... diverges and does not have a value in the usual sense.
The key is remembering that we're starting from one and adding natural numbers. There aren't any negatives. And we don't ever stop adding these numbers. It's an infinite sum. You couldn't prove this on a calculator because as soon as you pressed the equals key, it wouldnt be infinite.
This video is extremely misleading, and the math it uses is completely incorrect. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
kof_zpt ยท -1 points ยท Posted at 15:40:01 on May 25, 2016 ยท (Permalink)
Infinity isn't a real number. There exist (perfectly sane, well studied, well behaved and understood) number systems in which you can treat infinity. For example infinity is certainly a projective real number. It is also an affine real number, a projective complex number and a whole bunch of others.
you have to first show that a series converges to then be allowed to manipulate it like this.
simply because these operations are only defined on the real numbers. and it turns out that if the series converges and you do these operations the end result converges again to the expected result if you do it with the normal limits. thats why you can do it for convergent ones.
Would you mind citing sources disproving it? I don't claim to know enough to back up my claim, but I did see the numberphile video and read the wiki and a few other articles and it seemed to check out everytime.
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ยท ยท ยท is a divergent series. The nth partial sum of the series is the triangular number [snip] which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Numberphile actually has a followup video in which they clear some of the misconceptions that they had in the original video.
Piss_on ยท -1 points ยท Posted at 17:52:04 on May 25, 2016 ยท (Permalink)
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ยท ยท ยท is a divergent series.
The series is very obviously divergent and goes towards infinity. You can assign it a value (-1/12) with the zeta function.
tisom ยท 0 points ยท Posted at 03:04:46 on May 26, 2016 ยท (Permalink)
It is a divergent series, and it does appear to be heading towards infinity, but then the question comes up of what we mean by infinity. Of course, infinity is not really a number that is well defined, so we have to use the Riemann Zeta function to make sense of it. You seem to not like the idea of "assigning" it a value, but it actually comes from the idea of analytic continuation, which is a of critical importance to dealing with functions that have singularities. The fact that we can sum all these numbers and put a bounded answer on it is really important for things like calculating the Casimir force in physics (basically the idea is that electromagnetic fields are quantized or discreet, and each "mode" carries energy and can exert radiation pressure. If we run an experiment where we put two metal plates very close together, we actually restrict what modes can exist between them. We find that due to the lack of these modes, we also forbids vacuum fluctuations from occurring at these frequencies, and this causes the radiation pressure between the plates to be slightly less than on the outer edges, giving the places a small attractive force). The fact that electromagnetic fields can exist at frequencies that seem to diverge means that to understand them we have to be able to sum their contributions without just getting infinity, as you suggest by writing off my comment.
1+2+3+4.. does not equal -1/12. but as you said you can assign that value to it which does have physical meaning. but what you do when you assign that value to the series is kinda like saying that you made a mistake when you wrote 1+2+3... and should have wrote zeta(-1) which equals -1/12
tisom ยท 1 points ยท Posted at 12:40:02 on May 26, 2016 ยท (Permalink)*
What do you mean by a mistake? Isn't zeta(-1) = 1+ 2 + 3 + ... ?
Edit: ok I found an article which seems to support what you and u/flyingjam seem to be on the brigade about, that this result is "wrong:"
But at the same time, it explains how the Riemann Zeta function is just what you get when you use analytic continuation on the Euler Zeta function, extending the values you can plug in from x>1 to include x<=-1 as well as complex numbers. And when you do that, you get the -1/12. So are the author and you arguing that analytic continuation is wrong, even though it's a pretty important principle in complex analysis? At what stage do things go awry? Also, if the result of us assigning a value to the series is incorrect, but actually corresponds to experimentally verified results (for s=-3 because they are looking at 3D Casimir forces rather than 1D), then doesn't that validate the theory which you are claiming is wrong?
I'm not a mathematician, so please forgive me if I am missing some subtlety here, but I ask because I'm genuinely curious and want to learn.
zeta function is only defined by that series for s>1, which -1 isnt.
and -1/12 is what you get from the analytic continuation and plugging in -1. which is why you can assign the value -1/12 to is and why this appears in physics. what you do when you replace 1+2+3.. with -1/12 is that you say that you made a mistake when you wrote 1+2+3 and actually meant zeta(-1)(which isnt 1+2+3..) which is -1/12.
so there are ways to assign -1/12 to this series, but it is not the normal sum, as the series obviously diverges.
[deleted] ยท -1 points ยท Posted at 17:58:28 on May 25, 2016 ยท (Permalink)*
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ยท ยท ยท is a divergent series. The nth partial sum of the series is the triangular number [snip]
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
The series is divergent and doesn't not equal anything. But you can assign values to it with certain summation methods.
What is the difference between assigning a value to it and saying it's equal? I'm not a mathematician, and I'm genuinely curious. I like these videos that explaining better than I can:
https://www.youtube.com/watch?v=w-I6XTVZXwwhttps://www.youtube.com/watch?v=jcKRGpMiVTw
It's also related to the Riemann-Zeta function, which is used in explaining physical phenomenon (a lot in QED).
It's kinda like saying "This series diverges, BUT what if it didn't? What would happen if we used these summation methods which work for converging series and applied it to this divergent series?". The value you get is not the sum of the series, but it can still be useful. Really, the reason why this one is so famous is that it has applications in string theory regarding the number of dimensions needed to do what they want.
That on average one person dies on earth every 2 seconds..
So if you believe in Jesus you only have two seconds for that long, leisurely "walk and talk" with him like in "Footprints in the Sand" until the next person shows up for their long walk and talk lol.
.999... is equal to 1. ... is defined by an infinite series, and for .999..., it's the infinite series (9/10)n, which is equal to 1.
Caasi67 ยท 0 points ยท Posted at 18:48:09 on May 25, 2016 ยท (Permalink)
Those are the rules we define, and it works to solve problems, but isn't also technically correct to say .9... is infinitely close to 1 but not actually 1?
The sum of all whole numbers: 1+2+3+4+5...forever is -1/12. The sum of the cubes of all whole numbers: 13 + 23 + 33 + 43 + 53 + 63 + ... is +1/120. True story!
s0lv3 ยท 1 points ยท Posted at 18:44:19 on May 25, 2016 ยท (Permalink)
Okay if you are a mathematician or something PLEASE explain to me the first one and how that can be true. I've had it proved for me mathematically, and I get the math. But how is it that when you add positive integers, you get a negative number that is not an integer.
Neither of these statements is true. There are ways of assigning values to divergent infinite series, and under some (but not all) of these methods, the value -1/12 is assigned to the series 1+2+3+4+... But as you would correctly assume, if you are using the standard definitions, the series 1+2+3+4+... obviously diverges (grows larger without bound as you add more terms).
Nobody really knows "why" but these values emerge in the real world (eg, The Cassimir Effect uses 1/120 as a substitute for the sum of cubes, and it's proven as accurate). Some say that, really, it's -1/12 + infinity, or 1/120 + infinity, and that in solving these maths creatively the infinities cancel out. That's all I got!
s0lv3 ยท 1 points ยท Posted at 07:22:27 on May 26, 2016 ยท (Permalink)
So interesting I can't wait to learn these things.
The sum of all natural numbers is -1/12. Mind boggling
Matech ยท 1 points ยท Posted at 19:11:33 on May 25, 2016 ยท (Permalink)
Yup , my hatred for math grows. Even as Eli5 i still dont understand or agree, he even sayd its rounded.. The fuck? U cant just do that, thats a lie, you cant continually add whole numbers and get a fraction zero fucking sense you would just get a larger and larger whole number, ass hat math making something that isnt there.
as a child i was heavily into mental maths and crunching numbers...i had come up with a formula on my own back then...just pure dumb luck and lots of time at hand helped... true story and my own fav math fact...
At 3:10, why do they shift the second set of number to the right one place? That part right there seems like the "mathematical Hocus Pocus" they mention later.
cdleech ยท 2 points ยท Posted at 21:13:59 on May 25, 2016 ยท (Permalink)
That's just moving terms around on the paper, by lining them up you can see how they simplify. It's not changing any terms, like shifting decimal places.
I'd say the "hocus pocus" is assigning a value of 1/2 to S1, which is a divergent series. It's a valid way to assign a value to S1, which leads to the equally valid value of -1/12, but it's not the only summation method or a true limit value.
[deleted] ยท -1 points ยท Posted at 19:27:04 on May 25, 2016 ยท (Permalink)*
That site says "The general form of the Riemann zeta function for the argument "s" is: <sum of n^(-s) from 1 to infinity>"
This is completely and blatantly wrong. That is a representation of the Riemann zeta function only for Re(s)>1. The general formula is obtained through analytic continuation and is much more complicated.
[deleted] ยท -1 points ยท Posted at 20:32:43 on May 25, 2016 ยท (Permalink)
The series 1+2+3+4+... diverges, as you probably learned in Calc 2. There are other ways of assigning values to divergent series, and some (but not all) of these methods assign the value -1/12 to this series. But this does not mean that 1+2+3+4+...=-1/12.
Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
It is true that there is an interesting mathematical way of associating the number -1/12 with the sequence 1,2,3,4,5,... but it is most definitely not true that 1+2+3+4+...=-1/12. The article you linked to explains this in detail.
The article explains in detail how to calculate -1/12 using the sequence of 1+2+3...., and it is a fact that is used in physics. Watch numberphiles video on it. Its true
I have a PhD in math, and am a professional research mathematician. 1+2+3+... does not equal -1/12. Numberphile's (first) video is complete garbage.
Like I said, there are ways of associating the number -1/12 with that series. That does NOT mean that the SUM of the series is -1/12. It means that there is some other interesting mathematical relation between the sequence 1,2,3,4,... and the number -1/12.
I'm probably late for the party, but if you add up all the natural numbers, so 1+2+3+4+... and this goes forever the sum will be -1/12. This is proven, and is used today in different scientifical fields.
It is true that the Ramanujan summation of the function f(x)=x evaluated at the positive integers is -1/12. It is not true that 1+2+3+4+...=-1/12. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. Ramanujan summation is one example of these methods. But that does not mean that 1+2+3+...=-1/12.
Under most methods of assigning values to divergent series, this series is not assigned any value. No stable linear summation method can assign this series a value (see the wiki article if you want to know what those words mean). Even Ramanujan summation can assign this series different values. Ramanujan summation depends on the interpolating function you use. if you use the function f(x)=x, you get the value -1/12. If you use a different function such that f(n)=n for the positive integers, you'll get a different value. For example, you could take f(x)=x+sin(pi*x) or even f(x)=x+g(x)*sin(pi*x) for any function g.
Still not true. The sum 1+2+3+4+... is not equal to any real number (or any complex number for that matter). We can come up with some ways of assigning labels to such divergent sequences, which are sometimes useful. Some (but not all) of these methods happen to assign the label -1/12 to the sequence 1+2+3+4+5+... but that certainly does not mean that -1/12 is the sum of the sequence.
In fact as divergent sequences go 1+2+3+4+5 is quite a bad one. Most of the usual methods we have for labelling it simply do not work.
Here is an example of the sort of bad stuff which happens if you assume that the sequence has a finite sum:
x = 1 + 2 + 3 + 4 + 5 + 6...
Since x is just a finite number we can add 0 to it and not change anything:
So you can only "sum" this series in a number system in which 1=0. Certainly this is not true in the integers, rationals, reals, complex numbers or any extensions of such. Given the other axioms of the reals its actually possible to show that if 1=0 then every number equals zero. In other words asking for this series to have a sum leads to our number system becoming trivial.
[deleted] ยท -1 points ยท Posted at 23:18:14 on May 25, 2016 ยท (Permalink)
See my answer here. Setting this sum equal to any real number x allows you to derive 1 = 0 which contradicts with the axioms of the real numbers. Therefore this sum can't be equal to any real number (including x=-1/12). This fits with our intuition that this sum gets larger and larger and doesn't converge.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
[deleted] ยท -1 points ยท Posted at 23:26:04 on May 25, 2016 ยท (Permalink)
This series diverges, so you cannot set S1 equal to that series. Same problem with basically every line of your "proof." There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 1 points ยท Posted at 00:11:41 on May 26, 2016 ยท (Permalink)
Yeah, it's better as a Cesaro sum - but it's easier to explain on reddit using what i showed. But it is a thing. I didn't just make it up.
While you can interpret S1 as a Cesaro sum, 1+2+3+4+... is not Cesaro summable.
How is "assigned the value" and "=" different in any meaningful way in this context?
Maybe "associate a value" is a better term. There are many ways of associating a value to an infinite series. For example I could pick out the first term of the series, so 1+2+3+4+... gets the value 1, and 5+10+15+20+... gets the value 5, etc. Under a few methods of assigning values to infinite series (Dirichlet series continuation, zeta summation, Ramanujan summation applied to the function f(x)=x, etc.), the series 1+2+3+4+... gets the value -1/12. But none of the methods used to associate the value -1/12 to the series 1+2+3+... behave anything like summation. For example, no linear stable method can assign a value to this series.
See my answer here. Setting this sum equal to any real number x allows one to derive 1=0 which contradicts with the axioms of the real numbers.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
[deleted] ยท 1 points ยท Posted at 00:43:35 on May 26, 2016 ยท (Permalink)
The rule that you break is that you can only add a finite number of real numbers. The reals are closed under finite sums but an infinite sum is utterly meaningless. Some sequences have an additional property called convergence and it is convenient to talk about adding infinite sums which are convergent but that is only shorthand for mathematically rigorous operations including limits. We never (ever, ever, ever) actually add infinitely many terms.
Incidentally this is wrong:
subtracting 1/4 from any number shouldn't triple its size
Subtracting 1/4 from -1/8 triples its size.
[deleted] ยท -1 points ยท Posted at 23:28:24 on May 25, 2016 ยท (Permalink)
This is probably already said somewhere in these 10k comments, but if you take the sum of all the integers (infinitely): 1+2+3+4+5+... and so on, that sum will equal -1/12.
I mean that the series 1+2+3+4+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 1 points ยท Posted at 23:50:05 on May 25, 2016 ยท (Permalink)
So by your words, some of those methods come to that conclusion, and some do not. Having a degree in physics myself, I am more inclined to agree with the physics theory side of the problem. But it feels like this is coming to opinion more than anything.
So by your words, some of those methods come to that conclusion, and some do not.
No. None of these methods come to the conclusion that 1+2+3+...=-1/12. As I said, there are other ways of assigning a value to the series 1+2+3+..., and some of these methods assign the value -1/12 to this series. This does not mean that the sum of the series is -1/12. It just means that the number -1/12 has some other mathematical relation to the sequence of numbers 1,2,3,4,...
[deleted] ยท 2 points ยท Posted at 23:56:40 on May 25, 2016 ยท (Permalink)
Oh, I see what you mean by that. Also, that would make more sense as well with what Numberphile said in their video about this result being used in String Theory and other areas of theoretical physics. Thanks for the clarification.
The series 1+2+3+4+... diverges, so it does not have a value. As you add more terms, the sum grows larger without bound.
There are other ways of associating a number with an infinite series like this, and a few of these associate the number -1/12 to the series 1+2+3+4+..., but none of these claim that the sum of this series is -1/12.
Unfortunately the "fact" about pi in this video has not been proven. We do not yet know if the decimal expansion of pi contains every finite decimal string. This is conjectured to be true, but has not been proven.
[deleted] ยท -2 points ยท Posted at 03:06:01 on May 26, 2016 ยท (Permalink)
It's been proven. It was proven in 2010 at the University of Gundenberg Germany by a team of Mathematicians lead by Dr. Lichbaulz. He won the Nobel Prize for Computer Science that year. If you're interested in reading about it, the study is linked here: wwlichmybaulz.com
Infinity exists in math. You eventually have to round that last 9 up. But with infinity, there it's no last 9, it kees going. That's why limits approach a number, but don't hit it.
0.99... is really exactly equal to 1. The wikipedia article on it gives a load of proofs. 0.99... is not a process, it is a fixed and unchainging number.
That somehow, if you start adding numbers 1 + 2 + 3 + 4 + 5 +... to infinity, you wind up with... -1/12. I guess it's not so much a fact as it is a proof, but... but.... wow.
This video is extremely misleading, and the math it uses is completely incorrect. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
Well yes, it's a divergent series, but this way of looking at it is a fun little party trick, and I'd say it counts as my favorite math "fact". Or math trivia, if you will
R0kss ยท -2 points ยท Posted at 15:17:42 on May 25, 2016 ยท (Permalink)
Sum of all natural numbers is -1/12 ... I find that mindblowing
You cannot manipulate divergent series like that, or you get nonsense like this. A very simple proof to the contrary is to go to the definition of a limit, set epsilon to be 1/12. Then you would need there to be a natural number N>0 such that |(1+2+3+4+...+N)|<1/12, however this is clearly false for every N, as 1>1/12.
That's what you'd think. But it's an infinite series, and shit gets weird when you deal with infinities. Check out this video from numberphile where they give several proofs that it equals -1/12
the problems are that S1 doesnt converge(just do the cauchy test) and neither does S2, you thus cannot simply multiply,add or substract these serieses.
Predmid ยท 1 points ยท Posted at 15:04:51 on May 26, 2016 ยท (Permalink)*
Its what is used in places like the UK, and Australia (and, as far as I can tell, most other English speaking countries apart from the US). It comes from maths being short for mathematics (which is always plural).
Irrational numbers are numbers that can't be expressed as a ratio of integers (those would be rational numbers, which I think of as ratio-able numbers). Irrational numbers, when written in decimal form, have infinitely many digits on the right side of the decimal point that never repeat. Some famous examples are pi, sqrt(2), and e, but there are infinitely many irrational numbers. Actually, there are more irrational numbers than rational numbers.
If you were to decide on an encoding between digits and letters (like, for example, ASCII, which encodes the letter "A" as 65, and so on) then you could convert the digits in an irrational number to letters and punctuation.
Most of the converted digits would be gibberish (in fact, infinitely man of the converted digits would be gibberish); however, any sentence you can think of would also be in the converted sequence. As would all the works of Shakespeare, the bible, every novel, every textbook, and every publication that has ever been written. Also included are all future publications that haven't been written yet!
Instead of converting digits to ASCII symbols, we could instead use the digits in an irrational number to specify the amount of red, green, and blue in each pixel in a digital image. Inside your irrational number, you'll find that this choice of encoding will mostly be gibberish, but will also contain every digital image ever taken (as well as every image that ever will be taken).
edit: as pointed out by u/overconvergent, this doesn't hold for some irrational numbers such as 0.10100100010000100000...
edit 2: not sure why I'm being downvoted.... wtf? if you don't like this math fact, just move along?
Irrational numbers are numbers that can't be expressed as a ratio of numbers
Irrational numbers are numbers that can't be expressed as a ratio of integers
Most of the converted digits would be gibberish (in fact, infinitely man of the converted digits would be gibberish); however, any sentence you can think of would also be in the converted sequence.
This is true for every irrational number.
This is not true. For example, the number 0.101001000100001000001..... is irrational, but its decimal expansion never contains the digit 2.
For example, the number 0.101001000100001000001..... is irrational, but its decimal expansion never contains the digit 2.
Fair point that some irrationals contain patterns that preclude random information encoding. The issue of never containing digit 2 (or others) is less of a concern as the choice of encoding could instead be binary.
No you don't. This video is extremely misleading, and the math it uses is completely incorrect. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
This is not true. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท -9 points ยท Posted at 11:42:20 on May 25, 2016 ยท (Permalink)*
This video is extremely misleading, and the math it uses is completely incorrect. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท -3 points ยท Posted at 00:18:15 on May 26, 2016 ยท (Permalink)
That's not true. You just don't realise that you are using it every time you buy something, measure something, weigh out ingredients or budget your pay. It was drummed into you so much as a child that you use it without even knowing so.
I work in a smoke shop and have tons of customers that cant even estimate what a 15% off coupon will get them. We need math, at least to some level, even normal people.
And construction in general ("that door needs framed, use these one-bys. Opening is 38", need to keep it 36"."), operating a gas station ("If there are 20 inches of fuel left in the tank, how many gallons is that?"), baking ("The recipe calls for 1.5 tsp of baking powder but I'm tripling it, so I'll need..."), and so many other day-to-day things. Everything is math.
Are you my 14-year old son? We just had this conversation after I was working on a woodworking project and showed him how I had to use algebra and geometry to come up with some measurements. He insisted for way too long there was a way to do it without math, but he was sorely wrong.
That's actually one of my big gripes with people saying, "I don't ever use any of that math stuff I learned in school." Just because you're not using it exactly as the textbook showed you does not mean you're not using it. You are. But in real life, math is not a simple equation; it's a word problem where you have to separate the wheat from the chaff and use the numbers available to do something. That's also why you had to do all those word problems that were 'so stupid and not realistic at all.'
You might not need to be able to figure out how far apart two trains are after they left a town traveling in opposite directions at 60 miles an hour, but I can assure you there are multiple times in your life you will do a very similar problem in your head without realizing it. "Hmm... If I take the interstate, I can make $Town in 2 hours 45 minutes, but it'll be an extra 20 miles. If I go state roads, I save 20 miles, but it takes an extra 10 minutes. Which should I do?" You are now doing math and a cost-benefit analysis to see if the extra time or extra gas/wear and tear on the car are worth it.
Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results, some of which have applications in other fields such as complex analysis, quantum field theory, and string theory. Many summation methods are used in mathematics to assign numerical values even to a divergent series. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of โ1/12, which is expressed by a famous formula:[2]
bmorgy ยท 0 points ยท Posted at 16:23:47 on May 25, 2016 ยท (Permalink)
Oh but it does!
Lets start with the series: 1-1+1-1+1...that goes on for infinity. For simplicity's sake, I'll call this series "A". Now, Depending on where you stop (which is never if you go on for infinity), the answer to this series is either 1 or 0. With that logic, you can say that A = 1/2, which is the average of 1 and 0.
From there I'll direct you to the next series: 1-2+3-4+5...and so on, which we will call series "B". Using a bit of trickery, we can do the following (Its hard to format in reddit, but what is happening is that I am adding B to itself, but shifting the 2nd row over by one, which is allowed since this series goes on for infinity):
1-2+3-4+5-6
+1-2+3-4+5-6
1-1+1-1+1...
As you (hopefully) see above, I have just shown that B+B = A, or 2B = A. Since we already know that A = 1/2, that means that 2B = 1/4.
Finally, we are going to subtract B from the initial series, which we are going to call "C". That gives us:
. 1+2+3+4+5+6
-[1-2+3-4+5-6]
0+4+0+8+12...
By simplifying that answer, we get, 4+8+12+16... which can be reduced to 4(1+2+3+4...). So, what we have shown is:
C-B = 4C. We know B = 1/4, so solving for C we get: -B = 3C, so -1/4 = 3C, which gives us: C = -1/12!
Lets start with the series: 1-1+1-1+1...that goes on for infinity. For simplicity's sake, I'll call this series "A". Now, Depending on where you stop (which is never if you go on for infinity), the answer to this series is either 1 or 0. With that logic, you can say that A = 1/2, which is the average of 1 and 0.
Right there is the first error. The series does not converge, so it has no value under the usual meanings of converge.
[deleted] ยท -4 points ยท Posted at 20:02:19 on May 25, 2016 ยท (Permalink)
oighen ยท 1 points ยท Posted at 22:18:30 on May 25, 2016 ยท (Permalink)
It all boils down to the fact that there's no actual reason to change, writing 2ฯ or ฯ is the same thing, it's convention. Just use the symbol most people would recognize.
Saved comment
99999999999999999989 ยท 9218 points ยท Posted at 17:11:01 on May 25, 2016 ยท (Permalink)
99999999999999999989 is the largest prime number that can also be a Reddit username.
2_to_the_74207281-1 ยท 7356 points ยท Posted at 19:13:42 on May 25, 2016 ยท (Permalink)
hey, wait just a second...
imsometueventhisUN ยท 2427 points ยท Posted at 20:20:12 on May 25, 2016 ยท (Permalink)
Redditor for 4 months and this is your only comment. Beautiful.
2_to_the_74207281-1 ยท 384 points ยท Posted at 22:38:05 on May 25, 2016 ยท (Permalink)
I
amwas a committed lurker:-)
sdmitch16 ยท 8 points ยท Posted at 06:37:53 on May 26, 2016 ยท (Permalink)
Can I please ask what your username means?
h0suf ยท 14 points ยท Posted at 07:58:38 on May 26, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Largest_known_prime_number
Leash_Me_Blue ยท 7 points ยท Posted at 07:52:23 on May 26, 2016 ยท (Permalink)
It's a math equation.
It means 274207381 -1
sdmitch16 ยท 8 points ยท Posted at 08:20:50 on May 26, 2016 ยท (Permalink)
But what is 274207380? never mind. Someone already responded. Btw, you have the -1 superscripted which means the equation isn't the largest prime number.
SOncredible ยท 2 points ยท Posted at 06:22:51 on May 26, 2016 ยท (Permalink)
Just like a butterfly, waiting for the right moment
[deleted] ยท 71 points ยท Posted at 21:30:08 on May 25, 2016 ยท (Permalink)
Maybe it's OP's alt account
yaxamie ยท 28 points ยท Posted at 21:33:56 on May 25, 2016 ยท (Permalink)
Sweet lurking
sebastiankirk ยท 9 points ยท Posted at 22:42:46 on May 25, 2016 ยท (Permalink)
Don't spoil the fun! We choose to believe!
pilvlp ยท 18 points ยท Posted at 21:33:54 on May 25, 2016 ยท (Permalink)
He can delete comments.
imsometueventhisUN ยท 20 points ยท Posted at 21:35:38 on May 25, 2016 ยท (Permalink)
I WANT TO BELIEVE
dillionbowman ยท 4 points ยท Posted at 22:24:41 on May 25, 2016 ยท (Permalink)
sets back, cracks fingers well i know what im doing tonight
CrudelyAnimated ยท 6 points ยท Posted at 22:17:19 on May 25, 2016 ยท (Permalink)
"Gentlemen, our time is finally here."
addysol ยท 2 points ยท Posted at 23:14:51 on May 25, 2016 ยท (Permalink)
He's just been waiting for the right time to reveal himself
conquer69 ยท 4 points ยท Posted at 22:14:06 on May 25, 2016 ยท (Permalink)
Pretty sure it's his other account and he has been waiting months to post that. You people are really gullible.
99999999999999999989 ยท 12 points ยท Posted at 22:30:46 on May 25, 2016 ยท (Permalink)
Actually that is not me.
Jackpot777 ยท 18 points ยท Posted at 22:56:33 on May 25, 2016 ยท (Permalink)
So you're saying you didn't prime that response?
Ouroboron ยท 11 points ยท Posted at 23:43:17 on May 25, 2016 ยท (Permalink)
There aren't any factors to point to it.
99999999999999999989 ยท 5 points ยท Posted at 02:14:28 on May 26, 2016 ยท (Permalink)
Negative.
swordofthespirit ยท 3 points ยท Posted at 23:32:28 on May 25, 2016 ยท (Permalink)
I choose to believe this.
gnorty ยท 3 points ยท Posted at 23:23:01 on May 25, 2016 ยท (Permalink)
even so, it's a pretty sweet thing to behold, don't you think?
meistermichi ยท 1 points ยท Posted at 22:51:21 on May 25, 2016 ยท (Permalink)
Playing the long game
Sarcasrony ยท 1 points ยท Posted at 05:14:30 on May 26, 2016 ยท (Permalink)
I'm actually astonished
DattMownton ยท 1 points ยท Posted at 14:58:42 on May 26, 2016 ยท (Permalink)
And he gets gold for it....
dono111 ยท 1 points ยท Posted at 22:02:29 on May 25, 2016 ยท (Permalink)
He's been waiting 4 months for this!
HaplessMagician ยท 1 points ยท Posted at 23:43:58 on May 25, 2016 ยท (Permalink)
His comment karma is about 250 less than the two comments currently posted. This is his troll account. He just deletes the posts after. (I purge mine from time to time, so sometimes I have 30k comment karma and no comments)
ben1996123 ยท 91 points ยท Posted at 20:12:25 on May 25, 2016 ยท (Permalink)
I approve
[deleted] ยท 22 points ยท Posted at 21:05:53 on May 25, 2016 ยท (Permalink)
22 million digits. Since we're playing the bigger number game, let me just post a relevant link here. Enjoy the read!
Ninja edit: no fucks given the prime part. my bad.
Tommy2255 ยท 33 points ยท Posted at 22:37:25 on May 25, 2016 ยท (Permalink)
Haha, bite my shiny metal ass old article.
99999999999999999989 ยท 9 points ยท Posted at 22:41:32 on May 25, 2016 ยท (Permalink)
What sex manual are you using?
wannabesq ยท 8 points ยท Posted at 00:55:34 on May 26, 2016 ยท (Permalink)
Kama Sutra 2: Electric Boogaloo
99999999999999999989 ยท 1 points ยท Posted at 02:10:27 on May 26, 2016 ยท (Permalink)
FTFY
Cachinnatingcockatoo ยท 1 points ยท Posted at 18:10:06 on September 5, 2016 ยท (Permalink)
Ahem
https://en.wikipedia.org/wiki/AlphaGo_versus_Lee_Sedol
Tommy2255 ยท 2 points ยท Posted at 18:30:19 on September 5, 2016 ยท (Permalink)
3 months late and poor reading comprehension. Way to go.
Cachinnatingcockatoo ยท 1 points ยท Posted at 18:10:07 on September 5, 2016 ยท (Permalink)
Ahem
https://en.wikipedia.org/wiki/AlphaGo_versus_Lee_Sedol
99999999999999999989 ยท 5 points ยท Posted at 22:31:29 on May 25, 2016 ยท (Permalink)
A nice read as the others have said, but they completely ignored the factorial.
(BB(1000))!
hjqusai ยท 5 points ยท Posted at 01:59:11 on May 26, 2016 ยท (Permalink)
FTFY
methyboy ยท 1 points ยท Posted at 15:00:07 on May 26, 2016 ยท (Permalink)
They ignored the factorial because it's absolute child's play compared to the things discussed in the article.
99999999999999999989 ยท 1 points ยท Posted at 15:46:25 on May 26, 2016 ยท (Permalink)
Oh really? I don't see it that way. Factorial makes any number larger than 7 enormous relative to its original value.
Shaxys ยท 2 points ยท Posted at 16:23:04 on May 26, 2016 ยท (Permalink)
Wouldn't just taking the Busy Beaver function of 1005 instead of 1000 make that moot?
The factorial function grows very slowly compared to the functions discussed there, doesn't it?
99999999999999999989 ยท 1 points ยท Posted at 16:35:05 on May 26, 2016 ยท (Permalink)
Take the example of BB(4). BB(4) is 107. But 107! (which is (BB(4))!) = 1.23x10172.
So BB(4)! is profoundly larger than BB(4).
The same applies to BB(4!) which is BB(24) and is extremely large.
Shaxys ยท 1 points ยท Posted at 16:38:06 on May 26, 2016 ยท (Permalink)
But what is larger, BB(1000)! or BB(1005)?
Sure, the factorial increases the value a lot, but what's the point of taking f(a)! if f(a+2) is larger?
99999999999999999989 ยท 1 points ยท Posted at 16:46:20 on May 26, 2016 ยท (Permalink)
Well, yes. I think it will never be known which is a larger number. Heck BB(1001) could be larger.
I guess they were writing about making the "largest number" as a thought exercise to talk about the BB concept. But I'd still put the ! at the end to one up them.
methyboy ยท 1 points ยท Posted at 00:27:57 on May 27, 2016 ยท (Permalink)*
I'm sorry, but yes it is absolutely known which is bigger. BB(1001) is vastly, vastly, vastly larger than BB(1000)!. This is exactly what I meant when I said that factorials are child's play compared to things that are discussed in the article.
I mean, to try to give an idea of how fast it grows: it is not possible to compute BB(8000). It grows so damn fast that using our standard mathematical axioms, it is simply not possible to know what the value of BB(8000) is. It's just too big. Not in the sense that "we can't write it down in the universe" or something like that, but in the sense that we could never write down a well-defined mathematical expression and know for sure that it represents BB(8000), even in principle if we had as much space or time as we wanted.
Compare this to something like the factorial. It has a formula. Given enough time, we could, in principle, compute 8000! or 8000! or 99!99!99! or any other combination of any number of those symbols that you like. Even absurdly fast-growing things like Knuth's up-arrow notation, which most people already have a hard time getting their head around, is trivial compared to the Busy beaver function.
99999999999999999989 ยท 1 points ยท Posted at 00:32:09 on May 27, 2016 ยท (Permalink)
That may be, but in a contest I would write down BB(8000!)!. My point was that as enormous as these numbers are, they all can be increased immensely with just an exclamation point.
methyboy ยท 1 points ยท Posted at 00:40:43 on May 27, 2016 ยท (Permalink)*
And I would write down BB(BB(6)) and absolutely blow your number out of the water. In fact, you could write down 5 million extra factorials, and my BB(BB(6)) would still blow your number out of the water. You could write a factorial on every atom in the universe, and you would have wasted your time, since just writing one more BB() would have made more of an effect than all of those factorials combined.
In other words: my point is that factorials don't increasing things "immensely" from the point of view of the busy beaver function. Saying "BB(8000)! is immensely bigger than BB(8000)" is like saying "8000! + 1 is immensely bigger than 8000!".
methyboy ยท 1 points ยท Posted at 00:33:40 on May 27, 2016 ยท (Permalink)
To try to give a bit of a comparison here to explain why factorials are child's play:
You mentioned that BB(4)! is 1.23 x 10172 .
OK, but what is BB(BB(4)) (i.e., instead of doing an extra factorial, do an extra busy beaver)? Well, it's bigger than Graham's number, which is a number so large that you have to read a moderately lengthy Wikipedia article just to try to get a grasp on how big it is. It's a number that, even if you used power towers like 99999999... , there would not be enough space in the universe for you to write down a representation of it. You could write a 9 followed by a factorial sign on every atom in the observable universe, and you wouldn't have gotten close to Graham's number, which isn't even close to BB(BB(4)) (in fact, it's even less than BB(23)).
LoopyDagron ยท 1 points ยท Posted at 22:05:30 on May 25, 2016 ยท (Permalink)
I've been wondering where this went. Thank you.
thepeganator ยท 1 points ยท Posted at 22:12:04 on May 25, 2016 ยท (Permalink)
Great read. Feels very slightly dated but thoroughly interesting and well worth the full read to those interested.
genericlurker369 ยท 1 points ยท Posted at 22:25:56 on May 25, 2016 ยท (Permalink)
That was a good read, and it opened up many other paths for exploration. Thanks!
ImAScholarMother ยท 1 points ยท Posted at 00:55:43 on May 26, 2016 ยท (Permalink)
Holy shit, that was long.
See you tomorrow!
apodo ยท 31 points ยท Posted at 20:58:42 on May 25, 2016 ยท (Permalink)
He mersenne be allowed to get away with that.
GodICringe ยท 2 points ยท Posted at 00:35:39 on May 26, 2016 ยท (Permalink)
Ha better than any pun I could come up with.
Humpa ยท 8 points ยท Posted at 21:49:56 on May 25, 2016 ยท (Permalink)
Outstanding. Absolutely outstanding.
duncan_booty ยท 7 points ยท Posted at 22:08:58 on May 25, 2016 ยท (Permalink)
I just did my final about you
Jawas_Did_911 ยท 4 points ยท Posted at 22:55:16 on May 25, 2016 ยท (Permalink)
Mersenne-ger from God
punzybobo ยท 4 points ยท Posted at 23:16:04 on May 25, 2016 ยท (Permalink)
r/retiredusername
boomerangbro10 ยท 5 points ยท Posted at 19:25:19 on May 25, 2016 ยท (Permalink)
(username)
3pidividedby7degrees ยท 5 points ยท Posted at 20:05:05 on May 25, 2016 ยท (Permalink)
(username)*Times reddit post=0?
g18suppressed ยท 5 points ยท Posted at 22:19:40 on May 25, 2016 ยท (Permalink)
/r/museum_of_reddit
[deleted] ยท 2 points ยท Posted at 06:27:36 on May 26, 2016 ยท (Permalink)
I mean, if we are being technical, we can have a username that reads u/primetoobigforusernm
AStormofSwines ยท 1 points ยท Posted at 06:15:17 on May 26, 2016 ยท (Permalink)
you just destroyed Mr. 99989's whole reason d'etre. Well done.
[deleted] ยท 1 points ยท Posted at 13:59:41 on May 26, 2016 ยท (Permalink)
i hate you, you have 2 comments and more than 4500 karma
thePurpleAvenger ยท 1 points ยท Posted at 20:51:57 on May 25, 2016 ยท (Permalink)
Apparently they haven't heard of Mersenne primes! Well done sir, well done.
X7123M3-256 ยท 600 points ยท Posted at 18:44:18 on May 25, 2016 ยท (Permalink)
Unless you use hexadecimal
Halyon ยท 528 points ยท Posted at 18:52:26 on May 25, 2016 ยท (Permalink)
If you allow that, you could have 10 as a prime in base p, where p is the largest known prime :P
X7123M3-256 ยท 25 points ยท Posted at 18:57:36 on May 25, 2016 ยท (Permalink)
True. But you could fit the prime written in hexadecimal and the base it's written in (itself written in base 10) in a Reddit username:
Halyon ยท 21 points ยท Posted at 18:59:56 on May 25, 2016 ยท (Permalink)
True. I wonder what the largest such prime that can be expressed along with the base used to express it in a fixed number of characters is.
DanRoad ยท 11 points ยท Posted at 21:41:52 on May 25, 2016 ยท (Permalink)
WolframAlpha is your friend.
I've used a range of values for
xto find the largest primes in decimal, hexadecimal, base64, ASCII and extended ASCII (but those last two might be hard to post in a comment).I've also used
y=20to match the maximum reddit username length, but you can obviously change that if you want a larger number of characters.Sticking with reddit usernames:
Base 10 gives
99999999999999997_10.Base 16 gives
fffffffffffffffe9_16(295147905179352825833_10).Base 64 gives
________________f_64(5070602400912917605986812821471_10), but you have to remember that the final underscore is separating the number and the base and isn't part of the number itself.________________f_64 ยท 19 points ยท Posted at 21:54:07 on May 25, 2016 ยท (Permalink)
Excellent. I just took this one too. (99999999999999999989 here)
Thanks a lot! :)
b4b ยท -5 points ยท Posted at 22:06:47 on May 25, 2016 ยท (Permalink)
Why do you "collect" reddit user names? This is not cool. It just makes you a jerk. Someone one day might come out with such a clever name only to learn that it was used by you.
And technically you can be hit by a bus tomorrow + reddit does not really delete old accounts.
99999999999999999989 ยท 10 points ยท Posted at 22:27:50 on May 25, 2016 ยท (Permalink)
Well I only have like...four maybe. So there's that. And to be honest, this one is the most clever. And last time I checked, usernames were not some sort of commodity or anything.
EDIT: Mentally I just made my first million. A username parking scheme to sell especially clever ones to desperate people.
ManPumpkin ยท 1 points ยท Posted at 00:50:11 on May 26, 2016 ยท (Permalink)
Yeah but you have all the cool ones :(
99999999999999999989 ยท 1 points ยท Posted at 02:10:50 on May 26, 2016 ยท (Permalink)
So get some other coolness.
b4b ยท 0 points ยท Posted at 23:18:09 on May 25, 2016 ยท (Permalink)
Guess you never heard about /r/2ch and /r/3ch
99999999999999999989 ยท 2 points ยท Posted at 02:12:40 on May 26, 2016 ยท (Permalink)
Nope. But I do mod /r/usernameisnumbers
Halyon ยท 2 points ยท Posted at 22:40:42 on May 25, 2016 ยท (Permalink)
That's a clever use of NextPrime, never thought to use it like that! Very nice :) of course these are increasing in size for (relatively) small bases b but there must come a point if we include the base in the username where the base takes too much of the available space (if the base is 20 digits long, for instance) so I'd reason that a maximum over b exists - in the morning I may look into finding it, which should be reasonably straightforward (wolfram seems to be handling it well for x=1015 in your example).
DarthEru ยท 1 points ยท Posted at 23:32:17 on May 25, 2016 ยท (Permalink)
If you're ok with using arbitrary bases and unconventional conventions, I came up with an answer over here, and in a followup comment.
And yes, as you suspected the length of the base matters. For finding the largest number (non-prime), I basically just compared all the values of
{highest digit x times}_{9 (19-x) times} for x in 1..18. So if 9 was the highest digit I would have calculated999999999999999999_9to9_999999999999999999. From the few experiments I've done it looks like the base can take up about half the string before the value starts going down, although that's obviously not a proof.R3D1AL ยท 0 points ยท Posted at 21:11:26 on May 25, 2016 ยท (Permalink)
He writes the prime in hexadecimal and then writes the base in decimal.
If we could use different bases to write what base we're using then we could go back to /u/Halyon 's suggestion and just say 10_10. Which makes me realize how ridiculous writing base-10 is.
reply_to_R3D1AL ยท 2 points ยท Posted at 22:59:34 on May 25, 2016 ยท (Permalink)
Relevant webcomic: http://cowbirdsinlove.com/43
ableman ยท 6 points ยท Posted at 19:00:25 on May 25, 2016 ยท (Permalink)
But then why limit yourself to base 16, how many different characters does reddit accept for usernames? That's the base you should go to (although, I guess it'll get ambigious if you start using things other than letters and numbers, so you have to limit yourself to base 36, maybe 37 if you want to be weasily).
Rodents210 ยท 9 points ยท Posted at 19:53:13 on May 25, 2016 ยท (Permalink)
26 lowercase + 26 uppercase + 10 numeric +
-+_are the valid username characters, which together make the standard base64url format defined in RFC-4648.But if you adhere to the rule saying you need the
_to express the base at the end, that means you can only express it in Base63. There's no standard out there so while you could assume-to be high, you wouldn't intuitively know whether lowercase came before uppercase, etc. Then again, you can go down to Base62 and there's no standard for that, either...In the end either you can have Base64URL without expressing the base at the end or a nonstandard Base63/Base62 implementation, which could just be a Base64URL encoding without the
_(or-either, maybe, depending on which you choose) since_comes at the end of Base64URL.99999999999999999989 ยท 6 points ยท Posted at 20:05:07 on May 25, 2016 ยท (Permalink)
Somewhere I feel, there is a pre-doctoral Grad Student who will make this task his thesis.
Rodents210 ยท 10 points ยท Posted at 20:29:23 on May 25, 2016 ยท (Permalink)
I'm jealous of whoever has a thesis that could be completed with five minutes on Wolfram Alpha.
wolgo ยท 2 points ยท Posted at 21:10:40 on May 25, 2016 ยท (Permalink)
I would argue that you just need to express the base in a clear way, which might be clear with ร64. ร looks like a B of รase anyway..
Rodents210 ยท 1 points ยท Posted at 21:47:34 on May 25, 2016 ยท (Permalink)
That isn't a valid character for usernames.
wolgo ยท 1 points ยท Posted at 06:47:40 on May 26, 2016 ยท (Permalink)
O yeah >.<
DarthEru ยท 1 points ยท Posted at 22:31:15 on May 25, 2016 ยท (Permalink)
I was thinking the way you were thinking, but then I realized that you aren't actually limited to base 63 or 64. You're just limited to the first 63 (or 64 if you treat the last underscore as special) digits of whatever base you want! With that in mind, this is the largest number that can be expressed in that format that could also be a reddit username:
Convention: the digits go the following order
0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ-, the base is expressed in base 10, and we are disallowing_to be used in the number itself.That number in base 10 is
Which is pretty large. Note that it's not a prime. I'm planning to try to find the largest prime than can be expressed using the same convention, but it's a bit trickier. I just found the largest integer because I think it'll come in handy as an upper bound.
99999999999999999989 ยท 2 points ยท Posted at 22:40:17 on May 25, 2016 ยท (Permalink)
Right. First prime you get by subtraction starting there, then convert to your base. Kewl.
DarthEru ยท 1 points ยท Posted at 22:54:14 on May 25, 2016 ยท (Permalink)
Hah, yeah, it would be expressed as
---------Z_999999999. I thought I'd have to do a bit more work to find it. Oh well.Rodents210 ยท 1 points ยท Posted at 22:41:27 on May 25, 2016 ยท (Permalink)
I figured it was obvious that the username needs to be readable without guessing, given that I dedicated most of my post to that idea.
----------_999999999is purely meaningless because there is no standard for Base 999999999 and therefore no meaningful way to determine what-corresponds to in that base. Your "convention" is arbitrary and therefore useless.X7123M3-256 ยท 1 points ยท Posted at 19:50:12 on May 25, 2016 ยท (Permalink)
Yes, 16 is not the optimum, I just didn't bother to calculate what the actual highest prime you could get with this method would be.
eduardog3000 ยท 3 points ยท Posted at 21:43:24 on May 25, 2016 ยท (Permalink)
Or save a character by using
0xinstead of_16.titansabove ยท 1 points ยท Posted at 23:07:34 on May 25, 2016 ยท (Permalink)
Unfortunately that leaves 0xffffffffffffffffa3 as the username which is already taken...
Terdol ยท 2 points ยท Posted at 20:29:22 on May 25, 2016 ยท (Permalink)
Hey, why limit yourself to largest KNOWN prime? Let's go all out!
Halyon ยท 2 points ยท Posted at 20:48:34 on May 25, 2016 ยท (Permalink)
You gotta stop somewhere.
Deadmeat553 ยท 2 points ยท Posted at 22:33:05 on May 25, 2016 ยท (Permalink)
The problem with primes is that the higher you get, the rarer they get. As a limit, we can see that as we approach infinity, there are infinite whole numbers between one prime to the next. The "biggest prime" is undefined.
Halyon ยท 2 points ยท Posted at 22:34:43 on May 25, 2016 ยท (Permalink)
Oh I know that "biggest prime" is undefined. That was my point. With an infinitude of primes, you have to stop somewhere.
gnorty ยท -2 points ยท Posted at 23:26:36 on May 25, 2016 ยท (Permalink)
and his chosen stopping point was that the number could be fitted into a reddit username. I'm not seeing the point you are trying so hard to make...
akira410 ยท 2 points ยท Posted at 00:19:33 on May 26, 2016 ยท (Permalink)
Every base is base 10.
blightedfire ยท 1 points ยท Posted at 22:54:55 on May 25, 2016 ยท (Permalink)
Not really. There are an infinite number of primes. :P
NMDA ยท 1 points ยท Posted at 22:59:48 on May 25, 2016 ยท (Permalink)
But you would need to state which prime in the username or it isn't clearly defined. Checkmate!
[deleted] ยท 1 points ยท Posted at 04:24:31 on May 26, 2016 ยท (Permalink)
:10
99999999999999999989 ยท 12 points ยท Posted at 20:29:20 on May 25, 2016 ยท (Permalink)
FTFY
[deleted] ยท 2 points ยท Posted at 02:53:49 on May 26, 2016 ยท (Permalink)
99999999999999999989 ยท 2 points ยท Posted at 02:59:52 on May 26, 2016 ยท (Permalink)
Hey shaddap.
njofra ยท 2 points ยท Posted at 20:08:30 on May 25, 2016 ยท (Permalink)
Base 64 is where it's at.
[deleted] ยท 2 points ยท Posted at 21:15:02 on May 25, 2016 ยท (Permalink)
If we're going to be on the subject of annoying bases, -4 is more fun.
[deleted] ยท 1 points ยท Posted at 21:38:31 on May 25, 2016 ยท (Permalink)
I'm no mathematican and would need an eli5 but do prime numbers work differently when it's not Base 10?
X7123M3-256 ยท 1 points ยท Posted at 21:57:22 on May 25, 2016 ยท (Permalink)
No. A prime number is a number with no divisors other than itself and 1. This is independent of any specific choice of representation. A numerical base is just a way of writing things down.
[deleted] ยท 1 points ยท Posted at 22:04:15 on May 25, 2016 ยท (Permalink)
OK, I was more wondering if the fractions end up different when using bin, Oct, hex etc...
Deadmeat553 ยท 1 points ยท Posted at 22:25:10 on May 25, 2016 ยท (Permalink)
Base 12, baby.
iwiggums ยท 1 points ยท Posted at 23:16:22 on May 25, 2016 ยท (Permalink)
You guys are such nerds. I love it.
GMaestrolo ยท 1 points ยท Posted at 23:23:39 on May 25, 2016 ยท (Permalink)
Actually, you could base64 up in this bitch. Or at least a version of it.
a-z, A-Z, 0-9, -_
26 + 26 + 10 + 2 = 64
Eonexas ยท 1 points ยท Posted at 23:50:45 on May 25, 2016 ยท (Permalink)
But you don't have gold.
rphkhr ยท 12 points ยท Posted at 21:48:52 on May 25, 2016 ยท (Permalink)
/r/retiredusername
Eiroth ยท 10 points ยท Posted at 19:15:52 on May 25, 2016 ยท (Permalink)
How is this not a throwaway
99999999999999999989 ยท 30 points ยท Posted at 19:21:46 on May 25, 2016 ยท (Permalink)
Because that's how I roll, bitch!
delta_baryon ยท 7 points ยท Posted at 19:17:38 on May 25, 2016 ยท (Permalink)
...and you didn't even make the account just to answer the question.
jaredjeya ยท 12 points ยท Posted at 19:14:43 on May 25, 2016 ยท (Permalink)
Account Age: 2 years.
Neat :)
phillyeagle99 ยท 5 points ยท Posted at 20:28:05 on May 25, 2016 ยท (Permalink)
Username checks out.
redoubledit ยท 3 points ยท Posted at 19:17:31 on May 25, 2016 ยท (Permalink)
Long planned!
99999999999999999989 ยท 12 points ยท Posted at 19:22:00 on May 25, 2016 ยท (Permalink)
Nothing better than the long game.
I-Downloaded-a-Car ยท 3 points ยท Posted at 20:02:14 on May 25, 2016 ยท (Permalink)
Nothing better than the long dong
LordSoren ยท 3 points ยท Posted at 20:15:48 on May 25, 2016 ยท (Permalink)
Except the long dong con.
grande1899 ยท 2 points ยท Posted at 20:02:55 on May 25, 2016 ยท (Permalink)
Calling the gold
Kar0nt3 ยท 2 points ยท Posted at 20:55:23 on May 25, 2016 ยท (Permalink)
Now that's a fact I can use on my everyday life.
99999999999999999989 ยท 2 points ยท Posted at 20:59:11 on May 25, 2016 ยท (Permalink)
I surely do.
seanfish ยท 2 points ยท Posted at 22:59:24 on May 25, 2016 ยท (Permalink)
I like you.
99999999999999999989 ยท 2 points ยท Posted at 02:22:37 on May 26, 2016 ยท (Permalink)
I love you man!
seanfish ยท 2 points ยท Posted at 02:28:07 on May 26, 2016 ยท (Permalink)
<3
99999999999999999989 ยท 2 points ยท Posted at 02:30:52 on May 26, 2016 ยท (Permalink)
(no homo)
seanfish ยท 2 points ยท Posted at 02:41:22 on May 26, 2016 ยท (Permalink)
It's just bros hugging.
99999999999999999989 ยท 2 points ยท Posted at 02:44:07 on May 26, 2016 ยท (Permalink)
Exactly. Definitely not meeting up for kisses.
seanfish ยท 1 points ยท Posted at 03:07:07 on May 26, 2016 ยท (Permalink)
No. Nooooo. Nope. Definitely not.
99999999999999999989 ยท 2 points ยท Posted at 03:09:03 on May 26, 2016 ยท (Permalink)
[awkward shuffling of feet]
So, yeah. Yeah! How about them Yankees eh?
seanfish ยท 2 points ยท Posted at 03:12:09 on May 26, 2016 ยท (Permalink)
Yeah, they're playing a really sexy year this year.
Uh, great year. I meant great year. Haha how could a bunch of muscly guys be sexy, am I right? Hahaha ahahaha...
99999999999999999989 ยท 1 points ยท Posted at 03:15:30 on May 26, 2016 ยท (Permalink)
I hope my wife does not find this thread.
seanfish ยท 2 points ยท Posted at 03:19:05 on May 26, 2016 ยท (Permalink)
Me too although I'm sure she'd just laugh at me. :)
Either way, props for being that dedicated to prime numbers and finding a post that let it be known.
99999999999999999989 ยท 2 points ยท Posted at 03:21:05 on May 26, 2016 ยท (Permalink)
Wait. How do you know my wife? Have you been looking in my windows?
seanfish ยท 2 points ยท Posted at 03:26:23 on May 26, 2016 ยท (Permalink)
I don't know her; I'm just pretty sure she'd just laugh at me.
heirtotyrone ยท 1 points ยท Posted at 21:52:38 on May 26, 2016 ยท (Permalink)
That entire conversation sure was something.
cjan34 ยท 2 points ยท Posted at 23:51:15 on May 25, 2016 ยท (Permalink)
Username checks out.
becauzetheinternet ยท 1 points ยท Posted at 19:47:51 on May 25, 2016 ยท (Permalink)
Nice
[deleted] ยท 1 points ยท Posted at 20:14:27 on May 25, 2016 ยท (Permalink)
[deleted]
99999999999999999989 ยท 0 points ยท Posted at 20:28:49 on May 25, 2016 ยท (Permalink)
And I just saved 15% on my car insurance by switching to Geico!
SnipeCity73 ยท 1 points ยท Posted at 20:47:39 on May 25, 2016 ยท (Permalink)
Nice
Squibbles1 ยท 1 points ยท Posted at 21:45:02 on May 25, 2016 ยท (Permalink)
not anymore...
[deleted] ยท 1 points ยท Posted at 21:54:17 on May 25, 2016 ยท (Permalink)
[deleted]
99999999999999999989 ยท 1 points ยท Posted at 21:55:23 on May 25, 2016 ยท (Permalink)
Not prime
Deadmeat553 ยท 1 points ยท Posted at 22:22:44 on May 25, 2016 ยท (Permalink)
In base 10, maybe! Base 12 master race!
99999999999999999989 ยท 1 points ยท Posted at 22:28:22 on May 25, 2016 ยท (Permalink)
Meh. I took the Base 64 one too. So I think that seals it.
an_account_name_219 ยท 1 points ยท Posted at 23:15:50 on May 25, 2016 ยท (Permalink)
How can there be a largest prime number?
99999999999999999989 ยท 1 points ยท Posted at 02:06:50 on May 26, 2016 ยท (Permalink)
"that can also be a Reddit username"
an_account_name_219 ยท 1 points ยท Posted at 02:13:01 on May 26, 2016 ยท (Permalink)
Oh, I'm sorry. For some reason I read it as, "and can also...".
Senposai ยท 1 points ยท Posted at 23:17:37 on May 25, 2016 ยท (Permalink)
amazing. thank you. i hope you never comment again. or that you do if you want too.
99999999999999999989 ยท 1 points ยท Posted at 02:13:58 on May 26, 2016 ยท (Permalink)
Well the account is two years old so I'll probably keep going.
max81968 ยท 1 points ยท Posted at 23:26:35 on May 25, 2016 ยท (Permalink)
Lol.
Left4Head ยท 1 points ยท Posted at 23:46:14 on May 25, 2016 ยท (Permalink)
Did you get your username from Ali G?
99999999999999999989 ยท 1 points ยท Posted at 02:11:15 on May 26, 2016 ยท (Permalink)
No sir I did not.
ubspirit ยท 1 points ยท Posted at 00:01:55 on May 26, 2016 ยท (Permalink)
And it's also a code word for " failed out of high school math".
951402 ยท 1 points ยท Posted at 06:00:01 on May 26, 2016 ยท (Permalink)
Username checks out
funkyasl ยท 1 points ยท Posted at 06:25:09 on May 26, 2016 ยท (Permalink)
But, this is not a prime number. It's divisible by 3 and 9 to say the least.
99999999999999999989 ยท 1 points ยท Posted at 12:26:09 on May 26, 2016 ยท (Permalink)*
No. It is not. It is a prime number. There is an 8 in there.
xFlopsies ยท 1 points ยท Posted at 07:21:44 on May 26, 2016 ยท (Permalink)
Name checks out
countryboyathome ยท 1 points ยท Posted at 17:43:00 on May 26, 2016 ยท (Permalink)
Optimus?
The_________________ ยท 1 points ยท Posted at 20:17:11 on May 25, 2016 ยท (Permalink)*
Why not 99999999999999999999?
Edit: I completely overlooked the word "prime"
99999999999999999989 ยท 4 points ยท Posted at 20:27:56 on May 25, 2016 ยท (Permalink)
...
Because that is not a prime number.
boomerangbro10 ยท 2 points ยท Posted at 20:29:37 on May 25, 2016 ยท (Permalink)
11111111111111111111 * 9
NotSorryIfIOffendYou ยท 4842 points ยท Posted at 12:32:06 on May 25, 2016 ยท (Permalink)
You can almost perfectly convert miles and kilometers using the Fibonnaci sequence.
1 1 2 3 5 8 13 21 34....
Each number, after a few, is miles and the number after it is very nearly the corresponding number of kilometers and vice versa.
vidarino ยท 1801 points ยท Posted at 15:06:59 on May 25, 2016 ยท (Permalink)
Neat, never thought of that.
Makes perfect sense, though, since phi (the factor the sequence increases with) is 1.618, and there is 1.609 km in a mile.
[deleted] ยท 33 points ยท Posted at 17:22:27 on May 25, 2016 ยท (Permalink)
As an engineer I just use a factor of 0.5 when backpacking and need to translate for my American friends. I keep my gps in kilometers and they always want miles. It is close enough and super easy.
bobocalender ยท 34 points ยท Posted at 18:26:34 on May 25, 2016 ยท (Permalink)
It takes a tiny bit longer to do in your head, but just multiplying
mileskilometers by 3/5 is still pretty easy and gets an even closer estimate.pemboo ยท 30 points ยท Posted at 18:55:07 on May 25, 2016 ยท (Permalink)
If you're going to that trouble, 5 miles is about 8km...
revolucionario ยท 18 points ยท Posted at 19:07:58 on May 25, 2016 ยท (Permalink)
Yeah, that's how I do it. I count the 10s and 5s and convert them to 16s and 8s and vice versa.
firechill2004 ยท 1 points ยท Posted at 02:56:09 on May 26, 2016 ยท (Permalink)
You all convert miles and kilometers a lot?
revolucionario ยท 1 points ยท Posted at 08:16:17 on May 26, 2016 ยท (Permalink)
I grew up with km and now live in a country using miles.
Jiecut ยท 4 points ยท Posted at 19:09:42 on May 25, 2016 ยท (Permalink)
21 miles is about 34 km.
[deleted] ยท 2 points ยท Posted at 19:50:01 on May 25, 2016 ยท (Permalink)
34 miles is about 55km
phi186 ยท 3 points ยท Posted at 20:09:29 on May 25, 2016 ยท (Permalink)
55 miles is about 89 km.
Humpa ยท 7 points ยท Posted at 21:47:55 on May 25, 2016 ยท (Permalink)
89 miles is exactly 143.232 km
casey12141 ยท 11 points ยท Posted at 22:14:13 on May 25, 2016 ยท (Permalink)
load more comments (89 replies)
Yanman_be ยท 1 points ยท Posted at 22:26:15 on May 25, 2016 ยท (Permalink)
143.232 replies.
PacificBrim ยท 4 points ยท Posted at 20:17:48 on May 25, 2016 ยท (Permalink)
One could say this is a 3/5ths compromise
[deleted] ยท 1 points ยท Posted at 20:17:29 on May 25, 2016 ยท (Permalink)
If you're 3 clicks from the car it doesn't matter much. 1.5 miles is close enough to 1.8 miles, especially if you consider significant figures and round to the nearest whole mile, i.e., "about 2 miles."
[deleted] ยท 7 points ยท Posted at 19:08:59 on May 25, 2016 ยท (Permalink)
I use .5 and if the number's big I add another 10%.
2 km is about 1 mile and 20 km is about 12
I_MELT_STEEL_BEAMS ยท 2 points ยท Posted at 01:44:47 on May 26, 2016 ยท (Permalink)
I'm not alone!
spartanburt ยท 1 points ยท Posted at 22:32:13 on May 25, 2016 ยท (Permalink)
You need to help other people to divide by 2?
[deleted] ยท 1 points ยท Posted at 00:20:49 on May 26, 2016 ยท (Permalink)
Kilometers is completely foreign to most Americans. So is centigrade.
kangareagle ยท 1 points ยท Posted at 00:32:04 on May 26, 2016 ยท (Permalink)
As an engineer you do that. Ok.
[deleted] ยท 1 points ยท Posted at 00:41:21 on May 26, 2016 ยท (Permalink)
Thanks for your approval.
kangareagle ยท 1 points ยท Posted at 01:25:10 on May 26, 2016 ยท (Permalink)
As a tech writer, you're welcome.
[deleted] ยท 5 points ยท Posted at 20:38:59 on May 25, 2016 ยท (Permalink)
I always doubled the miles and then took off 20% since getting 20% is easy.
Never knew exactly how many km to a mile, but if those numbers are right, then you can get a ridiculously accurate estimate by averaging the Fibonacci answer and the minus 20% answer. Neat.
AddictiveSombrero ยท 3 points ยท Posted at 17:24:02 on May 25, 2016 ยท (Permalink)*
What do you mean by "the factor the sequence increases with"? I'm tired and just tried multiplying each value in the sequence by 1.618, which produced a result that was close. Granted, I've not covered this stuff yet in school.
vidarino ยท 38 points ยท Posted at 17:41:21 on May 25, 2016 ยท (Permalink)
It doesn't start off like that, but the factor approaches 1.618 - the golden ratio - as the sequence goes on.
AddictiveSombrero ยท 2 points ยท Posted at 18:06:39 on May 25, 2016 ยท (Permalink)
Ah, thanks. Looking forward to learning more about this stuff :D
pemboo ยท 4 points ยท Posted at 18:56:29 on May 25, 2016 ยท (Permalink)
Did you know you can write out an explicit formula to find the n-th number in the fibonacci sequence!?
Now that's mind blowing when you first find out!
DrShocker ยท 3 points ยท Posted at 19:26:29 on May 25, 2016 ยท (Permalink)
Why don't you share what that formula is then?
pemboo ยท 8 points ยท Posted at 19:39:47 on May 25, 2016 ยท (Permalink)
As with a lot of maths, the journey is as interesting, if not better, than the destination itself so I'll leave you with a video showing how you get there.
https://www.youtube.com/watch?v=whbjsLicdwM
ThePhantomOf ยท 3 points ยท Posted at 20:07:07 on May 25, 2016 ยท (Permalink)
There's a very elegant way you can get this formula via some linear algebra also :)
pemboo ยท 1 points ยท Posted at 20:14:31 on May 25, 2016 ยท (Permalink)
Yeah! That's the beauty of the result I think, a linear combination of 2 irrationals that gives integer results.
DrShocker ยท 1 points ยท Posted at 19:54:32 on May 25, 2016 ยท (Permalink)*
The most interesting things to me was that it actually has the golden ratio, phi, in there (it's (1+sqrt(5))/2 which is irrational, so you also need to divide my square root 5 to be able to get integers out of the formula.
Other than that, it reminded me of differential equations, and I thought I had moved past that stage in my life.
pemboo ยท 1 points ยท Posted at 20:11:57 on May 25, 2016 ยท (Permalink)
It is differential equations.
What's more interest is that it's a linear combination of 2 irrationals that leads to integer results.
MAFFS
DrShocker ยท 1 points ยท Posted at 20:14:39 on May 25, 2016 ยท (Permalink)
What are you trying to convey here?
casey12141 ยท 1 points ยท Posted at 22:42:34 on May 25, 2016 ยท (Permalink)
Not only that, but you can take it a step further and do it only using bit operations: https://paulhankin.github.io/Fibonacci/
[deleted] ยท 20 points ยท Posted at 17:52:28 on May 25, 2016 ยท (Permalink)
The ratio between two sequential numbers in the series approaches 1.618 as the numbers get larger. 3/2 = 1.5, 5/3 = 1.66, 8/5 = 1.6, 13/8 = 1.625 ... 144/89 = 1.6179.
If you're interested, this is called a "limit". A proof is here.
AddictiveSombrero ยท 4 points ยท Posted at 18:07:04 on May 25, 2016 ยท (Permalink)
Thanks :D
eltoro ยท 1 points ยท Posted at 00:42:55 on May 26, 2016 ยท (Permalink)
Phi is the most irrational number because it is the hardest to approximate accurately with fractions.
Related to the fact that the continued fraction is 1,1,1,1,1,...
lerjj ยท 8 points ยท Posted at 17:51:34 on May 25, 2016 ยท (Permalink)*
So first, we're going to do this by inspection - the first couple of Fibonacci numbers are 1,1,2,3,5,8,13,... The ratio between successive terms are 1,2,1.5,1.67,1.6,1.625... It would appear that the ratio is settling down to be something like 1.6 Checking successively higher values we find that it is very close to 1.618 which is approximately the golden ratio phi (which in turn is the positive solution to x2 =x+1). Now for the proof:
Assume that for sufficiently far in terms, they are in a fixed ratio of r. We'll now consider three terms: F1, F2 and F3. By the construction of the Fibonacci sequence, F3=F2+F1, and since they are in constant ratio, F2=rF1 and F3=r2F1. Plugging that in gives r2 =r+1, i.e. r=phi (where phi~1.618...)
Edit: Clarified Language
AddictiveSombrero ยท 5 points ยท Posted at 18:06:18 on May 25, 2016 ยท (Permalink)
Uh, I guess I should have clarified that I'm still in high school (England), so some of the vocabulary you're using is alien to me.
lerjj ยท 1 points ยท Posted at 18:23:02 on May 25, 2016 ยท (Permalink)
I tidied it up a little (some of what I wrote had tried to format itself which I didn't expect, and it didn't do a great job of it). I'm also (kinda) at school in England. (I'm on exam leave for A2s, so I've already had my official last day).
AddictiveSombrero ยท 2 points ยท Posted at 18:39:51 on May 25, 2016 ยท (Permalink)
Thanks for the help, and grats on finishing your exams :D I'm still mid-GCSEs, but they're probably incomparable to A2s/A levels.
lifelongfreshman ยท 0 points ยท Posted at 18:41:02 on May 25, 2016 ยท (Permalink)
F1, F2, and F3 here are just any random trio of sequential numbers in the sequence, called F, with what would be a subscript to let you tell the difference, if reddit allowed subscripts. It looks like r is the constant ratio mentioned above, 1.618.
Fixing his notation a bit, where reddit's markdown got weird, what he wrote is:
1. F3 = F2 + F1
2. F2 = r * F1
3. F3 = r2 * F1
4. Substituting Equations 2 and 3 into Equation 1 yields r2 * F1 = r * F1 + F1, which simplifies into r2 = r + 1
Where F1 is any number you care to choose in the sequence, F2 is the next number in the sequence after F1, and F3 is the next number in the sequence after F2. If it helps, we can define them as F1=3, F2=5, and F3=8. They could also be defined as F1=1, F2=2, and F3=3. Or F1=34, F2=55, and F3=89. It doesn't really matter, all that matters is that F1 is the number immediately before F2 in the sequence, and F2 is the number immediately before F3 in the sequence.
Equations 1 through 3 are the basic definitions of our pattern, the Fibbonaci Sequence. Equation 1 says that any position in the sequence is equal to the sum of the two numbers that came before it. Equation 2 says that any number in the sequence is also equal to some constant value multiplied by the number that came before it. Equation 3 extends this to say that any number in the sequence is equal to that constant value from before, squared, multiplied by the number that came two places before it. Finally, in Equation 4, we substitute the values in Equations 2 and 3 into Equation 1, which puts Equation 1 into terms of our variable F1. Since all the terms in our new substitution are multiplied by our variable F1, we can divide both sides of the equation by F1 to yield the simplified form.
What this does is allow us to isolate this constant multiple. If you were to take another look at Equation 2, you'd see that any number in the sequence divided by the number that came before it in the sequence is equal to r (or, to rewrite the equation: F2/F1 = r). A ratio is just the result of dividing any two numbers. However, the ratio in this sequence is special: No matter which two F2 and F1 you pick, so long as they share the defined relationship above, they will be within .5 of the same value as any other two. So yes, 2/1 = 2, but let's choose numbers farther along in the sequence. If F2 = 89 and F1 = 55, 89/55 = 1.618182. Take it to the next step beyond that, set F1 = 89 and F2 = 144, and you get 144/89 = 1.617978. And the numbers will keep getting closer to each other the farther along you get. We would normally call what's happening here a limit, but that's either pre-Calculus or Calculus material, and I'm not sure if you're that far yet.
He finished by saying r = phi, because phi is (from what I just looked up, so I didn't know this until just now) the symbol used when referring to the Golden Ratio, which is defined by simplifying the simplified form of Equation 4 up there to get r = 1 + 1/r. Phi, for what it's worth, is just a Greek letter. Mathematics, and just about every discipline that uses it, will use Greek letters as extra variables, or sometimes as specific variables, in order to note that whatever it is representing is different from a regular number.
I, uh. I tried my best to explain this simply, realized half way through that I was writing a wall of text, got to the end and now I'm fairly sure I've done nothing useful. But I put too much time into this to not post it. So I hope it helps.
AddictiveSombrero ยท 1 points ยท Posted at 19:24:49 on May 25, 2016 ยท (Permalink)
Thanks for putting in the effort, I think I understand now. In my understanding, if Fn is any position in the sequence, then
(http://i.imgur.com/F5XF24i.png) (This was the best text version I could make)
approaches Fn as n increases, with
being the aforementioned 1.618.
hobbycollector ยท 1 points ยท Posted at 20:13:51 on May 25, 2016 ยท (Permalink)
Thanks, never had the explanation.
agumonkey ยท 1 points ยท Posted at 23:20:33 on May 25, 2016 ยท (Permalink)
So a kilometer is just a phile ?
TheVeryMask ยท 1 points ยท Posted at 01:30:56 on May 26, 2016 ยท (Permalink)
Also works with any sequence of that format. Only really worth doing Fibonacci and Lucas numbers (1 3 4 7 11 18 29 47 76...), and then you only need to do the Lucas numbers up to 29 because after that they start approximating earlier numbers. 29 -> 47 is basically 3 -> 5 from Fibonacci.
ktkps ยท 1 points ยท Posted at 04:55:16 on May 26, 2016 ยท (Permalink)
The universe and our world is ruled by Pi Man.....
SleestakJack ยท 62 points ยท Posted at 15:14:02 on May 25, 2016 ยท (Permalink)
That ratio approaches phi, which is 1.618...
The ratio of miles to kilometers is 1.609.
Pretty close.
CharlieDancey ยท 12 points ยท Posted at 19:06:20 on May 25, 2016 ยท (Permalink)
Interestingly, you can start a pseudo-Fibonacci series with any two numbers and the ratio between consecutive numbers will still rapidly converge on phi: lets do 8 and 100 for the hell of it:
8, 100, 108, 208, 316, 524, 840, 1364...
1364/840 = 1.62380952380952 - pretty damn close.
Keep going and it will become exquisitely close.
happyfeett ยท 1 points ยท Posted at 09:06:59 on May 26, 2016 ยท (Permalink)
Ohhhh, is that why it's called the golden ratio?
[deleted] ยท 1 points ยท Posted at 21:06:45 on May 25, 2016 ยท (Permalink)
He said "almost perfectly"... but he actually meant "close approximation".
It's neat and all, but I can't calculate fibonnaci sequences off the top of my head. It's easier and more accurate to memorize the ratio and do the math than to memorize the Fibonacci ratio and do the math.
thegaysamosa ยท 396 points ยท Posted at 14:09:37 on May 25, 2016 ยท (Permalink)
Please illustrate
almightybob1 ยท 2154 points ยท Posted at 15:12:36 on May 25, 2016 ยท (Permalink)
The Fibbonacci sequence goes 1 1 2 3 5 8 13 21 34 55 89 etc etc. Skip the first few terms and...
thegaysamosa ยท 175 points ยท Posted at 16:28:23 on May 25, 2016 ยท (Permalink)
I get it now thanks!!
PM_me_twitch_cancer ยท 13 points ยท Posted at 22:02:08 on May 25, 2016 ยท (Permalink)
It's like the imperial system is almost making sense now.
EngineTrack ยท 11 points ยท Posted at 22:55:47 on May 25, 2016 ยท (Permalink)
Keyword: almost.
KypDurron ยท 8 points ยท Posted at 23:04:06 on May 25, 2016 ยท (Permalink)
No, it's just a coincidence that the ratio of miles to kilometers (1 mi = 1.6 km) is close to the ratio between consecutive numbers in the fibonacci sequence (phi, or 1.618ish)
Hungryforrobot ยท 2 points ยท Posted at 02:27:07 on May 26, 2016 ยท (Permalink)
That's a hell of a coincidence
thegaysamosa ยท 1 points ยท Posted at 02:04:13 on May 26, 2016 ยท (Permalink)
I was thinking the same thing
jugalator ยท 27 points ยท Posted at 17:30:18 on May 25, 2016 ยท (Permalink)
I'll be damned.
wgking12 ยท 5 points ยท Posted at 18:12:31 on May 25, 2016 ยท (Permalink)
Does this converge, stay roughly the same, or get worse with large numbers?
vezance ยท 6 points ยท Posted at 18:41:37 on May 25, 2016 ยท (Permalink)*
u/vidarino explained:
So as the numbers get larger, the difference would keep increasing. However, you wouldn't need to go to those distances for any practical purpose where you wouldn't anyway use a calculator.
Edit: had to come back to edit because I forgot something obvious - the ratio between consecutive numbers in the Fibonacci sequence itself converges to 1.618 as the numbers become greater (you can see how the ratio for the first few numbers are all over the place - 2/1 = 2, 3/2 = 1.5, 5/3 = 1.67, 8/5 = 1.60, etc.). It would be interesting to find out at what point the miles to km conversion using the Fibonacci sequence is the closest.
ellingjt ยท 1 points ยท Posted at 19:02:40 on May 25, 2016 ยท (Permalink)
It looks like the percent difference between the numbers stays roughly the same.
233 miles is about 374.977 km and the next fib # is 377 (0.54% difference) 11984 miles is about 19286.38 km and the next fib # is 19392 (0.55% difference)
wgking12 ยท 1 points ยท Posted at 19:18:33 on May 25, 2016 ยท (Permalink)
Makes sense! Seems to agree with the other reply to my comment, as fib's increase with ratio 1.618, and the km to miles ratio is ~1.609 If you divide the difference .009 by 1.618, you get the ~.55% difference.
FireDragon79 ยท 4 points ยท Posted at 17:15:37 on May 25, 2016 ยท (Permalink)
That is too fucking cool! Thanks!
architectdrone ยท 2 points ยท Posted at 18:33:03 on May 25, 2016 ยท (Permalink)
That is absolutely amazing.
becauzetheinternet ยท 2 points ยท Posted at 19:40:19 on May 25, 2016 ยท (Permalink)
Holy fuck
NijjioN ยท 2 points ยท Posted at 20:36:30 on May 25, 2016 ยท (Permalink)
How are you supposed to remember the sequence?
almightybob1 ยท 3 points ยท Posted at 21:05:07 on May 25, 2016 ยท (Permalink)
You can generate it yourself pretty quickly - just start with 1 1 and add the two previous numbers together.
StoneCold-JaneAustin ยท 1 points ยท Posted at 18:06:05 on May 25, 2016 ยท (Permalink)
Does this work when you start the sequence with a different number?
almightybob1 ยท 0 points ยท Posted at 18:52:49 on May 25, 2016 ยท (Permalink)
You mean start somewhere else in the Fibonacci sequence, or use different starting numbers and apply the Fibonacci rules (e.g. 2 2 4 6 10 16...)?
For the first, yes. For the second, no.
Mordreas ยท 4 points ยท Posted at 19:25:20 on May 25, 2016 ยท (Permalink)
welll....
https://docs.google.com/spreadsheets/d/1cdS2x7eVG_q27R8P_uj3zf8ebL9vlEbI4m48KP7MCzQ/edit?usp=sharing
I tried the second starting at 2,2 and 4,4 and 12,86 and for all of these the difference comes to less then a percent after 5 or 6 steps. so yes it does work for random starting numbers.
TGODie ยท 1 points ยท Posted at 19:26:20 on May 25, 2016 ยท (Permalink)
This is fucking dope. Cheers
[deleted] ยท 1 points ยท Posted at 20:14:35 on May 25, 2016 ยท (Permalink)*
[deleted]
almightybob1 ยท 3 points ยท Posted at 20:22:08 on May 25, 2016 ยท (Permalink)
Because the ratio in successive terms of the Fibonacci sequence tends towards the golden ratio which is ~ 1.618. And the conversion rate from miles to km is ~ 1.609. So the next term in the Fibonacci sequence is a very good approximation of the conversion of that number of miles to km.
[deleted] ยท 1 points ยท Posted at 20:32:45 on May 25, 2016 ยท (Permalink)*
[deleted]
MinkOWar ยท 1 points ยท Posted at 20:46:24 on May 25, 2016 ยท (Permalink)
They don't, and neither do the kilometres. The sequence has nothing directly to do with them. The relationship between adjacent numbers in the sequence is about the same as the relationship between kilometres and miles.
That's the extent of the 'math fact'. There's nothing else to it, the kilometres and miles don't line up to the sequence, the relationship between each adjacent number is just the same ratio. Pick any number and the adjacent number 'up' is that number converted to kilometres, and the adjacent number down is that number converted to miles.
almightybob1 ยท 1 points ยท Posted at 21:07:00 on May 25, 2016 ยท (Permalink)
They don't. I could have done it in reverse, started with km and said "use the previous number in the sequence to get the miles".
wanderingalice ยท 1 points ยท Posted at 22:16:35 on May 25, 2016 ยท (Permalink)
damn mind blown
[deleted] ยท 1 points ยท Posted at 22:20:26 on May 25, 2016 ยท (Permalink)
I misread your username as almightybot and was surprised there was a bot who responded so comprehensively to "please illustrate."
CyberTractor ยท 1 points ยท Posted at 00:57:06 on May 26, 2016 ยท (Permalink)
Over a larger section, does the sequence become more exact, less exact, or does it vary greatly?
almightybob1 ยท 1 points ยท Posted at 01:23:12 on May 26, 2016 ยท (Permalink)
More exact - or at least, it becomes wrong by a more consistent amount. The difference between the exact km conversion and the expected km amount using the next Fibonacci term tends towards 0.54%.
This is because the difference between two terms in the Fibonacci sequence tends towards a specific value - the golden ratio, ~ 1.618. This is pretty close to the mile/km conversion ratio of ~ 1.609 which is why this works, and why as the sequence tends towards a known ratio the error tends towards a fixed amount.
sirius4778 ยท 1 points ยท Posted at 02:35:29 on May 26, 2016 ยท (Permalink)
I'm so thankful you did this. I was really close to doing this on my crappy phone calculator, this was SO much more satisfying!
PotatoAlley ยท 1 points ยท Posted at 02:44:22 on May 26, 2016 ยท (Permalink)
Holy shit, this is absolutely astounding.
Charliek4 ยท 1 points ยท Posted at 18:07:42 on May 25, 2016 ยท (Permalink)
It might be more obvious if you switched the "approx km" and "exact km" columns to make the Fibonacci numbers next to each other. Just a suggestion
TLDM ยท 63 points ยท Posted at 14:45:22 on May 25, 2016 ยท (Permalink)
5 miles is approximately 8 km
13 miles is approximately 21 km
21 miles is approximately 34 km
etc.
johnnyfukinfootball ยท 1 points ยท Posted at 18:33:16 on May 25, 2016 ยท (Permalink)
34 miles is approximately 55 km
55 miles is approximately 89 km
89 miles is approximately 144 km
SignorSarcasm ยท 1 points ยท Posted at 16:11:44 on May 25, 2016 ยท (Permalink)
You're a hero.
Peregrine7 ยท 24 points ยท Posted at 14:55:15 on May 25, 2016 ยท (Permalink)*
Basically
(1,1,2,3,5,8,13...) 3 miles = 5km.
So we go up for miles->km
Reversed:
And we go down for km->miles
21km = 13 miles
using factors
50mph = 10x5 mph <--- taking 5 from the fibonnaci sequence. The next number in the sequence is 8 (1,1,2,3,5,8...) 10x8=80km/h
(real value is 80.46km/h)
The value of the ratio is pretty much identical amongst the entire fibonacci sequence from 5,8 onwards. So any number in the sequence above that is going to be exact to within 1or2%
skizfrenik_syco ยท 6 points ยท Posted at 14:48:04 on May 25, 2016 ยท (Permalink)
5 miles is about 8 km, 8 miles is about 13 km, 13 miles is about 21 km, and so on.
Schmetlappio ยท 3 points ยท Posted at 16:02:35 on May 25, 2016 ยท (Permalink)
The ratio of the n+1th term of the sequence to the nth converges on the conversion factor between miles and kilometers. Any sequence that converges on such a ratio would be similarly accurate as an approximation.
NotSorryIfIOffendYou ยท 2 points ยท Posted at 14:43:59 on May 25, 2016 ยท (Permalink)
13 miles is 20.9 km.
21 km is 13.05 miles.
Multai ยท 2 points ยท Posted at 15:06:38 on May 25, 2016 ยท (Permalink)
500 km = 310 miles
8 13 21 34 (took a bite out of the sequence)
500 / 34 * 21 = 308,8
500 / 21 * 13 = 309,5
500 / 13 * 8 = 307,6
None of them were off by more than 0,08%
CraigKostelecky ยท 2 points ยท Posted at 15:33:52 on May 25, 2016 ยท (Permalink)
1 mile is about 1.61 km. So 2 miles is 3 km (rounding to the nearest whole number). 3 miles is 5 km, 5 miles is 8 km, 8 miles is 13 km, and so on.
gmessad ยท 1 points ยท Posted at 21:16:36 on May 25, 2016 ยท (Permalink)
Math teachers always asking to show your work.
[deleted] ยท 12 points ยท Posted at 17:03:30 on May 25, 2016 ยท (Permalink)
So to effortlessly convert between miles and km, simply learn the fibonacci sequence.
AMasonJar ยท 3 points ยท Posted at 19:18:13 on May 25, 2016 ยท (Permalink)
And to learn the fibonacci sequence, just memorize how to convert between miles and kilometers!
drpinkcream ยท 1 points ยท Posted at 20:55:19 on May 25, 2016 ยท (Permalink)
Do you even listen to Tool?
[deleted] ยท 1 points ยท Posted at 21:12:35 on May 25, 2016 ยท (Permalink)
Spiral out.
Completeness_Axiom ยท 10 points ยท Posted at 14:53:24 on May 25, 2016 ยท (Permalink)
Holy shit that's genuinely awesome!
Zevee ยท 8 points ยท Posted at 17:21:53 on May 25, 2016 ยท (Permalink)
Best part, if you skip using miles, you dont even need to convert it.
.
Best wishes
/Europe (-UK)
thestickystickman ยท 0 points ยท Posted at 07:45:41 on May 26, 2016 ยท (Permalink)
MFW
rory_baxter ยท 5 points ยท Posted at 16:07:55 on May 25, 2016 ยท (Permalink)
This is due to the ratio between kilometres and miles being very close to the Golden ratio isn't it?
NotSorryIfIOffendYou ยท 3 points ยท Posted at 16:55:49 on May 25, 2016 ยท (Permalink)*
Yup. Ratio of F_n+1/Fn goes to phi as n increases. I'm not positive about this but that might imply that there's a range of values where the conversion is better than it is for arbitrarily high values.
Edit: For essentially all purposes this isn't the case as it converges very rapidly and the series of ratios is Cauchy based off of a very quick mental check. 2nd Edit: The series converges, there was no need to say it is Cauchy, that was a dumb thing of me to say.
Zero_Millennium ยท 2 points ยท Posted at 15:52:27 on May 25, 2016 ยท (Permalink)
So 5 miles is about 8 kilometres?
DreamCheeky ยท 2 points ยท Posted at 15:54:46 on May 25, 2016 ยท (Permalink)
I've remembered this for years because I'm a runner and we don't measure all our races with the same units.....grrrr
Karl_von_Moor ยท 3 points ยท Posted at 13:31:25 on May 25, 2016 ยท (Permalink)
Then how many miles are 520 kilometers?
Mini_Hobo ยท 22 points ยท Posted at 13:52:21 on May 25, 2016 ยท (Permalink)
Just use factors, or numbers which are at least close. For example, 520 = 40 * 13. 13 is a Fibonacci number, so if there are 520 km, there are roughly 40 * 8 miles.
Karl_von_Moor ยท 5 points ยท Posted at 13:59:10 on May 25, 2016 ยท (Permalink)*
You might want to double check that.Brainfart.
Still, if you can do factorials in your head you can multiply/divide a number by 1.6
NightmaresInNeurosis ยท 18 points ยท Posted at 14:30:38 on May 25, 2016 ยท (Permalink)
520km = 323mi. I think when we're dealing in the hundreds of miles, 320 could be considered "roughly" 323.
kDubya ยท 6 points ยท Posted at 14:40:29 on May 25, 2016 ยท (Permalink)
It's extremely close. 520 km is 323 miles.
adrianmonk ยท 10 points ยท Posted at 14:49:22 on May 25, 2016 ยท (Permalink)
There's another easy way. The actual conversion factor is 1.609 km per mile, but 1.6 is accurate to within 1%. (Note that 8 and 5 appear in the Fibonacci sequence, so that method contains this same approximation.)
1.6 is the same thing as 16/10. So you can do miles to km by doubling 4 times and then shifting the decimal point left by one position. And you can do km to miles by shifting the decimal point to the right once and then halving 4 times.
In your example, 520 becomes 5200, then you halve it to get 2600, halve again to 1300, and halve two more times to get 650 and then 325. The actual answer is 323.1 km, so it's pretty close. You made it easy by picking something that was a multiple of 8.
CraigKostelecky ยท 1 points ยท Posted at 15:30:05 on May 25, 2016 ยท (Permalink)
There are about 323 miles in 520 km. The closest consecutive Fibonacci numbers to those are 377 and 610.
Kered13 ยท 1 points ยท Posted at 22:21:39 on May 25, 2016 ยท (Permalink)*
500 km is 300 miles (Fibonacci terms multiplied by 100), 20 km is 12 miles (Using 1 to 0.6 conversion, multiplied by 20). 312 miles.
This is how I do it. Break it down into parts and use Fibonacci terms, 1 to 0.6,an 1.6 to 1 (these are actually equivalent to the Fibonacci terms 5:3 and 8:5, but I have memorized then this way), and easy multiples of those. It's accurate enough for everyday purposes.
nosnivel ยท 1 points ยท Posted at 15:51:04 on May 25, 2016 ยท (Permalink)
Wow.
woofwoofwolf ยท 1 points ยท Posted at 16:20:27 on May 25, 2016 ยท (Permalink)
This makes sense, as a kms = 1.6* miles and as the Fibonacci sequence goes on, the relationship between a number and the next gets closer and closer to ~1.6(the golden number)
Daniel_Yusim ยท 1 points ยท Posted at 16:24:03 on May 25, 2016 ยท (Permalink)
Ah, so that's where the logic of imperial units comes from. Some people like to divide by 10, some like to divide by Fibonnaci. I don't judge.
Erick2142 ยท 1 points ยท Posted at 17:22:42 on May 25, 2016 ยท (Permalink)
That just blew my mind
tommcdo ยท 1 points ยท Posted at 17:40:37 on May 25, 2016 ยท (Permalink)
Oh, I get it. So 0 miles = 1 kilometre, and 1 mile = 1 kilometer. Neat!
heroonebob ยท 1 points ยท Posted at 17:49:56 on May 25, 2016 ยท (Permalink)
This would be true for any sequence where you add the prior values together. 1,3,4,7,11,18 so 11miles is 18ish km. This is because the golden ratio applies to any sequence where the next value is the sum of the two previous ones.
rayrayheyhey ยท 1 points ยท Posted at 17:50:04 on May 25, 2016 ยท (Permalink)
Wow.
This is terrific. It just gave me shivers!
UselessGadget ยท 1 points ยท Posted at 18:07:57 on May 25, 2016 ยท (Permalink)
That is amazing. Not that I calculate this often, but whenever I would need to, I'd have to google. I'd think I can pretty much do it without now.
vgdiv ยท 1 points ยท Posted at 18:35:07 on May 25, 2016 ยท (Permalink)
Great, so now I gotta remember Fibonacci series if visiting US?
wasirapd ยท 1 points ยท Posted at 18:38:51 on May 25, 2016 ยท (Permalink)
This might be the most useful thing I've ever learned. Do you have one for kilograms? How about yards?
willyboy10 ยท 1 points ยท Posted at 18:39:51 on May 25, 2016 ยท (Permalink)
SPIRAL OUT
Soda ยท 1 points ยท Posted at 18:49:29 on May 25, 2016 ยท (Permalink)
The ratio between miles and kilometers is pretty close to the golden mean.
ManLeader ยท 1 points ยท Posted at 19:01:24 on May 25, 2016 ยท (Permalink)
These get a lot less impressive when you understand why,
casednova ยท 1 points ยท Posted at 19:12:22 on May 25, 2016 ยท (Permalink)
Planning on going to live to the US from Europe. You really saved my adult life, thank you
Kikiitani ยท 1 points ยท Posted at 19:19:18 on May 25, 2016 ยท (Permalink)
The square root of 69 is ate something right ? Cuz I've been trying to work it out awwwhhhhh
CalEPygous ยท 1 points ยท Posted at 19:25:15 on May 25, 2016 ยท (Permalink)*
It works for the obvious reason expressed by vidarino, but it isn't all that helpful since if it were a very large number you would have to generate the Fib sequence to generate the next term which would be harder (or the same) as multiplying by 1.6. Just sayin'
DericiousAprre ยท 1 points ยท Posted at 19:34:31 on May 25, 2016 ยท (Permalink)
Is there a there a simple trick to figuring out the next number in a Fibonnaci sequence?
NotSorryIfIOffendYou ยท 1 points ยท Posted at 19:37:21 on May 25, 2016 ยท (Permalink)
Just convert it to kilometers ;D
Seriously, not really. This is of limited usefulness for large numbers honestly I just always thought it was neat.
Meaningfulusername ยท 1 points ยท Posted at 19:38:07 on May 25, 2016 ยท (Permalink)
Holy shit, that's awesome.
bluegender03 ยท 1 points ยท Posted at 19:40:39 on May 25, 2016 ยท (Permalink)
Neat
JustAMomentofYerTime ยท 1 points ยท Posted at 20:04:32 on May 25, 2016 ยท (Permalink)
I picked my license plate directly because of this sequence. I've used cardboard to illustrate the sequence before and after my numbers, and am waiting to nerd out on the first officer to pull me over.
tfdavids ยท 1 points ยท Posted at 20:13:33 on May 25, 2016 ยท (Permalink)
You can also extend this to non-Fibonacci numbers by finding Fibonacci numbers that sum to it -- for example, to go from 28 miles to kilometers, 28 = 13 + 13 + 2, so it's about 21 + 21 + 3 = 45 kilometers.
[deleted] ยท 1 points ยท Posted at 20:20:01 on May 25, 2016 ยท (Permalink)
And the cool thing is you can convert any given number of miles into kilometers by using Zackendorf's theorem, which states that every positive integer can be interpreted as a sum of one or more distinct Fibonacci Numbers. For example : 7 (2+5) miles is nearly 11 (3+8) kilometers.
Gepetto_ ยท 1 points ยท Posted at 20:23:02 on May 25, 2016 ยท (Permalink)
boom goes the mind
thewilburbeast ยท 1 points ยท Posted at 20:51:31 on May 25, 2016 ยท (Permalink)
I never realized this, but have always been able to fairly accurately estimate the conversion in my head. Pretty much useless, living in the US, but still fun sometimes.
Solgir ยท 1 points ยท Posted at 21:00:40 on May 25, 2016 ยท (Permalink)
Holy shit! That is some amazing trick!
nahamed ยท 1 points ยท Posted at 21:53:50 on May 25, 2016 ยท (Permalink)
wow awesome
[deleted] ยท 1 points ยท Posted at 21:54:35 on May 25, 2016 ยท (Permalink)
This is amazing
meowplusderp ยท 1 points ยท Posted at 22:22:49 on May 25, 2016 ยท (Permalink)
I think I love you
spartanburt ยท 1 points ยท Posted at 22:32:43 on May 25, 2016 ยท (Permalink)
Just so happens the conversion rate is close to the golden ratio.
theodore_boozevelt ยท 1 points ยท Posted at 22:36:56 on May 25, 2016 ยท (Permalink)
Oh my GOD this is FUCKING COOL. Why did no math teachers ever tell me math could be this useful????
C413B7 ยท 1 points ยท Posted at 22:43:52 on May 25, 2016 ยท (Permalink)
So what's 7 miles?
jmpherso ยท 1 points ยท Posted at 22:48:48 on May 25, 2016 ยท (Permalink)
This is by far the most useful thing in the thread. Damn this is neat.
HatesTheLetterC ยท 1 points ยท Posted at 22:49:56 on May 25, 2016 ยท (Permalink)
Wow that's awesome. I will need to remember this. Kould have used it way bak in high skool
ryte4flyte ยท 1 points ยท Posted at 23:07:18 on May 25, 2016 ยท (Permalink)
I may have been born 15 years too early or 15 years too late. I've got nothing over nothing in understandability.
Vryl ยท 1 points ยท Posted at 23:25:46 on May 25, 2016 ยท (Permalink)
I was always "add a half plus a tenth". That is 0.5 + 0.1 = 0.6.
So, 10 miles = 10 + 5 + 1 =16 kilometres
120 miles = 120 + 60 + 12 = 192 kilometres
This is pretty accurate...
StoicStroke ยท 1 points ยท Posted at 23:42:44 on May 25, 2016 ยท (Permalink)
It's perfect or nothing buddy.
zanaohlala ยท 1 points ยท Posted at 23:54:38 on May 25, 2016 ยท (Permalink)
where can I get like a book of useful math knowledge like this??
01123581321sequence ยท 1 points ยท Posted at 01:36:15 on May 26, 2016 ยท (Permalink)
Just checking in.
TokyoCalling ยท 1 points ยท Posted at 01:49:34 on May 26, 2016 ยท (Permalink)
Brilliant!
clausport ยท 1 points ยท Posted at 02:35:48 on May 26, 2016 ยท (Permalink)
Interesting but almost useless. After the first half dozen or so numbers, I'm not likely to know what precedes or follows the number I am looking at in the Fibonacci series.
bucket888 ยท 1 points ยท Posted at 02:52:54 on May 26, 2016 ยท (Permalink)
I divide in half and add a tenth. Gets you real close.
12km = 6 + 1.2 miles
svanney ยท 1 points ยท Posted at 03:30:40 on May 26, 2016 ยท (Permalink)
miles:kilometers... ah! of course! the golden ratio.
Momskirbyok ยท 1 points ยท Posted at 03:46:54 on May 26, 2016 ยท (Permalink)
So awesome!
[deleted] ยท 1 points ยท Posted at 03:50:29 on May 26, 2016 ยท (Permalink)
Ride the spiral
1mrlee ยท 1 points ยท Posted at 03:54:55 on May 26, 2016 ยท (Permalink)
Sorry, I'm a bit slow. I'm trying to figure this out.
Can you ELI5
moomeansmoo ยท 1 points ยท Posted at 03:59:59 on May 26, 2016 ยท (Permalink)
I got a tattoo of the golden spiral and I have been inadvertently learning more about it ever since from so many different people. It's a wonderful experience. Honestly, it's the most I have ever enjoyed math, and all I had to do was put it permanently on my body.
LaLeeBird ยท 1 points ยท Posted at 09:12:14 on May 26, 2016 ยท (Permalink)
This is literally the most helpful thing I have ever learned on reddit. If I wasn't poor I would give you hold, thank you so much for this
nliausacmmv ยท 1 points ยท Posted at 17:27:54 on May 26, 2016 ยท (Permalink)
This works for any set of numbers created by adding the previous two terms, so long as the starting terms are both positive.
Project2r ยท 0 points ยท Posted at 15:23:15 on May 25, 2016 ยท (Permalink)
this. blows. my. mind.
does the same hold true for any other measurement conversion?
thedeejus ยท 7821 points ยท Posted at 13:43:23 on May 25, 2016 ยท (Permalink)*
this is more of a statistics fact, but if there is a 1 in x chance of something happening, in x attempts, for large numbers over 50 or so, the likelihood of it happening is about 63%
For example, if there's a 1 in 10,000 chance of getting hit by a meteor if you go outside, if you go outside 10,000 times, you have a 63% chance of getting hit with a meteor at some point. If there's a 1 in a million chance of winning the lottery and you buy a million (random) lottery tickets, you have a 63% chance of winning.
Edit: for the lottery example, the key word is random - yeah if you consciously buy every possible combination then it's 100%. If you buy one ticket in a million different lotteries, or a million randomly generated tickets for any one in a million lottery, then it's 63%
NoCanDoSlurmz ยท 272 points ยท Posted at 15:19:51 on May 25, 2016 ยท (Permalink)*
What he is calculating is 1 minus the odds of not winning on any of the attempts.
There are probable scenarios where you win 1 time, 2 times, 3 times, and so on. So to calculate the odds of winning at least once, the easier way than summing all of those possible winning scenarios is to find the odds of not winning, then reducing one by that value.
Say x = 100, so the odds of not winning 100 times in a row are (99/100)100
The compliment of that is simply 1 - (99/100)100 = 0.63397
sprucemoose101 ยท 5 points ยท Posted at 15:48:16 on May 25, 2016 ยท (Permalink)
why do you put it to the power of x (100) ?
NoCanDoSlurmz ยท 22 points ยท Posted at 15:51:23 on May 25, 2016 ยท (Permalink)
The odds of not winning are 99/100 for one try. For two attempts it's (99/100)2. What is special about this problem is that the 1 in 100 event is repeated, 100 times.
syropian ยท 0 points ยท Posted at 20:53:28 on May 25, 2016 ยท (Permalink)
This reminds me of when Kevin Spacey in 21 gives Jim Sturgess the Monty Hall problem.
Edit: I'm awful at math and have no idea if it actually applies, this whole thread just reminded me of that scene.
GGme ยท -3 points ยท Posted at 23:40:25 on May 25, 2016 ยท (Permalink)*
That is ridiculous.Once the 3rd door is open, there is a 50% chance for each of the unopened doors, regardless of when a final decision is made. The host knows where both goats are, so regardless of the contestant's initial pick, there is at least one door with a goat behind; or two. Either way, one door is opened revealing a goat, and the two closed doors now have 1 car and 1 goat. 50/50Edit: I see it now. 2/3 of the time, the host is forced to help your odds by eliminating a goat. 1/3 of the time he has no impact.
sweetcheeks1090 ยท 10 points ยท Posted at 00:20:23 on May 26, 2016 ยท (Permalink)
You're missing one key part of the problem. The host knows where the car is and always chooses the door it isn't behind. You have a 1/3 chance that you're correct on your first guess and therefore 2/3 it's one of the other doors. You can rule out one of the two when he opens the door and so the odds of it being the door you didn't choose are 2/3.
RedAnsem ยท 5 points ยท Posted at 02:12:51 on May 26, 2016 ยท (Permalink)
The problem is easier to understand if you increase the number of doors. Let's say you have 100 doors and after you pick one, the host eliminates 98 out of the 99 doors remaining. He can't eliminate the right door so either you picked the right one from the beginning or he got rid of 98 wrong answers for you leaving only the right door behind. The odds of you picking the right door from the beginning is only 1%. There is a 99% chance that you didn't and the host removed all the wrong doors for you.
ScrewAttackThis ยท 1 points ยท Posted at 03:02:19 on May 26, 2016 ยท (Permalink)
Nope. You always want to switch. The only way to lose is to pick the winning door initially. Since the host will always get rid of a losing door, you'll win anytime you initially pick a losing door.
So since you only have a 1/3 chance to lose, you have a 2/3 chance to win.
If you don't switch, you have 2/3 chance to lose. You can only win if you pick the winning door.
superiority ยท 1 points ยท Posted at 05:03:11 on May 26, 2016 ยท (Permalink)
Try drawing a probability tree.
ZephyrWarrior ยท 1 points ยท Posted at 02:28:12 on May 26, 2016 ยท (Permalink)
whoosh
The host knows where the car is and MUST open a door that does not have it. That is the factor you are ignoring.
CoolGuy9000 ยท 10594 points ยท Posted at 15:37:16 on May 25, 2016 ยท (Permalink)
So that's why 60% of the time it works every time.
roae ยท 1083 points ยท Posted at 16:25:42 on May 25, 2016 ยท (Permalink)
Mystery solved
[deleted] ยท 93 points ยท Posted at 16:38:06 on May 25, 2016 ยท (Permalink)
We did it Reddit
RiderEx ยท 1 points ยท Posted at 22:47:46 on May 25, 2016 ยท (Permalink)
63%*
Kirby999 ยท 29 points ยท Posted at 17:30:28 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
nrop_ ยท 10 points ยท Posted at 17:58:07 on May 25, 2016 ยท (Permalink)*
edited
666666t ยท 1 points ยท Posted at 19:15:57 on May 25, 2016 ยท (Permalink)
/r/itwasagraveyardgraph
adudeguyman ยท 2 points ยท Posted at 01:13:30 on May 26, 2016 ยท (Permalink)
I'm going to be a millionaire
goldontheceiling22 ยท 2 points ยท Posted at 02:40:40 on May 26, 2016 ยท (Permalink)
I may now rest in peace
CarcajouIS ยท 2 points ยท Posted at 18:15:57 on May 25, 2016 ยท (Permalink)
We did it, reddit
parentingandvice ยท 71 points ยท Posted at 15:53:00 on May 25, 2016 ยท (Permalink)
Holy shit Brian was smart.
Still smelled like bigfoot's dick though
CallRespiratory ยท 2 points ยท Posted at 18:19:27 on May 25, 2016 ยท (Permalink)
Like pure gasoline.
lucebree ยท 2 points ยท Posted at 22:47:48 on May 25, 2016 ยท (Permalink)
Like a turd covered in burnt hair.
WhatDoesTaiLopezDO ยท 23 points ยท Posted at 15:56:59 on May 25, 2016 ยท (Permalink)
holy shit
Funkit ยท 5 points ยท Posted at 17:04:10 on May 25, 2016 ยท (Permalink)
I'm gonna be honest with you, that smells like pure gasoline
Rodent_Smasher ยท 4 points ยท Posted at 17:14:38 on May 25, 2016 ยท (Permalink)
Does this apply to starting lawnmowers?
lazylion_ca ยท 2 points ยท Posted at 20:00:42 on May 25, 2016 ยท (Permalink)
Only if it takes over 50 pulls.
Areox ยท 3 points ยท Posted at 17:37:26 on May 25, 2016 ยท (Permalink)
I'll be dammed
ugotamesij ยท 7 points ยท Posted at 16:51:27 on May 25, 2016 ยท (Permalink)
Strictly speaking, about 63% of the time it works every time.
PM_ME_BALD_BEAVERS ยท 4 points ยท Posted at 16:40:33 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/FanTheories/comments/2m3y2t/anchorman_60_of_the_time_it_works_every_time/
ticktockaudemars ยท 2 points ยท Posted at 16:46:12 on May 25, 2016 ยท (Permalink)
... everytime
D_dark0 ยท 2 points ยท Posted at 17:14:35 on May 25, 2016 ยท (Permalink)
Holy shit
setofskills ยท 2 points ยท Posted at 17:43:06 on May 25, 2016 ยท (Permalink)
Mind. Blown.
Illsonmedia ยท 2 points ยท Posted at 18:13:33 on May 25, 2016 ยท (Permalink)
PRIMO!
dukemcrae ยท 2 points ยท Posted at 18:36:06 on May 25, 2016 ยท (Permalink)
Note to self: Buy: one million lottery tickets New bottle of sex panther.
hallykatyberryperry ยท 2 points ยท Posted at 18:49:27 on May 25, 2016 ยท (Permalink)
They've done study's you know..
colonelbyson ยท 0 points ยท Posted at 02:48:43 on May 26, 2016 ยท (Permalink)
*studies
hallykatyberryperry ยท 1 points ยท Posted at 03:49:06 on May 26, 2016 ยท (Permalink)
Swipe text bro
Beepbeepimadog ยท 2 points ยท Posted at 18:52:33 on May 25, 2016 ยท (Permalink)
Just gotta round down.
BrosBeforeHossa ยท 2 points ยท Posted at 18:53:37 on May 25, 2016 ยท (Permalink)
We all laughed about it for years, but he was right.
scraggledog ยท 2 points ยท Posted at 19:21:49 on May 25, 2016 ยท (Permalink)
If you do it enough
OSRS_Callgun ยท 4 points ยท Posted at 16:51:43 on May 25, 2016 ยท (Permalink)
That doesn't make sense
WitchHunterNL ยท 1 points ยท Posted at 19:31:51 on May 25, 2016 ยท (Permalink)
No, 60% of the time, it works
eject_eject ยท 1 points ยท Posted at 20:14:42 on May 25, 2016 ยท (Permalink)
When n is large!
dangerbird2 ยท 1 points ยท Posted at 20:23:51 on May 25, 2016 ยท (Permalink)
It still smells like Bigfoot's dick.
thatoneguy092 ยท 1 points ยท Posted at 20:40:29 on May 25, 2016 ยท (Permalink)
Wow
svengast ยท 1 points ยท Posted at 20:44:56 on May 25, 2016 ยท (Permalink)
/r/theydidtheshittymath
BitsofPanther ยท 1 points ยท Posted at 22:39:30 on May 25, 2016 ยท (Permalink)
Facts are facts.
Spore2012 ยท 1 points ยท Posted at 23:11:20 on May 25, 2016 ยท (Permalink)
i bet it has something to do with pi.
VisundrThePurple ยท 1 points ยท Posted at 23:37:57 on May 25, 2016 ยท (Permalink)
Sex panther. You smell like a used diaper filled with indian food. Desire smells like that to some people.
[deleted] ยท 1 points ยท Posted at 00:28:09 on May 26, 2016 ยท (Permalink)
Rounding
Arsenic99 ยท 1 points ยท Posted at 01:26:43 on May 26, 2016 ยท (Permalink)
That makes a lot of sense.
[deleted] ยท 1 points ยท Posted at 01:31:27 on May 26, 2016 ยท (Permalink)
I love lamp 60% of the time...
ivorymash ยท 1 points ยท Posted at 02:55:09 on May 26, 2016 ยท (Permalink)
17% of the time all the time greater bash
Owens783 ยท 1 points ยท Posted at 03:54:31 on May 26, 2016 ยท (Permalink)
I...i love you. Goddammit I love you.
WrathOfDionysus ยท 1 points ยท Posted at 04:26:55 on May 26, 2016 ยท (Permalink)
woah
BluntTruthGentleman ยท 1 points ยท Posted at 06:03:08 on May 26, 2016 ยท (Permalink)
"60% of the time it works 100% of the time."
trafcon ยท 1 points ยท Posted at 08:13:54 on May 26, 2016 ยท (Permalink)
That doesn't make sense.
angnagiisangajd ยท 1 points ยท Posted at 17:31:05 on August 18, 2016 ยท (Permalink)
Isn't it actually 50%? It either happens or it doesn't. xD
JaundiceCat ยท 0 points ยท Posted at 16:49:11 on May 25, 2016 ยท (Permalink)*
This blew my mind. Are you a wizard dude? Holy shit.
Dude if I had gold I would give it to you. '60% of the time it works every time' And you relate it to the probability answer of roughly 63%? I'm done. I'm just done. This is peak reddit, the singularity where memes become reality.
specopsjuno ยท 7 points ยท Posted at 17:14:50 on May 25, 2016 ยท (Permalink)
Calm down, Tumblr.
JaundiceCat ยท 0 points ยท Posted at 18:29:33 on May 25, 2016 ยท (Permalink)
Damn what an insult
DJTuret ยท 3 points ยท Posted at 17:35:29 on May 25, 2016 ยท (Permalink)
Charles Nelson Reilly?
JaundiceCat ยท 1 points ยท Posted at 21:35:59 on May 25, 2016 ยท (Permalink)
Hah. He's an older dude but I dont know what you're getting at. Do I have a similar way of writing? I'm a youngin sorry for my inexperience.
DJTuret ยท 2 points ยท Posted at 17:35:43 on May 25, 2016 ยท (Permalink)
Because you have his eloquence.
DJTuret ยท 1 points ยท Posted at 17:35:44 on May 25, 2016 ยท (Permalink)
Because you have his eloquence.
charlietango13 ยท 1 points ยท Posted at 18:10:19 on May 25, 2016 ยท (Permalink)
63% of the time
burtwart ยท 0 points ยท Posted at 17:48:38 on May 25, 2016 ยท (Permalink)
O shit waddup
thewildrose ยท 1413 points ยท Posted at 14:41:11 on May 25, 2016 ยท (Permalink)
I don't remember the reasoning behind it, but the mathematics is:
63% ~= 1 - (1/e)
NoCanDoSlurmz ยท 897 points ยท Posted at 15:24:48 on May 25, 2016 ยท (Permalink)
Correct, the limit of 1 - ((x-1)/x)x as x approaches infinity is 1 - (1/e)
If I remember correctly you end up using the "sandwich" method for that proof, and it was a good one.
VenomFire ยท 634 points ยท Posted at 15:40:36 on May 25, 2016 ยท (Permalink)
I think you're referring to the squeeze theorem if I'm not mistaken
NoCanDoSlurmz ยท 846 points ยท Posted at 15:41:57 on May 25, 2016 ยท (Permalink)
Yup, I like sandwiches better though.
VenomFire ยท 18 points ยท Posted at 15:42:42 on May 25, 2016 ยท (Permalink)
Fair enough, sandwiches are mighty delicious
NoCanDoSlurmz ยท 29 points ยท Posted at 15:44:39 on May 25, 2016 ยท (Permalink)
It's like we finish eachother's... sandwiches.
darkwing_duck_87 ยท 5 points ยท Posted at 16:47:56 on May 25, 2016 ยท (Permalink)
Take your dirty fucking hands of my sandwhich!
MeanwhileintheTARDIS ยท 1 points ยท Posted at 18:58:10 on May 25, 2016 ยท (Permalink)
Wow, kids movie to smut post in one comment.
Edit: I totally read that comment wrong
Bastard_Toby ยท 1 points ยท Posted at 21:39:20 on May 25, 2016 ยท (Permalink)
Sandwhiches
powerstriker ยท 3 points ยท Posted at 17:26:21 on May 25, 2016 ยท (Permalink)
That's what I was gonna say!
akasmira ยท 10 points ยท Posted at 16:00:59 on May 25, 2016 ยท (Permalink)
I use sandwich theorem for any reasoning of this sort myself, too. For example:
if a | b and b | a, then a = b
or
if a โค b and b โค a, then a = b
or
if A โ B and B โ A, then A = B
etc.
edit: added another example and some styling.
[deleted] ยท 6 points ยท Posted at 18:07:34 on May 25, 2016 ยท (Permalink)
I like certain types of squeezes more than certain types of sandwiches.
pointless_one ยท 3 points ยท Posted at 17:51:44 on May 25, 2016 ยท (Permalink)
The only thing I understood from all this is sandwiches.
frozengyro ยท 2 points ยท Posted at 18:10:39 on May 25, 2016 ยท (Permalink)
Idk, I like a good squeeze.
RandomCanadaDude ยท 4 points ยท Posted at 16:05:32 on May 25, 2016 ยท (Permalink)
I swear to god if someone told me you and /u/VenomFire were making this shit up, I would believe them.
GMY0da ยท 1 points ยท Posted at 20:57:24 on May 25, 2016 ยท (Permalink)
They're making that shit up
OV5 ยท 1 points ยท Posted at 16:54:11 on May 25, 2016 ยท (Permalink)
Yeah, ham sandwich sounds way better than ham squeeze. I prefer my squeezes to not be hams.
NoCanDoSlurmz ยท 2 points ยท Posted at 17:00:01 on May 25, 2016 ยท (Permalink)
unless it's on the side ;)
theHowSuspendedDo ยท 1 points ยท Posted at 07:55:07 on May 26, 2016 ยท (Permalink)
The sandwich theorem and the ham sandwich theorem are actually totally different theorems.
stfatherabraham ยท 1 points ยท Posted at 17:30:33 on May 25, 2016 ยท (Permalink)
Can't argue with that.
justSFWthings ยท 1 points ยท Posted at 18:03:24 on May 25, 2016 ยท (Permalink)
I like sandwiches, sandwiches are easy to eat.
MavGore ยท 2 points ยท Posted at 18:14:41 on May 25, 2016 ยท (Permalink)
I read this whilst eating a sandwich
Illsonmedia ยท 1 points ยท Posted at 18:14:06 on May 25, 2016 ยท (Permalink)
Leeeeeeel
Use_The_Sauce ยท 1 points ยท Posted at 18:51:45 on May 25, 2016 ยท (Permalink)
Footlong?
ShitLordByDesign ยท 1 points ยท Posted at 19:21:38 on May 25, 2016 ยท (Permalink)
This thread made me feel safe for some reason.
cattdaddy ยท 1 points ยท Posted at 19:31:32 on May 25, 2016 ยท (Permalink)
Potato potato...
SurprisedPotato ยท 1 points ยท Posted at 01:11:58 on May 26, 2016 ยท (Permalink)
Yes?
therealuser42 ยท 1 points ยท Posted at 22:06:03 on May 25, 2016 ยท (Permalink)
I like to make big sandwiches and squeeze them to make them thinner so I can take a bite. 63% of the time, the mustard doesn't come out from the sides.
sirius4778 ยท 1 points ยท Posted at 02:32:26 on May 26, 2016 ยท (Permalink)
The sandwich method is so much better hahaha
00Deege ยท 0 points ยท Posted at 18:10:39 on May 25, 2016 ยท (Permalink)
I like turtles.
Carotti ยท 29 points ยท Posted at 16:02:32 on May 25, 2016 ยท (Permalink)
Sandwich/Squeeze theorem is the same thing. I've also heard it called "the theorem of the wandering drunk and two policemen" which is a nice description
VenomFire ยท 1 points ยท Posted at 16:07:16 on May 25, 2016 ยท (Permalink)
I know what I'm calling it now, that's amazing!
leozinhu99 ยท 1 points ยท Posted at 21:20:13 on May 25, 2016 ยท (Permalink)
I've heard it as "Confrontation Theorem"
caustic_kiwi ยท 1 points ยท Posted at 09:39:30 on May 26, 2016 ยท (Permalink)
My teacher referred to the squeeze theorem as "The Two Policemen Theorem" once and declined to tell us where the name came from. For the longest time I had some... interesting notions about the reason for that name.
Edgecloser ยท 9 points ยท Posted at 16:37:23 on May 25, 2016 ยท (Permalink)
My professor taught this as the policemen theorem. He was a strange Russian named Boris who would make a joke, but since the class couldnt distinguish between sarcasm and normal tone, he would promptly yell 'JOKE!' at the end.
intrepid_i ยท 3 points ยท Posted at 17:41:26 on May 25, 2016 ยท (Permalink)
Same thing, different name. Yummier name.
Latex_Mane ยท 2 points ยท Posted at 16:28:50 on May 25, 2016 ยท (Permalink)
My professor used to say squeeth.
X5IMPLEX ยท 2 points ยท Posted at 16:59:53 on May 25, 2016 ยท (Permalink)
It's called Sandwich method in some countries, I learned it last semester as 'the sandwich lemma'
inherendo ยท 1 points ยท Posted at 22:19:16 on May 25, 2016 ยท (Permalink)
I wouldn't call it a method though that may be lost in translation from whatever language to english, french, or whatever it might have been translated to.
wumpa ยท 2 points ยท Posted at 17:07:10 on May 25, 2016 ยท (Permalink)
My undergrad lecturer called it the "sandwich theorem" and it's called that in some textbooks too, interchangeable nomenclature with the squeeze theorem.
IAmMosh ยท 2 points ยท Posted at 17:36:40 on May 25, 2016 ยท (Permalink)
(Some schools up here in Canada actually teach it as the 'sandwich method')
VenomFire ยท 1 points ยท Posted at 18:30:15 on May 25, 2016 ยท (Permalink)
I'm also from Canada, we learned squeeze. :P
IAmMosh ยท 1 points ยท Posted at 22:28:39 on May 25, 2016 ยท (Permalink)
Personally I learned squeeze at school in B.C. but I have engineering friends who looked at me like I was crazy.
marshmallowelephant ยท 2 points ยท Posted at 19:15:14 on May 25, 2016 ยท (Permalink)
I had a lecturer from Italy saying that over there, it's usually called the Policeman Theorem. The idea being that if you're stuck between two policeman, you're only going to one place - jail.
Pressondude ยท 2 points ยท Posted at 19:27:18 on May 25, 2016 ยท (Permalink)
My Russian (Soviet educated) calculus professor told us that when she was in school in Ukraine, it was taught to her as the "proof of the three policemen," wherein one is very, very drunk, and the other two are holding him up to walk him home.
DiamondSentinel ยท 2 points ยท Posted at 20:26:43 on May 25, 2016 ยท (Permalink)
In AP Calc and IB Maths, it's referred to as Sandwich Theorem. Must be old fangled maths courses.
Banbaur ยท 2 points ยท Posted at 21:01:43 on May 25, 2016 ยท (Permalink)
Theyre the same
Luo_Bo_Si ยท 2 points ยท Posted at 22:09:06 on May 25, 2016 ยท (Permalink)
I prefer the "Two policemen and a drunk" label, myself.
Radicle_ ยท 2 points ยท Posted at 00:00:56 on May 26, 2016 ยท (Permalink)
More like Satan's theorem
aglassofsherry ยท 2 points ยท Posted at 16:30:41 on May 25, 2016 ยท (Permalink)
Literally studying squeeze theorem right the fuck now (I'm sitting in Calculus as I type)
VenomFire ยท 4 points ยท Posted at 16:36:10 on May 25, 2016 ยท (Permalink)
It's not the worst theorem in the world, makes a lot of shit easy. :P
SurDin ยท 7 points ยท Posted at 16:23:57 on May 25, 2016 ยท (Permalink)
e= lim (1+1/n)n
(1+1/n)*(1-1/n)=(1-1/n2 )
(1-1/n2 )n ->1
Imugake ยท 1 points ยท Posted at 18:18:01 on May 25, 2016 ยท (Permalink)
Thank you
BLAZINGSORCERER199 ยท 3 points ยท Posted at 16:01:46 on May 25, 2016 ยท (Permalink)
You know what the best part of having just graduated high school ; seeing your maths class pay off by understanding a reddit maths fact.
Kered13 ยท 3 points ยท Posted at 21:48:34 on May 25, 2016 ยท (Permalink)*
In high school I proved this to myself using the binomial expansion of (1 - 1/x)x and the Taylor series for ex.
EDIT: Here's the full proof:
We wish to find Lim(x -> infinity, 1 - (1 - 1/x)x ). This is 1 - Lim(x -> infinity, (1 - 1/x)x ). Using the binomial theorem, (1 - 1/x)x expands to:
Let's focus on the x!/(k!(x-k)! * xk ) term:
Canceling terms in the binomial coefficient:
Expanding this product of binomials:
Where C_i is a constant. We don't care about the value of this constant, except that C_k=1, which is easy to see from the product of monomials. The rest of the C_i's will disappear when we take the limit. The above is a rational function, a ratio of two polynomials P(x) and Q(x), and a fact of rational functions, which is fairly easy to prove, is that if P(x) and Q(x) have the same degree (the degree of a polynomial is the highest power it contains) then the limit of P(x)/Q(x) as x goes to infinity is equal to the ratio of the coefficients of the largest degree. In our case both polynomials have degree k. The coefficient on top is C_k=1, and the coefficient on the bottom is k!. Therefore we have,
Now going back to our original problem:
From the taylor series for ex, we recognize that the above is e-1. So in conclusion,
darkieee ยท 2 points ยท Posted at 19:58:42 on May 26, 2016 ยท (Permalink)
Thanks man, beautiful proof!
RyGuy_42 ยท 2 points ยท Posted at 15:48:18 on May 25, 2016 ยท (Permalink)
the proof or the sandwich?
kyleqead ยท 2 points ยท Posted at 17:43:14 on May 25, 2016 ยท (Permalink)
No, easier way definitely than squeeze theorem. Lim [1 - ((x-1)/x)x] as x goes to infinity can be simplified to lim [1-(1-1/x)x]. set y=limit. take ln of both sides. Do l'hopitals and lastly take e to the power of both sides getting 1-(1/e)
Voxel_Brony ยท 2 points ยท Posted at 01:41:24 on May 26, 2016 ยท (Permalink)
There's a really pretty way to do it with inequalities and integrals
http://aleph0.clarku.edu/~djoyce/ma122/elimit.pdf
NoCanDoSlurmz ยท 2 points ยท Posted at 13:53:58 on May 26, 2016 ยท (Permalink)
This is the one I was talking about! And they say proofs can't be sexy.
[deleted] ยท 1 points ยท Posted at 15:54:33 on May 25, 2016 ยท (Permalink)
You could also use l'hospitals rule.
_illogical_ ยท 1 points ยท Posted at 17:10:36 on May 25, 2016 ยท (Permalink)
I think you mean the "hot dog" method.
theFunkiestButtLovin ยท 1 points ยท Posted at 17:14:46 on May 25, 2016 ยท (Permalink)
would you say it's...heroic?
DarthColleague ยท 1 points ยท Posted at 17:27:16 on May 25, 2016 ยท (Permalink)
Where do you use the sandwich theorem here? I can't spot anything where you have to.
anomalous_cowherd ยท 1 points ยท Posted at 18:13:20 on May 25, 2016 ยท (Permalink)
Proof by intimidation has a lot going for it too.
beingforthebenefit ยท 1 points ยท Posted at 18:28:42 on May 25, 2016 ยท (Permalink)
"sandwich" method is for oscillating functions. Exponentiate and the limit is pretty easy, depending on how you have defined e.
Mr___Roboto ยท 1 points ยท Posted at 20:33:40 on May 25, 2016 ยท (Permalink)
El mรฉtodo del "sรกndwich". Jaja se me habรญa olvidado
mangamaster03 ยท 1 points ยท Posted at 21:07:33 on May 25, 2016 ยท (Permalink)
So many painful memories of calculus one...
zxzCLOCKWORKzxz ยท 1 points ยท Posted at 21:08:54 on May 25, 2016 ยท (Permalink)
ELI5....
Teblefer ยท 1 points ยท Posted at 21:27:11 on May 25, 2016 ยท (Permalink)
Call the limit = y and take the ln of both sides. Rewrite the fun side as ln((x-1)/x)/(1/x) and apply L'Hopital's rule. You get -1 so you know that ln(y) = -1 so y (the variable i chose to represent the answer) is 1/e
ZachIsKill ยท 1 points ยท Posted at 22:21:42 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
Kenlurd ยท 1 points ยท Posted at 22:42:26 on May 25, 2016 ยท (Permalink)
... there is no limit!
udbluehens ยท 1 points ยท Posted at 00:38:50 on May 26, 2016 ยท (Permalink)
Thats true. Even easier is just to put x = 100000 into a calculator and get e.
[deleted] ยท 0 points ยท Posted at 16:31:40 on May 25, 2016 ยท (Permalink)
[deleted]
BOT_Allu ยท 2 points ยท Posted at 17:59:19 on May 25, 2016 ยท (Permalink)
But the limit does exist.... What are you talking about?
H3rQ133z ยท 0 points ยท Posted at 20:16:31 on May 25, 2016 ยท (Permalink)
Yes the limit as x approaches infinity is that, but infinity is an idea no stat can reach. One million isn't even close to infinity
Bolsen2 ยท -1 points ยท Posted at 16:49:12 on May 25, 2016 ยท (Permalink)
The limit does not exist
[deleted] ยท -1 points ยท Posted at 17:00:55 on May 25, 2016 ยท (Permalink)
can't comprehend
statist_steve ยท -2 points ยท Posted at 16:47:37 on May 25, 2016 ยท (Permalink)
Mmm, let's see. 1 - 1 + 2. Yep. Put a little x in there and an e and some parentheticals because math. Mmm hmm. Checks out.
smaug13 ยท 8 points ยท Posted at 15:27:05 on May 25, 2016 ยท (Permalink)
that is because eb is defined as the number that (1+b/x)x approaches when x goes to infinity. Let b=-1 and you get:
(1-1/x)x = e-1 = 1/e
So 1-(1-1/x)x = 1-1/e
If x approaches infinity. That doesn't happen in our case, but if you let x be a very very big number (like a thousand or so) it will get close enough to call it day.
dickskittles ยท 8 points ยท Posted at 15:40:37 on May 25, 2016 ยท (Permalink)
No, silly, eb is the note between D and E.
Alix1723 ยท 3 points ยท Posted at 16:11:43 on May 25, 2016 ยท (Permalink)
Now that's pretty noteworthy.
Taskforce58 ยท 2 points ยท Posted at 16:54:54 on May 25, 2016 ยท (Permalink)
I like the sound of that.
slver6 ยท 1 points ยท Posted at 15:50:03 on May 25, 2016 ยท (Permalink)
and by the time i saw you comment it had 63 upvotes HOLY SHIT
[deleted] ยท 1 points ยท Posted at 16:32:09 on May 25, 2016 ยท (Permalink)
[deleted]
yoitsthatoneguy ยท 3 points ยท Posted at 18:11:22 on May 25, 2016 ยท (Permalink)
The events have to be independent, but go for it.
FirstWorldAnarchist ยท 1 points ยท Posted at 16:35:04 on May 25, 2016 ยท (Permalink)
63/3=21
21*2=42
ChikenBBQ ยท 1 points ยท Posted at 16:52:42 on May 25, 2016 ยท (Permalink)
Euler you bastard! GET OUT OF MY HEAD!!!
roeravid ยท 1 points ยท Posted at 17:13:15 on May 25, 2016 ยท (Permalink)
e. 'Nuff said
roeravid ยท 1 points ยท Posted at 17:18:37 on May 25, 2016 ยท (Permalink)
e. 'Nuff said
Dunderost ยท 1 points ยท Posted at 17:38:43 on May 25, 2016 ยท (Permalink)
MY head hurts.
[deleted] ยท 1 points ยท Posted at 19:40:17 on May 25, 2016 ยท (Permalink)
Thank you for this! I noticed the trend toward 63% or so a few years years back (I was way too into obtaining shiny/perfect Pokemon in late middle school, so I wanted to know my odds in x hatches), but I didn't find the exact value.
NotGloomp ยท 1 points ยท Posted at 20:50:44 on May 25, 2016 ยท (Permalink)
Duuuuuuuuude so that's where ฯ comes from. Bruuuuuuh my mind is being blown by this thread. In both figurative senses.
Teblefer ยท 1 points ยท Posted at 21:12:20 on May 25, 2016 ยท (Permalink)
If you rolled a 6 sided die 6 times you would not get a 6 about a third of the time. It turns out that as you add more faces the odds of not getting a certain number after n rolls approaches 1/e. So since you either get at least one success or no success at all, the odds of no success at all approaches 1 - 1/e.
Yin4TheWin ยท 1 points ยท Posted at 22:57:45 on May 25, 2016 ยท (Permalink)
Complements counting. The probability of something happening at least once is 1 minus the probability of it not happening. If something has a 1/1000 chance of happening, then the probability of it not happening in 1000 tries is (1 - 1/1000)1000. Additionally, as x approaches infinity, (1 - 1/x)x approaches 1/e. Thus, for x large, the probability of something with a 1/x chance of happening over x tries is approximately (1 - 1/e)
jesset77 ยท 1 points ยท Posted at 23:04:11 on May 25, 2016 ยท (Permalink)
I experimentally saw this distribution as a kid (wrote a program to map out random picks out of 100 or more options, mapped which ones got picked, always got about 2/3 coverage and 1/3 distributed in some variant of duplicates), but mistook it most likely limiting to 66.6..%. :/
type_your_name_here ยท 0 points ยท Posted at 20:55:56 on May 25, 2016 ยท (Permalink)
I wonder if the converse is the secretary problem which approaches 37%.
ristoman ยท 394 points ยท Posted at 16:12:47 on May 25, 2016 ยท (Permalink)
What am I, Magellan?
thedailytoke ยท 19 points ยท Posted at 22:15:36 on May 25, 2016 ยท (Permalink)
There's a 63% chance you are
ristoman ยท 12 points ยท Posted at 00:58:15 on May 26, 2016 ยท (Permalink)
And the remaining 37%? Albert Einstein.
Honorable_Sasuke ยท 1 points ยท Posted at 07:52:48 on May 27, 2016 ยท (Permalink)
The remaining 37% is made of of that hack named Columbus
thenextguy ยท 7 points ยท Posted at 21:58:07 on May 25, 2016 ยท (Permalink)
I went outside once. I didn't like it.
UltimateShingo ยท 5 points ยท Posted at 22:21:40 on May 25, 2016 ยท (Permalink)
Neat graphics though.
[deleted] ยท 1 points ยท Posted at 07:42:18 on May 26, 2016 ยท (Permalink)
Could use an ENB mod tbh
BruteTartarus66 ยท 2 points ยท Posted at 22:51:45 on May 25, 2016 ยท (Permalink)
Only if you got that achievement in Civ V!
krung ยท 2 points ยท Posted at 05:17:39 on May 26, 2016 ยท (Permalink)
If you go outside every day, you only have to be around 30 years old to already have done it.
Tatsko ยท 1 points ยท Posted at 14:37:54 on May 26, 2016 ยท (Permalink)
So I'll need til 70 or so, got it.
ThatBelligerentSloth ยท 2 points ยท Posted at 06:04:55 on May 26, 2016 ยท (Permalink)
Who's Magellan?
Honorable_Sasuke ยท 2 points ยท Posted at 07:55:40 on May 27, 2016 ยท (Permalink)
The man who first circumnavigated Earth.
Tess47 ยท 1 points ยท Posted at 10:38:01 on May 26, 2016 ยท (Permalink)
Sorry, i was looking for you in the other direction.
[deleted] ยท 1 points ยท Posted at 13:58:43 on May 26, 2016 ยท (Permalink)
ayyyy gringo
Mesonit ยท 354 points ยท Posted at 14:33:05 on May 25, 2016 ยท (Permalink)
This is pretty counterintuitive!
crh23 ยท 1138 points ยท Posted at 14:44:55 on May 25, 2016 ยท (Permalink)*
That's because human intuitive understanding of statistics is surprisingly poor! Monty Hall problem, birthday paradox, gambler's fallacy, false positive paradox etc.
E: links, links, links!
youreawizerdharry ยท 51 points ยท Posted at 16:00:58 on May 25, 2016 ยท (Permalink)*
Love that Monty Hall problem.
Two simple ways to think about it:
Imagine he gives you the option to change your choice before he opens one with a goat, and this time if you agree to change, you get two doors. You obviously swap because why have one door when you could have two? Having agreed to swap, he then opens one of your own two doors, showing you that it's a goat - which one of your two will always be. Your remaining door therefore has a 2 in 3 chance of having the cash.
If there are 100 doors, and you pick one, and Monty opens 98 and asks if you want to switch, intuitively there is a much higher chance the money is not behind your door but in fact the one remaining - why else would he leave it closed, other than your 1 in 100 guess being correct?
WebStudentSteve ยท 31 points ยท Posted at 18:52:53 on May 25, 2016 ยท (Permalink)
Everyone skips over the most important part, and you kind of tacked it on at the end. The door he opens is always a goat, you know this BEFORE you switch doors. It's the most important part, because if he just eliminated a random door your odds don't change, but he always eliminates a goat door.
[deleted] ยท 7 points ยท Posted at 21:00:13 on May 25, 2016 ยท (Permalink)*
[deleted]
Schnoofles ยท 8 points ยท Posted at 22:45:38 on May 25, 2016 ยท (Permalink)
Apparently people are really bad at statistics, thus you're being downvoted :. Statistics don't care about intent, prior events or anything like that. The collective odds of the initial pick being right is always 1/3 regardless of what happens after it is picked. Switching is always the right choice.
[deleted] ยท 3 points ยท Posted at 23:30:40 on May 25, 2016 ยท (Permalink)
Thanks!
imyourfoot ยท 2 points ยท Posted at 01:20:06 on May 26, 2016 ยท (Permalink)*
Edit: To clarify, this post is referring to the alternate form where the host can reveal the car. In the standard form the host cannot reveal the car, and the usual "2/3 win when switching" answer is correct.
I went into more detail in response to looksfamiliar, but you're right that you'll pick the door with the car in 1/3 of all cases, and what happens afterward doesn't change whether you picked the car or not in any given case.
The complication is that the formulation of the problem specifies that the host reveals a goat, which effectively says "We're only looking at a subset of all possible games that could have occured." Because we're not looking at all games the odds can be (and indeed are) skewed by the criteria we choose to determine which games we include and exclude. By analogy, imagine if the problem specified that the host revealed the car. In that case your chance of having picked the car in the specified situation would be 0, even though your chance of picking the car in general would still be 1/3.
Because the host could have revealed the car, before the host opened any doors the possible outcomes would have been:
1/3 you pick the car * 0/2 the host reveals the car = 0
1/3 you pick the car * 2/2 the host doesn't reveal the car = 1/3 win by staying
2/3 you pick a goat * 1/2 the host reveals the car = 1/3 lose regardless
2/3 you pick a goat * 1/2 the host doesn't reveal the car = 1/3 win by switching
Since the host didn't reveal the car we can eliminate that possibility from consideration, and we divide the staying/switching win probabilities for these criteria (1/3) by the probability of the host not revealing the car (2/3) to get the 1/2 conditional probability of winning by either strategy, given that the host didn't reveal the car and we're limiting ourselves to games matching the criteria.
irishsultan ยท 1 points ยท Posted at 08:20:22 on September 5, 2016 ยท (Permalink)
Statistics don't care about intent or prior events, but in this case it still does matter. If the host accidentally reveals a goat you are not better of by switching, because he is more likely to reveal a goat (100% of the time in 1/3 of the cases) to reveal a goat when you picked the car than when you didn't (reveals a goat only 50% of the time, in 2/3 of the cases).
So now if you only know that he revealed a goat, but not that he did it deliberately, then you can't eliminate the possibility that he would have revealed a car. This means that you have a 1/3 possibility that the host reveals a car that you can remove, but the two other possibilities (host reveals goat, you picked the car; host reveals goat, you picked a goat) are equally likely.
If he did the picking of the goat deliberately this 1/3 possibility of the host revealing a car never exists, and so it can't be eliminated either.
imyourfoot ยท 1 points ยท Posted at 00:39:18 on May 26, 2016 ยท (Permalink)
Fake edit: this got a little long, sorry.
The Monty Hall problem boils down to the question "Given that the host has revealed a goat, what is the probability that the car is behind the door you initially selected?" In the standard form of the problem the host always reveals a goat, so the condition "Given that the host has revealed a goat" doesn't change the probabilities or reveal any new information and can be ignored.
In the alternate form of the question where he can reveal the car the condition is relevant and actually changes the probabilities. To show why, let's arbitrarily label the door hiding the car as door 1, the leftmost goat as door 2, and the rightmost goat as door 3. If we pick a door randomly and then the host randomly opens one of the remaining two doors without worrying about whether the car's behind it there are 6 possible outcomes:
#1: We pick door 1 (probability 1/3), host opens door 2 (probability 1/2), total: 1/3*1/2 = 1/6
#2: We pick door 1 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#3: We pick door 2 (1/3), host opens door 1 (1/2), total: 1/3*1/2 = 1/6 <--- car
#4: We pick door 2 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#5: We pick door 3 (1/3), host opens door 1 (1/2), total: 1/3*1/2 = 1/6 <--- car
#6: we pick door 3 (1/3), host opens door 2 (1/2), total: 1/3*1/2 = 1/6
If case #3 or #5 occurs the host reveals the car and our chances of winning by either staying or switching to the third door drop to 0. What if he doesn't reveal the car? Then we're in one of cases #1, #2, #4, or #6. In #1 and #2 we win by staying and in #4 and #6 we win by switching. Since the chances of each case occurring are equal, we have even odds for either strategy, and thus win 1/2 of the time given that the host didn't reveal the goat.
Your overall chances of winning by staying are still 1/3, as you still win if and only if you pick the door with the goat initially (2 of the 6 cases). What changes is that by imposing the condition "Given that the host has revealed a goat" we're limiting ourselves to considering 4 cases, and in 2/4 of those cases we win by switching.
So why doesn't that happen in the standard form? The difference is that the rules prevent the host from opening the door with the car. In case #3 we pick door 2 with a goat, and the host would open door 1 with the car, but he's not allowed to, so he's forced to open door 3 instead. That effectively morphs #3 into #4, which increases the overall chances of winning when switching by 1/6. Likewise #5 morphs into #6, increasing the switching odds by another 1/6 for a total of 4/6=2/3.
Creating another list like before we get:
#1: We pick door 1 (probability 1/3), host opens door 2 (probability 1/2), total: 1/3*1/2 = 1/6
#2: We pick door 1 (1/3), host opens door 3 (1/2), total: 1/3*1/2 = 1/6
#3: We pick door 2 (1/3), host opens door 3 (1), total: 1/3*1 = 1/3
#4: We pick door 3 (1/3), host opens door 2 (1), total: 1/3*1 = 1/3
We still have a 1/3 chance to pick each door, but this time if we pick a door with a goat there's only one possible case per door since there's only one available door with a goat behind it for the host to reveal. It's only the 1/3 chance where we pick the car door that we have two subcases, and these two equally likely subcases split the 1/3 probability into two halves of 1/6 probability. Thus we have 1/6+1/6 = 1/3 chance to win by staying (or lose by switching), and 1/3+1/3=2/3 chance to win by switching.
[deleted] ยท 2 points ยท Posted at 01:40:21 on May 26, 2016 ยท (Permalink)
Damn. You are right. I didn't think you were and sought out to prove you wrong, but the intention does matter. I keep making tables of possibilities and if the intention of the host was to pick a door at random, and they just so happen to pick a goat, switching to the other door only yields a success rate of 1/2. If the intention of the host was to always reveal a door that contains a goat, switching success rate is 2/3 and the one I initially choose is 1/3.
[deleted] ยท 1 points ยท Posted at 11:01:25 on May 26, 2016 ยท (Permalink)
Whilst you are right, you make the decision to switch after the host opens his door. Therefore it doesn't matter the total probability. As I said, if he reveals the car, you have lost. If he reveals a goat then we are back to 1/3 to 2/3. It's that simple.
Your analysis shows that it reduces your chance as you stand before he opens the door because there is always a chance he will reveal the car with his random choice (in this modified ruleset for others confused by us) and force you into losing.
imyourfoot ยท 1 points ยท Posted at 18:36:57 on May 26, 2016 ยท (Permalink)
Imagine a third variation of the game where everything is the same as the standard and alternate variations, except that the host always reveals the car if you didn't pick it initially. In that case switching will always lose, because either the host already revealed the car or the car was behind the door you picked initially. In that case the conditional probability of (the car being behind the third door, given that the host revealed the goat) is 0, since that never happens even though he sometimes reveals a goat.
That shows that changing the algorithm the host uses to choose which door to open can change the distribution of possible outcomes, which in turn changes the conditional probability of (the car being behind the third door, given that the host revealed a goat).
Suppose you have two possibilities A and B with probabilities > 0 where exactly one of them must occur, so there's no overlap or third alternative. If the overall probability of an event happening across A and B combined is 1/3, then either the probability is 1/3 in both of them, or it's greater than 1/3 in one of them and less than 1/3 in the other. The exact ratios will depend on the probability of A happening vs. B happening, but that generalization holds for any combination of probabilities having an overall 1/3 probability; the math just wouldn't work otherwise.
We agree that the probability of the car being behind the door you picked, given that the host hasn't opened a door yet, is 1/3. There are two possible outcomes of the host opening the door: either he reveals the car, or he doesn't. If he does reveal the car then the probability that the car is behind your door drops to 0. Using the general reasoning above, if he doesn't reveal the car that must mean that the probability that the car is behind your door rises. If that wasn't the case the probability of the goat being behind your door would be less than 1/3 in situation A (host reveals the car) and less than or equal to 1/3 in situation B (host doesn't reveal the car), which would only work if the overall chance of you picking the car was less than 1/3.
Conversely, in the standard problem where situation A (the host reveals the car) never happens all of the probability comes from situation B, and so the chance of the car being behind your door in situation B (he reveals a goat) must equal the overall probability of that happening, 1/3.
[deleted] ยท 1 points ยท Posted at 18:47:41 on May 26, 2016 ยท (Permalink)
OK, so I agree with this:
But I dont agree with this:
and I'm not sure why. However if he reveals the car, you have new information. But if he reveals a goat (by chance with these rules) then you dont have any new information. It should still be 1/3 to 2/3.
imyourfoot ยท 1 points ยท Posted at 01:23:55 on May 27, 2016 ยท (Permalink)
In the variation of the game where the host can reveal the car, before the host opens the door it's possible he will indeed reveal the car. If he then reveals a goat the new information is that he didn't reveal the car.
Looking at it another way:
Because the probability of (the host reveals the car) is different before and after the host opens the door, there must have been new information that led to that probability changing.
Conversely, in the standard problem where the host can't reveal the car, the fact that the host reveals a goat doesn't provide any new information. This is because the player knew there was a 100% chance the host would reveal a goat, so no probabilities change.
madewith-care ยท 66 points ยท Posted at 17:30:51 on May 25, 2016 ยท (Permalink)
Bonus fact about the Monty Hall problem: when the correct interpretation was advanced in a column by a female mathematician in 1990, despite the solution being provable with some very simple computer modelling in a way that wasn't possible when it was first explained, she was accused of using "female logic" and her "incompetence" derided by a number of people who somehow had attained PhDs despite not being able to do some quite basic maths.
(You are now subscribed to Stats Facts)
bloouup ยท 17 points ยท Posted at 18:02:18 on May 25, 2016 ยท (Permalink)
Marilyn vos Savant was also recognized by the Guinness Book of World Records as having the highest IQ of all time.
fistkick18 ยท 3 points ยท Posted at 19:47:26 on May 25, 2016 ยท (Permalink)
Hence the expression, I'm guessing?
Pijlpunt ยท 3 points ยท Posted at 20:14:59 on May 25, 2016 ยท (Permalink)
That would be quite a coincidence, given that "savant" means "learned" in French. Let's see.
This is what Merriam-Webster says:
ivecometosavetheday ยท 4 points ยท Posted at 20:31:22 on May 25, 2016 ยท (Permalink)
Huh. What are the odds of that...
sunshinesasparilla ยท 22 points ยท Posted at 20:35:35 on May 25, 2016 ยท (Permalink)
About 63%
Binny999 ยท 1 points ยท Posted at 21:57:57 on May 25, 2016 ยท (Permalink)
So meta
fistkick18 ยท 1 points ยท Posted at 00:44:58 on May 26, 2016 ยท (Permalink)
huh. thats weird on both fronts, considering "savant" usually means unusually gifted, not experienced (learned).
GroovingPict ยท 0 points ยท Posted at 21:10:33 on May 25, 2016 ยท (Permalink)
so... Marilyn vos Savant was savant?
Hobartastic ยท 2 points ยท Posted at 00:24:13 on May 26, 2016 ยท (Permalink)
It blows my mind that someone could both get a PhD and be convinced that "female logic" is a thing.
stinkyfastball ยท 2 points ยท Posted at 19:39:41 on May 25, 2016 ยท (Permalink)
The best part about the problems is this.
"In her book The Power of Logical Thinking, Vos Savant (1996, p. 15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer". Pigeons repeatedly exposed to the problem show that they rapidly learn always to switch, unlike humans (Herbranson and Schroeder, 2010)." from the wiki article.
That just cracks me up. The brightest of humanity consistently being outdone by pigeons.
crappenheimers ยท 1 points ยท Posted at 16:19:31 on May 25, 2016 ยท (Permalink)
Whoa your second point blew my mind. I'm trying to figure it out still, though. I believe it works based on the data, but don't understand. Switching from door 1 to door 2 gives a 2/3 chance of success, but couldn't the same be said for switching from door 2 to door 1? It makes sense for the 100 doors thing, but I don't get the three door problem.
President_SDR ยท 9 points ยท Posted at 16:34:33 on May 25, 2016 ยท (Permalink)
It doesn't matter which for you picked first, the act of switching gives you a two thirds chance of winning.
The key is that the host is always going to reveal a goat, he'll never reveal a car. The revealing is really just a formality, you're making a choice between the door you pick and all the doors you didn't pick.
ILikeMasterChief ยท 3 points ยท Posted at 17:56:20 on May 25, 2016 ยท (Permalink)
Finally! This did it for me. I've read dozens of explanations for this, but this one is the only one to help me get it. I knew it would finally happen. Thanks!
crappenheimers ยท 1 points ยท Posted at 01:57:47 on May 26, 2016 ยท (Permalink)
That was the best ELI5 I've seen about this! I actually understand it now, thanks.
Twilightdusk ยท 3 points ยท Posted at 17:01:36 on May 25, 2016 ยท (Permalink)
It still leaves me reeling a bit but here's the best explanation I remember:
There are 3 doors. One of them has the prize behind it. You have no further information, so whichever door you pick has a 1/3 chance of being correct, and a 2/3 chance of being incorrect.
Now Monty reveals one of the wrong doors, and asks you if you want to switch. On its face, you are making a new choice between two doors, 50/50 either way right? However in reality, he's asking you "Do you think your original choice was correct?"
Your original choice still has a 1/3 chance of being correct, because that's what it was when you picked it and that hasn't actually changed. So if you stick with that door, you'll have won 1/3 of the time and lost 2/3 of the time, same as if he revealed the winning door right away. Since the only other option is to switch, then switching provides a 2/3 chance of being the winning door, since the one you originally picked is only correct 1/3 of the time.
EsquireSandwich ยท 3 points ยท Posted at 17:22:39 on May 25, 2016 ยท (Permalink)*
The nice thing about the Monty Hall problem is that its so small you can actually just work out the possibilities to show that it works.
Lets say you pick door 1 and stick with it. There are thee options for what will happen:
The car is behind door 1 and you win
the car is behind door 2 and you lose
the car is behind door 3 and you lose
very simple 1 in 3 chance of winning.
Lets say you pick door 1 and switch. Your outcomes become
The car was behind door number one, he showed you either door 2 or 3 (it doesn't matter which) you switched to the other and now you lose.
The car was behind door number two, he showed you door 3, you switched and won.
The car was behind door number three, he showed you door 2, you switched and won.
2 in 3 chance of winning by switching.
The other way to think about it is that if initially pick a goat and switch, you will win. You will pick the goat 2 out of 3 times. The only way switching makes you lose if you happened to get the 1 out of 3 chance that you correctly picked the car the first time.
sarcbastard ยท 1 points ยท Posted at 20:21:43 on May 25, 2016 ยท (Permalink)
The problem with the Monty Hall problem is that way too many people don't pose the question in a manner that makes it clear that the bold parts can not happen.
[deleted] ยท 2 points ยท Posted at 16:39:30 on May 25, 2016 ยท (Permalink)
[deleted]
orangestegosaurus ยท 1 points ยท Posted at 17:09:43 on May 25, 2016 ยท (Permalink)
The simple way to understand this is that due to always opening the remainong empty doors, you're actually trying to pick an empty door as the "correct" door so you can then simply change your choice to the other non opened door. Your chances of winning then after opening the remaining empty doors simply reflect your chances of choosing an empty door.
So A% equals your chance of choosing the empty door while B% is the chance of choosing the door with a prize. While choosing a door you have B% chance of choosing the correct door but after opening the remaining empty doors you have the A% chance that you chose an empty door and swapping doors is the right move to get the prize.
DoctorWaluigiTime ยท 1 points ยท Posted at 17:32:11 on May 25, 2016 ยท (Permalink)
Your pick: 1/100 could have the money
Your non-pick: 99/100 could have the money
After the host reveals that 98 of those 99 other doors don't have the money, that last door is still in the second bucket: 99/100 chance of having the money.
The same applies to 3 doors: 1/3 correct, 2/3 incorrect. Host removes on of those two doors, but the second bucket is still "2/3".
throwaway903444 ยท 1 points ยท Posted at 19:37:48 on May 25, 2016 ยท (Permalink)
I tried REALLY FUCKING HARD to make sense of it using only the Wikipedia article and failed, and then reading this makes me feel like a complete idiot. It's so obvious.
[deleted] ยท 1 points ยท Posted at 21:54:19 on May 25, 2016 ยท (Permalink)
You once looked at three doors the same, even if you were unsure of the odds to begin with after the host reveals the contents of one of the other two doors you now see only two doors the same way. One, is your choice you previously without any knowledge about any one of the three doors. The other, is the one and only choice left you did not make based on the same information you had when you made your first choice. Now, you have new information not only about the goat door but about your odds of winning between the other two doors. You will have to ask yourself questions that frankly seem to have nothing to do with statistics but rather logistics.
If you had picked the WINNING door(assuming a goat isn't all you ever dream of) would the host announce you the winner (assuming they, or an informant of theirs knows the contents of each door) right away without any further play?
Should this not be a sudden happy ending, what are the chances they're trying to pawn another goat off on you?
If your chances were 1/3 at the start and 50/50 now, even though making a different choice will actually result in a different outcome rather you knew it or not, does it make a statistical difference?
Looking at two doors with hidden contents hoping for one to be the winner(when the other is not) is always a 50/50 without any prior knowledge. Looking at one opened door and two closed doors hoping for the same is still a 50/50 whether or not you had previously made a choice or not. They are separate events because your initial choice was never revealed. The fact the contestants would win in this situation 63% of the time is a separate statistic because it doesn't reflect anything about either of the two scenarios. Just before you make your choice to change or stay with door X it is still a 50/50, you've only had one door eliminated from the choosing. You still have no way of certainly telling if you would have won the game had you made the right choice the first time.
Honestly, This was really hard to explain whether I'm right or wrong but ultimately I would change my choice.
[deleted] ยท 17 points ยท Posted at 15:46:55 on May 25, 2016 ยท (Permalink)
That Monty Hall one really messes with me.
I'm going to have to read it more intently when I'm not at work.
AbsolutShite ยท 41 points ยท Posted at 16:12:37 on May 25, 2016 ยท (Permalink)
Imagine there were 100 doors with 1 prize.
I ask you to pick a number and you say 14. I open every door except 14 and 83. Would you swap?
pogtheawesome ยท 7 points ยท Posted at 18:11:02 on May 25, 2016 ยท (Permalink)
holy shit I get it now
[deleted] ยท 11 points ยท Posted at 16:14:41 on May 25, 2016 ยท (Permalink)
I don't see these as the same situation.
My answer is yes, definitely.
N546RV ยท 22 points ยท Posted at 16:18:14 on May 25, 2016 ยท (Permalink)
Why not?
[deleted] ยท 14 points ยท Posted at 16:20:59 on May 25, 2016 ยท (Permalink)
I'm having a hard time articulating it.
Which is obviously because my feeling is wrong and they're identical situations...
I guess it's because I chose 14 and the game chose 83. So no matter which one I picked, it would be that number or 83, in the end.
To me, it's less likely that I picked x out of 100 correct, therefore, the other option must be more likely. (as it is not truly out of 100)
N546RV ยท 22 points ยท Posted at 16:27:40 on May 25, 2016 ยท (Permalink)
But the same logic applies regardless of the number of doors; it's simply made more obvious by examining the extreme case of 100 doors. In all cases, you're likely to have picked the wrong door initially. The host then eliminates all but two doors, one of which is the one you picked. Since your first guess was most likely wrong, this means that the other remaining door is most likely right.
Practically speaking, the 100-door example would be much more useful. In that case, you could be pretty frickin sure that the other door was the right choice. I'm not a statistics guy, but I'd suspect that the chances of the other door containing the prize would be the opposite of the chances of your first guess being right, eg you had a 1/100 chance of your first guess being right, ergo there's a 99/100 chance that switching is the right decision.
With the three-door problem, the margin is much smaller. It's still a win statistically - you go from 1/3 to 2/3 chance of winning - but it's not the same open-and-shut case as the 100-door problem.
heybrother45 ยท 5 points ยท Posted at 17:34:56 on May 25, 2016 ยท (Permalink)
Important to note that this ONLY works if the host knows which door is correct.
[deleted] ยท 1 points ยท Posted at 17:55:04 on May 25, 2016 ยท (Permalink)
Correct. If the host can open a prize door then you learn nothing useful about the remaining doors.
[deleted] ยท 1 points ยท Posted at 19:54:06 on May 25, 2016 ยท (Permalink)*
[deleted]
[deleted] ยท 1 points ยท Posted at 20:13:12 on May 25, 2016 ยท (Permalink)*
No, because there isn't a transfer of information going on, because the host does not have information to transfer. If you pick the wrong door he only has a 2/3*(1/2) chance of opening a door with a goat.
The original problem only works because the host knows which door is the correct answer. If he does not there is no information gained when he opens a door, because he could have chosen the prize.
Here's a more detailed answer why: http://itsastatlife.blogspot.com/2013/09/the-monty-hall-problem.html
soniclettuce ยท 1 points ยท Posted at 04:20:07 on May 29, 2016 ยท (Permalink)
Doesn't it still work as long as the host doesn't actually open the prize door? In the 100 door case, if the host opens 98 doors and they all have goats, it would still make sense to switch.
[deleted] ยท 0 points ยท Posted at 05:46:12 on May 29, 2016 ยท (Permalink)
Nope, because either you or the host just got lucky.
soniclettuce ยท 1 points ยท Posted at 06:06:07 on May 29, 2016 ยท (Permalink)
Why does the host doing it by luck matter vs doing it by intention? Sure, it's very unlikely they avoid the prize by chance, but when they do, you're in the exact same situation.
[deleted] ยท 1 points ยท Posted at 06:33:21 on May 29, 2016 ยท (Permalink)
It means that there is a 50/50 chance that they guessed right or you did.
The difference is if they know which door it isn't they can't accidentally open it, so all of those possibilities are lost, so the remaining door grabs the probability. On the other hand if both of you are just randomly guessing the probability distributes evenly.
Basically when you say "given they don't select the prize" you need to divide by the probability they don't select the prize door. This completely kills off the additional probability that would be added if they are randomly guessing. If they aren't this prob is 1, so the remaining door absorbs the prob from the other doors.
[deleted] ยท 3 points ยท Posted at 16:31:51 on May 25, 2016 ยท (Permalink)
But, if switching is a 50% chance...how is not switching not a 50% chance as well?
That's the part I can't reconcile.
After it's revealed that door 3 is a goat, we learn that it was a 50% choice the entire time....how does switching a 50% chance choice make a difference?
President_SDR ยท 10 points ยท Posted at 16:39:53 on May 25, 2016 ยท (Permalink)
When you switch you don't have a 50% chance of winning, you have a two thirds chance if winning.
The key is that there host is always going to show a goat.
If you start by picking a goat (2/3 chance), the host will reveal the other good, leaving behind the prize, so if you switch you'll always win in this scenario.
If you pick the prize first (1/3 chance) the host will reveal one of the goats, leading behind the other goat, so if you switch you'll always lose.
There's a 2/3 chance of being in a winning position when you always switch, and a 1/3 chance of being in a losing position when you always switch, so you have 2/3 odds.
Rainuwastaken ยท 5 points ยท Posted at 17:10:07 on May 25, 2016 ยท (Permalink)
It still hurts my simple brain a little, but I think I get it. Any situation in which you picked a goat is one where you want to switch, and two thirds of the time you have a goat, so switching is usually the better answer. Am I getting it right?
I think originally I wasn't seeing the big picture. I was super focused on only the final "2 doors" choice, that I never looked at it from the "examine all outcomes" point of view.
EsquireSandwich ยท 4 points ยท Posted at 17:25:43 on May 25, 2016 ยท (Permalink)
That is exactly it. If you go in planning on switching, then you just need to pick the goat initially, which is a 2/3 chance.
d0ntblink ยท 3 points ยท Posted at 18:25:14 on May 25, 2016 ยท (Permalink)
But I want a goat
[deleted] ยท 3 points ยท Posted at 16:43:16 on May 25, 2016 ยท (Permalink)
This helped me resolve it mentally.
Looking at it backwards helped. 2/3 chance of choosing goat to start with instead of a 1/3 chance of choosing the car.
Thank you!
station_nine ยท 1 points ยท Posted at 18:17:36 on May 25, 2016 ยท (Permalink)
The best way to "get" it is to actually play the game, as Monty. This is what I did a long time ago.
You take 3 playing cards (Ace, Jack, Jack, let's say), and ask a friend to choose one. Now show your friend one of the remaining Jacks and give them a chance to stay or switch. Do this a couple dozen times and you'll realize that when it's time for you to reveal a Jack, you more often than not have only one card you can reveal. So more often than not, you're revealing where the Ace really is.
Pixelologist ยท 1 points ยท Posted at 16:48:59 on May 25, 2016 ยท (Permalink)
This was the only explanation that made sense to me, thanks.
[deleted] ยท 1 points ยท Posted at 16:40:39 on May 25, 2016 ยท (Permalink)
Think of this way: when presented with three doors, with a prize behind one of them, would you rather open one door or open two?
devotion304 ยท 1 points ยท Posted at 17:42:22 on May 25, 2016 ยท (Permalink)
Think about it this way, there are three possible scenarios according to which box you chose:
Door You picked: Goat A. Door He opened: Goat B. Swap door: Car.
Door He opened: Goat A. Door you picked: Goat B. Swap Door: Car.
Door He opened: Goat A. Swap Door: Goat B. Door you picked: Car.
In two of these scenarios swapping gets you the car, in only one of them sticking gets you the car. So you should always swap because your odds are better.
[deleted] ยท 1 points ยท Posted at 17:53:37 on May 25, 2016 ยท (Permalink)
Because the host is revealing information he knows that you do not know. If the host does not know which door is correct and opens randomly then there is a 50/50 chance of the door you started with being the winner, assuming he did not reveal the prize. But if the host knows and won't reveal the winning door then there was a 2/3 chance it was one of the other doors initially, and once he reveals a goat the remaining door gains that entire probability, because if you were right, which happens 1/3 of the time he could have picked either door. If you were wrong which happens 2/3 of the time, though, he had no choice of which door to pick. So overall you end up with a 2/3 chance of winning if you switch, since you picked the wrong door 2/3 of the time, and if you picked the wrong door the remaining door MUST be correct.
okuRaku ยท -3 points ยท Posted at 16:35:03 on May 25, 2016 ยท (Permalink)
It's only 50% if you switch, because when you picked the door it was 33%
ThirdFloorGreg ยท 2 points ยท Posted at 16:56:04 on May 25, 2016 ยท (Permalink)
When you pick a door, there is a 1/3 chance you picked the car and a 2/3 chance you picked a goat. In either case, the host has at least one goat to show you, which he does. This does not affect the probability that your original choice was a car. If you switch, you are betting that your initial choice was a goat, and you have a 2/3 chance of being right, since the host revealing one of the goats has no effect on the probability that you chose a car. Nothing is a 50% chance.
[deleted] ยท -3 points ยท Posted at 16:36:46 on May 25, 2016 ยท (Permalink)
Only because we didn't have the info we get later.
It's still 50%.
Not switching is a choice, just like switching is. Both doors have a 50% chance. they always did, we just didn't know it yet.
wwwstuff ยท 7 points ยท Posted at 16:41:45 on May 25, 2016 ยท (Permalink)
66% chance you picked a goat -> switching gives you a car.
33% chance you picked a car -> switching gives you a goat.
Not switching means you're more likely to end up with a goat. Switching means you're more likely to end up with a car.
PRDX4 ยท 4 points ยท Posted at 21:06:00 on May 25, 2016 ยท (Permalink)
I GET IT NOW.
You're saying that the act of switching gives you a 66% chance of success. I think what I and others were hung up on is that we're counting the number of doors and the number of prizes. 1 prize out of two doors is 1/2, intuitively.
ThirdFloorGreg ยท 4 points ยท Posted at 16:52:17 on May 25, 2016 ยท (Permalink)
No. Not at all.
TheVeryMask ยท 2 points ยท Posted at 23:49:10 on May 25, 2016 ยท (Permalink)
When you choose in the beginning you have a 1/3 chance. If you switch, what you're betting on is that your first choice was wrong. It's between the door you pick first and "any other door besides this one". After you make your choice, the dealer eliminates every thing you didn't pick except one, but your choice is still betting on getting it right the first time vs getting it wrong the first time.
Goddamnit_Clown ยท 1 points ยท Posted at 11:29:52 on May 26, 2016 ยท (Permalink)
Imagine that instead of the host opening 98 doors for you and leaving the last one to you, you got to open all 99 doors.
Or you could stick with door 14 and open that.
null_work ยท 1 points ยท Posted at 19:52:00 on May 25, 2016 ยท (Permalink)
Because while the two situations are congruent in some sense, in some sense there is a dissimilarity. I would wager that if you rephrased the question so that there's 100 doors, you pick one, the host opens 1 empty door and asks you if you want to stay with what you have or choose another door, people would be equally confused as they are with the 3 door version of the problem. Of course, in this variant, it still makes statistical sense to choose another door, as each one of those other doors has a slightly higher chance than the one you initially chose as well.
heybrother45 ยท 1 points ยท Posted at 17:33:11 on May 25, 2016 ยท (Permalink)
If you switch here you have a 99% chance of winning
chromeless ยท 1 points ยท Posted at 04:27:58 on May 26, 2016 ยท (Permalink)
You're right in this case. The idea that having 100 doors illuminates the problem is something I feel to be a mental trap that prevents people from actually understanding the problem and frequently only fools them into thinking they do.
Having 100 doors means that the chance of randomly picking a door with the car and happening to be correct is low enough that you may as well assume that when Monty eliminates all the other doors, that it's more likely that he's deliberately chosen to eliminate all the other answers except for what you reasonably believe is likely to be the car.
The thing is, this logic doesn't actually apply to the original three door problem directly, as even if both you and Monty are actually choosing randomly (if the reasoning behind his actions is not specified), there's a decent chance that you'll end up in the situation specified by the original scenario. Then, if you suspect Monty is likely acting randomly, him revealing a goat actually provides additional evidence that your next choice is 50/50, which is less likely to be the case in the 100 door problem.
All of this is irrelevant if you know exactly how Monty must act beforehand though.
[deleted] ยท 1 points ยท Posted at 10:09:41 on May 26, 2016 ยท (Permalink)
Thank you for articulating this.
It helps.
LexUnits ยท 3 points ยท Posted at 17:26:25 on May 25, 2016 ยท (Permalink)
The key is that Monty knows where the prize is, right? I don't know, I've had this explained to me so many times and I still have a hard time wrapping my head around it.
AbsolutShite ยท 3 points ยท Posted at 18:13:10 on May 25, 2016 ยท (Permalink)
Yeah, Monty can't open the door with the prize behind it so you have much more information after he opens the door.
[deleted] ยท 2 points ยท Posted at 20:07:26 on May 25, 2016 ยท (Permalink)
[deleted]
LexUnits ยท 1 points ยท Posted at 20:10:40 on May 25, 2016 ยท (Permalink)
Hmm.
[deleted] ยท 3 points ยท Posted at 20:03:15 on May 25, 2016 ยท (Permalink)
This is the best way to illustrate the logic behind Monty Hall problem that I've seen yet.
bl1nds1ght ยท 1 points ยท Posted at 21:31:41 on May 25, 2016 ยท (Permalink)
OOOOOOOOOHHHHHH, I finally get it. Thank you.
TopSecretSpy ยท 2 points ยท Posted at 18:09:22 on May 25, 2016 ยท (Permalink)
You're looking at the two doors in isolation and thinking each has a 50% chance. The problem is, you can't consider them in isolation because the host's actions (opening the other doors) has added new information that has to be considered.
The way I usually state it is that if there are X doors, your chance of choosing correctly on the first guess is 1/X. That means, crucially, that the chance you chose wrong is (X-1)/X. In the classic MH problem, it's 1/3 chance right, 2/3 chance wrong. By the host selectively opening doors, he's adding new information -- namely, a selection of doors that are now known to be wrong choices. It is that new information that changes things, because now the odds of you having chosen correctly never change even though there are now fewer doors left closed. The original odds remain 1/X, and the odds you were wrong remain (X-1)/X. And that's ultimately what you fight against at the end -- it isn't "is it this one door or that one door," it's "was I likely right when I guessed at first when there were X number of doors, or was I more likely to be wrong."
Of course, the MH problem as we think of it now technically wasn't how the real game operated. Sometimes he's open your door to reveal a win, or a loss, directly. Sometimes if you guessed wrong he'd open the winning door directly. They adjusted that in order to help control how much they actually had to pay out in prizes.
Dr-K-G ยท 1 points ยท Posted at 17:08:13 on May 25, 2016 ยท (Permalink)
Look at switching as betting on that your first choice was wrong. By switching you say "I think it's more likely that I got the wrong door the first try than that I got the right door and this is why I should switch".
EsquireSandwich ยท 1 points ยท Posted at 17:23:36 on May 25, 2016 ยท (Permalink)*
The nice thing about the Monty Hall problem is that its so small you can actually just work out the possibilities to show that it works.
Lets say you pick door 1 and stick with it. There are thee options for what will happen:
The car is behind door 1 and you win
the car is behind door 2 and you lose
the car is behind door 3 and you lose
very simple 1 in 3 chance of winning.
Lets say you pick door 1 and switch. Your outcomes become
The car was behind door number one, he showed you either door 2 or 3 (it doesn't matter which) you switched to the other and now you lose.
The car was behind door number two, he showed you door 3, you switched and won.
The car was behind door number three, he showed you door 2, you switched and won.
2 in 3 chance of winning by switching.
The other way to think about it is that if initially pick a goat and switch, you will win. You will pick the goat 2 out of 3 times. The only way switching makes you lose if you happened to get the 1 out of 3 chance that you correctly picked the car the first time.
[deleted] ยท 1 points ยท Posted at 17:41:13 on May 25, 2016 ยท (Permalink)
If you land on the donkey he can only switch you to the car not another donkey. That was the part that constantly tripped me up.
Randomawesomeguy ยท 1 points ยท Posted at 00:10:02 on May 26, 2016 ยท (Permalink)
During the initial choosing you have a 2/3 chance of picking a goat. He always opens a goat door. If you switch, odds are you will switch to the correct door, or rather the one you want, because of the odds in the initial choosing.
superiority ยท 1 points ยท Posted at 05:06:50 on May 26, 2016 ยท (Permalink)
If (and only if) you picked a goat the first time around, then switching doors when you're given the opportunity will win you the car.
So the probability that you win if you switch is the same as the probability that you picked a goat.
The probability you picked a goat on your first guess is two-thirds.
Therefore the probability that you'll win a car if you switch doors is two-thirds.
fruitcakefriday ยท -2 points ยท Posted at 16:09:52 on May 25, 2016 ยท (Permalink)*
From my other comment,
edit updated because wrong
President_SDR ยท 2 points ยท Posted at 16:44:08 on May 25, 2016 ยท (Permalink)
That's an incorrect way of looking at it and actually the exact fallacy that trips up people. You're not going from 1/3 to 50%, but 1/3 to 2/3.
fruitcakefriday ยท 1 points ยท Posted at 18:12:35 on May 25, 2016 ยท (Permalink)
God damn it.
[deleted] ยท -1 points ยท Posted at 16:13:06 on May 25, 2016 ยท (Permalink)
But not picking again has a 50% chance as well...
The actual chances don't change. What is behind each door is set.
What is the point in switching your response to a coin-flip situation?
LaughingVergil ยท 3 points ยท Posted at 17:01:09 on May 25, 2016 ยท (Permalink)
Actually, your original choice remains at 33.33...%
Consider this scenario. The setup is just like the Monty Hall scenario: three doors, one good result, and you choose your door randomly. However, instead of picking a certain loser to open, the host opens the first door that you didn't pick - door 2 if you pick door 1, door 1 if you pick 2 or 3.
1/3 of the time, you will lose as soon as the door is opened. The rest of the time, you will have a 1/2 (50%) chance of winning. But the total chance of losing is 2/3 of the time -- 1/3 + 1/2 of 2/3 = 2/3 -- whether or not you change your pick.
If both unpicked doors are opened at the same time in the above scenario, your pick still has a 2/3 chance of losing.
In the Monty Hall problem, the first pick will never be a loser. Although your first choice only has a 1/3 chance of winning no matter what (because you chose one door out of three), removing one door from consideration sets up a different problem with only two doors.
Now, if you can not change your door at this point, you are still playing the game where two out of three doors are losers. It doesn't matter what order the doors are opened, you are still playing a game where 2/3 of the doors lose.
If you stay with your first choice, it is the same as if you were not allowed to change doors - you still lose two out of three times. However, if you change your choice, you are playing a new game, where there are only two doors, and one of the doors has the prize. Instead of staying in the game where you lose more than you win, changing to the game where you have even odds increases your chance of winning.
Hopefully this helps clarify things.
screen317 ยท 1 points ยท Posted at 16:52:34 on May 25, 2016 ยท (Permalink)
Look at the extreme case with a million doors.
Goddamnit_Clown ยท 14 points ยท Posted at 15:34:53 on May 25, 2016 ยท (Permalink)
I always felt that Monty Hall is so much more of a sticking point than other examples because of the extra ambiguity around the rules the host plays by.
Glitch29 ยท 15 points ยท Posted at 15:53:35 on May 25, 2016 ยท (Permalink)
Preach it.
It's a pet peeve of mine when people set up Monty Hall problems in an ambiguous way. For the problem to be solvable, it's not sufficient to say what the third party did - you need to also say what they would have done in each scenario.
boarhog ยท 1 points ยท Posted at 04:16:59 on May 26, 2016 ยท (Permalink)
In each scenario they would open a door that doesn't have the prize behind it. Can you explain what you're referring to?
Glitch29 ยท 1 points ยท Posted at 07:14:38 on May 26, 2016 ยท (Permalink)
That clarification is what I'm referring to. There's a huge difference between
and
The second allows for situations like this:
In this scenario, the contestant should be indifferent to swapping or not, as either gives a 50/50 once they've gotten to that stage.
kcMasterpiece ยท 12 points ยท Posted at 15:41:01 on May 25, 2016 ยท (Permalink)
I think nobody ever just broke it down as 2/3 of the time you will pick wrong. And then be asked to switch between a right and wrong answer.
I failed to reason that logic out for myself when I was 16.
fruitcakefriday ยท 0 points ยท Posted at 15:59:50 on May 25, 2016 ยท (Permalink)*
It took me a while to get it, and when I did, I didn't understand why the explanations to the problem I had seen were so obtuse.
Basically, at the start you have three doors and a 66.66% chance of selecting the wrong door. When asked if you want to switch your answer, you have two doors and so a
50%66.66% chance of success if switching, vs a 33.33% chance of having selected the right door from the start.If asked, "Do you want to stick with your 33.33% chance, or switch to the
50%66.66% chance?" the correct decision is obvious.edit I'm annoyed I got it wrong still after thinking I had sussed it...but the logic works out.
As others have said, increasing the number of doors makes it clearer. If there are 10 doors, you have a 90% chance of selecting the wrong door initially, so once given the choice to switch after all invalid doors are closed, the other door has a 90% chance of being the winning one, while you current door retains the initial 10% chance of being the right door.
kcMasterpiece ยท 6 points ยท Posted at 16:20:29 on May 25, 2016 ยท (Permalink)
Ah, I might be misremembering the rules as the other guy said, but I always thought they always got rid of a losing door. So at the end there is a winning door and a losing door.
So the 33% of the time you picked the right door the first time you will be switching to a losing door, the 66% of the time you will be switching to a winning door.
So if the rules are like that, you always switch. And have a 66% chance of winning that way.
ThirdFloorGreg ยท 4 points ยท Posted at 16:58:50 on May 25, 2016 ยท (Permalink)
Switching gives you a 2/3 probability of winning, not 50%. You are being asked to bet that your initial choice was bad (switch, 2/3 probability of winning, or that it was good (stay, 1/3 probability of winning.
InappropriateHandle ยท 1 points ยท Posted at 16:17:14 on May 25, 2016 ยท (Permalink)
It's also a little easier to understand if you start with a higher number of doors. Maybe there's 100 doors, you pick one, and he opens 98. It's much easier to understand there's a higher likelihood that you chose the wrong door initially, and apply it to the 3-door problem.
thisisnotdan ยท 7 points ยท Posted at 15:12:57 on May 25, 2016 ยท (Permalink)
I feel smart because I understood all three of those references.
lala447 ยท 5 points ยท Posted at 15:21:26 on May 25, 2016 ยท (Permalink)
i didn't. ELI5?
asdfqwertyfghj ยท 21 points ยท Posted at 15:27:35 on May 25, 2016 ยท (Permalink)
The birthday problem I am assuming is you only need 23 people to have a 50% chance that two people have the same birthday and the gamblers fallacy is that you believe your chances of winning go up the longer you haven't won bc eventually you've got to win sometime even though in reality you have the same chance of winning your first time as you did you last time.
Edit: deleted some words for correct wording.
Mystery_Hours ยท 15 points ยท Posted at 15:43:12 on May 25, 2016 ยท (Permalink)
People also believe that when you're on a 'hot streak' you're more likely to keep winning.
KilKidd ยท 29 points ยท Posted at 16:12:49 on May 25, 2016 ยท (Permalink)
So, essentially, whatever happens people will belive they should win?
PessimiStick ยท 24 points ยท Posted at 16:17:06 on May 25, 2016 ยท (Permalink)
Yeah that's pretty much the entire psychology behind casinos.
If people were rational, no one would gamble, because you always lose long-term.
[deleted] ยท 0 points ยท Posted at 16:34:47 on May 25, 2016 ยท (Permalink)*
[deleted]
Barimen ยท 1 points ยท Posted at 17:01:59 on May 25, 2016 ยท (Permalink)
"Intristic satisfaction" doesn't fall under rational. You win, your brain is flooded with nice, juicy and addictive neurochemicals and you are happy... for a moment.
And PessimiStick clearly said "long run". You're talking about short run. :)
kogasapls ยท 2 points ยท Posted at 17:04:07 on May 25, 2016 ยท (Permalink)*
His claim:
The reason given is
He says rational people would not gamble (at all) because of the long-run consequences. He doesn't say rational people would not gamble only in the long run.
If your goal is to maximize satisfaction and gambling gives more satisfaction than not gambling, isn't the rational choice to gamble? Rational decision-making isn't really possible without some kind of a goal. Otherwise there is no way to distinguish rational from irrational choices. He's presupposing that the goal is to maximize profit, in which case long-run gambling is a poor strategy. But if intrinsic satisfaction per gamble outweighs the average cost then it could be a rational endeavor in the long run (it just generally doesn't, so it isn't).
big_cheddars ยท 1 points ยท Posted at 19:22:53 on May 25, 2016 ยท (Permalink)
Essentially yeah. Gambler's fallacy is people believing a string of one value must eventually break. Hot streak fallacy is people believing the exact opposite about the same situation, that a string of values are more likely to not break.
phlegminist ยท 1 points ยท Posted at 17:12:15 on May 25, 2016 ยท (Permalink)
That case is more superstition than a misunderstanding of probability though.
RabidRapidRabbit ยท 1 points ยท Posted at 18:09:49 on May 25, 2016 ยท (Permalink)
to be fair variance dictates that it gets less and less likely to lose AGAIN the more often you repeat throwing the dice. Their sample size is just too small for it to be of relevance
chetlin ยท 1 points ยท Posted at 16:30:31 on May 25, 2016 ยท (Permalink)
Is it also the gambler's fallacy when people say Chicago is "due" to get hit by a strong tornado or Florida is "due" to get hit by a hurricane this year because it's been longer than normal since the last time those things happened? Previous years really don't have much of an influence on this one.
asdfqwertyfghj ยท 2 points ยท Posted at 16:47:16 on May 25, 2016 ยท (Permalink)
I believe there are other contributing factors when dealing with the weather. So probably not as much as you would think.
CGRCC ยท 0 points ยท Posted at 17:26:56 on May 25, 2016 ยท (Permalink)
Except much of weather is provably cyclical
[deleted] ยท 5 points ยท Posted at 15:26:21 on May 25, 2016 ยท (Permalink)
Not an ELI5, but the Monty Hall problem, the Birthday problem and the Gambler's fallacy.
lala447 ยท 3 points ยท Posted at 15:27:26 on May 25, 2016 ยท (Permalink)
Thanks!
sharkinaround ยท 2 points ยท Posted at 16:39:06 on May 25, 2016 ยท (Permalink)
there is no ELI5 for the Monty Hall problem... a simple explanation that will get you to grasp it simply doesn't exist. I hate going down the inevitable rabbit hole every time i rehash that problem in my head.
Goddamnit_Clown ยท 1 points ยท Posted at 11:44:02 on May 26, 2016 ยท (Permalink)
Sure there is: There are some doors, you get to pick one, then you get a choice. You can either open [your door] or [every other door].
The mechanics of playing are very simple but the gameshow trappings are very confusing. The host is only dramatically opening known losing doors from the [every other door] category for entertainment purposes.
The prize doesn't care whether he opens some and you open some, whether he opens them all or you open them all. Either way you're going home with what's behind your door or what's behind every other door put together.
IAM_deleted_AMA ยท -1 points ยท Posted at 19:21:14 on May 25, 2016 ยท (Permalink)
I'm in no way an expert but I believe I understand it. When he tells you to open one of 3 doors, you have 1/3 chances to win (or 33%). But then he opens a not winning door, which leaves you with the one you picked and another door, now you're asked if you want to keep your door or change for the other one, but this time you have 1/2 chances to win (or 50%), 50% is higher than 33% so theoretically you have better chances to win if you switch, because when you picked your first door, your chances of winning were smaller.
The 3 door scenario doesn't really make it easy to understand, it's way better if you imagine it with 100 doors, say you pick one (that's 1% chances of winning) he opens 98 losing doors, that leaves you with 2 (50% chance), the one you picked and another one. Would you really believe you picked the winning door out of a 100??
sharkinaround ยท 1 points ยท Posted at 19:45:33 on May 25, 2016 ยท (Permalink)
yeah I was sort of joking, I understand the logic behind it. I think the part I struggled with (still struggle with) was that it seems that the whole problem hinges on the fact that it would have to be established that he is going to open a losing door prior to the game starting. If I was told that going into the game then I agree on the principal. I know people will say that doesn't matter. But that removes the concept of the switch offer potentially only being given if you picked the winning door, etc.. Definitely thinking from a different angle on that one beyond just pure probability analysis which isn't the point of the problem, but I feel like the math implies that the switch offer is always in play the whole time, every time, yet the question is phrased that it is introduced only after the selection is made. (if that makes any sense)
[deleted] ยท 2 points ยท Posted at 15:50:32 on May 25, 2016 ยท (Permalink)
A nice visualization and presentation of the false positive paradox, as well:
https://www.ted.com/talks/peter_donnelly_shows_how_stats_fool_juries?language=en
Jacques_R_Estard ยท 3 points ยท Posted at 15:27:23 on May 25, 2016 ยท (Permalink)
First one is the problem with the three doors and goats/cars behind them. Birthday paradox (not really a paradox) is that if you get 23 people in a room there's a 50% chance of two people sharing a birthday and the gambler's fallacy is assuming that if you flip a (fair) coin a hundred times and get heads each time, you have a better than 50% chance at a tails next time you flip it. Although if that happens, I'd tend to suspect the person who told me the coin was fair was full of it.
ThirdFloorGreg ยท 1 points ยท Posted at 17:02:08 on May 25, 2016 ยท (Permalink)
In a fifth grade lesson on probability I flipped coins in groups of three and got either all heads or all tails like 8 times in a row.
Jacques_R_Estard ยท 2 points ยท Posted at 17:28:18 on May 25, 2016 ยท (Permalink)
The probability of that happening is (2 * (1/2)3)8, or 1 in 65536. Not bad.
3kindsofsalt ยท 2 points ยท Posted at 15:55:09 on May 25, 2016 ยท (Permalink)
The false positive one doesn't seem that hard to grasp. If the likelihood that your test gives a false positive is greater than the actual percentage of positives, a positive is just numerically more likely to be a false positive. "3% of people are infected. This test screws up 10% of the time for the uninfected. A positive test is pretty unreliable".
[deleted] ยท 4 points ยท Posted at 15:37:16 on May 25, 2016 ยท (Permalink)
[deleted]
lala447 ยท 3 points ยท Posted at 15:44:51 on May 25, 2016 ยท (Permalink)
Thank you! That makes a lot of sense!
kogasapls ยท 3 points ยท Posted at 16:49:27 on May 25, 2016 ยท (Permalink)
Your explanation of the birthday paradox is slightly misleading. It implies that there is a 69% chance that a group of 23 has a shared birthday, while the actual chance is ~50.7%. It also implies that a group of 20 is sufficient for >50% chance, which is false.
It's easiest to think of it in terms of "the chances of two people not sharing a birthday." The first person is guaranteed a unique birthday for any of the 365 days: 365/365.
The second person has a unique birthday on 364 of the remaining days, so their combined probability is 365/365 * 364/365. Dividing by 1 = 365/365 to simplify things leaves you with just 364/365.
Then the third person can pick 363 of the remaining days, and so on:
365/365 * 364/365 * 363/365 ... = (365 * 364 * 363 ... )/(365 * 365 * 365 ...)
which is equal (after dividing by 365/365 again) to
(364 * 363 ... (365-n))/(365n )
The numerator can be rewritten as 365!/(365 - n)!, leaving you with
365!/[(365 - n)! * 365n ]
which gives you the correct probability P(n) for a group of n people not sharing a birthday. The probability for that group having a shared birthday is then 1 - P(n) > 0.5 for n>22
PianoMastR64 ยท 1 points ยท Posted at 16:07:21 on May 25, 2016 ยท (Permalink)
Fun fact: dice is actually plural, even though many people treat it as singular. Die is the singular term.
acEightyThrees ยท 2 points ยท Posted at 15:26:25 on May 25, 2016 ยท (Permalink)
The birthday paradox has always made my head hurt. I'm actually good at math, and pretty intelligent, but the birthday paradox messes me up.
kogasapls ยท 1 points ยท Posted at 17:02:57 on May 25, 2016 ยท (Permalink)
Figure out the odds that n people do not share a birthday by looking at the number of possible days left that haven't already been "taken." For the first person, all 365 are available, so he has 365/365 available days: a probability of 1.
The second person has only 364/365 available days IF the first person has a unique day (P=365/365). So the combined probability of the first person having a unique day then the second person having a unique day is their product: 365/365 * 364/365.
The third person has 363/365 IF the first AND the second both have unique days (P=365/365 * 364/365). So their combined probability is 364/365 * 363/365 = (365 * 364 * 363)/(365 * 365 * 365) = (365 * 364 * 363)/(3653 )
As you can see, the numerator is following the pattern: (365 * 364 * 363 * 362 * 361 ...) while the denominator is simply (365 * 365 * 365 *365 * 365 ...). You can rewrite the numerator as 365!/(365 - n)! and the denominator as 365n to give you the equation P(n) to find the probability of a group of n people all having unique birthdays.
P(n) = 365!/[(365 - n)!(365n )]
So the probability of the opposite case, where at least one shared birthday exists, is 1 - P(n), which is greater than 0.5 for n=23.
thiney49 ยท 1 points ยท Posted at 15:34:15 on May 25, 2016 ยท (Permalink)
I should read all the of these later when I want to not work.
myshieldsforargus ยท 1 points ยท Posted at 15:57:35 on May 25, 2016 ยท (Permalink)
there are perfectly good explanations for 'human intuition' in those cases. It has to do with the fact that the human brain is evolved to operate on conditional probability in the real world. For example, if you roll a die 100 times and you get head every time, conditional probability would tell you that the probability of the next one being head is very high, just as if you had dropped an apple and it fell to the ground 100 times it's a pretty good chance the next time you drop it it's gonna fall.
AbsolutShite ยท 2 points ยท Posted at 16:13:25 on May 25, 2016 ยท (Permalink)
What die are you rolling that you get head?
Can I borrow it?
crh23 ยท 1 points ยท Posted at 16:07:15 on May 25, 2016 ยท (Permalink)
Of course! That is why the sorts of things that don't come up in nature (like a dude with cars and goats behind doors) are the things we struggle with.
BEEFTANK_Jr ยท 1 points ยท Posted at 16:18:06 on May 25, 2016 ยท (Permalink)
I have to say. It took me a long time reading the Monty Hall entry to agree with the correct conclusion.
[deleted] ยท 1 points ยท Posted at 16:20:13 on May 25, 2016 ยท (Permalink)
Monty Hall isn't really that confusing imo. You initially had a 2/3 chance that the door you pick had a goat behind it, so once a goat is revealed, there is now a higher chance that the door you didn't initially pick isn't a goat.
I think what gets people is that once a goat is revealed, they stop thinking about the doors in terms of the initial situation.
imGnarly ยท 1 points ยท Posted at 17:17:55 on May 25, 2016 ยท (Permalink)*
Monty Hall's is one of my favourite math problems. So simple, yet so hard for people to grasp. It can be explained so easily by just checking the arrangement table. The reason this works is simply because the host never opens the door with the car in it. The behaviour of the host, just as the article explains, is what makes the door-switching strategy the most successful.
[deleted] ยท 1 points ยท Posted at 18:04:05 on May 25, 2016 ยท (Permalink)
The Monty Hall problem is my favourite. I actually learned about it through reading the curious case of the dog at night time.
bl1y ยท 1 points ยท Posted at 18:14:53 on May 25, 2016 ยท (Permalink)
Don't forget the puppy problem!
A person calls a pet store and asks if they have any male puppies. The clerk at the counter says there are 2 puppies, but they're in the back getting washed, so he calls to the dog washer a the back and asks "Hey, do we have any male puppies?" The dog washer checks and says "Yes."
Then the person on the phone asks "What about 2 male puppies?"
What are the odds both puppies are male?
Intuitively, we'd say there's a 1/2 chance. One puppy is male, and there's a 50% chance the other is male, so 50% chance they're both male.
In fact, it's only a 1/3 chance!
The combination for any 2 puppies is M/M, M/F, F/M, and F/F, and it's important to understand that M/F and F/M are not the same, and are two separate possibilities. It can help to name the puppies to make that clear -- Spot female, Rascal male, and Spot male, Rascal female are different.
However, knowing that there is 1 male puppy already eliminates the F/F possibility, leaving us with M/M, M/F, and F/M. These all occur with equal odds, so M/M is only a 1 in 3 chance, much less than the 1 in 2 we would have thought.
true_unbeliever ยท 1 points ยท Posted at 18:17:20 on May 25, 2016 ยท (Permalink)
Lots of deserved love for Monte Hall.
I like Shermer's article. Similar to John Allen Paulos' book Innumeracy.
The probability calculations of a dream premonition of a loved one dying is good.
The birthday problem is also a good one.
NlNTENDO ยท 1 points ยท Posted at 18:30:04 on May 25, 2016 ยท (Permalink)
Thanks! As a data analyst, I get to justify my redditing at work now
Datduckdo ยท 1 points ยท Posted at 18:34:50 on May 25, 2016 ยท (Permalink)
I dont like monty hall because of the human variable, what if the host opened 3 because he knew 1 had the car
takotaco ยท 1 points ยท Posted at 18:44:33 on May 25, 2016 ยท (Permalink)
Case in point though; even when we try to do statistics right, we often don't.
pogrmman ยท 1 points ยท Posted at 19:33:20 on May 25, 2016 ยท (Permalink)
Also, stats is just weird. Look at Simpson's Paradox
For instance, Texas has low high school graduation rates, overall. But, for whites, Hispanics, and African Americans, it has among the highest graduation rates for each race
rivade ยท 1 points ยท Posted at 19:48:50 on May 25, 2016 ยท (Permalink)
Can you explain why gambler's fallacy doesn't directly apply in the situation OP was describing with the meteor?
Nugz123 ยท 1 points ยท Posted at 20:26:29 on May 25, 2016 ยท (Permalink)
Flipping a coin 100 times vs asking a group of people to fake it.
The coin always has longer streaks because people faking it don't understand statistics / probability.
crh23 ยท 2 points ยท Posted at 20:39:42 on May 25, 2016 ยท (Permalink)
There are a set of tests of randomness for coin flips: on average, half are heads and half are tails (which humans simulate quite well), but also half of sets of two consecutive coins are the the same and half are different, and half of adjacent pairs are both the above, ad infinitum
andropogon09 ยท 1 points ยท Posted at 20:36:15 on May 25, 2016 ยท (Permalink)
I hear stuff like this all the time on the Weather Channel. If we experience a few days that are unusually cool or warm, then we can expect a few days to compensate because of "the law of averages".
Odesit ยท 1 points ยท Posted at 20:42:05 on May 25, 2016 ยท (Permalink)
I was about to post the birthday paradox here because I love it. It really goes to show how statistics can be confusing intuitively. Also I think it's great to win bets against people who don't know it. E.g. I bet you in this chamber of 23 people there's at least two people who share birthday. If this bet doesn't work, you double it in the next room you go to with 23 people eventually recovering your loss.
NotGloomp ยท 1 points ยท Posted at 20:52:38 on May 25, 2016 ยท (Permalink)
Yeah Denombration and Probabilities were really trippy in highschool.
flexpercep ยท 1 points ยท Posted at 21:07:24 on May 25, 2016 ยท (Permalink)
I love all of these!
[deleted] ยท 1 points ยท Posted at 21:22:06 on May 25, 2016 ยท (Permalink)
From your first link:
Ironic that this ignores the concept above. Should be like 0.8 miracles per month, no?
SergeantGrumblz ยท 1 points ยท Posted at 23:33:00 on May 25, 2016 ยท (Permalink)
cool article except he's wrong about evolution. you can witness evolution in a human lifetime, just not human evolution. you can witness evolution in successive generations of fruit flies or nematodes or whatever. organisms where the time between birth and reproduction is very short.
nanotubes ยท 1 points ยท Posted at 23:53:25 on May 25, 2016 ยท (Permalink)
I understand the math for gambler's fallacy...but I have to really disagree with what people usually understands it as. People usually understand it as that whatever number of tosses come next, you can't have more probability due to the previous records. (See /u/asdfqwertyfghj's explanation) However, that only holds true for the very next toss, because head/tail is always 50/50.
For example fair coin = 50/50 chance. Meaning, if in first 50 toss of are heads biased, then your next 50 toss will be tail biased to average out the toss pattern. Assuming this is a fair coin. If you say, no no no, that's gambler's fallacy, then you probably understood it wrong. It has to tail biased to average it out. If you continue to have head biased, then yea, your 100 toss is probably more like 75/25, then you can bet your next 100 toss will be tail biased. In order for the whole set to be averaged out to 50/50
IMO, gambler's fallacy only applies to the very next bet because regardless, head/tail is always 1/2 chance. However, if a gambler is looking at a set of data at a time, gambler's fallacy no longer applies to its full extent.
Teh_Mongoose ยท 1 points ยท Posted at 00:15:30 on May 26, 2016 ยท (Permalink)
The thing about that though is people are often better at understanding the real world against statistics. Taking the monty hall problem, statistically it's a better bet to switch, but outside sterile statistics it actually is irrelevant. The prize has already been placed, it hasnt moved.
[deleted] ยท 1 points ยท Posted at 07:50:50 on May 26, 2016 ยท (Permalink)
Daniel Kahneman's 'Thinking, Fast and Slow' also has some great examples demonstrating poor human intuitive grasp of statistics. More from a decision-making and judgement perspective as in cognitive psychology, but still very relevant.
[deleted] ยท 4 points ยท Posted at 18:01:03 on May 25, 2016 ยท (Permalink)
That's because it is worded poorly. The right way to see it is, there is a 1 in N chance of an event occurring. The probably that the event occurs at least once in N attempts is about 63%.
guy99877 ยท 2 points ยท Posted at 16:36:12 on May 25, 2016 ยท (Permalink)
It is pretty intuitive!
wedgiey1 ยท 2 points ยท Posted at 15:42:33 on May 25, 2016 ยท (Permalink)
It is? Is the intuitive response that it should be 100%?
queue_cumber ยท 2 points ยท Posted at 17:47:55 on May 25, 2016 ยท (Permalink)
If you think about the odds, what it means to have odds of 1 out of 100 is that out of 100 times it should happen at least once. That's what the odds mean: it happens 1 time out of every 100 times. So the idea that it's a different number is counter intuitive.
wedgiey1 ยท 2 points ยท Posted at 17:50:50 on May 25, 2016 ยท (Permalink)
By that logic every two times you flip a coin it should come up heads once and tails once...
queue_cumber ยท 3 points ยท Posted at 17:54:04 on May 25, 2016 ยท (Permalink)
Yes, it should, the odds for each are 2:1 so you would expect each to come up once in two flips. In reality, since there is randomness, you would need to repeat the experiment many many (infinite) times to get that outcome of 50%. So what's the problem again?
Hara-Kiri ยท 2 points ยท Posted at 18:11:43 on May 25, 2016 ยท (Permalink)
Well not 100%, but if the odds of something were 1 in 100, I'd imagine it would be more likely to happen than 63%.
wedgiey1 ยท 1 points ยท Posted at 19:22:36 on May 25, 2016 ยท (Permalink)
Yeah, when I think about it, I think each time I do Y, there's a 1% chance that X will happen. So it's like how many times do you need to roll a 1d100 until you get a 1... As a tabletop gamer, it seems like this happens way more than 1% of the time, but really you could roll it 1,000 times and never see a '1' come up... I guess when you start adding up a bunch of 1% chances over time it averages out to 63%?? I dunno.
droodic ยท 3 points ยท Posted at 15:57:11 on May 25, 2016 ยท (Permalink)
I don't know why it's surprising to hear that to people who haven't studies statistics, hearing something having odds of 1 out of 100 would usually yield a 100% result if tried 100 times
sharkinaround ยท 7 points ยท Posted at 16:47:23 on May 25, 2016 ยท (Permalink)
yeah I'd think you just add the probabilities up. e.g. two 1:100 chances, 1/100 + 1/100 so 1/50 times you'd win. I think anyone claiming that reaching 63% as the answer is more intuitive then reaching 100% is either lying or desperately trying to sound smart.
Idontlikesundays ยท 6 points ยท Posted at 17:22:09 on May 25, 2016 ยท (Permalink)
If you flip a coin twice is the likelihood of getting heads 100%? Obviously not.
sharkinaround ยท 1 points ยท Posted at 14:16:46 on May 26, 2016 ยท (Permalink)
no but on average you would get 1 heads... which I think is where the confusion arises for a lot of people.
[deleted] ยท 3 points ยท Posted at 17:26:07 on May 25, 2016 ยท (Permalink)
[deleted]
sharkinaround ยท 3 points ยท Posted at 19:36:00 on May 25, 2016 ยท (Permalink)*
You're the one that initially responded with a high-brow "It is?" like you are so surprised anyone wouldn't be as smart as you and realize this immediately. Why do you think the fact is the top comment on the thread? Perhaps because it isn't very obvious.
The original fact presented could easily be given as a textbook example of counter-intuition.
What are the odds of tossing a 6-sided die and getting a 1? 1:6, obviously.
What about if you get two throws and have to throw a "1" at least once? Majority of people would assume your odds would increase to 2:6. Intuition says that if you get double the chances, you would double your odds. Many people would apply the same logic to the 1:100 chance. The first probability site I pulled up reiterates that to be standard train of thought.
Secondly, people also may confuse probability of 1 (or 100%) to mean that if you do something with a 1/100 chance 100 times, and then repeat this process many times, you will win once on average in each set of 100 attempts. Hence why /u/droodic said it would "usually yield." I don't think anyone is claiming or thinks that it is guaranteed to happen.
[deleted] ยท 1 points ยท Posted at 20:40:32 on May 25, 2016 ยท (Permalink)
[deleted]
sharkinaround ยท 1 points ยท Posted at 21:30:28 on May 25, 2016 ยท (Permalink)
I'm not so sure you fully grasp what intuition implies. If you are applying things you've learned in statistics or math courses, or even thinking deeply into the problem at all, that is no longer intuitive thinking. I didn't say that "anyone that claims they agree that 63% makes more sense to them as the answer than 100% is lying." or "anyone that understands why it is 63%", etc. I said anyone that claims that their basic intuition (which implies instinctual thought, not having been instructed on principals of statistics or probabilites, and by definition, not applying conscious reasoning) would have led them to an answer closer to 63% than 100% is either lying or desperately trying to sound smart.
You use the Monty Hall problem as an example. So you are claiming you immediately knew the correct answer to the problem without even having to think it through? If not, then you prove my point that that problem is also counter-intuitive. Again, that doesn't mean that you don't fully understand it in and out, or that you couldn't figure it out after breaking it down, but then it ceases to be intuition that helped you reach the answer.
My opening line of the last message clearly was directed to a comment earlier in the thread which I wrongfully assumed was from you. I'm quite surprised your intuition didn't deduce that one.
ThirdFloorGreg ยท 5 points ยท Posted at 17:04:34 on May 25, 2016 ยท (Permalink)
Anyone who thinks 100% is not obviously wrong is just a fucking idiot, so literally any other result should be more intuitive.
vakula ยท 1 points ยท Posted at 18:34:17 on May 25, 2016 ยท (Permalink)
I like your terms :-)
_mainus ยท 4 points ยท Posted at 16:11:00 on May 25, 2016 ยท (Permalink)
I always assumed 50%
wedgiey1 ยท 1 points ยท Posted at 16:30:54 on May 25, 2016 ยท (Permalink)
It either happens or doesn't! 50%!
_mainus ยท 6 points ยท Posted at 16:38:41 on May 25, 2016 ยท (Permalink)
I was thinking more along the lines of the top of a bell curve
Numendil ยท 1 points ยท Posted at 16:28:40 on May 25, 2016 ยท (Permalink)
It's always 50%: it either happens or it doesn't
sharkinaround ยท 2 points ยท Posted at 16:49:14 on May 25, 2016 ยท (Permalink)
Wow, so I have a 50% chance of growing wings and flying away right when I submit this comment? I like those odds.
_mainus ยท 1 points ยท Posted at 16:38:33 on May 25, 2016 ยท (Permalink)
I was thinking more along the lines of the top of a bell curve
lazyant ยท 1 points ยท Posted at 15:53:14 on May 25, 2016 ยท (Permalink)
Think about rolling dice and getting a '6', if you roll it 6 times you are not getting a 6 all the time, but only some of the time, if you bet 1-1 with a friend that he won't get it 1/3 of the time you would be ahead in the long term.
nejc311 ยท 1 points ยท Posted at 18:00:41 on May 25, 2016 ยท (Permalink)
It's only because we usually forget about the possibility of multiple successes is why it's counterintuitive. In the lottery example, there is a small chance that we win more than once. Hence more than 50% chance of winning at least once.
ggpwntthxbai ยท 1 points ยท Posted at 18:05:18 on May 25, 2016 ยท (Permalink)
It's really not, if you understand how e arises from the process of interest compounding upon itself, in the limit that that process becomes continuous.
For a process where something is repeatedly increased by an amount proportional to itself (compounding interest), e arises in the limit of that process becoming continuous. This statistics problem is constructed such that the probability of failure is inversely proportional to the #of trials. The probability of failing each consecutive trial is then a process of repeatedly attenuating a term by an amount proportional to itself (like the opposite of interest compiling upon itself). Therefore when this process of repeated attenuation is taken to the limit of being continuous (# of trials -> inf), the term 1/e arises in the exact same manner that the term e arises in compounding interest.
just like how e arises in x=x' or how 1/e arises in x=-x'
[deleted] ยท 1 points ยท Posted at 18:43:36 on May 25, 2016 ยท (Permalink)
It's just because of doubles and triples of certain outcomes occurring. You wouldn't expect every possible number in a set of 10000 to come up exactly once in 10000 random draws. as the number of draws approached something like 100 septillion, yea you'd expect each number to be drawn roughly equally. But 10000 is a very poor sample size when there are 10000 possible draws.
UBKUBK ยท 1 points ยท Posted at 21:01:44 on May 25, 2016 ยท (Permalink)
What does your intuition say should be the answer?
Mesonit ยท 1 points ยท Posted at 21:30:34 on May 25, 2016 ยท (Permalink)
100%, because the phrase "1 in x" makes me think that I should expect it to happen once in x trials, at least if x were big enough. I know it's probably basic statistics, but it still made me think twice about it.
UBKUBK ยท 1 points ยท Posted at 22:15:37 on May 25, 2016 ยท (Permalink)
This way of thinking about it might help: On average a win will occur 1 in a million times. So if you did groups of one million trials over and over again, let's say 1000 times you would get about 1000 wins. But they would be occurring randomly so sometimes a certain group of a million trials might have 2 or 3 wins. This means that some other groups of a million trials must have no wins.
dudeguymanthesecond ยท 0 points ยท Posted at 16:57:29 on May 25, 2016 ยท (Permalink)
And why the lottery makes so much money (unless some MIT smarties figure out a loophole.)
sharknado-enoughsaid ยท 6 points ยท Posted at 15:30:16 on May 25, 2016 ยท (Permalink)
Runescape learnt me this
umopapsidn ยท 3 points ยท Posted at 15:50:21 on May 25, 2016 ยท (Permalink)
Figuring out how (un)lucky you are is always fun.
[deleted] ยท 5 points ยท Posted at 15:57:08 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 19:55:10 on May 25, 2016 ยท (Permalink)
try 1 - 1/e if you want to see the number that's approached as x goes up
MystyrNile ยท 4 points ยท Posted at 15:23:33 on May 25, 2016 ยท (Permalink)
And the chance of success falls as x rises, though it never falls below 63%.
For example, it's fairly simple to calculate that if you flip a coin twice (i.e. x=2) and want heads at least once, there's a 75% chance of success.
skirtsniffer ยท 5 points ยท Posted at 15:37:13 on May 25, 2016 ยท (Permalink)
This means i would have to fly 11 million times to have a 63% chance of dying in a plane crash. I feel slightly better now...i think.
destinybond ยท 4 points ยท Posted at 16:11:02 on May 25, 2016 ยท (Permalink)
I am 0% surprised about you throwing around a statistics fact
reallydumb4real ยท 1 points ยท Posted at 16:58:22 on May 25, 2016 ยท (Permalink)
We really out here
crimsontideftw24 ยท 1 points ยท Posted at 18:15:23 on May 25, 2016 ยท (Permalink)
We everywhere bruv
oh_no_aliens ยท 9 points ยท Posted at 16:09:05 on May 25, 2016 ยท (Permalink)
So you're saying...60% of the time, it works 100% of the time?
d0ntblink ยท 0 points ยท Posted at 18:29:26 on May 25, 2016 ยท (Permalink)
No, I think he is saying that you have a 60% chance of it happening one time.
RagingCacti ยท -1 points ยท Posted at 17:48:19 on May 25, 2016 ยท (Permalink)
NO, NO, NO! 100% of the time, it works 60% of the time.
a_casserole ยท 3 points ยท Posted at 15:40:15 on May 25, 2016 ยท (Permalink)
Very cool fact haha
JStray63 ยท 2 points ยท Posted at 16:09:55 on May 25, 2016 ยท (Permalink)
Great percentage!
_mainus ยท 2 points ยท Posted at 16:10:34 on May 25, 2016 ยท (Permalink)
That's weird, I always assumed it would be 50%
_mainus ยท 1 points ยท Posted at 16:38:11 on May 25, 2016 ยท (Permalink)
More like the top of a bell curve
nobodyperson ยท 2 points ยท Posted at 19:51:07 on May 25, 2016 ยท (Permalink)
A visual calculation for those who are still like wtf mate? https://imgur.com/TeqzIA7
ioftheneedle ยท 1 points ยท Posted at 15:51:03 on May 25, 2016 ยท (Permalink)
so if I buy 2 million tickets i have a 125% chance of winning? Think we beat the lottery with math here!
darls ยท 0 points ยท Posted at 16:20:55 on May 25, 2016 ยท (Permalink)
keep in mind that odds of winning powerball jackpot is 1 in 292,000,000
TriggerCut ยท 0 points ยท Posted at 16:47:27 on May 25, 2016 ยท (Permalink)
Actually, there is some sound logic to your thinking..
[deleted] ยท 2 points ยท Posted at 15:59:55 on May 25, 2016 ยท (Permalink)*
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paracelsus23 ยท 3 points ยท Posted at 16:16:42 on May 25, 2016 ยท (Permalink)
Yeah his lottery example was bad. In a traditional lottery, if you buy 1 million tickets when the odds are 1 in a million, you've got a 100% chance of winning assuming each ticket is different.
Scratch off tickets are better because the chance of winning is random for each ticket. If the odds of winning with a single ticket are 1 in million, and you buy a million random tickets, you've got a 63% chance of having purchased a winning ticket.
TheWetMop ยท 2 points ยท Posted at 19:04:49 on May 25, 2016 ยท (Permalink)
The lottery is a bad example because his fact is for unrelated events. The 200th coin flip is not influenced by the first 199, etc.
In a traditional lottery, each time you buy a ticket and lose the next one becomes more likely to win.
[deleted] ยท 1 points ยท Posted at 15:03:33 on May 25, 2016 ยท (Permalink)*
[deleted]
thedeejus ยท 1 points ยท Posted at 15:06:21 on May 25, 2016 ยท (Permalink)
either, theoretically
Retbull ยท 2 points ยท Posted at 15:23:56 on May 25, 2016 ยท (Permalink)
Only if you buy the same tickets twice. If you buy all unique tickets you will always win.
obamaluvr ยท 3 points ยท Posted at 15:35:53 on May 25, 2016 ยท (Permalink)
it applies if tickets are randomly, as then a mean of 63% of all combinations will be bought.
thedeejus ยท 2 points ยท Posted at 15:29:10 on May 25, 2016 ยท (Permalink)
right, that's why i said random
tiajuanat ยท 1 points ยท Posted at 15:36:01 on May 25, 2016 ยท (Permalink)
This is also equal to 1-(1/e), which is also a time constant when working with RLC circuits!
RancidLemons ยท 1 points ยท Posted at 15:46:45 on May 25, 2016 ยท (Permalink)
That is absolutely fascinating. Thank you, I've caught myself wondering about that!
How many times would you need to do something to push it to 99%?
thedeejus ยท 1 points ยท Posted at 16:09:12 on May 25, 2016 ยท (Permalink)
just plug the probability and #attempts into the equation and see for yourself. the probability is that 1/x in the parentheses, and the exponent is the number of attempts
Plasmodicum ยท 1 points ยท Posted at 22:24:49 on May 25, 2016 ยท (Permalink)
Depends on what the chance is. Here's an example using 1 in 50.
So for something with a 1 in 50 chance of happening, 228 attempts would have a 99% chance of success. Step 5 can be generalized for other numbers.
chironomidae ยท 1 points ยท Posted at 15:46:58 on May 25, 2016 ยท (Permalink)
This particular example is a bit misleading. A lottery might have 1 in a million odds because the only possible plays are 1-1,000,000. So if you bought every single possible number you'd have 100% chance of winning.
thedeejus ยท 1 points ยท Posted at 16:08:25 on May 25, 2016 ยท (Permalink)
chironomidae ยท 1 points ยท Posted at 16:34:57 on May 25, 2016 ยท (Permalink)
ah right
gHaDE351 ยท 1 points ยท Posted at 15:49:28 on May 25, 2016 ยท (Permalink)
Mmmmmm.... This sounds like a logical fallacy but i cant remember the name.
PUR3SK1LL ยท 1 points ยท Posted at 15:50:59 on May 25, 2016 ยท (Permalink)
wait so if I have a 1 in 100 chance of unboxing a knife in cs:go and I open 100 boxes I have a 67% chance of actually getting it ? I'm surprised since I came up with this in school and asked how to calculate my chances to get it since you obviously doesn't have a 100% chance of getting it with 100 boxes and he said that you can not calculate it but with each try I just have a 1 in 100 chance.
[deleted] ยท 1 points ยท Posted at 18:39:59 on May 25, 2016 ยท (Permalink)*
[deleted]
PUR3SK1LL ยท 1 points ยท Posted at 00:50:28 on May 26, 2016 ยท (Permalink)
wow that's what I call a good math teacher :D
lzilhao ยท 1 points ยท Posted at 16:00:51 on May 25, 2016 ยท (Permalink)
I was not at all aware of this. Is it related to the central limit theorem?
cyberspacecowboy ยท 1 points ยท Posted at 16:03:39 on May 25, 2016 ยท (Permalink)
IANA math person, but that would only be true if there are more than a million tickets actually available. If you buy all the tickets, and there's 1 winning, your chance is 100%. right?
thedeejus ยท 1 points ยท Posted at 16:07:48 on May 25, 2016 ยท (Permalink)
if you get a million randomly generated tickets for one lottery (or any ticket for a million different lotteries) then this works. If you purposely buy different tickets to use up each possibility, then it will be higher (or 100% if you buy every possible combo). The key word is "random"
rhythmrice ยท 1 points ยท Posted at 16:10:26 on May 25, 2016 ยท (Permalink)
If its a 1 in a million chance and you buy a million tickets shouldnt it be 100 % chance of winning?
thedeejus ยท 1 points ยท Posted at 16:15:06 on May 25, 2016 ยท (Permalink)
the key word is random - yeah if you buy every possible combination then it's 100%. If you buy one ticket in a million different lotteries, or a million randomly generated tickets for any one in a million lottery, then it's 63%
docbrown_ ยท 1 points ยท Posted at 16:11:28 on May 25, 2016 ยท (Permalink)
We need to get a lottery pool going. Of course we'll probably get no where near 63% chance, but if we got 10,000 people to play and we hit the jackpot, that is 8,000 grand each. If we got 1,000 people to play, we could win 80,000 each.
insertacoolname ยท 1 points ยท Posted at 16:15:14 on May 25, 2016 ยท (Permalink)
Unless you buy 1 million lottery tickets at the same time.
lonelypaperclip ยท 1 points ยท Posted at 16:16:55 on May 25, 2016 ยท (Permalink)
This is more than I learned my whole semester in statistics.
classicharlie ยท 1 points ยท Posted at 16:17:45 on May 25, 2016 ยท (Permalink)
Is this a Poisson distribution?
Whydoibother1 ยท 1 points ยท Posted at 16:20:38 on May 25, 2016 ยท (Permalink)
Excellent! Of course if a thousand people did this they would win 1 each on average. 37% may not win any, but some people would win twice or more, so on average it will be 1.
[deleted] ยท 1 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
I'm never going outside again.
ThatIneptGuy ยท 1 points ยท Posted at 16:23:39 on May 25, 2016 ยท (Permalink)
I knew this because of a game called Path of Exile lol
Brocolli123 ยท 1 points ยท Posted at 16:23:48 on May 25, 2016 ยท (Permalink)
can somebody test this by going out and back in 10,000 times
Inthethickofit ยท 1 points ยท Posted at 16:24:29 on May 25, 2016 ยท (Permalink)
this is a great heuristic. Thanks for shoving it into my brain.
spinkers ยท 1 points ยท Posted at 16:25:48 on May 25, 2016 ยท (Permalink)
So you're telling me that there is a 63% chance that everybody gets hit by meteor and that there is possible for there to be a 63% chance of winning the lottery
mkid75 ยท 1 points ยท Posted at 16:30:57 on May 25, 2016 ยท (Permalink)
this lady's and gentlemen is how RNG in video games work. Well played good sir, well played.
Zman14q ยท 1 points ยท Posted at 16:31:54 on May 25, 2016 ยท (Permalink)
Does that 63% also include the times you got struck by a meteor more than once in the 10,000 attempts? Which basically, in the long run, makes up for the 37% of the time you weren't struck?
wicked-dog ยท 1 points ยท Posted at 16:32:41 on May 25, 2016 ยท (Permalink)
Is there any real world proof of this? Like can we calculate the odds of getting hit by lighting, then look at a large enough group of people and find that 63 of them were struck by lightning?
gnutun ยท 1 points ยท Posted at 16:33:00 on May 25, 2016 ยท (Permalink)
Piggybacking on /u/NoCanDoSlurmz's reply, I think it would be helpful to explicitly provide for the case of the event occurring multiple times in the description. For example:
arxv ยท 1 points ยท Posted at 16:34:29 on May 25, 2016 ยท (Permalink)
in what way, if any, can this be applied to gambling?
ilovesquares ยท 1 points ยท Posted at 16:36:21 on May 25, 2016 ยท (Permalink)
Wow I might be retarded. I always thought that if I was trying to do something that had 1% chance of success statistically I would achieve it in 100 attempts. TIL
SmokeyUnicycle ยท 1 points ยท Posted at 16:39:45 on May 25, 2016 ยท (Permalink)
So if the odds are 1/2...
okuRaku ยท 1 points ยท Posted at 16:40:02 on May 25, 2016 ยท (Permalink)
So have I been wrong when thinking about expected values like: "it's a 1 in 13 chance so the expected value is 1/13?"
plonce ยท 1 points ยท Posted at 16:42:31 on May 25, 2016 ยท (Permalink)
Please fix this.
dangz ยท 1 points ยท Posted at 16:45:32 on May 25, 2016 ยท (Permalink)
So there is a 63% chance I'll pull an ace of spades out of this standard deck of cards?
thedeejus ยท 1 points ยท Posted at 16:47:19 on May 25, 2016 ยท (Permalink)
there's a 1/52 (about 2%) on one try.
If you do it 52 times (with replacement and shuffling so there's a fresh start each time) then there's a 63% chance of pulling the ace of spades at some point in the 52 tries.
dangz ยท 1 points ยท Posted at 16:52:49 on May 25, 2016 ยท (Permalink)
Alright cool. Thanks! I was tripping out like "Did I understand it wrong my whole life."
Deadeye_Marksman ยท 1 points ยท Posted at 16:57:25 on May 25, 2016 ยท (Permalink)
It's used in physics for nuclear calculations and in electricity. (basically any exponential monotone evolution)
sapador ยท 1 points ยท Posted at 16:59:09 on May 25, 2016 ยท (Permalink)
When I was 12 and playing world of warcraft I thought its 50%. I have no idea but it made sense to me, until a friend asked me why. Then I tried (1/2)*(1/2) and it wasnt 50% :P
tdug ยท 1 points ยท Posted at 17:04:31 on May 25, 2016 ยท (Permalink)
That being said, the lottery thing is kinda meaningless since if multiple people win a jackpot, they split the pot.
Edit: Also, is there a formula to determine the distribution of the amount of times the event would occur?
feeblegoat ยท 1 points ยท Posted at 17:05:04 on May 25, 2016 ยท (Permalink)
I figured this one out one night. I was so pumped it was 1-1/e I made a Facebook post about it. :) Which is my second greatest maths accomplishment, the greatest being solving the switching zero coin flipping problem. (With a lot of help from wolfram ;) ) Which is far cooler
[deleted] ยท 1 points ยท Posted at 17:05:18 on May 25, 2016 ยท (Permalink)
LOL I love your edit. Why the hell would you even have to explain that? Some people....
SushiAndWoW ยท 1 points ยท Posted at 17:11:55 on May 25, 2016 ยท (Permalink)*
Funny you should mention that. Not that long ago, I wondered – if drop rate for an item in a game is 1/N, what's the probability of still not getting that item in N attempts. That probability is ((n-1)/n)n, which approaches 1/e, yes :) About 36.79%.
It also converges fast. For N=2,3,4,5,... – corresponding to drop rates 50%, 33%, 25%, 20% – the probabilities of not getting the item after N attempts are 0.25, 0.296296, 0.316406, 0.32768, ...
iIsMe95 ยท 1 points ยท Posted at 17:12:18 on May 25, 2016 ยท (Permalink)
I've gone outside for roughly 7,308 days. How likely am I to be hit be space debris?
BubbleTeaFiend ยท 1 points ยท Posted at 17:21:28 on May 25, 2016 ยท (Permalink)
I haven't taken statistics in ages, so you'll have to excuse my ignorance, but I always thought it was a common misconception that the more you do something, the higher the probability there is of a particular event occuring. Using a coin flip as an example, if someone flips 10 heads in a row they might think that the next flip is very likely to be tails, but isn't it still 50%?
thunderfvck ยท 1 points ยท Posted at 17:24:29 on May 25, 2016 ยท (Permalink)
2/pi D:
JackBond1234 ยท 1 points ยท Posted at 17:40:44 on May 25, 2016 ยท (Permalink)
I discovered this by chance on my own while playing Pokemon. I believe the Masuda method yields a shiny Pokemon from breeding with 1/1365 odds. It took me around 1500 attempts, so I was slightly unlucky. I actually drew out the curve to see what I could expect.
TurboChewy ยท 1 points ยท Posted at 17:40:49 on May 25, 2016 ยท (Permalink)
In other words, if I picked a million truly random numbers, between one and a million, I'll likely get approximately 63% of the numbers?
Is this at all related to the birthday problem, what are the odds of two people in the room having the same birthday for any number of people in the room?
heisenberger42 ยท 1 points ยท Posted at 17:42:13 on May 25, 2016 ยท (Permalink)
I once proved that without knowing about it and felt really proud of it. Now it just makes me feel like all the good proofs are taken! My teacher was impressed though, I think(hope)
ravendarklord76 ยท 1 points ยท Posted at 17:50:54 on May 25, 2016 ยท (Permalink)
James?
[deleted] ยท 1 points ยท Posted at 17:57:30 on May 25, 2016 ยท (Permalink)
I have a 1/2 chance to flip tails. I flip a coin twice. You're tellin' me there's a 63% chance I hit tails one time?
I have a 50% chance the first time. I have a 50% chance the second time.
Edit: ohhhh, large numbers. Nvm.
riskybusinesscdc ยท 1 points ยท Posted at 17:57:43 on May 25, 2016 ยท (Permalink)
So there's a 63% chance of intelligent life elsewhere in the universe right now? Cool!
Denziloe ยท 1 points ยท Posted at 18:00:44 on May 25, 2016 ยท (Permalink)
No, the key word is independent. The outcome of the lottery thing is still "random" if you bought every ticket but one.
fowlraul ยท 1 points ยท Posted at 18:03:09 on May 25, 2016 ยท (Permalink)
So if I go out ~40% more times going forward, meteor time got it.
RabidRapidRabbit ยท 1 points ยท Posted at 18:04:31 on May 25, 2016 ยท (Permalink)
the same reason as why you would have to go out about 30 000 times to surely get hit. (probability reaches ~99.99 percent for sigma = 3)
one of my most used estimates
Stukya ยท 1 points ยท Posted at 18:06:08 on May 25, 2016 ยท (Permalink)
But how many times would i have to go outside before a girl smiles at me?
Nautique210 ยท 1 points ยท Posted at 18:07:55 on May 25, 2016 ยท (Permalink)
Aka a standard deviation
rondosfinger ยท 1 points ยท Posted at 18:10:46 on May 25, 2016 ยท (Permalink)
1-1/e
throwaway_holla ยท 1 points ยท Posted at 18:10:52 on May 25, 2016 ยท (Permalink)*
I think your statement is appallingly incorrect. It sounds like you are misquoting one example that ended up at 63% solely because that example was based on a 1% chance tried 100 times. https://www.reddit.com/r/explainlikeimfive/comments/25qsv7/eli5_if_i_attempt_something_with_1_probability/chjuh04
There is a big mathematical difference between a 1 in 100 chance tried 100 times (99100) and a 1 in 1,000,000 chance tried 1,000,000 times (999,9991,000,000).
SrirachaFlash ยท 1 points ยท Posted at 18:11:28 on May 25, 2016 ยท (Permalink)
You miss 37% of the shots you don't take
CromulentAsFuck ยท 1 points ยท Posted at 18:14:42 on May 25, 2016 ยท (Permalink)
Doesn't everyone go outside at least 10,000 times in a lifetime?
perkco ยท 1 points ยท Posted at 18:18:21 on May 25, 2016 ยท (Permalink)
Can someone explain to me the implications of this for expected values? I would have thought that if I had a 1/x chance in each attempt (with a payoff of 1 if successful), and I did x attempts, my expected value would be 1 (i.e., 1/x * x). Does this mean that, instead, the expected value of x attempts is .63?
ButtGardener ยท 1 points ยท Posted at 18:20:37 on May 25, 2016 ยท (Permalink)
So what you're saying is that if I buy a million lottery tickets I will become a millionaire?
[deleted] ยท 1 points ยท Posted at 18:22:24 on May 25, 2016 ยท (Permalink)
There are a lot of interesting math shortcuts dealing with large exponents of numbers near 1 which you can do in your head with a little practice. They're the kind of shortcuts that make your friends think you're the next Feynman. MIT has an excellent (free) book and course online containing many of these "tricks."
samsdeadfishclub ยท 1 points ยท Posted at 18:25:44 on May 25, 2016 ยท (Permalink)
100% of the time it works 63% of the time. Got it.
IDRINKYOURMILK-SHAKE ยท 1 points ยท Posted at 18:26:03 on May 25, 2016 ยท (Permalink)
AAYYY Lazlo Hollyfeld.
[deleted] ยท 1 points ยท Posted at 18:26:19 on May 25, 2016 ยท (Permalink)
In the same vein is the game show statistic. The game is to guess which door the car is behind, door 1, door 2 or door 3. You pick one and the host starts opening the other doors. The 1st one has no car behind it. He adks you if you'd like to switch your answer. Should you? The answer is yes. You now have a 1/2 chance of winning instead of 1/3 chance. It's hard to wrap your head around this fact but it's true
[deleted] ยท 1 points ยท Posted at 18:27:24 on May 25, 2016 ยท (Permalink)*
[deleted]
Deethreekay ยท 1 points ยท Posted at 12:00:41 on May 26, 2016 ยท (Permalink)
It's a simplified version of the Probability Mass Function for the Binomial distribution. Have a look on Wikipedia and keep in mind that for this example k=0.
OldOrder ยท 1 points ยท Posted at 18:28:58 on May 25, 2016 ยท (Permalink)
Shouldn't you be looking up Corey Kluber's K/9 rate and how it ranks historically to Fernando Valenzuela or something?
supremecrafters ยท 1 points ยท Posted at 18:31:40 on May 25, 2016 ยท (Permalink)
Huh. I would expect it to be 68.27%.
JooJoona ยท 1 points ยท Posted at 18:36:57 on May 25, 2016 ยท (Permalink)
1 sigma.
MacBelieve ยท 1 points ยท Posted at 18:37:33 on May 25, 2016 ยท (Permalink)
Is it 63% for 1 or >=1?
[deleted] ยท 1 points ยท Posted at 18:39:11 on May 25, 2016 ยท (Permalink)
So then what? I get a 1 in 1.58 chance that I'll get hit by a metior if I go outside 10,000 times. So if I go outside 15,800 times do I now have a new 63% chance of getting hit by a meteor? Am I going to dilute the possibility of ever getting hit by going outdoors more? How does anything ever happen?!
freudian_nipple_slip ยท 1 points ยท Posted at 18:46:44 on May 25, 2016 ยท (Permalink)
This is due to the Poisson approximation of the binomial distribution
ShortBusBully ยท 1 points ยท Posted at 19:00:18 on May 25, 2016 ยท (Permalink)
Does this in any way have to do with Benford's Law?
nojerryitsjerky ยท 1 points ยท Posted at 19:01:42 on May 25, 2016 ยท (Permalink)
So in the case that there are over 10,000 meteors falling, I should probably stay inside? Got it, continue life as normal;Check.
usernumber36 ยท 7545 points ยท Posted at 11:43:47 on May 25, 2016 ยท (Permalink)*
there are exactly 10! seconds in six weeks
EDIT: oh shit this comment blew up and I remembered a way better fact later.
If you add up the numbers 1 to 36, it adds to 666. AND if you draw a perfect pentagram, the internal angles of the star are all 36 degrees. How the fuck did I not talk about my own damn number.
Peregrine7 ยท 4394 points ยท Posted at 14:41:11 on May 25, 2016 ยท (Permalink)
Ten exciting seconds every six weeks...? Sounds about right.
pm_steam_keys_plz ยท 1937 points ยท Posted at 15:04:51 on May 25, 2016 ยท (Permalink)
that about sums up my sex life
jk I don't have a sex life
[deleted] ยท 72 points ยท Posted at 16:41:34 on May 25, 2016 ยท (Permalink)
[deleted]
EhhWhatsUpDoc ยท 2 points ยท Posted at 00:14:42 on May 26, 2016 ยท (Permalink)
Found the married
amalgam_reynolds ยท 45 points ยท Posted at 16:36:32 on May 25, 2016 ยท (Permalink)*
0!
Edit: thanks, I get it guys, 0!=1 despite otherwise common sense.
Avcdo ยท 18 points ยท Posted at 17:09:56 on May 25, 2016 ยท (Permalink)
At least you aren't a virgin
telegetoutmyway ยท 7 points ยท Posted at 17:32:00 on May 25, 2016 ยท (Permalink)
so just 1 boring second
GokuMoto ยท 4 points ยท Posted at 17:51:11 on May 25, 2016 ยท (Permalink)
=1 bruh
PhantomLord666 ยท 1 points ยท Posted at 22:08:50 on May 25, 2016 ยท (Permalink)
Eh, not really. It's =1 by definition. The factorial is used to calculate the number of ways a set of numbers can be arranged (permuted).
So, if you have a set of 3 numbers, [1,2,3] you can arrange them 6 ways (123, 132, 312, 321, 231, 213), so 3! tells you how many permutations or arrangements you can have. A set of n numbers can be arranged in n! ways.
if you have a set of 'no numbers', or as it is properly called the Empty Set, n=0. You can only arrange (permute) the Empty Set one way - [] so n!=0!=1
[deleted] ยท 1 points ยท Posted at 01:08:40 on May 26, 2016 ยท (Permalink)
im pretty sure a factorial is all the numbers below and including the numbers multiplied together.
nuclearwaffle121 ยท 2 points ยท Posted at 02:57:36 on May 26, 2016 ยท (Permalink)
That's another definition, yeah
PhantomLord666 ยท 1 points ยท Posted at 05:51:19 on May 26, 2016 ยท (Permalink)
That is the way you calculate it, but it doesn't explain why 0!=1.
[deleted] ยท 1 points ยท Posted at 21:57:29 on May 26, 2016 ยท (Permalink)
Number phile did a good job of explaining it. this link
[deleted] ยท 1 points ยท Posted at 23:00:00 on May 25, 2016 ยท (Permalink)
numberphile did an amazing job explaning why 0! = 1. It's because of a pattern in factorials.
5! = 6! / 6 = 120
4! = 5! / 5 = 24
3! = 4! / 4 = 6
2! = 3! / 3 = 2
1! = 2! / 2 = 1
0! = 1! / 1 = 1
factorial is the product of all the integers below and including a number. But a factorial can also be then number ahead divided by that number. Hope that explains why. If you still don't get it go to this link by numberphile youtube channel.
amalgam_reynolds ยท 1 points ยท Posted at 00:27:24 on May 26, 2016 ยท (Permalink)
"You've broken maths, Brady, stop that!" I love Numberphile, great video thank you!
Peregrine7 ยท 1 points ยท Posted at 01:29:48 on May 26, 2016 ยท (Permalink)
Or, stepping away from mathematical purity and into logic, factorials can be used to describe the amount of ways something can be arranged. A set with 0 items can only be arranged one way (as opposed to a set of 5 items, 1,2,3,4,5 , which can be arranged 4,2,3,1,5 for example) and the factorial mirrors this.
quick_escalation24 ยท 0 points ยท Posted at 18:44:31 on May 25, 2016 ยท (Permalink)
So 1?
thecoolracer ยท 0 points ยท Posted at 18:59:32 on May 25, 2016 ยท (Permalink)
0! = 1
Denroll ยท 4 points ยท Posted at 16:59:22 on May 25, 2016 ยท (Permalink)
a/s/l? Let's cyber.
pm_steam_keys_plz ยท 6 points ยท Posted at 17:37:46 on May 25, 2016 ยท (Permalink)
Over 300/male/dagobah
Denroll ยท 5 points ยท Posted at 17:42:56 on May 25, 2016 ยท (Permalink)
Ooh. Would you like to snarfle my garflack?
piperiain ยท 5 points ยท Posted at 17:49:56 on May 25, 2016 ยท (Permalink)
ooooohhhh... stick your finger in my thresha!
jolsiphur ยท 2 points ยท Posted at 19:27:15 on May 25, 2016 ยท (Permalink)
My Jagon is so hard.
pm_steam_keys_plz ยท 3 points ยท Posted at 17:47:58 on May 25, 2016 ยท (Permalink)
( อกยฐ อส อกยฐ)
physalisx ยท 4 points ยท Posted at 18:43:34 on May 25, 2016 ยท (Permalink)
I put on my robe and wizard hat.
PM_ME_YOUR_SPUDS ยท 3 points ยท Posted at 18:29:55 on May 25, 2016 ยท (Permalink)
Cool story Mark. Anyways, how's your sex life?
colonspiders4u ยท 2 points ยท Posted at 20:30:12 on May 25, 2016 ยท (Permalink)
You poor thing. Here, have some sex.
You received item <Sex>!
omar1993 ยท 1 points ยท Posted at 18:27:29 on May 25, 2016 ยท (Permalink)
:(
There there...
Aldrai ยท 1 points ยท Posted at 18:54:20 on May 25, 2016 ยท (Permalink)
What, Jill doesn't come visit?
EntropyJunkie ยท 1 points ยท Posted at 20:25:57 on May 25, 2016 ยท (Permalink)
Found the married man!
Source: am married
LivingShadowz ยท 1 points ยท Posted at 21:39:56 on May 25, 2016 ยท (Permalink)
That's not what my mom said
ForceBlade ยท 1 points ยท Posted at 22:17:55 on May 25, 2016 ยท (Permalink)
I know
[deleted] ยท 1 points ยท Posted at 22:26:30 on May 25, 2016 ยท (Permalink)
U wanna fuck
MaltaNsee ยท 1 points ยท Posted at 22:31:38 on May 25, 2016 ยท (Permalink)
are you actually looking for steam keys?
datbooty12 ยท 1 points ยท Posted at 23:50:01 on May 25, 2016 ยท (Permalink)
Do you wanna have a sex life?
sypersonic ยท 1 points ยท Posted at 02:29:02 on May 26, 2016 ยท (Permalink)
Three minutes of ecstasy... several nights a month...
Maxtsi ยท -1 points ยท Posted at 15:57:45 on May 25, 2016 ยท (Permalink)
thatsthejoke.jpg
bumlove ยท 8 points ยท Posted at 15:37:59 on May 25, 2016 ยท (Permalink)
It's funny because it's true. Sigh.
shadow6654 ยท 3 points ยท Posted at 16:13:06 on May 25, 2016 ยท (Permalink)
Must be nice :'(
g3t0nmyl3v3l ยท 2 points ยท Posted at 15:53:11 on May 25, 2016 ยท (Permalink)
Sex is great isn't it?
Peregrine7 ยท 1 points ยท Posted at 01:22:37 on May 26, 2016 ยท (Permalink)
Only the last 1/16th of a second for me, the rest is hard work.
[deleted] ยท 2 points ยท Posted at 16:24:48 on May 25, 2016 ยท (Permalink)*
Funny that this is nearly the exact same conversation of
the lastanother 'What's your favourite maths fact?' thread.But they called them enthusiastic seconds or something
Edit: Found it
[deleted] ยท 3 points ยท Posted at 19:45:47 on May 25, 2016 ยท (Permalink)
AskReddit repeats exact conversations all the time, gets grating after a while
serklinika ยท 2 points ยท Posted at 17:36:34 on May 25, 2016 ยท (Permalink)*
In England they used to call the ! symbol "admiration" When referring to factorials
Peregrine7 ยท 1 points ยท Posted at 01:21:00 on May 26, 2016 ยท (Permalink)
Well, it wasn't particularly clever. Goddamn how'd it get upvoted so much, it's things like this that make me spill terrible jokes in reality.
LaughingVergil ยท 2 points ยท Posted at 17:08:34 on May 25, 2016 ยท (Permalink)
Wouldn't that be ten Jeb! seconds every six weeks?
tha-snazzle ยท 2 points ยท Posted at 19:21:30 on May 25, 2016 ยท (Permalink)
10 brilliant chess moves in 6 weeks.
Anton-LaVey ยท 5 points ยท Posted at 15:04:35 on May 25, 2016 ยท (Permalink)
found the married guy
ectish ยท 2 points ยท Posted at 15:18:43 on May 25, 2016 ยท (Permalink)
Or gal
[deleted] ยท 3 points ยท Posted at 16:48:52 on May 25, 2016 ยท (Permalink)
[deleted]
Peregrine7 ยท 2 points ยท Posted at 01:20:06 on May 26, 2016 ยท (Permalink)
I know bby.
Not_Stalin ยท 1 points ยท Posted at 17:13:23 on May 25, 2016 ยท (Permalink)
A great ten seconds
JakeEddyCarpenter ยท 1 points ยท Posted at 18:21:43 on May 25, 2016 ยท (Permalink)
Just like there's one exciting panic at the Disco.
AmishElectricity49 ยท -3 points ยท Posted at 15:31:37 on May 25, 2016 ยท (Permalink)
! in math means a factorial. Check out stuff on 52! that shit is crazy. A regular deck of cards is so many math facts about it, it is unreal
josephdevon ยท 11 points ยท Posted at 15:50:19 on May 25, 2016 ยท (Permalink)
He was making with the humor.
AmishElectricity49 ยท 0 points ยท Posted at 17:53:34 on May 25, 2016 ยท (Permalink)
For to make the laughs happy?
Derptard25 ยท -2 points ยท Posted at 16:22:36 on May 25, 2016 ยท (Permalink)
Found someone who didnt pass algebra
Mirrorboy17 ยท 9439 points ยท Posted at 13:11:45 on May 25, 2016 ยท (Permalink)
Let's figure this one out...
So, 6 weeks is 1 second x 60 x 60 x 24 x 7 x 6
Straight away there we have our 1, 7 and 6 - now we just need the rest
60 = 2 x 3 x 10
60 = 5 x 4 x 3
24 = 8 x 3
We have 2 extra 3s here, so take two of them: 3ร3 =9
Now we have 1x2x3x4x5x6x7x8x9x10 and that's 6 weeks
[deleted] ยท 1123 points ยท Posted at 14:22:06 on May 25, 2016 ยท (Permalink)
I'm glad you did this!
ZombieAlpacaLips ยท 94 points ยท Posted at 14:52:44 on May 25, 2016 ยท (Permalink)
How do you find the factorial of this?
[deleted] ยท 81 points ยท Posted at 14:55:37 on May 25, 2016 ยท (Permalink)
this x that x t'other
Psychwrite ยท 4 points ยท Posted at 17:40:45 on May 25, 2016 ยท (Permalink)
This is great. Thank you.
cascer1 ยท 0 points ยท Posted at 17:36:51 on May 25, 2016 ยท (Permalink)
Duh. Who doesn't know that
EquationTAKEN ยท 9 points ยท Posted at 17:21:48 on May 25, 2016 ยท (Permalink)
this! = this x this-1 x this-2 x this-3 x this-4 x ... x 2 x 1
Aaaand the word just stopped making sense.
highphive ยท 27 points ยท Posted at 15:26:41 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial
ZombieAlpacaLips ยท 2 points ยท Posted at 15:29:22 on May 25, 2016 ยท (Permalink)
There's a subreddit for everything!
pf2- ยท 6 points ยท Posted at 17:01:14 on May 25, 2016 ยท (Permalink)
/r/ofcoursethatsathing
Timothy_Claypole ยท 1 points ยท Posted at 19:04:25 on May 25, 2016 ยท (Permalink)
WTAF...
i_am_useless_too ยท 5 points ยท Posted at 15:48:49 on May 25, 2016 ยท (Permalink)
in javascript
[deleted] ยท 2 points ยท Posted at 17:35:56 on May 25, 2016 ยท (Permalink)
TxHxixS. As you can see, it is one of the few words that has an imaginary factorial.
Dr_Legacy ยท 2 points ยท Posted at 20:31:28 on May 25, 2016 ยท (Permalink)
'this' is base 36 for 1375732, per Wolfram Alpha, which also gives 1375732! as 1.22433069887918754190508636513318769451534501450378357285932310011240528537021063229328167365626537612760027381027635721490513568578769889176366164801250721892503278930162368497443723597943081636085321499675375050080224972046615350639180719588150311524155989379588960968564907643809003381862707661500245161757608237729511162492680906126617328609184841959277430994780111890577964855088263106282897810276315011511287358861073115376746502352144636310โฆ ร 107847508
thestickystickman ยท 1 points ยท Posted at 07:41:24 on May 26, 2016 ยท (Permalink)
Using base-36.
setfire3 ยท 9 points ยท Posted at 17:03:08 on May 25, 2016 ยท (Permalink)
I Can't Believe He've Done This
yumyumgivemesome ยท 3 points ยท Posted at 17:34:59 on May 25, 2016 ยท (Permalink)
This is the rendition I choose to support.
[deleted] ยท 7 points ยท Posted at 15:29:45 on May 25, 2016 ยท (Permalink)
I'm glad he used this approach instead of finding the totals for each and comparing.
SonumSaga ยท 4 points ยท Posted at 16:45:00 on May 25, 2016 ยท (Permalink)
I can't believe you've done this!
[deleted] ยท 2 points ยท Posted at 17:10:26 on May 25, 2016 ยท (Permalink)
I can't believe you've done this!
WarLordM123 ยท 2 points ยท Posted at 18:05:28 on May 25, 2016 ยท (Permalink)
I can't believe he's done this!
PirateNinjaJedi ยท 2 points ยท Posted at 18:36:58 on May 25, 2016 ยท (Permalink)
I can't believe you've done this!
svengast ยท 2 points ยท Posted at 20:49:16 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial
[deleted] ยท 1 points ยท Posted at 20:51:04 on May 25, 2016 ยท (Permalink)
There really is a subreddit for everything.
Ubersheep ยท 2 points ยท Posted at 23:27:24 on May 25, 2016 ยท (Permalink)
GeorgeK is that you? :O
[deleted] ยท 2 points ยท Posted at 11:34:42 on May 26, 2016 ยท (Permalink)
So after many, MANY replies, I finally know what I accidentally referred to in my earlier post. I was so confused(factorial)
Ubersheep ยท 1 points ยท Posted at 20:50:56 on May 26, 2016 ยท (Permalink)
Ah, I guess you're not George K. Sorry, Google QuantumSheep, it's that guy
Aloysius7 ยท 1 points ยท Posted at 17:44:08 on May 25, 2016 ยท (Permalink)
What, or how, did he do it?
hornwalker ยท 1 points ยท Posted at 21:09:08 on May 25, 2016 ยท (Permalink)
R/theydidit
sirius4778 ยท 1 points ยท Posted at 02:52:53 on May 26, 2016 ยท (Permalink)
I'm glad I saw it!
ImWatchingYouPoop ยท 843 points ยท Posted at 14:43:26 on May 25, 2016 ยท (Permalink)
Whoa. Stuff like this is why math is so cool. Never in a million years would I have thought prove it this way.
d-scott ยท 1818 points ยท Posted at 15:30:46 on May 25, 2016 ยท (Permalink)
Here I am sitting here with my stopwatch for 6 weeks and this guy proves it in 30 seconds
[deleted] ยท 622 points ยท Posted at 16:34:59 on May 25, 2016 ยท (Permalink)*
[deleted]
TeebsGaming ยท 40 points ยท Posted at 17:56:07 on May 25, 2016 ยท (Permalink)
Whoa. Stuff like this is why stopwatches are so cool. Never in a million years would I have thought to count it this way.
AMasonJar ยท 17 points ยท Posted at 19:20:06 on May 25, 2016 ยท (Permalink)
Here I am sitting with my calculator for 30 seconds and this guy proves it in 6 weeks
DrShocker ยท 5 points ยท Posted at 19:28:35 on May 25, 2016 ยท (Permalink)
Here I am looking at the timestamps on the posts, and this other guy, wait no, actually that's the easiest way.
SharKCS11 ยท 1 points ยท Posted at 19:40:33 on May 25, 2016 ยท (Permalink)
Whoa! Stuff like this is why I'm still on Reddit. Never in a million years would I have thought to create a rabbit-hole pun thread.
ProtoKun7 ยท 2 points ยท Posted at 18:19:47 on May 25, 2016 ยท (Permalink)
He was watching Countdown.
Mozambique_Drill ยท 0 points ยท Posted at 18:45:19 on May 25, 2016 ยท (Permalink)
The name of that show confuses me. The clock starts at 0 and counts to 30. Shouldn't it be called "Countup" or, at the very least, "Count"?
ProtoKun7 ยท 2 points ยท Posted at 18:46:10 on May 25, 2016 ยท (Permalink)
Nah, the hand moves down.
jasonrubik ยท 1 points ยท Posted at 03:55:05 on May 26, 2016 ยท (Permalink)
Why is the rotational axis of your clock hands perpendicular to your frame of reference?
bonerofalonelyheart ยท 2 points ยท Posted at 18:20:01 on May 25, 2016 ยท (Permalink)
You could have done it in 10!
[deleted] ยท 1 points ยท Posted at 02:44:11 on May 26, 2016 ยท (Permalink)
Bo. Nero. Falon. Ely. Heart.
Redditor_1138 ยท 1 points ยท Posted at 19:10:25 on May 25, 2016 ยท (Permalink)
Well, that's valid; it's usually good to pair theoretical and empirical testing.
ManuGinosebleed ยท 1 points ยท Posted at 19:44:10 on May 25, 2016 ยท (Permalink)
Here I am sitting here trying to come up with a comment for 30 weeks and this guys does it in 6 seconds
KhabaLox ยท 1 points ยท Posted at 19:47:54 on May 25, 2016 ยท (Permalink)
Or 30/10! 6-weeks.
DearKC ยท 1 points ยท Posted at 20:18:09 on May 25, 2016 ยท (Permalink)
On the other hand, you could have put the arithmetic into your calculator. If your spm on a 10 key is fast enough, you get the # of seconds in a week: 3628800 and 10!: 3628800. Proof. IT's not good for understanding how it works, merely that it does work. but I'd argue it's faster than what this guy did :)
mikk0384 ยท 1 points ยท Posted at 05:09:30 on May 26, 2016 ยท (Permalink)
You stopwatch works in factorials? That seems a pointless overcomplication...
FireDragon79 ยท -1 points ยท Posted at 17:11:15 on May 25, 2016 ยท (Permalink)
No, it's 10! seconds.
GalaxyClass ยท 11 points ยท Posted at 15:14:04 on May 25, 2016 ยท (Permalink)
I know, I would have just done the math.
Thynomeus ยท 1 points ยท Posted at 17:35:12 on May 25, 2016 ยท (Permalink)
Perhaps because it's a very unintuitive process of proof due to the fact that everyone carries around a calculator these days.
[deleted] ยท 1 points ยท Posted at 19:24:12 on May 25, 2016 ยท (Permalink)
And mostly why I was never never good with math..
ThachWeave ยท 1 points ยท Posted at 20:45:26 on May 25, 2016 ยท (Permalink)
I was going to try to think of an example for my favorite maths fact, but /u/Mirrorboy17's proof depicts it better than any of the examples I had in mind could:
With virtually all math problems you work with, there are multiple ways to break the problem down into steps -- multiple paths to the solution you seek. But unlike a more subjective field, the path you take won't influence the solution; all techniques, assuming they are valid, will reach the same answer, every time. You can completely adapt your approach to your own preferences, and still arrive at the same answer as someone doing a completely different approach. Every valid approach is equally so.
Maths are the language of the universe, the one true objectivity, and the closest thing we'll ever see to absolute perfection. They're beautiful in their own way.
ImWatchingYouPoop ยท 2 points ยท Posted at 21:04:52 on May 25, 2016 ยท (Permalink)
Yes! Exactly this! Back when I was in college I used to tutor math at one of the local public libraries (K-12 students). During my first week, there were a few times I noticed that a kid would solve a problem in a completely different way than I would do it. Because of this, I started having kids try to solve the problem from beginning to end to the best of their abilities then showing them where they went wrong instead of walking them through the way I would do it which could potentially just confuse them more. I always got really excited when a student and I would get the same answer using totally different methods. It was cool to see possible applications of concepts above their level too like when the younger kids had to add lots of numbers instead of just multiply or high school geometry problems that could be solved using calculus.
kyune ยท 1 points ยท Posted at 06:12:42 on May 26, 2016 ยท (Permalink)
Six weeks is Math's happy little accident. Bob Ross would be proud.
ewic ยท 1 points ยท Posted at 15:54:14 on May 25, 2016 ยท (Permalink)
Never in 31,556,952,000,000 seconds
Obi-Wan_Kannabis ยท 1 points ยท Posted at 01:10:27 on May 26, 2016 ยท (Permalink)
No. Math is cool because of the technology, engineering, physics and understanding it has brought to us. Not because of some coincidence.
[deleted] ยท 0 points ยท Posted at 15:38:53 on May 25, 2016 ยท (Permalink)*
[deleted]
sinsinkun ยท 9 points ยท Posted at 16:11:20 on May 25, 2016 ยท (Permalink)
Well... You could just... calculate out 10! and then calculate out 1x60x60x24x7x6 and compare them...
[deleted] ยท 0 points ยท Posted at 16:18:10 on May 25, 2016 ยท (Permalink)*
[deleted]
Aj16ay ยท 8 points ยท Posted at 16:58:23 on May 25, 2016 ยท (Permalink)
I mean... not really. Multiplying out 6 numbers on calculator and comparing to 10! is pretty simple
[deleted] ยท 1 points ยท Posted at 20:41:44 on May 25, 2016 ยท (Permalink)
The calculator is pretty complicated, though
Illsonmedia ยท -2 points ยท Posted at 18:16:22 on May 25, 2016 ยท (Permalink)*
Umm. I didn't take "proof" or "logic" or whatever. And certainly no advanced math courses in college. What exactly is happening here.
Where are we getting 60 x 60 x 24 x 7 x 6.edit: Okay I got this, it's hours x seconds x minutes x days x weeks. It's 3,628,800 (seconds in 6 weeks), which happens to equal 10!, after I manually multiplied 1-10. But still confused on my part belowWhy are we running a bunch of calculations to pull out numbers 1 through 10. What does that "prove" and what are these numbers sourced from (e.g. the 60 = 2 x 3 x 10)Edit2: holy shit I get it now. That's weird and cool.
dwmfives ยท 51 points ยท Posted at 15:32:30 on May 25, 2016 ยท (Permalink)
Wait so I never did high level math in school.... the ! operator just means multiple this and every real whole number before it? So 5! would be 1x2x3x4x5?
klawehtgod ยท 55 points ยท Posted at 15:50:03 on May 25, 2016 ยท (Permalink)
Yes. It's called a Factorial.
dwmfives ยท 11 points ยท Posted at 15:52:35 on May 25, 2016 ยท (Permalink)
Neato.
[deleted] ยท 10 points ยท Posted at 16:37:30 on May 25, 2016 ยท (Permalink)
[deleted]
dwmfives ยท 13 points ยท Posted at 16:40:52 on May 25, 2016 ยท (Permalink)
Yea I ended up reading some crazy shit with playing cards and 52!. Something about walk around the world emptying the ocean a drop at a time and stacking the paper for each ocean emptied and stacking it to somewhere in space and then I smoked a joint and brought my dog for a walk.
gtalley10 ยท 8 points ยท Posted at 17:21:34 on May 25, 2016 ยท (Permalink)
That's statistics for you.
aviationmaybe ยท 3 points ยท Posted at 17:07:09 on May 25, 2016 ยท (Permalink)
http://czep.net/weblog/52cards.html
Plsdontreadthis ยท 2 points ยท Posted at 21:43:18 on May 25, 2016 ยท (Permalink)
There are more combinations of shuffles in a deck of cards than atoms in our solar system.
anomalous_cowherd ยท 3 points ยท Posted at 18:16:03 on May 25, 2016 ยท (Permalink)
Protip: if you're working it out step by step you can skip the 'x1' because maths.
Also, don't start from zero.
dwmfives ยท 7 points ยท Posted at 18:21:31 on May 25, 2016 ยท (Permalink)
Instructions unclear, dick stuck in an event horizon.
anomalous_cowherd ยท 4 points ยท Posted at 18:40:21 on May 25, 2016 ยท (Permalink)
No, you got it right.
kenlubin ยท 4 points ยท Posted at 18:55:17 on May 25, 2016 ยท (Permalink)
And you pronounce "ten factorial" by shouting "10!" really excitedly.
dwmfives ยท 1 points ยท Posted at 15:30:08 on May 27, 2016 ยท (Permalink)
Is that 10 EXCLAMATION or 10 BANG?
kenlubin ยท 1 points ยท Posted at 16:55:13 on May 27, 2016 ยท (Permalink)
TEN!!!!
GokuMoto ยท 2 points ยท Posted at 17:50:19 on May 25, 2016 ยท (Permalink)
here is something that will blow your mind then 0!=1
ikcaj ยท 2 points ยท Posted at 20:18:22 on May 25, 2016 ยท (Permalink)
For someone who never did high level math, (like me), you sure did figure that out fast, (unlike me).
dwmfives ยท 1 points ยท Posted at 02:16:02 on May 26, 2016 ยท (Permalink)
I never did my homework. I'm not bad at math, just never got to take advanced courses.
PM_Sinister ยท 1 points ยท Posted at 23:56:23 on May 25, 2016 ยท (Permalink)
The definition of n! can also be written as n! = n*(n-1)!. By definition, 0! = 1 because it's impossible to have positive integers less than 0. Every other factorial can be found by using this as a defined value. This also makes it easier to see why the factorial for negative integers is undefined since it would necessarily be the case that 0! = 0*(-1)!. If (-1)! were a real number, this statement could not be made true no matter what (-1)! is; therefore, it must not be a real number.
[deleted] ยท 1 points ยท Posted at 00:13:44 on May 26, 2016 ยท (Permalink)
[deleted]
christian-mann ยท 1 points ยท Posted at 01:17:20 on May 26, 2016 ยท (Permalink)
Maybe there's a programming background?
dwmfives ยท 1 points ยท Posted at 02:17:21 on May 26, 2016 ยท (Permalink)
IT, but I dunno they taught the word in regular math when I was in grade school in the early 90s.
Shadax ยท 1 points ยท Posted at 00:23:46 on May 26, 2016 ยท (Permalink)
Strange that you're using other words at the same or higher math level than factorials.
dwmfives ยท 1 points ยท Posted at 02:17:51 on May 26, 2016 ยท (Permalink)
I got through regular high school math, just never an advanced course.
press-control-w ยท 8 points ยท Posted at 15:25:57 on May 25, 2016 ยท (Permalink)
As a math major, I love you
[deleted] ยท 3 points ยท Posted at 16:16:54 on May 25, 2016 ยท (Permalink)
r/theydidthemath
Inthethickofit ยท 5 points ยท Posted at 16:09:18 on May 25, 2016 ยท (Permalink)
do you teach math to middle schoolers? Because if you don't you should. it's clearly your calling.
Mirrorboy17 ยท 6 points ยท Posted at 16:44:32 on May 25, 2016 ยท (Permalink)
Wow thanks, I'm not a teacher - stopped after my degree. Always something I've though about though
anomalous_cowherd ยท 1 points ยท Posted at 18:17:48 on May 25, 2016 ยท (Permalink)
I know several ex-maths teachers.
All of them quit because they loved maths and loved teaching but found that they really didn't like kids. And senseless bureaucracy.
IAm_From_2045_AMA ยท 6 points ยท Posted at 14:44:35 on May 25, 2016 ยท (Permalink)*
So is this just an incredible coincidence, or did someone plan to have a week* be exactly 10! seconds somehow?
Edit: six weeks
Goddamnit_Clown ยท 17 points ยท Posted at 15:28:40 on May 25, 2016 ยท (Permalink)
Coincidence. We already divided time into nice numbers with lots of factors like 24 and 60, we just happened to pick just the right nice numbers and pick 7 days for our week to fill in the gap.
WendellSchadenfreude ยท 6 points ยท Posted at 17:22:22 on May 25, 2016 ยท (Permalink)
And just to make it clear that the coincidence isn't all that unlikely: if our week only had 6 days, then 10! seconds would be exactly 7 weeks instead, and it would still look faszinating.
And there would be other fun coincidences for different numbers of hours per day or minutes per hour.
RoboticChicken ยท 3 points ยท Posted at 16:37:11 on May 25, 2016 ยท (Permalink)
6 weeks = 10! seconds
ohitsasnaake ยท 1 points ยท Posted at 15:34:34 on May 25, 2016 ยท (Permalink)
I think you'd have to go ask the ancient Babylonians or something, I think they started at least the 60 minutes in a degree/hour thing, probably also 24 hours in a day. 60 seconds per minute is a much more modern thing, but was a direct imitation of the minutes per hour. No idea about the 7-day week. Romans? Greeks? Babylonians?
Vidyogamasta ยท 1 points ยท Posted at 16:02:19 on May 25, 2016 ยท (Permalink)
Kind of a coincidence, but kind of not. Time bases were chosen to be highly divisible (e.g. 12 can be divided evenly by 1, 2, 3, 4, 6), a side effect of which being that they have many factors.
To get 10!, we need to find the numbers 2 through 10, or the factors of these numbers. That gives us eight 2s, four 3s, two 5s, and a 7. The 7 is easy, that's days in a week!
A day can be separated in 24 hours, which can be separated into three 2s and a 3. (5, 3, 2 left). Hours are separated into 60 minutes, which is two 2s, a three, and a 5 (3, 2, 1). Same can be said for seconds ( 1, 1, 0). That leaves a factor of one 2 and one 3 left. 2*3 = 6 weeks.
Basically, 10! is the first factorial that contains all of the factors needed to build up to a "number of weeks" value (to get that second factor of 5). Once you factor it all out, the remaining factors are the number of weeks you have. You can do something slightly less impressive with 5! being exactly 2 minutes, for example, since 5! contains all of the factors needed for a minute (2, 2, 3, 5).
lengau ยท 1 points ยท Posted at 17:08:17 on May 25, 2016 ยท (Permalink)
The choice of 6 weeks is deliberate to fit the one missing number in the factorial (6)
Black_Antidote ยท 2 points ยท Posted at 15:53:21 on May 25, 2016 ยท (Permalink)
Can someone explain what just happened here? I understand how this works, but this isn't how I did it growing up. Is this the preferred method? It seems like a lot more effort to me.
klawehtgod ยท 4 points ยท Posted at 16:05:07 on May 25, 2016 ยท (Permalink)
I don't know about preferred, but I thought checking all the factors was brilliant. This is a great way to do it if you didn't have a calculator on hand.
And because it shows how they're equivalent without doing any real arithmetic, I think it's more intuitive.
pepedelapijagrande ยท 2 points ยท Posted at 17:27:17 on May 25, 2016 ยท (Permalink)
I am so fucking lost
v1z10 ยท 2 points ยท Posted at 17:37:35 on May 25, 2016 ยท (Permalink)
Beautifully explained
-PM_ME_PANTY_PICS ยท 7 points ยท Posted at 14:59:47 on May 25, 2016 ยท (Permalink)
/r/theytookabath
inphx ยท 3 points ยท Posted at 15:12:41 on May 25, 2016 ยท (Permalink)
Is this common core?
Mirrorboy17 ยท 10 points ยท Posted at 16:06:39 on May 25, 2016 ยท (Permalink)
Honestly I've no idea, I just sort of winged it
[deleted] ยท 3 points ยท Posted at 18:15:59 on May 25, 2016 ยท (Permalink)
I think the purpose of common core is to get you to understand relationships like this.
ObliviousScrublord ยท 0 points ยท Posted at 14:57:31 on May 25, 2016 ยท (Permalink)
I'm honestly not sure if I'm looking at real math or if this is a joke. Probably should have paid attention in high school
Stef100111 ยท 9 points ยท Posted at 15:23:36 on May 25, 2016 ยท (Permalink)
True. 10!=10ยท9ยท8ยท7ยท6ยท5ยท4ยท3ยท2ยท1=3,628,800.
How many seconds in a week?
60 seconds per minuteยท60 minutes per hourยท24 hours per dayยท7 days per weekยท6 weeks= 3,628,800 seconds
Tasonir ยท 2 points ยท Posted at 17:25:47 on May 25, 2016 ยท (Permalink)
This is how I would have proved it, although seeing them break it down into factors was also pretty cool.
Alfaron ยท 2 points ยท Posted at 15:20:51 on May 25, 2016 ยท (Permalink)
same here
pronouncedayayron ยท 1 points ยท Posted at 15:38:59 on May 25, 2016 ยท (Permalink)
10! seconds, not 10 seconds.
rubiscoisrad ยท 1 points ยท Posted at 18:07:30 on May 25, 2016 ยท (Permalink)
Real math. He just used a way to prove it that most people wouldn't have thought of.
[deleted] ยท 1 points ยท Posted at 18:17:52 on May 25, 2016 ยท (Permalink)
It's just the associative property of multiplication, it's not complicated.
sup3rdr01d ยท 1 points ยท Posted at 15:24:48 on May 25, 2016 ยท (Permalink)
Holy fuck
FarSightXR-20 ยท 1 points ยท Posted at 15:32:53 on May 25, 2016 ยท (Permalink)
-5 for no units.
weezyheff ยท 1 points ยท Posted at 15:37:11 on May 25, 2016 ยท (Permalink)
You sir are the real MVP
JustALuckyShot ยท 1 points ยท Posted at 15:37:31 on May 25, 2016 ยท (Permalink)
It's like suduko, but more confusing
tael89 ยท 1 points ยท Posted at 15:56:22 on May 25, 2016 ยท (Permalink)
As others said, this is an awesome way to solve the statement. Thanks.
notacabaret ยท 1 points ยท Posted at 15:58:38 on May 25, 2016 ยท (Permalink)*
This proof is so pretty I want to cry. I've never seen it done so perfectly and beautifully.
Edit: It deserves gold.
cartmancakes ยท 1 points ยท Posted at 16:09:41 on May 25, 2016 ยท (Permalink)
that was beautiful
trevmiller ยท 1 points ยท Posted at 16:17:14 on May 25, 2016 ยท (Permalink)
THIS is what blows me away about math and numbers. Everything's modular, you can just break it up into different chunks to see them in a different way. Thanks for proving that the way you did, that was pretty cool.
Darkohuntr ยท 1 points ยท Posted at 16:26:08 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
DietCherrySoda ยท 1 points ยท Posted at 16:29:42 on May 25, 2016 ยท (Permalink)
That was fantastic, really thinking outside the box!
[deleted] ยท 1 points ยท Posted at 16:34:06 on May 25, 2016 ยท (Permalink)
you don't need to find the "1"
setfire3 ยท 1 points ยท Posted at 17:01:37 on May 25, 2016 ยท (Permalink)
as an engineering graduate student, this is probably the cleanest proof I have ever fucking seen.
Subject1337 ยท 1 points ยท Posted at 17:25:50 on May 25, 2016 ยท (Permalink)
-1. Didn't show work.
LexUnits ยท 1 points ยท Posted at 17:29:22 on May 25, 2016 ยท (Permalink)
I really enjoyed how you did that.
ghandpivot ยท 1 points ยท Posted at 17:30:57 on May 25, 2016 ยท (Permalink)
I read all the comments and I'm still not sure if this is a correct way to prove the 10! or just a messy toss-around with the numbers that somehow turned out right.
cametosayshadk ยท 1 points ยท Posted at 17:42:08 on May 25, 2016 ยท (Permalink)
Excellent post
PointyOintment ยท 1 points ยท Posted at 17:45:16 on May 25, 2016 ยท (Permalink)
Well that's a different meaning of /r/unexpectedfactorial than usual.
Nicekicksbro ยท 1 points ยท Posted at 17:56:49 on May 25, 2016 ยท (Permalink)
Wow that was really intrigiung yet straight-forward. Thanks!
reddditaccount2 ยท 1 points ยท Posted at 18:13:12 on May 25, 2016 ยท (Permalink)
Oh! So this is how the common core math is supposed to be used.
[deleted] ยท 1 points ยท Posted at 18:23:52 on May 25, 2016 ยท (Permalink)
i dont get it
darexinfinity ยท 1 points ยท Posted at 18:26:50 on May 25, 2016 ยท (Permalink)
You got gold for simple math. I'm willing to do simple math problems for gold!
[deleted] ยท 1 points ยท Posted at 18:30:03 on May 25, 2016 ยท (Permalink)
I give it a 10! A fucking 10!
R.I.P. Paul
baube19 ยท 1 points ยท Posted at 18:33:17 on May 25, 2016 ยท (Permalink)
So that's what the ! is for on calculators haha I had no idea.. I don't know exactly how I got my diploma but at this point I'm too afraid to ask..
Solagnas ยท 1 points ยท Posted at 18:34:24 on May 25, 2016 ยท (Permalink)
That's really funny. Last time this was posted, I did the math and someone gave me gold.
[deleted] ยท 1 points ยท Posted at 18:35:26 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial
Although I guess it's not unexpected in a math thread...
Zartonk ยท 1 points ยท Posted at 18:37:02 on May 25, 2016 ยท (Permalink)
Holy shit, that's a pretty cool way to prove that.
S2_Statutes ยท 1 points ยท Posted at 18:37:15 on May 25, 2016 ยท (Permalink)
I'm going to tell people this but I'm just going to yell ten seconds loudly.
hotcarl8 ยท 1 points ยท Posted at 18:39:19 on May 25, 2016 ยท (Permalink)
hey that was fucking cool
TheHamCaptain ยท 1 points ยท Posted at 18:42:52 on May 25, 2016 ยท (Permalink)
Very very cool.
rafael000 ยท 1 points ยท Posted at 18:52:24 on May 25, 2016 ยท (Permalink)
slow clap
KickassMcFuckyeah ยท 1 points ยท Posted at 18:54:31 on May 25, 2016 ยท (Permalink)
Very cool proof!
ThatchedRoofCottage ยท 1 points ยท Posted at 19:05:04 on May 25, 2016 ยท (Permalink)
That's a fantastic way of showing why this is true. Far better than just calculating both and comparing answers.
Richard-Butts ยท 1 points ยท Posted at 19:11:27 on May 25, 2016 ยท (Permalink)
Wow, I am truly impressed.
[deleted] ยท 1 points ยท Posted at 19:17:43 on May 25, 2016 ยท (Permalink)
Isn't this the more complicated way of solving this? I would have just done 1 x 60 x 60 x 24 x 7 x 6 but I guess I did take longer to write down and keep track of where I was/use a calculator
gagnonca ยท 1 points ยท Posted at 19:24:16 on May 25, 2016 ยท (Permalink)
that's a real dumbass way of solving the problem... You could have also just seen if 10! == 60 x 60 x 24 x 7 x 6
daSMRThomer ยท 1 points ยท Posted at 19:31:29 on May 25, 2016 ยท (Permalink)
/u/Sellasella123 and you hated on me a few months ago for doing this same exact thing
Sellasella123 ยท 1 points ยท Posted at 22:40:54 on May 25, 2016 ยท (Permalink)
Hated get hated life son
DBREEZE223 ยท 1 points ยท Posted at 19:39:42 on May 25, 2016 ยท (Permalink)
I DONT REMEMBER ANY OF THIS
[deleted] ยท 1 points ยท Posted at 19:39:53 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
Alysx ยท 1 points ยท Posted at 19:40:24 on May 25, 2016 ยท (Permalink)
This is brilliant!
Teive ยท 1 points ยท Posted at 20:04:57 on May 25, 2016 ยท (Permalink)
You should post this as its own comment
DerBK ยท 1 points ยท Posted at 20:13:04 on May 25, 2016 ยท (Permalink)
Ooooooh pretty
Et_tu__Brute ยท 1 points ยท Posted at 20:19:27 on May 25, 2016 ยท (Permalink)
That was hot.
LookingForOreos ยท 1 points ยท Posted at 20:20:14 on May 25, 2016 ยท (Permalink)
Wow neat way to prove it. I never would've thought to do it like that
[deleted] ยท 1 points ยท Posted at 20:24:08 on May 25, 2016 ยท (Permalink)
That's pretty radical.
the-ace ยท 1 points ยท Posted at 20:25:51 on May 25, 2016 ยท (Permalink)
Thanks for explaining factorials once and for all for me.
chappersyo ยท 1 points ยท Posted at 20:28:58 on May 25, 2016 ยท (Permalink)
See I would have just worked out the exact number of seconds and compared it to 10! Your way is much more elegant and I like it.
your_mind_aches ยท 1 points ยท Posted at 20:31:03 on May 25, 2016 ยท (Permalink)
Lol nice!
[deleted] ยท 1 points ยท Posted at 20:34:53 on May 25, 2016 ยท (Permalink)
I also figured it out but I did it the lame way:
Calculator - 10!
Calculator - 60602476
Both equal 3628800.
[deleted] ยท 1 points ยท Posted at 20:42:16 on May 25, 2016 ยท (Permalink)
This actually demonstrates the reason we have 60 seconds in a minute and 60 minutes in an hour.
When the Babylonians wanted to divide up time, they wanted highly divisible numbers. 60 was chosen because it's divisible by 2, 3, 4, 5, 6 and all the cofactors.
NotGloomp ยท 1 points ยท Posted at 20:44:31 on May 25, 2016 ยท (Permalink)
This is problem solving. You start with what you know and work forward until you reach your goal. Glad I figured this out eventually.
FalseEnvision ยท 1 points ยท Posted at 21:17:26 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
[deleted] ยท 1 points ยท Posted at 21:45:24 on May 25, 2016 ยท (Permalink)
I fucking loled
guitarkow ยท 1 points ยท Posted at 21:47:39 on May 25, 2016 ยท (Permalink)
The lack of units is hurting my engineering brain.
xoxota99 ยท 1 points ยท Posted at 22:01:16 on May 25, 2016 ยท (Permalink)
Where's the six? Edit:Nevermind, I'm an idiot.
Mriswith88 ยท 1 points ยท Posted at 22:03:01 on May 25, 2016 ยท (Permalink)
That's Numberwang!
mattsk8n ยท 1 points ยท Posted at 22:27:25 on May 25, 2016 ยท (Permalink)
This seems too much like new math to me. I'd just calculate 1sec x 60sec x 60min x 24 hr x 7 day x 6 weeks = 3,628,800 seconds.
Then conversely, 10! = 10x9x8x7x6x5x4x3x2x1 = 3,628,800.
Bam done.
cakefairy ยท 1 points ยท Posted at 22:32:30 on May 25, 2016 ยท (Permalink)
I would have just used the factorial function on the calculator
Auxcaliber ยท 1 points ยท Posted at 04:27:51 on May 26, 2016 ยท (Permalink)
I was expecting illuminati confirmed or Busch did 9/11
ktkps ยท 1 points ยท Posted at 04:56:17 on May 26, 2016 ยท (Permalink)
hey wait a minute there...
LegacyLemur ยท 1 points ยท Posted at 08:23:45 on May 26, 2016 ยท (Permalink)
I would have never thought to break it down like that...
Trevita17 ยท 1 points ยท Posted at 11:59:45 on May 26, 2016 ยท (Permalink)
I can only get so erect.
procrastinating_hr ยท 1 points ยท Posted at 12:55:12 on May 26, 2016 ยท (Permalink)
Outstanding breakdown and while I understood what you did, could you please elaborate why taking away the extra 3s doesn't change the end result?
hosalabad ยท 1 points ยท Posted at 15:49:51 on May 25, 2016 ยท (Permalink)
This is like the bullshit math they are teaching my kids in elementary school, except you explained it in a fashion that made sense.
Thanks =)
gloid_christmas ยท 690 points ยท Posted at 14:03:25 on May 25, 2016 ยท (Permalink)
There are exactly 11! seconds in 66 weeks!
PiperArrow ยท 383 points ยท Posted at 14:22:13 on May 25, 2016 ยท (Permalink)
There are exactly 12! seconds in 792 weeks!
fuccimama79 ยท 450 points ยท Posted at 15:20:21 on May 25, 2016 ยท (Permalink)
There are exactly 13! Seconds in 10,296 weeks
Move over r/counting. Here come factorials!
RoboticChicken ยท 98 points ยท Posted at 16:39:02 on May 25, 2016 ยท (Permalink)
There are exactly 14! seconds in 144 144 weeks!
Jaytho ยท 213 points ยท Posted at 16:49:40 on May 25, 2016 ยท (Permalink)
I think it's funny that 10! seconds are 6 weeks, not that long ago or in the future. That's barely 1.5 months, a pretty short time.
14! seconds are 2772 years. Rome was founded 14! seconds ago in 753 BC.
ticktockaudemars ยท 92 points ยท Posted at 16:52:21 on May 25, 2016 ยท (Permalink)
that is exciting!! why is everyone yelling?
DarthJones1 ยท 15 points ยท Posted at 20:07:16 on May 25, 2016 ยท (Permalink)
I can give you 1! reason
[deleted] ยท 6 points ยท Posted at 22:15:12 on May 25, 2016 ยท (Permalink)
[deleted]
Come_To_r_Polandball ยท 4 points ยท Posted at 22:57:25 on May 25, 2016 ยท (Permalink)
/r/itwasagraveyardgraph
ticktockaudemars ยท 3 points ยท Posted at 02:29:35 on May 26, 2016 ยท (Permalink)
I DON'T GET IT!
[deleted] ยท 1 points ยท Posted at 04:00:12 on May 26, 2016 ยท (Permalink)
an "!" means "factorial" in math.
for "n!", it is the product of all positive integers less than or equal to n. For example,
ticktockaudemars ยท 1 points ยท Posted at 10:47:41 on May 26, 2016 ยท (Permalink)*
YAY! LETTERS TOO!? M!
GokuMoto ยท 0 points ยท Posted at 17:55:23 on May 25, 2016 ยท (Permalink)
in math "!" is the symbol for factoral. which is essentially how many different ways you can arrange a group of things. you can arrange a group of 10 objects 3,628,800 different ways. so 10!=3,628,800 and there are 3,628,800 seconds in 6 weeks: 6(weeks) x 7(days per week) x 24(hours per day) x 60(minutes per hour) x 60(seconds per minute)= 3,628,800
DanTheStripe ยท 10 points ยท Posted at 18:12:27 on May 25, 2016 ยท (Permalink)
IF YOU SAY SO!!!
GokuMoto ยท 1 points ยท Posted at 18:14:34 on May 25, 2016 ยท (Permalink)
I KNOW SO!!!!
ticktockaudemars ยท 2 points ยท Posted at 19:38:44 on May 25, 2016 ยท (Permalink)
THIS IS FUN! YEAH MATH!
ย
EVERYBODY SHOUT OUT YOUR FAVORITE NUMBER! 14!
ย
ย
GokuMoto ยท 0 points ยท Posted at 19:49:32 on May 25, 2016 ยท (Permalink)
your favourite number is 87,178,291,200?
Gstreetshit ยท 1 points ยท Posted at 18:14:04 on May 25, 2016 ยท (Permalink)
Wut? You can arrange ten items 3,628,800 ways? That doesn't seem right....then again I also barely passed college algebra.
joeydee93 ยท 8 points ยท Posted at 18:42:27 on May 25, 2016 ยท (Permalink)
So I am going to show 3! Which is a nice small number as an example and not a proof.
3! = 1ร2ร3 3! = 6
Now you have 3 objects named A,B,C how many different ways can you arrange thoses objects?
A B C
A C B
B A C
B C A
C A B
C B A
so that is 6 which is 3!
This is useful for stats and probability.
CharlieDancey ยท 1 points ยท Posted at 18:57:59 on May 25, 2016 ยท (Permalink)
While this isn't a proof our friend /u/Gstreetshit will find that the exercise of laying out all the possible permutations of A,B,C,D with pencil and paper will make everything clear.
There are 4! = 1 x 2 x 3 x 4 = 24 possibilities. Try it!
Gstreetshit ยท 1 points ยท Posted at 13:14:08 on May 26, 2016 ยท (Permalink)
Makes sense now.
Its the same as 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 *2 * 1
I suppose that is probably what the ! means?
joeydee93 ยท 1 points ยท Posted at 13:59:04 on May 26, 2016 ยท (Permalink)
Ya the ! symbol means factorial in math. and the way to compute a factorial is multiply every counting number smaller then it self
so n! = n *(n-1)! for all counting numbers
Flamingtomato ยท 3 points ยท Posted at 18:39:19 on May 25, 2016 ยท (Permalink)*
It's true though - think of it like this:
You've got 10 "slots" to fill with 10 objects in any arrangement, and to make it easier we're gonna do them one at a time, starting with the left one.
For the first slot you can put any of the 10 numbers, so we have 10 ways to arrange the first slot.
For the second slot you put any of the nine remaining numbers. Meaning the first 2 slots can be arranged in 10*9 different ways.
For the third slot there are 8 numbers remaining, so the first 3 slots can be arranged in 10 * 9 * 8 ways
And you continue like this, and end up with 123456789*10 (EDIT: 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 formatting is a pain sometimes) in the end. This is what 10! means, and if you try putting in a calculator you're gonna find it equals 3,628,800
Gstreetshit ยท 1 points ยท Posted at 13:10:07 on May 26, 2016 ยท (Permalink)
10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1?
Flamingtomato ยท 1 points ยท Posted at 13:14:00 on May 26, 2016 ยท (Permalink)
well shit that went badly...
Gstreetshit ยท 1 points ยท Posted at 13:19:28 on May 26, 2016 ยท (Permalink)
Thank you for the clarification
Flamingtomato ยท 1 points ยท Posted at 13:21:27 on May 26, 2016 ยท (Permalink)
I need to learn to look through my post after posting it to make sure it is formatted correctly
GokuMoto ยท 1 points ยท Posted at 19:04:24 on May 25, 2016 ยท (Permalink)
1 2 3 4 5 6 7 8 9 10
1 3 2 4 5 6 7 8 9 10
1 2 4 3 5 6 7 8 9 10
1 2 3 5 4 6 7 8 9 10
keep doing this for every possible formation
vesomortex ยท 2 points ยท Posted at 16:54:37 on May 25, 2016 ยท (Permalink)
Not any more. That second just passed.
InukChinook ยท 2 points ยท Posted at 21:54:28 on May 25, 2016 ยท (Permalink)
This is gonna be a TIL
mirziemlichegal ยท 1 points ยท Posted at 22:22:49 on May 25, 2016 ยท (Permalink)
let's make a factorial calendar.
yerba-matee ยท 0 points ยท Posted at 17:21:28 on May 25, 2016 ยท (Permalink)
what the fuck are you guys on about!?
Blitzilla ยท 11 points ยท Posted at 17:36:01 on May 25, 2016 ยท (Permalink)
The ! symbol following an integer is called a factorial. It's really simple.
5!= 5x4x3x2x1
6!= 6x5x4x3x2x1
10!= 10x9x8x7x6x5x4x3x2x1
And so on. As you can see from the thread, these factorials can grow drastically in very few increments. 10! seconds equals six weeks while 14! seconds is over 2770 years.
yerba-matee ยท 1 points ยท Posted at 15:44:45 on May 26, 2016 ยท (Permalink)
wow. nice.
now I'm gonna spend hours not sleeping beacuse I have to work out how many years they are in my head..
imGnarly ยท 2 points ยท Posted at 17:31:05 on May 25, 2016 ยท (Permalink)
The enervating charm of math, of course.
statist_steve ยท 7 points ยท Posted at 16:50:22 on May 25, 2016 ยท (Permalink)
There are exactly I don't know what I'm doing! seconds in this thread!
casualdelirium ยท 1 points ยท Posted at 22:32:14 on May 25, 2016 ยท (Permalink)
Why do you keep shouting those numbers???
Wont_Edit_If_Gilded ยท 3 points ยท Posted at 20:24:10 on May 25, 2016 ยท (Permalink)
That escalated quickly
666666t ยท 2 points ยท Posted at 19:26:00 on May 25, 2016 ยท (Permalink)
/r/factorials?
Sabalabajaybum ยท 1 points ยท Posted at 18:24:58 on May 25, 2016 ยท (Permalink)
What is what, who is who, how is how, where is were, you are now.
phil_doe ยท 1 points ยท Posted at 18:33:42 on May 25, 2016 ยท (Permalink)
boomerangbro10 ยท 1 points ยท Posted at 19:20:30 on May 25, 2016 ยท (Permalink)
(factorials)(factorials-1)(factorials-2)...(4)(3)(2)
spiral6 ยท 1 points ยท Posted at 19:51:22 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial
sirius4778 ยท 1 points ยท Posted at 02:55:33 on May 26, 2016 ยท (Permalink)
There are exactly 9! seconds in 6.3 days!
DanTilkin ยท 1 points ยท Posted at 23:50:04 on May 31, 2016 ยท (Permalink)
https://www.reddit.com/r/counting/comments/1v8fth/counting_in_factorial/ch8x20o
ciaisi ยท 6 points ยท Posted at 14:55:22 on May 25, 2016 ยท (Permalink)
There are Nine Days in 257 Weeks.
โซAnd its so sad, you're so good and I'm so bad!โซ
aaaaaandimatwork ยท 7 points ยท Posted at 15:10:27 on May 25, 2016 ยท (Permalink)
Of all the places to see a Nine Days reference...
Anonpornaccnt ยท 1 points ยท Posted at 16:40:07 on May 25, 2016 ยท (Permalink)
There's 104 days of summer vacation!
Pun-Master-General ยท 3 points ยท Posted at 15:53:49 on May 25, 2016 ยท (Permalink)
Well, that escalated quickly,
frugalNOTcheap ยท 2 points ยท Posted at 15:35:52 on May 25, 2016 ยท (Permalink)
Damn those factorials add up fast
Enchiladas4Real ยท 1 points ยท Posted at 20:33:49 on May 25, 2016 ยท (Permalink)
I'm feeling so excited!
zamadatix ยท 1 points ยท Posted at 02:53:47 on May 26, 2016 ยท (Permalink)
There are exactly 74! seconds in 10489235925670301916094400945625754126892543500156486909265979415125927057996307884933120000000000000 years!
rzezzy1 ยท 13 points ยท Posted at 14:53:05 on May 25, 2016 ยท (Permalink)
/r/expectedfactorial
bobocalender ยท 2 points ยท Posted at 18:16:15 on May 25, 2016 ยท (Permalink)
That was a very strange experience.
[deleted] ยท -1 points ยท Posted at 14:56:42 on May 25, 2016 ยท (Permalink)
No it isn't. He wanted to put 10 factorial.
rzezzy1 ยท 7 points ยท Posted at 15:58:09 on May 25, 2016 ยท (Permalink)
Yes, that's why I didn't link /r/unexpectedfactorial
Mirsky814 ยท 17 points ยท Posted at 15:00:14 on May 25, 2016 ยท (Permalink)
Not if you're a physicist or computer scientist/programmer. You got to love leap seconds.
https://www.youtube.com/watch?v=-5wpm-gesOY
featherfooted ยท 1 points ยท Posted at 18:13:49 on May 25, 2016 ยท (Permalink)
If you're a physicist, you're probably more interested in the fact that ten pi million seconds is approximately a year, to within 0.5% tolerance.
Ten pi million = 31415926.53589... seconds
One year = 60 * 60 * 24 * 365.25 = 31557600.0 seconds
Difference = -141673.4641099982 seconds
Error = -0.0044
Percent = about 0.4% less than expected
WolverineMan016 ยท 13 points ยท Posted at 15:11:04 on May 25, 2016 ยท (Permalink)
This can quickly be turned into joke form:
Bob and Joe were sitting in their math class one day when their teacher suddenly shouts โPop quiz! If you donโt answer this question correctly, then you will fail the classโ
Both Bob and Joe are taken aback.
The teacher turns to Joe, โJoe! Quickly, how many seconds are there in six weeks?โ Joe takes a few seconds to think about it, and then with a smile on his face quickly exclaims, โthere are exactly 10!โ
The teacher then turns to Bob, โWhat do you think, Bob?โ Bob is perplexed with Joeโs answer. How can there only be 10 seconds in six weeks? However, not being great at math, Bob decides to agree with Joe and says, โthere are exactly 10 seconds in six weeks.โ
The teacher then turns back to Joe with a smile, โGreat work, Joe. You pass!โ Then she turns to Bob shaking her head. โBob, looks like I will be seeing you again next year. You fail.โ
GokuMoto ยท 3 points ยท Posted at 18:07:19 on May 25, 2016 ยท (Permalink)
only good in a written form
saucywaucy ยท 1 points ยท Posted at 17:33:27 on May 25, 2016 ยท (Permalink)
Thankfully Joe wasn't too excited and didnt say "there are exactly 10!!!"
TypicalCricket ยท 2 points ยท Posted at 15:13:53 on May 25, 2016 ยท (Permalink)
When I was learning about factorial in high school, my math teacher was explaining to the class: "This here is six factorial, and not SIX!"
He bellowed the SIX part so loud that a girl who was dozing off at the front of the class fell out of her desk.
AmishElectricity49 ยท 2 points ยท Posted at 15:32:14 on May 25, 2016 ยท (Permalink)
It took me a good 5 minutes to figure out that you meant 10 factorial and not just an exciting 10 seconds
AcclimateToMind ยท 2 points ยท Posted at 15:35:58 on May 25, 2016 ยท (Permalink)
psshh, you math people trying to sound smart? There are way more then 10 seconds in six weeks. You can't fool me
Missing_Intestines ยท 2 points ยท Posted at 16:28:41 on May 25, 2016 ยท (Permalink)
Sounds like Panic! at the Disco for mathletes.
superawesomepandacat ยท 2 points ยท Posted at 16:34:01 on May 25, 2016 ยท (Permalink)
HOW MANY SECONDS!?
[deleted] ยท 2 points ยท Posted at 16:45:55 on May 25, 2016 ยท (Permalink)
/r/expectedfactorial
/r/unexpectedfactorial
Reignbringer ยท 2 points ยท Posted at 17:02:25 on May 25, 2016 ยท (Permalink)
Took me way to long to realize that was 10 factorial. I read it as you were excited about 10...
lurgi ยท 2 points ยท Posted at 17:10:35 on May 25, 2016 ยท (Permalink)
There are roughly pi * 10 million seconds in a year.
zrrt1 ยท 1 points ยท Posted at 19:18:58 on May 25, 2016 ยท (Permalink)
There are roughly c seconds a year
thisismycuntaccount ยท 2 points ยท Posted at 17:33:38 on May 25, 2016 ยท (Permalink)
Given how bad my maths is and the fact I barely passed at the lowest level, I genuinely thought you were just really excited about there being 10 seconds in a week and my thinking, "well I know that's not right.."
10! seconds
DoWhile ยท 2 points ยท Posted at 14:33:56 on May 25, 2016 ยท (Permalink)
this fact got gold once
Arsonslwrd ยท 1 points ยท Posted at 16:26:12 on May 25, 2016 ยท (Permalink)
In the same cathegory: PI seconde equals a nanocentury
wicked-dog ยท 1 points ยท Posted at 16:35:10 on May 25, 2016 ยท (Permalink)
How long is 100! seconds?
featherfooted ยท 2 points ยท Posted at 18:16:11 on May 25, 2016 ยท (Permalink)
~ 2.95739248 ร 10150 years
wicked-dog ยท 2 points ยท Posted at 18:25:17 on May 25, 2016 ยท (Permalink)
Damn, that is way less interesting
usernumber36 ยท 2 points ยท Posted at 08:53:08 on May 26, 2016 ยท (Permalink)
fucken long man
PrrrromotionGiven ยท 1 points ยท Posted at 17:35:03 on May 25, 2016 ยท (Permalink)
Wow! So I take it this must have been done deliberately when people were wondering "So, what units should we use for time?"
I always thought they just made them up pretty randomly, but this seems to precise for that to be true. TIL.
ThebocaJ ยท 1 points ยท Posted at 17:49:19 on May 25, 2016 ยท (Permalink)
Except on leap second weeks.
Third__Wheel ยท 1 points ยท Posted at 17:58:55 on May 25, 2016 ยท (Permalink)
Adding on to this, the year is actually fundamentally based on Pi, one year is Pi * 107 seconds
friends_found_my_acc ยท 1 points ยท Posted at 18:03:59 on May 25, 2016 ยท (Permalink)
ELI5?
peanutismint ยท 1 points ยท Posted at 18:29:30 on May 25, 2016 ยท (Permalink)
What does ! stand for?
99shadow25 ยท 2 points ยท Posted at 21:46:03 on May 25, 2016 ยท (Permalink)*
Factorial, which is just that number times that number minus one times the number minus two, etc until 1. So 5! is the same as 5*4*3*2*1, or 120.
peanutismint ยท 1 points ยท Posted at 10:10:07 on May 26, 2016 ยท (Permalink)
I'm lernding!
But seriously, thanks.
narwhals_narwhals ยท 1 points ยท Posted at 18:37:38 on May 25, 2016 ยท (Permalink)
It's not quite as math-y as the explanation of this one below, but there are approximately pi * 107 seconds in one year. That's accurate to within 0.5%, so it's perfectly acceptable when doing quick estimates of things.
garblegarble12342 ยท 1 points ยท Posted at 18:39:46 on May 25, 2016 ยท (Permalink)
I get that you are enthusiastic about it, but that does not make it true.
Tephrite ยท 1 points ยท Posted at 18:54:41 on May 25, 2016 ยท (Permalink)*
also something i ended up at after thinking about this, is that if you take n!, then the number of times 2 is a factor of n! tends to n as n tends to infinity.
e.g. 2999987 is a factor of 999999!
You can do similar things with other prime factors, p;
pn/(p-1) is a factor of n as n-> infinity
so for the first few primes (p:number of times p is a factor); 2:n 3:n/2 4:n/3 etc
cosmoceratops ยท 1 points ยท Posted at 19:26:46 on May 25, 2016 ยท (Permalink)
(Panic)x(Pani)x(Pan)x(Pi)x(P) At The Disco
[deleted] ยท 1 points ยท Posted at 19:32:32 on May 25, 2016 ยท (Permalink)
There are pi seconds in a nano-century.
Lympwing2 ยท 1 points ยท Posted at 20:30:32 on May 25, 2016 ยท (Permalink)
What the fuck is going on in this comment chain
Morningred7 ยท 1 points ยท Posted at 20:36:22 on May 25, 2016 ยท (Permalink)
You don't have to yell.
Mefic_vest ยท 1 points ยท Posted at 21:14:57 on May 25, 2016 ยท (Permalink)
Except when you get leap seconds.
Yeah, leap seconds. Think on that one for a sec.
baconmanlovesbacon ยท 1 points ยท Posted at 21:34:31 on May 25, 2016 ยท (Permalink)
I just learned about ! In pre calc, cool to see it
WilliamWallace2K14 ยท 1 points ยท Posted at 21:47:37 on May 25, 2016 ยท (Permalink)
Why are you shouting
D-Shap ยท 1 points ยท Posted at 21:59:58 on May 25, 2016 ยท (Permalink)
R/expectedfactorial
Stkrdknmiblz ยท 1 points ยท Posted at 22:12:23 on May 25, 2016 ยท (Permalink)
Why are you shouting the 10?
CinnamonDolceLatte ยท 1 points ยท Posted at 23:43:05 on May 25, 2016 ยท (Permalink)
And about Pi billion seconds in a century.
Screen_Watcher ยท 1 points ยท Posted at 00:15:10 on May 26, 2016 ยท (Permalink)
0! = 1
sunnyjum ยท 1 points ยท Posted at 02:02:35 on May 26, 2016 ยท (Permalink)
Seems to check out!
= secondsperminute * minutesperhour * hoursperday * daysperweek * weeks
= 60 * 60 * 24 * 7 * 6
= 60 * ( 60 * 6 ) * 24 * 7
= 60 * 360 * 24 * 7
= ( 10 * 6 ) * ( 9 * 8 * 5 ) * ( 4 * 3 * 2 ) * 7
= 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 10!
Yggsdrazl ยท 1 points ยท Posted at 05:19:42 on May 26, 2016 ยท (Permalink)
/r/expectedfactorial
WantDiscussion ยท 1 points ยท Posted at 06:42:24 on May 26, 2016 ยท (Permalink)
There are exactly 10! seconds in 3! weeks
ixora7 ยท 1 points ยท Posted at 09:36:47 on May 26, 2016 ยท (Permalink)
Okay okay. You don't have to yell.
[deleted] ยท 1 points ยท Posted at 09:38:23 on May 26, 2016 ยท (Permalink)
Isn't a Jewish star of David really similar to that as well?
countryboyathome ยท 1 points ยท Posted at 17:47:03 on May 26, 2016 ยท (Permalink)
This is great.. that means 10!/42 = seconds in a day. 42 is the answer to everything
ktkps ยท -21 points ยท Posted at 12:15:20 on May 25, 2016 ยท (Permalink)
FTFY
[deleted] ยท 6 points ยท Posted at 13:30:30 on May 25, 2016 ยท (Permalink)
You forgot to shout "ten!"
usernumber36 ยท 7 points ยท Posted at 12:22:32 on May 25, 2016 ยท (Permalink)
you did not. 10! as in 10 factorial. 10x9x8x7x6x5x4x3x2x1
Myblfrenk ยท 1 points ยท Posted at 12:39:41 on May 25, 2016 ยท (Permalink)
Whoosh.
ktkps ยท -1 points ยท Posted at 12:23:26 on May 25, 2016 ยท (Permalink)
oh..i though this is the weekly grammar thread
[deleted] ยท -5 points ยท Posted at 12:42:32 on May 25, 2016 ยท (Permalink)
thatsthejoke
usernumber36 ยท 8 points ยท Posted at 13:07:32 on May 25, 2016 ยท (Permalink)
dude I'm into maths we have no sense of humour. lol
Runixo ยท 5 points ยท Posted at 13:52:49 on May 25, 2016 ยท (Permalink)
So you're saying math is no laughing matter?
[deleted] ยท -4 points ยท Posted at 13:58:09 on May 25, 2016 ยท (Permalink)
Speak for yourself I like humor and math (and I spell them right too haha)
mdifmm11 ยท 0 points ยท Posted at 15:14:31 on May 25, 2016 ยท (Permalink)
This isn't a math fact (other than utilizing a factorial). It's a coincidence.
Nuns_Love_Guns ยท 0 points ยท Posted at 15:52:53 on May 25, 2016 ยท (Permalink)
10! there are more than 10 seconds in a week!
BluntTruthGentleman ยท 0 points ยท Posted at 16:00:07 on May 25, 2016 ยท (Permalink)
Why are you yelling the 10?
nimria ยท 0 points ยท Posted at 16:24:02 on May 25, 2016 ยท (Permalink)
Why is the 10 so excited!
heyhey91 ยท 0 points ยท Posted at 16:32:00 on May 25, 2016 ยท (Permalink)
Am I the only one who read 10!, and yelled TEN in my head, as if it was meant as an exclamation point?
elee0228 ยท 4307 points ยท Posted at 12:34:05 on May 25, 2016 ยท (Permalink)*
International Paper Sizes (e.g. A4) use a 1:โ2 ratio. If you cut them in half
lengthwisecrosswise, the same ratio will be maintained. It's great for scaling up or down.Edit: fixed error
NotHereToHaveFun ยท 351 points ยท Posted at 15:09:50 on May 25, 2016 ยท (Permalink)
That, the fact that A0 has an area of 1 m2 , and that each subsequent size is just half of the previous one is all you need to define the whole series of sizes (A1, A2, A3, ...).
DCallejasSevilla ยท 149 points ยท Posted at 15:31:43 on May 25, 2016 ยท (Permalink)
Plus, the weight of an A0 sheet of paper is equal to its density (in kg/m2 ).
Or conversely, if you have 16 sheets of A4 paper with density 80 g/m2 , their weight is 80 g.
[deleted] ยท 43 points ยท Posted at 15:44:14 on May 25, 2016 ยท (Permalink)
So it's like the mole, but for paper.
lostguru ยท 4 points ยท Posted at 23:19:16 on May 25, 2016 ยท (Permalink)
Holy shit.
nico-demus ยท 1 points ยท Posted at 16:53:57 on May 27, 2016 ยท (Permalink)
Hah
Sickboy22 ยท 15 points ยท Posted at 18:00:00 on May 25, 2016 ยท (Permalink)
That's not a bonus ("plus") but a consequence of the area of 1m2
LiquidSilver ยท 9 points ยท Posted at 18:38:08 on May 25, 2016 ยท (Permalink)
The weight of 1 m2 of paper which weighs x kg per m2 is x kg. Mind blown.
ars-derivatia ยท 12 points ยท Posted at 19:27:41 on May 25, 2016 ยท (Permalink)
Yeah, seems silly at first, but what he/she meant is that paper stock density is defined in grams per m2 and knowing that A0 is exactly that allows for easy calculation of all other formats.
So we can easily calculate that single sheet of A4 is 5 grams, or a 96-page notebook weighs 240 grams. Or that two hundred blank A8 business cards made from 350g stock weigh 340 grams. It's cool when you work in printing-related industry :)
TribeWars ยท 1 points ยท Posted at 19:51:04 on May 25, 2016 ยท (Permalink)
Finally a useful fact
gnorty ยท 3 points ยท Posted at 23:33:32 on May 25, 2016 ยท (Permalink)
Is "density" really the name for this? surely density is kg/m3. the weight of a piece of paper could be related to density (ie the fibres are closely packed with less air) but equally could be the thickness of the sheet (a very airy sheet 1mm thick might weigh more than a tight packed sheet 0.01mm thick.
If density really is the name for that, then OK I guess, but it does seem like a meaningless value
[deleted] ยท 1 points ยท Posted at 10:48:42 on May 26, 2016 ยท (Permalink)
It's how much paper (or cellulose, or whatever) goes into this paper. And because "3" is hard to compare, it's set it into some relation.
density is usually really good for this, but if you want to calculate "how heavy will this letter (package) be and how much postage must I pay" or want a tangible way of comparing paper, "grams per mยฒ" provides useful.
Of course "thickness" is technically wrong, but what should be meant in this case is "strength" of the paper, not unlikely in lack of a better english word, as the "a4"-denomination is commonly used in europe, but only to a lesser extent in the USA.
The further benefit of "grams per mยฒ" is the above demonstrated calculation of weight, an "Ax" size paper with "y g/mยฒ" will weigh y / 2x gram.
elgskred ยท 1 points ยท Posted at 00:03:29 on May 26, 2016 ยท (Permalink)
this comes in handy when some angry officer comes into your office and yells at you "give me 300 A4 pages, IMMEDIATELY!". no need to count that, just tell him bitch i got this, then give him (300/16*80)g of paper.
jf908 ยท 1 points ยท Posted at 15:55:51 on May 25, 2016 ยท (Permalink)
Doesn't that depend on the thickness of the paper?
siliconespray ยท 9 points ยท Posted at 16:01:26 on May 25, 2016 ยท (Permalink)
The density /u/DCallejasSevilla is quoting is "mass per unit area," aka "area density." Regular "density" is "mass per unit volume." To get from "density" to "area density," you multiply by the thickness. That's how the thickness comes into play.
jf908 ยท 2 points ยท Posted at 16:30:19 on May 25, 2016 ยท (Permalink)
Oh right yeah, my bad.
LikeImGonnaLoseYou ยท 5 points ยท Posted at 18:25:09 on May 25, 2016 ยท (Permalink)
A0 = A1 + A2 + A3 + .......
1 = 1/2 + 1/4 + 1/8 + .......
anomalous_cowherd ยท 6 points ยท Posted at 18:33:18 on May 25, 2016 ยท (Permalink)
Also, envelopes come in C0-C5 etc sizes, where C4 is the right size for an A4 sheet without folding, C5 would fit it when folded in half etc.
There's also the metric B sizes which are in between the A sizes but have the same ratios. The short side of B0 is 1m long.
CircumcisionKnife ยท 2 points ยท Posted at 19:41:12 on May 25, 2016 ยท (Permalink)
The B series is the geometric mean of the A series, where B1 is between A0 and A1. The C series is the geometric mean of the A and B series, where C1 is between A1 and B1.
anomalous_cowherd ยท 4 points ยท Posted at 20:04:59 on May 25, 2016 ยท (Permalink)
Agreed. But here in metricland we only ever really see A sizes in paper and C sizes in envelopes!
CircumcisionKnife ยท 1 points ยท Posted at 23:56:41 on May 25, 2016 ยท (Permalink)
Neat! I'm Canadian, so all I know about the international paper size is from what I read about them on Wikipedia when I got bored.
What if the only reason the B series is even defined is so they can have a better size for the C series for envelopes.
anomalous_cowherd ยท 1 points ยท Posted at 08:59:34 on May 26, 2016 ยท (Permalink)
B is bigger than C, those envelopes would have too much slack in them.
http://www.theinternetprinter.com.au/info/Paper_Sizes.aspx
iprobably8it ยท 2 points ยท Posted at 20:23:17 on May 25, 2016 ยท (Permalink)
Its not exactly that simple. If I told someone to make a piece of paper with an area of 1m2 without any other instructions, I'd probably get 1 sq. m of paper, which doesn't conform to AX ratios.
NotHereToHaveFun ยท 3 points ยท Posted at 21:39:42 on May 25, 2016 ยท (Permalink)
Right. But the parent comment to mine states that the aspect ratio is โ2 .
Put these two pieces of information together, and consider a rectangle (OK, I forgot to say it's a rectangle) with sides a and b.
The aspect ratio means that:
b = (โ2 ) a
The area gives usthat:
a b = 1 m2
solving for a we get:
a (โ2 ) a = 1 m2
a2 = (1 m2 )/(โ2 )= (โ(1/2)) m2
a = (1/2)1/4 m = 0.841 m
With the aspect ratio and the total area you get A0, with the third fact (that each subsequent one is half the area of the previous one) you can construct the rest.
Jaredlong ยท 1 points ยท Posted at 16:39:47 on May 25, 2016 ยท (Permalink)
So there's no standard paper size larger than A0?
youngeng ยท 3 points ยท Posted at 17:24:49 on May 25, 2016 ยท (Permalink)
There are at least two, 2A0 and 4A0. Unsurprisingly, 2A0 means twice as bigger as an A0, 4A0 four times as bigger as an A0. They belong to a German standard which is not very famous. See http://www.paper-sizes.com/uncommon-paper-sizes/german-extension-paper-sizes
MerleCorgi ยท 1 points ยท Posted at 18:28:57 on May 25, 2016 ยท (Permalink)
I've also heard of "elephant" and "double elephant"
AadeeMoien ยท 2 points ยท Posted at 17:22:48 on May 25, 2016 ยท (Permalink)
Why would you need a standard paper size larger than a square meter?
Jaredlong ยท 1 points ยท Posted at 17:33:12 on May 25, 2016 ยท (Permalink)
I was thinking for posters.
AadeeMoien ยท 1 points ยท Posted at 19:43:59 on May 25, 2016 ยท (Permalink)
Posters aren't usually made with standard paper. They're either on a glossy specialty paper or, for a presentation, they're going to be custom made by a printer.
marnues ยท 1 points ยท Posted at 21:47:28 on May 25, 2016 ยท (Permalink)
I can arrange a page many ways to be 1 m2. One of the dimensions or a ratio would be helpful too!
NotHereToHaveFun ยท 2 points ยท Posted at 22:04:55 on May 25, 2016 ยท (Permalink)
Right, but the parent comment to mine specified an aspect ratio, the square root of 2.
Then you can solve for the two sides, as I did here
[deleted] ยท -1 points ยท Posted at 18:20:18 on May 25, 2016 ยท (Permalink)*
[removed]
Sayakai ยท 4 points ยท Posted at 18:42:37 on May 25, 2016 ยท (Permalink)
No, that's not how areas work. 1m2 is 1m x 1m. 10cm x 10cm is 0.01 m2, or 100cm2. 100cm = 1m, 10,000cm2 = 1m2.
[deleted] ยท 1 points ยท Posted at 18:47:45 on May 25, 2016 ยท (Permalink)*
[removed]
Sayakai ยท 2 points ยท Posted at 18:51:46 on May 25, 2016 ยท (Permalink)
My whole point is: It isn't. 100cm2 is only 1% of 1m2.
[deleted] ยท 1 points ยท Posted at 18:56:43 on May 25, 2016 ยท (Permalink)*
[removed]
Sayakai ยท 1 points ยท Posted at 18:59:09 on May 25, 2016 ยท (Permalink)
Correct. For areas, all conversion units are squared as well, for volumes, cubed. 1002 = 10,000.
markjs ยท 1937 points ยท Posted at 15:13:32 on May 25, 2016 ยท (Permalink)
And A0 has an area of 1 square metre.
Which means:
So basically the area of an Ax piece of paper is 1/2x m2
DrummerVim ยท 580 points ยท Posted at 15:45:15 on May 25, 2016 ยท (Permalink)
Really? Holy crap that's beautiful.
wordserious ยท 775 points ยท Posted at 16:16:06 on May 25, 2016 ยท (Permalink)
Metric, biatch :)
DrummerVim ยท 17 points ยท Posted at 18:59:31 on May 25, 2016 ยท (Permalink)
I'm European but I wasn't familiar with this fact about paper sizes. :)
superyiwu ยท 11 points ยท Posted at 19:31:56 on May 25, 2016 ยท (Permalink)
I'm European and im always surprised that not much people know about this :)
DrummerVim ยท 8 points ยท Posted at 19:37:30 on May 25, 2016 ยท (Permalink)
Yeah, it seems to be a pretty obscure fact. I knew of course that A4 was half the size of A3 etc. but the actual area of them being a proper number I had no clue.
[deleted] ยท 7 points ยท Posted at 22:12:45 on May 25, 2016 ยท (Permalink)
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Ray57 ยท 6 points ยท Posted at 22:29:06 on May 25, 2016 ยท (Permalink)
The Imperial system exists as "soft" protectionism for the US manufacturing sector.
It's a battle that can't be won by scientists, but by diplomats with trade deals.
NbdySpcl_00 ยท 4 points ยท Posted at 23:02:46 on May 25, 2016 ยท (Permalink)
It's not so nefarious as all that. Two two important things are true. (1) Changing to the metric system is expensive (2) US is principally a consumer, not a seller. The buyer gets to set the standards.
When the trade balance shifts (and it really will) US manufacturers will have to meet their buyer's standards if they want to compete. Everything will standardize through vertical integration simply under the drive of supply and demand. But it just isn't going to be be worth it to anyone to make the change, no matter how sensible it is from a maths perspective, until the cost of not doing it hits the bottom line.
jkelleyrtp ยท 1 points ยท Posted at 02:45:42 on May 26, 2016 ยท (Permalink)
Most scientists, engineers, and academics would prefer to use the metric system. It's not even trade deals or consumerism that prevents the switch; it's the sheer amount of infrastructure and existing machinery that was built using the imperial system. Specifically tooling for and maintenance equipment would have to be converted from imperial to metric which is just about impossible and ungodly expensive. The united states is proliferated with drill bits, end mills, material thickness, and fastener sizes in fractions of an inch without a metric equivalent. It seems that reddit believes switching to metric is much easier than it really is.
Ray57 ยท 1 points ยท Posted at 02:57:20 on May 26, 2016 ยท (Permalink)
Well that might be an argument. Except almost every other country from highly industrialised western countries to third-world shit holes have managed to do it.
Never attribute to incompetence that which is adequately explained by greed.
jkelleyrtp ยท 1 points ยท Posted at 03:26:19 on May 26, 2016 ยท (Permalink)
Considering you're going to disregard an argument of difficultly as greed, whatever I post probably won't mean much, but I'll still bite.
This is a history of metrication in the world.
Aside from the UK in 1965, there hasn't been a metrication by a country that has been historically known for manufacturing in the past 50 years. My original point still stands that conversion to metric is extraordinarily difficult and expensive for the United States, primarily because we've waited so long. It's not as easy as telling teachers to stop teaching imperial; private businesses and whole industries have invested millions of dollars into tooling that would be obsolete after the switch. Everyone on reddit might be up for a switch, but the metric/imperial argument affects them so little compared to countless businesses and the entire country's infrastructure history and standards.
Ray57 ยท 1 points ยท Posted at 03:45:49 on May 26, 2016 ยท (Permalink)
Well then what about the UK then?
What magic do they have that you don't?
No-one says it is easy. We choose to do these things because they are hard.
[deleted] ยท 14 points ยท Posted at 17:28:33 on May 25, 2016 ยท (Permalink)
[deleted]
wordserious ยท 8 points ยท Posted at 17:33:37 on May 25, 2016 ยท (Permalink)
Don't know about reddit, but I am sure foreigners living in the US will relate.
hugglesthemerciless ยท 2 points ยท Posted at 21:27:35 on May 25, 2016 ยท (Permalink)
As do foreigners in Canada. Sure we're officially metric but the population seems to have only partially caught on to that fact
ChiefFireTooth ยท 2 points ยท Posted at 18:52:44 on May 25, 2016 ยท (Permalink)
Yes.
(source: I am foreigner living in the US. I do relate)
bearsnchairs ยท 18 points ยท Posted at 17:25:44 on May 25, 2016 ยท (Permalink)
I had no idea the metric system was based on reciprocal powers of 2...
wordserious ยท 8 points ยท Posted at 17:32:32 on May 25, 2016 ยท (Permalink)
Oh you...
bearsnchairs ยท 20 points ยท Posted at 17:40:40 on May 25, 2016 ยท (Permalink)
ISO is different from SI.
ChuckWiles ยท 3 points ยท Posted at 20:01:18 on May 25, 2016 ยท (Permalink)
Not really metric, if you did it in furlongs it would be true as well. However, since 220 square yards of paper is a lot of paper, we use the meter which is large enough to be usable when cut in halves or quarters, but small enoughto be kind of absurd but still useful
It's more of a math thing than a metric thing
rtomek ยท 2 points ยท Posted at 22:53:59 on May 25, 2016 ยท (Permalink)
I wasn't aware the metric system considered fractions a thing
wordserious ยท 3 points ยท Posted at 22:57:45 on May 25, 2016 ยท (Permalink)
eh? Fractions and decimal points are just mathematical notation. It's certainly easier to use 0.5 m2, 0.25m2 and 0.125 m2, but nobody stops you from notating in fractions.
itz4mna ยท 3 points ยท Posted at 19:05:11 on May 25, 2016 ยท (Permalink)
Not really, it would be just as reasonable to define A0 as a square yard. It wouldn't break the scaling properties.
wordserious ยท 20 points ยท Posted at 19:57:17 on May 25, 2016 ยท (Permalink)
every little piece of the imperial system can be fixed within its little universe; but there is no overall connection with everything else like there is in the IS (which ISO uses in this case).
This is the hardest thing to explain to Americans: yes, inches work, feet work, cups and pounds and Fahrenheit. But there is no relationship between them, making any sort of work more complex than cooking a lot harder than it could be.
AshtarB ยท -4 points ยท Posted at 20:56:16 on May 25, 2016 ยท (Permalink)
The metric system isn't perfect, either, but at least it's an international standard. It's a large leap forward from Imperial, at least.
To begin with, it's based on 10, which, although adequate for multiples, doesn't really work for divisions of the base unit. You would expect a metre to be divisible by 3, but the decimal system doesn't really allow that. Base 12 would be better, but our number system is already base 10, so it would be more impractical.
Yes, some of these conversion factors are very close to a power of ten. There's the density of water at 999.972 kg/m3, and standard gravity at 9.80665 m/s2. It would make sense in that respect to use the decisecond, decimetre and kilogram as the base units to keep these as close to 1 as possible, or to use 98.0665 mm and 943.083 g to make them exactly 1.
Then there are the conversion factors that don't mesh well with decimal, like 4184 joules to raise 1 kg of water 1 Kelvin. Fahrenheit has its 0 and 100 points in a range comfortable for humans. Celsius doesn't, but it makes up for it by having 0 and 100 be the phase changes of water. But even across the earth's surface, gravity is much more stable than the boiling point of water, which can go under 80 ยฐC in more mountainous regions. It seems better to me to keep the freezing point at a round absolute temperature and let the boiling point be free.
But that's just an idealist's dream. SI is here to stay.
DMAredditer ยท 1 points ยท Posted at 01:22:54 on May 26, 2016 ยท (Permalink)
Those are all problems with decimals, not metrics though. It's pretty well accepted (at least scientifically) that a base 12 system would be better.
AshtarB ยท 1 points ยท Posted at 01:38:54 on May 26, 2016 ยท (Permalink)
That's just my second paragraph. The random conversion factors are still a problem. In dozenal, 2508 joules is still an awkward number.
KitKatKittens ยท 2 points ยท Posted at 02:17:29 on May 26, 2016 ยท (Permalink)
You can't make a system that has nice conversions for every physical scenario. It's impossible. And there is nothing scientifically special about water that demands we define units in terms of it. In fact, as you said, water is not perfectly consistent and is a terrible way to do science. Your system has to be arbitrary, but as long as it's based on something consistent, you're fine.
Everything SI has some physical definition, and it's not all about water. In fact, if anything has to do with water, it's because water is a common, stable substance that allowed scientists in the past, with their imperfect tools, to base units off of it. But now that we have better measurement devices and know that the properties of water change very easily, we've based the units on something else, something more consistent in nature.
Both the SI and the imperial system are based off of something consistent (or are in the progress of being so), which is why they both work. The problem is that the imperial system is literally defined in terms of SI units. A meter is defined in terms of the speed of light, but a foot is literally defined in terms of meters. Not only is it unnecessary, but it also takes away your ability to use a simple decimal system to scale your units or convert between different SI units (like meters and and newtons).
Finally, yes, the decimal system is imperfect. Base 12 is "better" (more convenient when working with certain simple fractions), but base 10 is definitely here to stay. And while base 10 isn't very nice when it comes to thirds, it's way better than most of the ugly imperial conversions.
AshtarB ยท 2 points ยท Posted at 04:55:11 on May 26, 2016 ยท (Permalink)
Yes. This was what I meant. The SI isnโt perfect, but itโs a lot more practical when actually doing calculations than the imperial system.
The only relationship with water is precisely "conceptual" definitions. A second is conceptually the 86400th part of a mean solar day, a metre is conceptually the ten millionth part of the distance from the poles to the equator, a kilogram is conceptually the mass of a cubic decimetre of water, and a kelvin is conceptually a hundredth of the difference between the freezing and boiling point of water at sea level.
The actual definitions have been refined several times, to keep up with the precision and accuracy that modern tools are capable of, but that obviously introduces extraneous conversion factors if you want to keep the units within the range of error of the previous definition.
But that doesnโt matter anymore. If a system is consistent with the physical world by itself, itโs that much better than a system defined in terms of another, and the SI is already here, and itโs an international standard, so trying to reform it puts you out of step with the rest of the world.
Wyand1337 ยท 1 points ยท Posted at 12:08:38 on May 26, 2016 ยท (Permalink)
Those "conversion factors" are just as random as the random states/points you chose to look at them. You chose to pick one specific gravitational accelleration out of the infinite values you could find for it just on this planet. You chose one of the infinite densities that water can have. Sure, I get that you picked a popular one that water has for a very specific (randomly chosen) set of parameters. But even if you would define that to be exactly 1, a second later the very same water would have a slightly different density. Same goes for the specific heat capacity you named for water for which you chose a value of 4184 J/kgK. water can have that value, but it is not a constant.
So what exactly would be the point of redefining base units just to get some derived functions to have a value of exactly 1 for a very specific set of parameters?
itz4mna ยท -5 points ยท Posted at 20:41:19 on May 25, 2016 ยท (Permalink)
I think the way we do it in the UK is pretty good, we use both depending on the situation. Kilometres are kind of a crap measurement for road distance, a car typically travels around 60mph or a mile a minute, the average man walks around 3mph or a mile every 20 minutes. In metric that works out to driving 100km/h so a kilometre every 1.7 minutes, hardly a convenient number. If want to design a car you'd use metric measurements. Imperial units which developed from real-life use tend to be much more relatable to humans than metric ones which were mandated by the intellectuals of the French revolution, which is why for human things like body weight and height are more often than not given in stone and feet in day to day life, if you're at the doctors getting a bone fixed then they'll use metric.
The other problem I have with the metric system is that 10 is a shitty choice of number to base a system of measure on. It only divides cleanly by 5 and 2. Compare that to say the foot of 12 inches which divides by 2, 3, 4 and 6. The base-60 measuring system we use for time which the French famously tried to get rid of is even better, 60 divides by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.
I won't defend Americans using volume measurements for literally everything in cooking though, that's just silly.
hugglesthemerciless ยท 3 points ยท Posted at 21:32:05 on May 25, 2016 ยท (Permalink)
The strength of base 10 though is how easy it is to multiply and divide. Take a square metre. You know a metre is 100cm, so a square metre ought to be 10,000cm2. Which is easy to do and most people can somewhat easily do in their heads if they think about it. In a base 12 system though you'd run into all sorts of problems trying to convert, doing for example 120x120=14,400 and similar, which far fewer people can do in their heads.
bearsnchairs ยท 0 points ยท Posted at 22:32:25 on May 25, 2016 ยท (Permalink)
Quick how many seconds are in an hour?!
hugglesthemerciless ยท 2 points ยท Posted at 22:33:49 on May 25, 2016 ยท (Permalink)
Convert 475 seconds into hours, and then convert 475 centimetres into metres and tell me which one took more time.
bearsnchairs ยท 1 points ยท Posted at 22:36:37 on May 25, 2016 ยท (Permalink)
That goes with my point, the entirety of SI isn't base ten. Time is still hexadecimal harking back to ease of division.
hugglesthemerciless ยท 1 points ยท Posted at 22:46:23 on May 25, 2016 ยท (Permalink)
Yea but that is the earths fault, we haven't yet found the technology to slow our rotation down to 10 hour days ;)
bearsnchairs ยท 2 points ยท Posted at 22:48:51 on May 25, 2016 ยท (Permalink)
Not really, units are human constructs and can be redefined. The second and meter were already redefined to natural and repeatable phenomenon, they were just refined very very close to their original values. Nothing is stopping us from base 10, or 100, time except convention.
[deleted] ยท 1 points ยท Posted at 11:24:26 on May 26, 2016 ยท (Permalink)
It's not the earth we have to change, but our way of counting time passing. You have to keep in mind that even with 10 hour days, it doesn't change the minutes or seconds.
1 hour = 60 minutes.
1 minutes = 60 seconds.
86400s in 24 hours. We could make one minute 100 seconds long, and an hour 100 minutes long, but then we would only have 8,64 hours in a day.
What if we change what a second is instead? Lets say we use the new Second (nS), which is slightly faster than the old second, so there is 100 000 seconds in a day (that way there would be 10 hours per day), the new second would be ca. 1,157 times faster than the old second.
The reason we count time as we dose is because of historical reasons and some old mathematics using 60 as a base (which is also why there is 360 (or 60x6) degrees in a circle. And changing it would mean changing all clocks, time measuring equipment we have worldwide. It could be done, but so far no one has agreed or suggested doing that.
itz4mna ยท -2 points ยท Posted at 21:37:04 on May 25, 2016 ยท (Permalink)
You'd have to be pretty awful at maths to not be able to realise 122 is 144 and therefore a square foot is 144 square inches. If people were taught from primary school how to do it they'd have no problem, I mean for most of our history we used ยฃsd money which is arguably harder to work with than feet and inches.
hugglesthemerciless ยท 2 points ยท Posted at 21:51:13 on May 25, 2016 ยท (Permalink)
Simplified the example, point being our number system is base 10 so it's a lot more intuitive for people to also do measurements in base 10.
You'd also be surprised by just how bad people are at math this side of the pond
DMAredditer ยท 1 points ยท Posted at 01:25:28 on May 26, 2016 ยท (Permalink)
Lol, look at international tests and you'll see generally Europe is ahead of the US, by quite a gap as well.
[deleted] ยท 1 points ยท Posted at 11:29:01 on May 26, 2016 ยท (Permalink)
I think he was talking about people in US being bad at math, as in agreeing with you.
[deleted] ยท 3 points ยท Posted at 21:39:56 on May 25, 2016 ยท (Permalink)
All of those are only related to what you are used to. I can just as easily figure out how long a trip somewhere will take based on kilometers because I'm used to that. Using multiple units for the same thing is very counter productive.
Ouroboron ยท 2 points ยท Posted at 00:38:14 on May 26, 2016 ยท (Permalink)
And where I live, we talk about distance in time. I don't live thirty miles away from my parents. I live about forty five minutes away from them. Oh*o is about an hour away. I lived about fifteen minutes from school on my bike.
omniscient_glutton ยท 2 points ยท Posted at 00:08:48 on May 26, 2016 ยท (Permalink)
You're argument here is largely based on life experience. It's measures you have used for a long time that are familiar and comfortable to you.
I've grown up exclusively with metric measures. These are natural second nature to me.
Why divide your hour up to a third to get one mile? My average walking speed is pretty much bang on 5km/h. 1km every 12min. My car at 100km/h will cover 25km in a quarter hour. My point being that we can all find nice points on both scales that work for us in our everyday life, but these do not contribute to an effective argument for or against.
As it happens I quite like imperial. There's an extra mouth full in each beer pint :)
Shadesbane43 ยท 1 points ยท Posted at 21:07:50 on May 25, 2016 ยท (Permalink)
Thank you for explaining the way England uses the Imperial system. I always knew you guys used a sort of mix, but wasn't sure if it was just because of everybody around you using Metric. As an American, I recognize how much better the Metric system is in scientific applications, but all we've got over here are 2L bottles of soda.
Interesting with the stone measurement too. Over here we just use pounds for everything.
itz4mna ยท 4 points ยท Posted at 21:10:44 on May 25, 2016 ยท (Permalink)
No worries! Stone's only really used for body weight, I think it's from agriculture but that's all metric now. Most stuff's either given in kilograms or pounds depending on what you're buying and who you're asking.
computeraddict ยท -4 points ยท Posted at 20:36:43 on May 25, 2016 ยท (Permalink)
Good thing we have computers and "ease of unit conversion" is kind of a moot selling point! The Imperial System has survived the ages in which it might have been killed, sorry.
Also, it has nothing to do with what area you choose for a piece of paper, which will likely never be subject to unit conversions.
bearsnchairs ยท -2 points ยท Posted at 21:53:34 on May 25, 2016 ยท (Permalink)*
Edit 2: I will buy reddit gold for anyone who can show a relationship between degrees Celsius and another SI dimensional base unit!
What is the relationship between Celsius and other SI units like: meters, liters, kilograms? There isn't one.
And I'm a chemist and use SI every day.
Edit: instead of downvoting I'd really like people to think back to their high school education. The dimension of temperature is not relatable to mass or length. Nor the other four base dimensions of current, luminosity, time, or moles.
Celsius came 50 years before the base ten metric system and 200 years before the SI system was codified...
wordserious ยท 4 points ยท Posted at 22:02:06 on May 25, 2016 ยท (Permalink)
Oh yes, there is, and this is exactly the point:
Source: this thread with contributions from /u/MartinSchou, /u/koshgeo, and myself.
jkelleyrtp ยท 2 points ยท Posted at 02:50:05 on May 26, 2016 ยท (Permalink)
I believe his point is that technically there isn't a better reason as to why water is used other than it being what we use. It's better than most options but still arbitrary.
bearsnchairs ยท 1 points ยท Posted at 04:03:24 on May 26, 2016 ยท (Permalink)
That is close to my point. Celsius/centrigrade has no connection to the other units/dimensions in SI, no temperature scale does. But apparently you can't point that out without people getting mad.
Aussierotica ยท 1 points ยท Posted at 09:33:54 on May 26, 2016 ยท (Permalink)*
If you took your Newton of force, and a gram of water, then moved the water over a distance of 4.182 metres (at NIST Standard Temperature and Pressure, and with zero losses other than into the water), you have raised the temperature of the water by 1 degree celsius (and expended 4.182 J, and 1 cal).
Take this interval and take 20 away from the starting temperature. You now have water's freezing point. Multiply the interval by 100 and add to the water's freezing point, and you now have boiling (at the NIST standard pressure). Take this 0-100 scale, and you now have Celsius.
EDIT -
An alternative is to climb vertically in the atmosphere until you reach the base of a cloud. For every hundred metres of altitude gain inside a cloud, the ambient temperature will drop 0.5 degrees Celsius (moist adiabatic lapse rate). Alternatively, if you are in a desert at sea level in the middle of summer (so a really dry air parcel above you), you will lose 0.98 degrees Celsius per 100 metres of altitude gain (dry adiabatic lapse rate).
Of course, if we're being entirely consistent, it's an effect of pressure, but altitude is much easier to measure given our starting point of derived values.
bearsnchairs ยท -5 points ยท Posted at 22:07:56 on May 25, 2016 ยท (Permalink)*
That didn't address what I asked at all and some of that is wrong. Do you really think I didn't know how distance, area, and volume are related?
How is Celsius related to any of the other units? That is what I wanted to know.
One liter of water is only 1 kg at 4 ยฐC.
Southforwinter ยท 0 points ยท Posted at 21:16:17 on May 25, 2016 ยท (Permalink)
It would, if American paper sizes used the 1:โ2 aspect ratio, instead the aspect ratio of American paper alternates with each size, which is silly.
dharmadhatu ยท 2 points ยท Posted at 21:25:28 on May 25, 2016 ยท (Permalink)
Of course, it would work just as well for standard (1 sq ft, 1/2 sq ft, 1/4 sq ft, ...).
HughManatee ยท 1 points ยท Posted at 01:16:17 on May 26, 2016 ยท (Permalink)
Really has nothing to do with the system of measurement.
ScrewAttackThis ยท 1 points ยท Posted at 03:26:02 on May 26, 2016 ยท (Permalink)
Am I just crazy or does this have nothing to do with metric? It works so well because of the ratio, not the units.
datbooty12 ยท 0 points ยท Posted at 23:47:55 on May 25, 2016 ยท (Permalink)
There's a list of countries that use the Metric system. Then there's the list of countries with Successful Mars landings...
Bmandk ยท 12 points ยท Posted at 17:15:42 on May 25, 2016 ยท (Permalink)
The metric system is generally beautiful
bearsnchairs ยท 16 points ยท Posted at 17:41:16 on May 25, 2016 ยท (Permalink)
It isn't the metric system... it is ISO.
imGnarly ยท 9 points ยท Posted at 17:32:08 on May 25, 2016 ยท (Permalink)
And yet Americans won't use it, just like with the metric system. Why won't they like math perfection?
blackn1ght ยท 3 points ยท Posted at 21:11:39 on May 25, 2016 ยท (Permalink)
TIL Americans don't use A4.
bearsnchairs ยท 0 points ยท Posted at 17:43:11 on May 25, 2016 ยท (Permalink)*
Our paper sizes work the same way...letter is half the size of
legalledger and so onThese are the US printing paper sizes.
A: 8.5" x 11" (letter)
B: 11" x 17"
C: 17" x 22"
D: 22" x 34"
E: 34" x 44".
Each one is half the size of the next one.
https://en.wikipedia.org/wiki/Paper_size?wprov=sfla1
realzealman ยท 12 points ยท Posted at 17:58:12 on May 25, 2016 ยท (Permalink)
it kinda doesn't work tho. a standard architectural drawing size is 24x36, and a true half scale of that is a 12x18, which is a non-standard paper size. A1 to A3 scales perfectly.
bearsnchairs ยท 4 points ยท Posted at 18:05:48 on May 25, 2016 ยท (Permalink)*
Do people do architectural drawings on printing paper? I know nothing about that. Also the dimensions you listed aren't ANSI standard anyways, so it isn't surprising that half of a non-standard size is also non-standard.
imGnarly ยท 5 points ยท Posted at 18:45:21 on May 25, 2016 ยท (Permalink)
Yes. I work with architects and they'll do architectural drawings everywhere.
bearsnchairs ยท 2 points ยท Posted at 18:52:46 on May 25, 2016 ยท (Permalink)
According to Wikipedia there are non ANSI architectural standards that are used for their drawing paper.
imGnarly ยท 2 points ยท Posted at 19:05:42 on May 25, 2016 ยท (Permalink)
I was just kidding, but as a civil engineer I can tell you that the common practice is to use 60x90cm to print blueprints, at least the ones we handled to our clients. The ones we used for revision were mostly A5 sized.
fournameslater ยท 5 points ยท Posted at 19:19:45 on May 25, 2016 ยท (Permalink)
PC LOAD LETTER
ChiefFireTooth ยท 1 points ยท Posted at 18:53:49 on May 25, 2016 ยท (Permalink)
Yup. Exactly the same as the metric system. Super logical and easy to remember!
It sounds like you've never seen a piece of legal size paper.
bearsnchairs ยท 1 points ยท Posted at 18:57:08 on May 25, 2016 ยท (Permalink)
But those paper standards are ISO, not SI... Quick what are the dimensions of an A0 sheet without looking it up?
ChiefFireTooth ยท 3 points ยท Posted at 21:25:31 on May 25, 2016 ยท (Permalink)
I think you missed what I was saying, which is that legal paper is most definitely not twice the area as letter size.
bearsnchairs ยท 2 points ยท Posted at 21:27:31 on May 25, 2016 ยท (Permalink)
Good catch, I meant ledger size, not legal.
[deleted] ยท 1 points ยท Posted at 20:12:22 on May 25, 2016 ยท (Permalink)
16* the dimensions of A4 so about.
21cm16 30cm16
Thing is because of how ISO paper works I never need to know the sizes. I just double or half the sizes I'm familiar with.
bearsnchairs ยท 1 points ยท Posted at 20:17:16 on May 25, 2016 ยท (Permalink)
4 times actually. My point is that the ISO scaling has nothing to do with the SI base ten system.
And if you forgot my original point it is the same with the ANSI system. Double the width to get the new length.
atyon ยท 1 points ยท Posted at 22:42:48 on May 25, 2016 ยท (Permalink)
It can't be the same system, because the DIN/ISO system only works with a ratio of 1:โ2. With any other ratio, you can't repeatedly fold the paper to get two of the next smaller size.
If your aspect ratio isn't 1:โ2, folding just once will change the ratio.
bearsnchairs ยท 1 points ยท Posted at 22:46:33 on May 25, 2016 ยท (Permalink)
I never claimed it was...Just that the 1/2x relationship with area also holds in ANSI printing sizes.
atyon ยท 1 points ยท Posted at 23:01:40 on May 25, 2016 ยท (Permalink)
Ah, the confusion starts because you talked about letter and legal, which have none of these properties.
The ANSI series (containing letter and ledger, but not legal) is actually interesting, because it alternates between two different ratios. Which isโฆ kinda neat, but not the same.
grodgeandgo ยท 0 points ยท Posted at 17:46:50 on May 25, 2016 ยท (Permalink)*
bearsnchairs ยท 0 points ยท Posted at 17:54:30 on May 25, 2016 ยท (Permalink)
Are you serious? I just told you.
[deleted] ยท -1 points ยท Posted at 17:59:24 on May 25, 2016 ยท (Permalink)*
[deleted]
bearsnchairs ยท 1 points ยท Posted at 18:04:35 on May 25, 2016 ยท (Permalink)
But that isn't what we're talking about right now...
The comment that spawn this specific thread was how international sheets are half the size of the preceding sheet.
There is no wasted space stacking letter on legal either. 8.5 x 11 and 11 x 17.
King_of_Avalon ยท 4 points ยท Posted at 18:40:50 on May 25, 2016 ยท (Permalink)
But that's not the point of ISO. The A-series sheets never change aspect ratio, meaning you can scale them up and down without any losses or distortions. However, going from 8.5x11 to 11x17 changes the aspect ratio, meaning that if you enlarge or reduce, either the image will be distorted or you will have blank spaces along one side.
For this reason, most photocopiers in the rest of the world have an 'A3->A4' button, useful for shrinking two pages of an A4 book side by side to fit on one sheet of A4 with no cropping or stretching. That is the whole point of maintaining the 1:sqrt2 aspect ratio
bearsnchairs ยท 3 points ยท Posted at 18:45:33 on May 25, 2016 ยท (Permalink)
That is true, but I wasn't addressing that just the halving. Every two steps in ANSI has the same aspect ratio though.
I haven't had to photocopy and shrink enough things for a function like that too be useful, and with computer printer scaling it isn't an issue at all.
[deleted] ยท 1 points ยท Posted at 18:24:32 on May 25, 2016 ยท (Permalink)
I read that in Peter Griffin's voice.
DrummerVim ยท 2 points ยท Posted at 19:00:13 on May 25, 2016 ยท (Permalink)
Well that makes me feel smart. :(
[deleted] ยท 1 points ยท Posted at 19:39:15 on May 25, 2016 ยท (Permalink)
Offense, none meant.
DrummerVim ยท 1 points ยท Posted at 20:03:26 on May 25, 2016 ยท (Permalink)
To be honest, not sure who I'd rather be from the Family Guy guys.
Lythor ยท 1 points ยท Posted at 20:46:47 on May 25, 2016 ยท (Permalink)
lol, a sudden orange comment :P
DrummerVim ยท 1 points ยท Posted at 21:03:11 on May 25, 2016 ยท (Permalink)
Orange you glad I'm in your friends list?
Lythor ยท 1 points ยท Posted at 21:08:44 on May 25, 2016 ยท (Permalink)
"get out"
DrummerVim ยท 1 points ยท Posted at 21:19:05 on May 25, 2016 ยท (Permalink)
You can't lock up the puns.
Lythor ยท 1 points ยท Posted at 21:20:23 on May 25, 2016 ยท (Permalink)
A great, strong and powerful woman probably can
rylnalyevo ยท -8 points ยท Posted at 16:00:51 on May 25, 2016 ยท (Permalink)*
The US paper sizes work as follows:
A: 8.5" x 11" (letter)
B: 11" x 17"
C: 17" x 22"
D: 22" x 34"
E: 34" x 44"
If you fold a size B sheet in half, the result measures 8.5" x 11". This works for each of the larger sheets as well,
making it far easier to stack multiple sheet sizes neatly than would be the case for the metric sizes.Edit: found a better source showing it works for metric sizes too.
-KR- ยท 8 points ยท Posted at 16:07:12 on May 25, 2016 ยท (Permalink)
Um, no. It's exactly the same in ISO 216.
rylnalyevo ยท 2 points ยท Posted at 16:08:13 on May 25, 2016 ยท (Permalink)
I was just going by that figure posted above. I came out with 0.5 mm mismatches on some of the measurements.
Smithy2997 ยท 3 points ยท Posted at 16:12:57 on May 25, 2016 ยท (Permalink)
ISO 216 paper sizes are defined to the neared mm, so A4 is 210*297, then A5 is 148*210, and is rounded
Edit: damn you markdown, stealing my asterisks, and also, I'd imagine that the 0.5mm difference isn't much larger than the tolerances on manufacture either.
mormotomyia ยท 0 points ยท Posted at 17:38:21 on May 25, 2016 ยท (Permalink)
yeah but therefor we must give up on our freedom. cannot have nice units and freedom.
Angs ยท 4 points ยท Posted at 17:42:40 on May 25, 2016 ยท (Permalink)
And a single A4 sheet of regular 80g/m2 paper will weight about 80g/16=5g. Might be useful when calculating postage prices.
TleilaxTheTerrible ยท 4 points ยท Posted at 17:14:44 on May 25, 2016 ยท (Permalink)
And the B sizes follow a similar pattern, with B0 being โ2 m on the long side and 1 m on the short side, with subsequent sizes halving in size every step.
Pilotted ยท 8 points ยท Posted at 15:46:49 on May 25, 2016 ยท (Permalink)*
Not quite. Your Ax = 1/2x m2 doesn't quite work for the A3 there. Although you have "basically"EDIT: I'm a dumbass.
CrapKnees ยท 11 points ยท Posted at 15:51:52 on May 25, 2016 ยท (Permalink)
But it does though.
Pilotted ยท 12 points ยท Posted at 15:55:26 on May 25, 2016 ยท (Permalink)
Aw fuck exponents not multiplication. I'm just being dense this morning. Good look my dude.
198jazzy349 ยท 6 points ยท Posted at 17:41:06 on May 25, 2016 ยท (Permalink)
Props for owning it. :-) and an upvote for your worthless karma!
markjs ยท 3 points ยท Posted at 15:54:24 on May 25, 2016 ยท (Permalink)
How does it not work for A3? The caveat is that the official A0 size has the lengths rounded to the nearest millimetre and the other sizes are then deduced from that. The formula gives a fairly accurate number but it gets less accurate the smaller the paper size.
Pilotted ยท 6 points ยท Posted at 15:59:04 on May 25, 2016 ยท (Permalink)
No no I'm just an idiot this morning. You're all good my man.
jf908 ยท 4 points ยท Posted at 15:55:08 on May 25, 2016 ยท (Permalink)
But 23 = 8
Pilotted ยท 5 points ยท Posted at 15:58:34 on May 25, 2016 ยท (Permalink)
Yeah yeah. Apparently I forget how to do exponents when I sleep in. I was thinking just straight multiplication and that A3 would equal 1/6 m2.
jf908 ยท 3 points ยท Posted at 16:31:33 on May 25, 2016 ยท (Permalink)
Happens to the best of us
PrrrromotionGiven ยท 2 points ยท Posted at 17:31:31 on May 25, 2016 ยท (Permalink)
Well, once you have the first size (A0, that is, or any other one. It doesn't matter), you can confirm just visually that the surface area halves each time you increase the number, and therefore doubles each time you decrease it.
san_salvador ยท 2 points ยท Posted at 19:27:05 on May 25, 2016 ยท (Permalink)
Live by the DIN, die by the DIN!
Bramthedev ยท 1 points ยท Posted at 18:26:53 on May 25, 2016 ยท (Permalink)
O really? what about A(-1) area?
Didn't think of that, did you, Einstein!
markjs ยท 1 points ยท Posted at 20:55:18 on May 25, 2016 ยท (Permalink)
Firstly, the maths still checks out fine with a value of -1:
1/2-1 = 1/0.5 = 2 m2
Secondly, the size above A0 is 2A0 (and then 4A0).
So maybe I (or the people that designed the system) did think about that ;)
MasterFubar ยท 1 points ยท Posted at 18:44:11 on May 25, 2016 ยท (Permalink)
One should add that this rule also defines the proportions of the sides.
In order to keep the same aspect when cut in half, the sizes have a sqrt(2) / 1 aspect ratio.
For instance, A4 is 210 mm x 297 mm. A3 is 420 mm x 297 mm. To get the dimensions of the next bigger size, multiply the smallest side by 2.
All I memorized is the A4 dimensions, from those I can get the dimensions of any other size in the A series.
anonymousme712 ยท 1 points ยท Posted at 19:34:33 on May 25, 2016 ยท (Permalink)
Yeah! We had a printing paper business and we used to supply materials to the printing press in the area. We used to have 1meter iron racks in the shop to store reams of paper. A sheet from the ream of paper would get you 4 A/4 size papers.
CKyle22 ยท 1 points ยท Posted at 20:15:21 on May 25, 2016 ยท (Permalink)
Are there paper sizes larger than A0? What's the notation in that case?
markjs ยท 1 points ยท Posted at 20:55:59 on May 25, 2016 ยท (Permalink)
2A0 and then 4A0. Self explanatory how they work.
stm2a ยท 1 points ยท Posted at 20:21:35 on May 25, 2016 ยท (Permalink)
Is there an A-1 piece of paper?
markjs ยท 1 points ยท Posted at 20:56:21 on May 25, 2016 ยท (Permalink)
Double the size of A0 is known as 2A0 (and next up, 4A0).
Southforwinter ยท 1 points ยท Posted at 21:14:35 on May 25, 2016 ยท (Permalink)
And finally, each B, C, and D size sits at 1/4, 1/2 and 3/4 of the way between the corresponding pair of A sizes. This means that folded A1 paper fits easily in a B1 envelope, B1 paper in a C1 envelope and so on.
samuelmackson ยท 1 points ยท Posted at 22:47:22 on May 25, 2016 ยท (Permalink)
The formula should be 1/2x I think man
Harbinger2001 ยท 1 points ยท Posted at 23:25:42 on May 25, 2016 ยท (Permalink)
This was done to have zero waste when making paper sizes. Just manufacture A0 and you can make any other size. US sizes lead to a lot of waste and has to be pulped and recycled.
Still, A4 and A5 sure feels weird to read.
hazily ยท 1 points ยท Posted at 05:51:54 on May 26, 2016 ยท (Permalink)
By the same logic A0 has infinite size? Since 1/(2x0) = Inf...
markjs ยท 1 points ยท Posted at 06:19:29 on May 26, 2016 ยท (Permalink)
It's 2 to the power of x. And 2 to the power of 0 is 1.
boarhog ยท 1 points ยท Posted at 08:33:08 on May 26, 2016 ยท (Permalink)
Also, international envelope sizes, the so called C sizes will fit corresponding A paper.
C4 is for A4, C5 is for A5 and so on. I don't think there is a C0 envelope though.
ShiningRaven ยท 1 points ยท Posted at 08:34:11 on May 26, 2016 ยท (Permalink)
Only, it doesn't work with A0, which is not 0 m2 ;)
The_Farting_Duck ยท 0 points ยท Posted at 15:56:00 on May 25, 2016 ยท (Permalink)
So, shouldn't A3 = 1/6 m2 ?
markjs ยท 4 points ยท Posted at 15:57:45 on May 25, 2016 ยท (Permalink)
No it is 2 to the power of x. So 2x2x2x2... x times. So 2 to the power of 3 (denoted as 23 ) is 2x2x2 = 8.
bearsnchairs ยท 1 points ยท Posted at 18:33:00 on May 25, 2016 ยท (Permalink)
If you're reading on an app it might show the formatting wrong.
nothing_clever ยท 0 points ยท Posted at 17:19:23 on May 25, 2016 ยท (Permalink)
What the fuck. Who had enough time on their hands to work some beautiful math into the size of paper?
Zweiffel ยท 1 points ยท Posted at 17:58:50 on May 25, 2016 ยท (Permalink)
Apparently this guy
nothing_clever ยท 1 points ยท Posted at 18:55:04 on May 25, 2016 ยท (Permalink)
Somehow I am not remotely surprised he was German.
IrishPrime ยท 0 points ยท Posted at 18:27:24 on May 25, 2016 ยท (Permalink)
Damn it, they even have metric paper?
Come on, America; Europe is making us look like fools out there!
Peregrine7 ยท 1161 points ยท Posted at 14:49:54 on May 25, 2016 ยท (Permalink)
For those who don't get it, here's an image
scottishdrunkard ยท 69 points ยท Posted at 15:19:42 on May 25, 2016 ยท (Permalink)
Wait, why are "legal" A4 and "letter A4" different?
ohitsasnaake ยท 276 points ยท Posted at 15:22:15 on May 25, 2016 ยท (Permalink)
They're not, those are the US legal and letter paper sizes, drawn for comparison. There is just one A4.
scottishdrunkard ยท 12 points ยท Posted at 15:30:22 on May 25, 2016 ยท (Permalink)
Oh, thanks fir the explanation.
MaximaFuryRigor ยท 41 points ยท Posted at 15:46:24 on May 25, 2016 ยท (Permalink)*
FYI, letter is slightly wider and shorter than A4.
If you travel abroad with a North American duo-tang or folder, A4 paper WILL stick out the top. You'll be the laughing stock of all your European friends, I tell you!!
Edit: Apparently no one knows what a duo-tang is...
SirNoName ยท 13 points ยท Posted at 16:16:53 on May 25, 2016 ยท (Permalink)
Er...what's a Duo-tang?
[deleted] ยท 11 points ยท Posted at 18:26:16 on May 25, 2016 ยท (Permalink)*
[deleted]
b4b ยท 2 points ยท Posted at 21:58:16 on May 25, 2016 ยท (Permalink)
Sounds like some chinese food
MaximaFuryRigor ยท 4 points ยท Posted at 17:29:03 on May 25, 2016 ยท (Permalink)
http://whatsdifferentincanada.tumblr.com/post/52061906901/duo-tangs
insane_contin ยท 4 points ยท Posted at 17:38:25 on May 25, 2016 ยท (Permalink)*
Holy shit, I though duo-tang's where common everywhere.
Damn it, I was looking through that tumblr and just learned there's gonna be a new area code in my area. Now I have to remember 3 sets of numbers.
MaximaFuryRigor ยท 2 points ยท Posted at 18:25:41 on May 25, 2016 ยท (Permalink)
Yeah, my province just got a second one a few years back. Though I still haven't seen any numbers that use it.
casey12141 ยท 1 points ยท Posted at 21:57:40 on May 25, 2016 ยท (Permalink)
Teachers used to call them that in southestern PA, USA, which is pretty far from Canada
superiority ยท 1 points ยท Posted at 05:56:27 on May 26, 2016 ยท (Permalink)
In my country, there are five area codes: 3, 4, 6, 7, & 9.
(There are also the mobile phone area codes: 21, 22, 27, & 28.)
kappaislove ยท 1 points ยท Posted at 09:24:40 on May 26, 2016 ยท (Permalink)
We have them in the Netherlands although we call them differently.
dexr23 ยท 1 points ยท Posted at 16:20:14 on May 25, 2016 ยท (Permalink)
two people do tango. isn't it obvious?
ohitsasnaake ยท 4 points ยท Posted at 18:07:19 on May 25, 2016 ยท (Permalink)
Also annoying when one wants to print pdf files laid our for letter on A4 paper (printers tend to be able to handle both, but I'm not sure letter-size paper is easily/cheaply available outside the US). The whole page will probably end up scaled down a bit so that it fits horizontally, and then you also end up with extra large white areas at the top and bottom of the page.
MaximaFuryRigor ยท 6 points ยท Posted at 18:28:17 on May 25, 2016 ยท (Permalink)
omg yes. The fact that it then centres it vertically just looks that much more unprofessional.
I'd rather it align to the top and have all the extra white space at the bottom, but it takes so much finicking to do that.
[deleted] ยท 2 points ยท Posted at 22:58:39 on May 25, 2016 ยท (Permalink)
To add to the fun, most of the world uses two-hole binders. Which are also incompatible with the US two-hole binders.
jamesaj23 ยท 1 points ยท Posted at 21:48:54 on May 25, 2016 ยท (Permalink)*
You are looking at for a map
MaximaFuryRigor ยท 2 points ยท Posted at 21:57:59 on May 25, 2016 ยท (Permalink)
Never heard that term before, but after a quick search, a manilla folder doesn't appear to require hole-punching, so no, I don't believe a duo-tang is the same thing.
Stingray88 ยท 0 points ยท Posted at 16:51:10 on May 25, 2016 ยท (Permalink)
wtf is that?
MaximaFuryRigor ยท 1 points ยท Posted at 17:28:59 on May 25, 2016 ยท (Permalink)
http://whatsdifferentincanada.tumblr.com/post/52061906901/duo-tangs
BacardiBatman11 ยท 11 points ยท Posted at 16:33:18 on May 25, 2016 ยท (Permalink)
Another reason the metric system makes more sense
[deleted] ยท 20 points ยท Posted at 16:45:39 on May 25, 2016 ยท (Permalink)
1:โ2 ratio paper could have been done with any measures and isn't a part of the metric system, but I do agree that it's has some advantages over US letter size.
i_am_useless_too ยท -5 points ยท Posted at 15:47:29 on May 25, 2016 ยท (Permalink)
C4 is da bomb
ohitsasnaake ยท 1 points ยท Posted at 18:13:32 on May 25, 2016 ยท (Permalink)
Ignoring your lameish joke (judging by personal taste and your downvotes), IIRC C4 is the envelope size that you can easily fit an A4 inside. C5 for A5 paper or A4s that have been folded in half are much more common though.
heliorm ยท 58 points ยท Posted at 15:22:40 on May 25, 2016 ยท (Permalink)
There is no A4 letter and A4 legal. The USA legal and letter formats were just overlaid on the graph for info.
karlexceed ยท 31 points ยท Posted at 16:37:45 on May 25, 2016 ยท (Permalink)
The real question is why the US doesn't just use A4 instead of letter
mcfandrew ยท 8 points ยท Posted at 20:09:03 on May 25, 2016 ยท (Permalink)
Because Marge in Accounting would shit a brick and vote twice for Trump if we forced sensible ideas like A(x) paper and metric measurements into her stupid antiquated "system."
illyndor ยท 18 points ยท Posted at 17:20:47 on May 25, 2016 ยท (Permalink)
To have the right paper for when your printer says to "PC load letter".
orthag ยท 4 points ยท Posted at 16:50:20 on May 25, 2016 ยท (Permalink)
We're a stubborn bunch.
KSPReptile ยท 2 points ยท Posted at 20:58:16 on May 25, 2016 ยท (Permalink)
Same reason why they don't use metric (for the most part that is).
Comrade-Napoleon ยท 2 points ยท Posted at 16:40:41 on May 25, 2016 ยท (Permalink)
They'll throw you in jail for using an A4 for letters, obviously
[deleted] ยท 11 points ยท Posted at 15:31:53 on May 25, 2016 ยท (Permalink)
Holy fucking shit. I work with paper a lot and this image made all of these sizes click. Before, I'd just basically remembered proportions and the ratios of each paper relative to each other. Looking at the odd/even numbering - how in the fuck did I not notice this sooner?
I should say that I just kinda landed in a position that dealt with a lot of printing, so I never had an training in it. Just self-taught. And this is why being self-taught sucks. heh
gerryn ยท 10 points ยท Posted at 17:50:41 on May 25, 2016 ยท (Permalink)
Most likely because you are not thinking by default in metric. Everything in metric makes sense, not so much with imperial.
Toppo ยท 3 points ยท Posted at 18:32:21 on May 25, 2016 ยท (Permalink)
A-sizes are independent of metrics though, and only the size of A0 fits nicely to metric measurements. The same principle could be used with inches too.
gerryn ยท 2 points ยท Posted at 19:19:59 on May 25, 2016 ยท (Permalink)
Ah, good point. The cm measurement of an A4 for example are not "uniform" as one would see it.
The A4 size print measures 21.0 x 29.7cm, 8.27 x 11.69 inches
Doesn't fit into the "niceness" of 100, 10, 1, etc. Very true - I was mistaken. Thanks for your post.
Peregrine7 ยท 2 points ยท Posted at 01:26:17 on May 26, 2016 ยท (Permalink)
A0 is one square meter, dividing down the dimension of the paper is still designed with utility in mind, rather than pure mathematics, because this is a situation where usability is more important than keeping to metrics.
So the area of each page is exactly half of the A before it, meaning they're easy to cut, and the dimension of the page is designed with usability, text count, and margins factored in.
gerryn ยท 1 points ยท Posted at 01:30:21 on May 26, 2016 ยท (Permalink)
Yup, for me it makes perfect sense, it just doesn't translate to the uniformality (yeah, I just made that word up) of metric - 100 10 1 :) I have no idea how feet, inches and shit work, all I know is how much 14 inches is, or 20 inches, or 27, from monitor sizes :D
Peregrine7 ยท 2 points ยท Posted at 01:40:05 on May 26, 2016 ยท (Permalink)
*Uniformity :)
Yeah, it's not part of metric. After all, it's paper, not a scientific unit.
And yeah, me too on inches and feet. 12 inches in a foot... 3 feet in a yard... a yard is about a meter.... fuck it I'm using metric.
gerryn ยท 1 points ยท Posted at 01:49:25 on May 26, 2016 ยท (Permalink)
:)
oh_no_aliens ยท 5 points ยท Posted at 16:11:19 on May 25, 2016 ยท (Permalink)
A0 is MASSIVE. I've seen one, but forgot what they were used for.
Pm_me_any_dragon ยท 7 points ยท Posted at 16:37:25 on May 25, 2016 ยท (Permalink)
Mostly for plotting complex machinery.
Altough you may even need multiple a0 papers to plot the very complex stuff (eg. A cpu)
https://en.wikipedia.org/wiki/Plotter
Mizzet ยท 4 points ยท Posted at 17:34:47 on May 25, 2016 ยท (Permalink)
Architectural drafting for one, and for large format posters/presentation boards. Printed my fair share and they still seem huge to me.
gostan ยท 3 points ยท Posted at 18:22:29 on May 25, 2016 ยท (Permalink)
A0 is used a lot for science posters
Frexxia ยท 2 points ยท Posted at 17:29:18 on May 25, 2016 ยท (Permalink)
I've used A0 for posters before.
[deleted] ยท 1 points ยท Posted at 20:34:18 on May 25, 2016 ยท (Permalink)
I use them at work for connection schematics. A system overview of a ship requires space.
Zweiffel ยท 4 points ยท Posted at 17:48:15 on May 25, 2016 ยท (Permalink)
or watch this video
[deleted] ยท 4 points ยท Posted at 16:20:54 on May 25, 2016 ยท (Permalink)
Ah, the golden ratio appears in nature once again.
absentbird ยท 4 points ยท Posted at 19:41:35 on May 25, 2016 ยท (Permalink)
That's not the golden ratio and not in nature but other than that you are correct.
ric2b ยท 2 points ยท Posted at 18:49:42 on May 25, 2016 ยท (Permalink)
nature
jdovew ยท 1 points ยท Posted at 15:40:52 on May 25, 2016 ยท (Permalink)
I worked in a print shop for 3 years and never realized this...
[deleted] ยท 1 points ยท Posted at 15:54:20 on May 25, 2016 ยท (Permalink)
Wait. So there is no legal size is this system?
wordserious ยท 8 points ยท Posted at 16:14:20 on May 25, 2016 ยท (Permalink)
No, and the rest of the world doesn't miss it.
EDIT: actually, there's no letter either. A4 is the closest approximation of both.
jaulin ยท 1 points ยท Posted at 18:34:20 on May 25, 2016 ยท (Permalink)
When is the legal size even used? It looks awkwardly long compared to its width. Also the difference between it and letter is so small anyway.
Peregrine7 ยท 2 points ยท Posted at 01:37:34 on May 26, 2016 ยท (Permalink)
It is awkwardly long, it's also a half cut of an incredibly common dimension of paper (foolscap) that was used in the 1500's onwards. Like most imperial things, it was chosen by chance and then used in the legal system until it became the norm. Because of the sheer number of legal documents written in legal size from then onwards, legal size was maintained in order to ensure backwards compatibility with previous documents, amongst other reasons.
Beat_the_Deadites ยท 1 points ยท Posted at 16:59:41 on May 25, 2016 ยท (Permalink)
Ok, so this fits in well with the overall logic/simplicity of the metric system, with one exception: why are the A0 dimensions 1189 x 841 mm?
Why not 1414 x 1000, or 1000 x 707, or 1448 x 1024 so at least one of the numbers is a nice meter or easily divided by 2?
Edit: /u/markjs has the answer below, apparently 1189 x 841 mm gives you a total area of 1 square meter.
eddie_koala ยท 1 points ยท Posted at 17:22:51 on May 25, 2016 ยท (Permalink)
What about A9?
Mypopsecrets ยท 1 points ยท Posted at 17:45:39 on May 25, 2016 ยท (Permalink)
Except for legal sized paper apparently
thatssorelevant ยท 1 points ยท Posted at 18:15:55 on May 25, 2016 ยท (Permalink)
Oh god. I looked at this image so many times when I was a Graphic Design undergrad.
TheRoss23 ยท 1 points ยท Posted at 18:44:25 on May 25, 2016 ยท (Permalink)
so hamburger style, not hot dog.
Deto ยท 1 points ยท Posted at 18:45:33 on May 25, 2016 ยท (Permalink)
It's...so....beautiful!
KhabaLox ยท 1 points ยท Posted at 19:50:45 on May 25, 2016 ยท (Permalink)
That's Golden.
umbongo_ ยท 1 points ยท Posted at 21:31:05 on May 25, 2016 ยท (Permalink)
Does that mean paper sizes are a geometric sequence?
bigb1 ยท 1 points ยท Posted at 23:49:42 on May 25, 2016 ยท (Permalink)
A2 is 420mm wide, but how high is it?
DrFegelein ยท 1731 points ยท Posted at 14:19:15 on May 25, 2016 ยท (Permalink)
I was so confused when I learned the US doesn't use the same paper size as the rest of the world. Why can't they be standard with anyone else on anything?
saxy_for_life ยท 1739 points ยท Posted at 14:32:11 on May 25, 2016 ยท (Permalink)
Don't you dare take away our 8.5x11
albe00 ยท 901 points ยท Posted at 14:51:10 on May 25, 2016 ยท (Permalink)
8.5 by 11 cm seems really small!
[deleted] ยท 139 points ยท Posted at 14:56:18 on May 25, 2016 ยท (Permalink)
It's fine, because it scales.
anorakofdreams ยท 16 points ยท Posted at 17:28:14 on May 25, 2016 ยท (Permalink)
When you fold it in half it doubles in size
blebaford ยท 2 points ยท Posted at 18:35:53 on May 25, 2016 ยท (Permalink)
in thickness you mean
Korlus ยท 5 points ยท Posted at 16:12:31 on May 25, 2016 ยท (Permalink)
Most people use wood pulp to make paper, not scales.
TheLoneExplorer ยท 1 points ยท Posted at 16:47:23 on May 25, 2016 ยท (Permalink)
I make paper using my scale all the time... my mom says i need to go on a diet.
DestinationVoid ยท 1 points ยท Posted at 22:08:38 on May 25, 2016 ยท (Permalink)
Is it web scale?
nissepik ยท 1 points ยท Posted at 22:56:20 on May 25, 2016 ยท (Permalink)
hehe americans cant get on scales theyll break
Sir_Illo ยท 1029 points ยท Posted at 15:00:49 on May 25, 2016 ยท (Permalink)
AMERICAN INCHES REIGN SUPREME YOU PLEBEIAN
DEATH BEFORE METRIC
/s
manly_lumberjack ยท 288 points ยท Posted at 15:07:11 on May 25, 2016 ยท (Permalink)
Give me standard or give me death
dwmfives ยท 34 points ยท Posted at 15:36:35 on May 25, 2016 ยท (Permalink)
If you insist. How would you prefer to die, sentenced to walk 10,000 miles with only 8 fl. ozs of water? To be dropped 100 yards with a 200 pound weight tied to your leg? To be buried 6 feet deep? To be burned in an oven set at 500 degrees....Fahrenheit?
HivemindRock ยท 13 points ยท Posted at 16:36:58 on May 25, 2016 ยท (Permalink)
The irony is, in a convoluted sort of way, you're giving him both.
dwmfives ยท 8 points ยท Posted at 16:39:00 on May 25, 2016 ยท (Permalink)
That's all freedom. If some dirty gypsie european wants to steal some freedom, they are FREE to do so.
uizanfagit ยท 2 points ยท Posted at 20:18:31 on May 25, 2016 ยท (Permalink)
What's the point in having a 200 lb weight attached to your legs? You won't fall faster...(I get its a joke but still)
humplick ยท 1 points ยท Posted at 20:30:59 on May 25, 2016 ยท (Permalink)
I was thinking the same thing! You'd still drop 300ft though, but it's not like the weight is adding any sort of danger.
xeronotxero ยท 1 points ยท Posted at 20:39:38 on May 25, 2016 ยท (Permalink)
If the weight was shaped in a way to have massive air resistance, maybe you would land first and then get crushed by it?
intangiblesniper_ ยท 6 points ยท Posted at 15:49:05 on May 25, 2016 ยท (Permalink)
Let them eat metric!
manly_lumberjack ยท 5 points ยท Posted at 16:40:07 on May 25, 2016 ยท (Permalink)
All 10cm of it
jeffbell ยท 9 points ยท Posted at 15:31:03 on May 25, 2016 ยท (Permalink)
The official US standard is metric.
You are thinking of US customary.
karlexceed ยท 2 points ยท Posted at 16:39:33 on May 25, 2016 ยท (Permalink)
Since 1988, I believe. And yet, here we are...
candycv30 ยท 19 points ยท Posted at 15:15:16 on May 25, 2016 ยท (Permalink)
Freedom Units!
AHucs ยท 7 points ยท Posted at 18:15:27 on May 25, 2016 ยท (Permalink)
I love the irony of calling them "Freedom Units". The reason they're called "Imperial" is because they were the standard units of the British Empire (although at the time of the AR I think they were still just called English units).
AHucs ยท 4 points ยท Posted at 18:15:28 on May 25, 2016 ยท (Permalink)
I love the irony of calling them "Freedom Units". The reason they're called "Imperial" is because they were the standard units of the British Empire (although at the time of the AR I think they were still just called English units).
Retrograde_Lectin ยท 2 points ยท Posted at 16:45:04 on May 25, 2016 ยท (Permalink)
Give me lithium or give me meth
fks_gvn ยท 2 points ยท Posted at 18:05:05 on May 25, 2016 ยท (Permalink)
COMMUNISTS DETECTED ON AMERICAN SOIL. LETHAL FORCE ENGAGED!
minimim ยท 2 points ยท Posted at 15:34:52 on May 25, 2016 ยท (Permalink)
So... metric? It's the standard.
ObitoUchiha41 ยท 1 points ยท Posted at 16:34:41 on May 25, 2016 ยท (Permalink)
Big_pekka ยท 1 points ยท Posted at 16:48:13 on May 25, 2016 ยท (Permalink)
1 gallon of death. Coming up.
thetate ยท 1 points ยท Posted at 20:04:10 on May 25, 2016 ยท (Permalink)
That was the Challengers motto too
wolfman92 ยท 1 points ยท Posted at 21:23:43 on May 25, 2016 ยท (Permalink)
"Standard"
Acupriest ยท 1 points ยท Posted at 22:33:40 on May 25, 2016 ยท (Permalink)
Use oz. instead of ml the next time you take a medicine. You'll almost certainly get your death.
throwaway_entreprene ยท 0 points ยท Posted at 15:15:20 on May 25, 2016 ยท (Permalink)
Metric System anyone?
Rappaccini ยท 0 points ยท Posted at 18:22:10 on May 25, 2016 ยท (Permalink)
Your terms are.... acceptable.
loads freedom shotgun of inconsistency
hoodie92 ยท 57 points ยท Posted at 15:51:31 on May 25, 2016 ยท (Permalink)
Also known as the Mars Orbiter approach.
Sir_Illo ยท 12 points ยท Posted at 16:00:16 on May 25, 2016 ยท (Permalink)
rip
mangamaster03 ยท 2 points ยท Posted at 21:12:52 on May 25, 2016 ยท (Permalink)
Harsh
fosterthechildren ยท 2 points ยท Posted at 18:31:03 on May 25, 2016 ยท (Permalink)
Oh shit, you went there.
[deleted] ยท 2 points ยท Posted at 21:44:32 on May 25, 2016 ยท (Permalink)
Renounces the empire; keeps imperial measurement system
You kept the worst thing about the empire. Good job.
xXTowelieXx ยท 2 points ยท Posted at 16:49:57 on May 25, 2016 ยท (Permalink)
DEATH IS A PREFERABLE ALTERNATIVE TO METRIC
Rubcionnnnn ยท 2 points ยท Posted at 17:15:46 on May 25, 2016 ยท (Permalink)
I see the sarcasm, but the american measurement system is actually great for engineering. You can divide measurements in half easier because it uses a binary like system. For example, in your head, take 1cm and divide it in half, then in half, and then in half again and what do you get?
1cm/2 = 5mm
5mm/2 = 2.5mm
2.5mm/2 = 1.25mm
1.25mm/2 = 0.625mm
0.625mm/2 = 0.3125mm
0.3125mm/2 = 0.15625mm
See how you start getting all these long numbers? Now take the good ol' American system and divide it in half.
1" /2 = 1/2
1/2" /2 = 1/4
1/4" /2 = 1/8
1/8" /2 = 1/16
1/16" /2 = 1/32
1/32" /2 = 1/64
Fellou ยท 3 points ยท Posted at 17:56:41 on May 25, 2016 ยท (Permalink)
Then you could say the same about dividing by 5 or 10 for metrics. The reason we use base 10 is that we write numbers that way.
Kered13 ยท 1 points ยท Posted at 22:05:22 on May 25, 2016 ยท (Permalink)
How often do you divide by 5? How often do you divide by 2?
We write in base 10 and that's bad enough, don't make us measure in base 10 as well.
Fellou ยท 1 points ยท Posted at 23:01:53 on May 27, 2016 ยท (Permalink)
I that base 10 is not the best base, 12 or 8 would be better. But what is wosre is having different bases in different things. That mean converting the numbers each time you do a calculus using different bases.
reytr0 ยท 6 points ยท Posted at 17:59:57 on May 25, 2016 ยท (Permalink)
Ummm.... if you really wanted to:
1cm /2 = 1/2cm
1/2cm /2 = 1/4cm
1/4cm /2 = 1/8cm
1/8cm /2 = 1/16cm
1/16cm /2 = 1/32cm
1/32cm /2 = 1/64cm
What's the difference?
Rubcionnnnn ยท 1 points ยท Posted at 19:12:58 on May 25, 2016 ยท (Permalink)
Because nobody measures like that. Tools like tape measures and wrenches will use 0.75mm rather than 3/4mm.
RabidRapidRabbit ยท -1 points ยท Posted at 18:21:56 on May 25, 2016 ยท (Permalink)
is it?
0,45359 / 0,0254ยฒ = ??? kg /mยฒ I mean WHAT
POUNDS PER SQUARE INCH YOU FUCKING WOT MATE
wakeupwill ยท 1 points ยท Posted at 19:00:46 on May 25, 2016 ยท (Permalink)
You already have them though.
cavilier210 ยท 1 points ยท Posted at 20:40:19 on May 25, 2016 ยท (Permalink)
I mean it without the sarcasm!
hookersandblackjack ยท 1 points ยท Posted at 06:16:09 on May 26, 2016 ยท (Permalink)
British*
Trumps_the_main_man ยท -4 points ยท Posted at 15:19:29 on May 25, 2016 ยท (Permalink)
Americans MUST stick with Standard. Too many of us are too stupid to change anything in their tiny little minds. Not all of us, just those who think that Donald Trump anything but a huckster out to destroy the nation with his racism and ignorance-is-cool kind of lifestyle.
Source: Ask a Trumpster if they'll switch to metric.
Sir_Illo ยท 3 points ยท Posted at 15:36:54 on May 25, 2016 ยท (Permalink)
I know you are just trolling but could you calm down a bit?
[deleted] ยท 2 points ยท Posted at 16:23:23 on May 25, 2016 ยท (Permalink)
I use metric all the time as a US Citizen. Give me 750mL of whiskey please.
12 ounces of beer?? Who the fuck measures liquid by weight?
Sir_Illo ยท 2 points ยท Posted at 16:42:00 on May 25, 2016 ยท (Permalink)
No not that portion. Metric is the better system, I was asking him to calm down in reference to his obviously inflammatory pro Trump rhetoric.
[deleted] ยท 3 points ยท Posted at 16:54:41 on May 25, 2016 ยท (Permalink)
I was actually responding to a comment way above ours. I don't like the way Reddit does this. The trees become far too branched and split in several areas. Hell, I don't even know who I was talking to. I just put my comment under yours so the single thread would continue outward rather than adding another split.
Ugh, I miss the days of forums where the next comment/post would simply fall below the one above it! :P
nivlark ยท 1 points ยท Posted at 18:20:21 on May 25, 2016 ยท (Permalink)
He's not actually saying that though:
i.e. unless you are anti trump, you are too stupid to learn metric. (His words not mine)
Trumps_the_main_man ยท 1 points ยท Posted at 16:41:40 on May 25, 2016 ยท (Permalink)
Why calm down? Why do you think it's trolling to point out to everyone, everywhere, that supporters of Trump are morons?
RabidRapidRabbit ยท -1 points ยท Posted at 18:17:42 on May 25, 2016 ยท (Permalink)
never will I calculate with psi again NEVER
For someone used to a real numeric system it's like rainbows per unicorn
0,45359 / 0,0254ยฒ = ??? kg /mยฒ I mean WHAT
cerettala ยท 7 points ยท Posted at 15:31:01 on May 25, 2016 ยท (Permalink)
I'm sorry that /u/saxy_for_life didn't convert it to "countries that haven't been to the moon" units.
And yes, I know, NASA uses the metric system....
[deleted] ยท 3 points ยท Posted at 16:59:23 on May 25, 2016 ยท (Permalink)
Just make that "countries that have been on the moon in the past 40 years" units.
cerettala ยท 2 points ยท Posted at 17:27:31 on May 25, 2016 ยท (Permalink)
I should have phrased it "put people on the moon"
Saoirse-on-Thames ยท 2 points ยท Posted at 06:34:46 on May 26, 2016 ยท (Permalink)
Also the fact that they weren't the first to put people in space, the first to have a spacecraft reach the surface on another planet, or create the first probe to return direct measurements from another planet's atmosphere. Getting to the moon was a seriously big achievement, but a lot of the other advancements of the time are often overlooked.
[deleted] ยท 2 points ยท Posted at 09:11:20 on May 26, 2016 ยท (Permalink)
The Soviets were also the first to put a spacecraft in orbit around the sun, the first to land a spacecraft on the moon (ten years before Apollo 11), the first to take pictures of the far side of the moon, the first to take pictures from the surface of the moon, the first to put a spacecraft in orbit around the moon, the first to put a remote-controlled vehicle on the moon, the first manned space station, etc.
Saoirse-on-Thames ยท 2 points ยท Posted at 18:22:06 on May 26, 2016 ยท (Permalink)
That's pretty impressive!
Apart from landing on the moon, what else was America first at, seeing as you seem to know a thing or two :) ?
[deleted] ยท 2 points ยท Posted at 20:33:44 on May 26, 2016 ยท (Permalink)
Pretty much everything related to space observatories and really long-range probes. You could make a very long list of "firsts" for either country.
bearsnchairs ยท 1 points ยท Posted at 17:22:15 on May 25, 2016 ยท (Permalink)
"Countries that haven't been on Mars or the outer solar system" units if that makes you happy.
[deleted] ยท 1 points ยท Posted at 23:01:25 on May 25, 2016 ยท (Permalink)
Don't forget the Nazi scientists. Now, put someone on the moon without Nazis and then I'll be impressed by your units.
[deleted] ยท 1 points ยท Posted at 09:14:17 on May 26, 2016 ยท (Permalink)
I'm pretty sure that no one has ever put anything on the moon without using Nazi rocket scientists.
railmaniac ยท 3 points ยท Posted at 18:20:51 on May 25, 2016 ยท (Permalink)
That's a ridiculous name for a unit system. The US uses imperial and Russia, India, China and Japan all use metric.
bearsnchairs ยท 2 points ยท Posted at 18:38:46 on May 25, 2016 ยท (Permalink)
The US does not use imperial, the British did. The British codified their system of measurements into the Imperial System after the Americans had codified their US Customary System. British Imperial units aren't even the same as US Customary units.
nivlark ยท 2 points ยท Posted at 18:21:19 on May 25, 2016 ยท (Permalink)
As do China and Russia (who have also been to the Moon)
cerettala ยท 3 points ยท Posted at 19:26:52 on May 25, 2016 ยท (Permalink)
Not in person.
shittylyricist ยท 2 points ยท Posted at 18:47:09 on May 25, 2016 ยท (Permalink)
Yes, but you make up for it in volume!
ThinkingCrap ยท 3 points ยท Posted at 15:05:11 on May 25, 2016 ยท (Permalink)
They don't know cm either tho
SKR47CH ยท 3 points ยท Posted at 15:46:45 on May 25, 2016 ยท (Permalink)
Feels good when measuring dick.
dishwiz ยท 2 points ยท Posted at 17:58:19 on May 25, 2016 ยท (Permalink)
What's this cm nonsense? We use Freedom Units over here.
Vairman ยท 2 points ยท Posted at 17:24:05 on May 25, 2016 ยท (Permalink)
maybe so but 8.5" x 11" sounds just perfect. And has a touch of freedom to it also. mmmmm.....
klparrot ยท 1 points ยท Posted at 16:59:52 on May 25, 2016 ยท (Permalink)
That's pretty close to C7.
ShutUpTodd ยท 1 points ยท Posted at 15:07:38 on May 25, 2016 ยท (Permalink)
It would be an unfortunate girth and length...
lwarB ยท 1 points ยท Posted at 15:26:59 on May 25, 2016 ยท (Permalink)
She said it was average... :(
swaldron ยท 0 points ยท Posted at 20:16:17 on May 25, 2016 ยท (Permalink)
There are two types of measurement systems. Metric, and THE ONE THAT PUT MAN ON THE MOON
tominsj ยท 17 points ยท Posted at 15:01:41 on May 25, 2016 ยท (Permalink)
Plus we have Tabloid AND legal!
QuineQuest ยท 9 points ยท Posted at 19:52:12 on May 25, 2016 ยท (Permalink)
And Government Letter (8x10.5). And Ledger (17x11 (same as tabloid, but on its side)). And Junior legal (8x5
tominsj ยท 4 points ยท Posted at 20:45:17 on May 25, 2016 ยท (Permalink)
Not to mention 9x12!
And Foolscap in 13 x 8!
roomandcoke ยท 2 points ยท Posted at 16:07:26 on May 25, 2016 ยท (Permalink)
A tabloid (I've always known it as ledger from my Staples Copy & Print Center days) cut in half makes a letter. At least we have that.
QuineQuest ยท 5 points ยท Posted at 19:54:03 on May 25, 2016 ยท (Permalink)
Tabloid and Ledger are completely different sizes. Tabloid is 17x11 inches, where as Ledger is 11x17 inches.
8andahalfby11 ยท 16 points ยท Posted at 16:33:19 on May 25, 2016 ยท (Permalink)
I'm not going anywhere...
AgentKuma ยท 16 points ยท Posted at 16:46:14 on May 25, 2016 ยท (Permalink)
Everything changed after 8.5x11.
drinks_antifreeze ยท 10 points ยท Posted at 18:02:30 on May 25, 2016 ยท (Permalink)
There's something so delightfully musical about the phrase "Eight-'n-a-half-by-eleven"
lagerbaer ยท 7 points ยท Posted at 16:16:09 on May 25, 2016 ยท (Permalink)
But that is so dangerously close to 9x11.
nickins ยท 24 points ยท Posted at 15:10:59 on May 25, 2016 ยท (Permalink)
We use the same in Canada (8.5x11) and I am NOT letting my paper go to some International Paper Overlord!
kcdwayne ยท 5 points ยท Posted at 15:05:07 on May 25, 2016 ยท (Permalink)
Freedom papers! Wait a minute...
fuckitimatwork ยท 1 points ยท Posted at 17:12:03 on May 25, 2016 ยท (Permalink)
fuck letter - legal master race
smfarrel ยท 1 points ยท Posted at 17:15:16 on May 25, 2016 ยท (Permalink)
Canadian here, 8.5 x 11 solidarity yo
arnedh ยท 1 points ยท Posted at 18:23:15 on May 25, 2016 ยท (Permalink)
Never forget! 8.5-11
deltablazing ยท 1 points ยท Posted at 22:36:20 on May 25, 2016 ยท (Permalink)
It's the best for paper airplanes by far.
Firewolf420 ยท 1 points ยท Posted at 01:03:37 on May 26, 2016 ยท (Permalink)
The size of freedom
Krombopulos_Mikhail ยท -7 points ยท Posted at 16:06:26 on May 25, 2016 ยท (Permalink)
8.5x11 is fucking awful. It's too short and way too wide.
fancyfilibuster ยท 9 points ยท Posted at 16:25:33 on May 25, 2016 ยท (Permalink)
It's less than 1/4 inch wider than a4
Krombopulos_Mikhail ยท -9 points ยท Posted at 16:27:53 on May 25, 2016 ยท (Permalink)
Which is a lot. It was enough to make transferring my resume over look like shit. It was a huge pain in the ass on most other documents too. It's a lot easier to present more information neatly and with good use of white space on A4.
latman ยท 1 points ยท Posted at 18:59:29 on May 25, 2016 ยท (Permalink)
Nah your resume looked like shit anyway
goldman60 ยท 1 points ยท Posted at 19:14:16 on May 25, 2016 ยท (Permalink)
My resume automatically scales, you just feed latex the paper size and render it to a PDF. You must just be a scrub.
AUGUST_BURNS_REDDIT ยท 9 points ยท Posted at 15:35:49 on May 25, 2016 ยท (Permalink)
Canada does.
antidense ยท 16 points ยท Posted at 15:00:45 on May 25, 2016 ยท (Permalink)
So we can have the PC LOAD LETTER error message.
[deleted] ยท 1 points ยท Posted at 15:07:46 on May 25, 2016 ยท (Permalink)*
[deleted]
Stingray88 ยท 3 points ยท Posted at 16:52:30 on May 25, 2016 ยท (Permalink)
You can swear on the internet buddy.
AUS_Doug ยท 149 points ยท Posted at 14:48:52 on May 25, 2016 ยท (Permalink)
Because Freedom Units
mr_lab_rat ยท 57 points ยท Posted at 15:10:46 on May 25, 2016 ยท (Permalink)
You realize these units come from an imperium you fought hard to separate from, no?
__Noodles ยท 87 points ยท Posted at 15:13:51 on May 25, 2016 ยท (Permalink)
Uh huh. And just like everything else we like, it's ours now.
tophermeyer ยท 28 points ยท Posted at 15:36:20 on May 25, 2016 ยท (Permalink)
Manifest Destiny bitches.
itz4mna ยท 3 points ยท Posted at 19:04:19 on May 25, 2016 ยท (Permalink)
Not really, we still use Imperial for a lot of things in the UK like the roads and pubs. If you ordered 50cl of beer or a 250g steak in a pub you'd get a funny look as well.
__Noodles ยท 1 points ยท Posted at 21:40:49 on May 25, 2016 ยท (Permalink)
Yea, it's weird that you still use miles as well. In this case UK really has no business in the Metric vs Best standards debate ;)
bearsnchairs ยท 0 points ยท Posted at 17:23:54 on May 25, 2016 ยท (Permalink)*
Actually they don't all. The US Customary units are very slightly different in value from British Imperial units.
ProgramTheWorld ยท 2 points ยท Posted at 15:36:44 on May 25, 2016 ยท (Permalink)
We must have enough fuel units!
[deleted] ยท 1 points ยท Posted at 21:45:45 on May 25, 2016 ยท (Permalink)
*imperial
escalat0r ยท 1 points ยท Posted at 22:36:41 on May 25, 2016 ยท (Permalink)
The most free countries use the metric system though, except for New Zealand.
[deleted] ยท 1 points ยท Posted at 16:02:31 on May 25, 2016 ยท (Permalink)
I heard Hillary supported moving to Metric!
th3davinci ยท 0 points ยท Posted at 16:56:10 on May 25, 2016 ยท (Permalink)
I like how it's called freedom units while the official lengths are the measures from a king...
[deleted] ยท 3 points ยท Posted at 18:10:26 on May 25, 2016 ยท (Permalink)
Interesting. I never knew. Henry I. Previously it was an average of the feet Of 16 random people walking out of church. Fascinating.
alumpoflard ยท 7 points ยท Posted at 15:03:28 on May 25, 2016 ยท (Permalink)
what about bullet sizes? Americans use ALL OF THEM
[deleted] ยท 10 points ยท Posted at 15:40:19 on May 25, 2016 ยท (Permalink)
Wait, fuck, what size paper does the rest of the world use?
splat313 ยท 31 points ยท Posted at 15:45:55 on May 25, 2016 ยท (Permalink)
The rest of the world uses 'A4' as their standard letter size.
A4 paper is 8.26" x 11.69" so a little narrow and taller than US letter size.
[deleted] ยท 4 points ยท Posted at 16:11:30 on May 25, 2016 ยท (Permalink)
Weeeeeeeeeiiiird.
Damn, the US always insists on being different.
tripletstate ยท -1 points ยท Posted at 16:54:05 on May 25, 2016 ยท (Permalink)
We used the letter size way before they standardized theirs. Why do you think it's so close to the same size?
[deleted] ยท 11 points ยท Posted at 19:22:40 on May 25, 2016 ยท (Permalink)*
[deleted]
tripletstate ยท -13 points ยท Posted at 19:36:00 on May 25, 2016 ยท (Permalink)
That's bullshit.
[deleted] ยท 7 points ยท Posted at 19:42:03 on May 25, 2016 ยท (Permalink)*
[deleted]
tripletstate ยท 0 points ยท Posted at 08:58:53 on May 26, 2016 ยท (Permalink)
You keep editing your comment so many times it's a joke. Europeans copied the American format.
tripletstate ยท -7 points ยท Posted at 21:39:32 on May 25, 2016 ยท (Permalink)
We only used letter format since 1995? What a fucking joke. We were using that for hundreds of years. The Europeans roughly copied the same size, and used that for their system, which I agree is better.
CookieTheSlayer ยท 4 points ยท Posted at 06:26:52 on May 26, 2016 ยท (Permalink)
Dont you just love Americans?
tripletstate ยท -2 points ยท Posted at 08:57:28 on May 26, 2016 ยท (Permalink)
I love how Europeans try their best rewrite history by bringing up the most obscure artifacts, to pretend they don't copy everything Americans do.
CookieTheSlayer ยท 3 points ยท Posted at 08:59:54 on May 26, 2016 ยท (Permalink)
I am Australian.
tripletstate ยท -2 points ยท Posted at 09:03:13 on May 26, 2016 ยท (Permalink)
I'm only stating a fact. Look at that guy and who so many times edited his comment to make it look like America only used the Letter format since the late 90's. We used that format way longer than they ever came up with some clever system on how to divide paper. I'm pretty sure the Chinese taught us all, but the Europeans are smug idiots.
CookieTheSlayer ยท 4 points ยท Posted at 09:14:07 on May 26, 2016 ยท (Permalink)
Smug idiots that don't have ego issues it seems.
Tramagust ยท 2 points ยท Posted at 08:25:53 on May 26, 2016 ยท (Permalink)
Sane ones.
ThachWeave ยท 3 points ยท Posted at 21:03:45 on May 25, 2016 ยท (Permalink)
We drive on the right side of the road, just like 95% of the world.
redweasel ยท 2 points ยท Posted at 07:14:29 on May 26, 2016 ยท (Permalink)
I just learned the other day -- on Facebook, of all places! -- that the US standard geometry for a 45rpm "single" vinyl record is different than the world standard (which I had never heard of and which blew my mind when I guy posted a video of it): in the US a 45 rpm single has a "large" central hole about one inch (?) in diameter, whereas in the rest of the world it has the same "small" central hole (about 1/4 inch) as all the other (e.g. 33.3... rpm albums) kinds of records (which are the same in the US).
boreas907 ยท 7 points ยท Posted at 15:51:03 on May 25, 2016 ยท (Permalink)*
It's one of those "more hassle than it's worth" things. A4 is, mercifully, the same width as A (letter) size (edit: apparently A is slightly wider), and only about 20 mils longer, so there's no functional benefit to switching out, aside from perhaps a one-time stimulus boost to the binder industry as everybody suddenly needs slightly longer things to hold their papers in. And ANSI sizes scale similarly to the way that ISO ones do, so it's not like we don't also get the benefit of maintaining aspect ratios.
Edits: I oopsed some facts.
seansand ยท 13 points ยท Posted at 16:08:00 on May 25, 2016 ยท (Permalink)
It's not actually the same width. Letter is slightly wider than A4.
lengau ยท 5 points ยท Posted at 19:58:24 on May 25, 2016 ยท (Permalink)
Actually they don't scale in quite the same way.
You double one dimension and not the other, but because it doesn't have an aspect ratio of 1:sqrt(2), the aspect ratio of letter is different from the aspect ratio of ledger/tabloid (secretly the same paper, just rotated). So if you want a double-size print of an A4 page, you can print it on A3 paper and it'll look fine. If you try to print a letter page on tabloid paper, it'll be stretched.
boreas907 ยท 2 points ยท Posted at 21:10:48 on May 25, 2016 ยท (Permalink)
Yeah, I learned this after I said that. My bad.
VikingCoder ยท 6 points ยท Posted at 14:54:45 on May 25, 2016 ยท (Permalink)
WHEN WE CONQUER ALL OF YOU, EVERYONE ELSE WILL BE STANDARD WITH US!
AMasonJar ยท 13 points ยท Posted at 15:13:26 on May 25, 2016 ยท (Permalink)
FTFY
VikingCoder ยท 5 points ยท Posted at 15:27:40 on May 25, 2016 ยท (Permalink)
Yeah, we're going to liberate the fuck out of all of you! DEMOCRAZY! WOOOO!
WhyYouLetRomneyWin ยท 2 points ยท Posted at 17:44:53 on May 25, 2016 ยท (Permalink)
From my perspective, the rest of the world is non-standard!
Daimoth ยท 3 points ยท Posted at 15:21:18 on May 25, 2016 ยท (Permalink)
WE LEARNED IT FROM YOU!
Provided you're English, that is. We occupy a massive chunk of a continent, not nearly as much pressure from our neighbors to standardize. We have far more infrastructure built using the old system than any European nation. It's tricky.
Dob-is-Hella-Rad ยท 5 points ยท Posted at 16:07:44 on May 25, 2016 ยท (Permalink)*
I doubt they're English, an English person would know that England's system of measurement is closer to the US's than to mainland Europe's (and much worse than the US's. They could at least be consistent. That should be the number one priority)
nivlark ยท 2 points ยท Posted at 18:40:23 on May 25, 2016 ยท (Permalink)
Not really, we are taught fairly exclusively metric and the vast majority of things are measured in metric. There are a few weird exceptions though: road signs are still mostly in Imperial, beer and milk are still sold by the pint (an Imperial pint, which is different from the US pint), and older generations still measure their weight in stones and pounds.
[deleted] ยท 1 points ยท Posted at 20:05:23 on May 25, 2016 ยท (Permalink)
So what you're saying is... it's inconsistent.
[deleted] ยท 1 points ยท Posted at 20:39:23 on May 25, 2016 ยท (Permalink)
In very few specific cases
fb5a1199 ยท 4 points ยท Posted at 14:52:12 on May 25, 2016 ยท (Permalink)
When you leave crumpled sheets of A4 on the moon, then we'll think about it.
SoupinCup ยท 5 points ยท Posted at 15:17:46 on May 25, 2016 ยท (Permalink)
Don't litter in space :P
stupidfatchocobo ยท 2 points ยท Posted at 15:30:00 on May 25, 2016 ยท (Permalink)
Why change?
mainsworth ยท 2 points ยท Posted at 15:48:16 on May 25, 2016 ยท (Permalink)
Because the system we established long before international standardization existed works for us, and because the US has the economic clout to sustain non-standardization, it continues.
It obviously isn't that big of an issue for us.
King_of_Avalon ยท 4 points ยท Posted at 18:29:34 on May 25, 2016 ยท (Permalink)
No, the A4 standard has been around since the 1940s and was basically ubiquitous by the '60s. The US didn't make 8.5x11 the national standard until Reagan decreed it in the 1980s. Before that, the US had all sorts of nonstandard paper sizes for different applications.
mainsworth ยท 1 points ยท Posted at 20:41:26 on May 25, 2016 ยท (Permalink)
Well, shit.
ALittlePunk ยท 1 points ยท Posted at 14:51:14 on May 25, 2016 ยท (Permalink)
Because the government thinks it's funny
[deleted] ยท 1 points ยท Posted at 16:04:03 on May 25, 2016 ยท (Permalink)
Sometimes I think this too but then realise I'm British, and we're weird enough with our plugs and driving on the left.
I mean we're correct, but still uncommon
YetAnotherDumbGuy ยท 1 points ยท Posted at 16:08:21 on May 25, 2016 ยท (Permalink)
Joke answer: Because of Lunar Lander Awesomeness, that's why!
Real answer: the USA is a huge market with very low barriers to entry, and thus suppliers and manufacturers don't feel much economic pressure to adapt. If I make something in a small town in the States, I can sell it across an entire continent, in a market with 300million people, some more than 3000 miles away, with no currency exchange, no import/export taxes, no language barrier, and no trouble about metric vs imperial units. Maybe it interferes me selling it in Finland, but I probably wasn't to be selling in Finland, so I don't care that much.
When the metric system was cooked up, units like ell (https://en.wikipedia.org/wiki/Ell) were completely nonstandard from one country to the next, which was a big problem for merchants across Europe. The metric system solved a real problem. But that problem wasn't as seriously felt here in the States, so the pressure to adopt metric wasn't as high.
I think a switch would be pretty painless, all told. They've been selling soda in two-liter bottles for decades, and I don't remember anyone eve so much as blinking about it. I suspect the same would be true of many other changes, and we could go metric without anyone really bothering about it, if only anyone could be bothered to do it.
gologologolo ยท 1 points ยท Posted at 16:09:43 on May 25, 2016 ยท (Permalink)
Same reason as pounds. Snobbiness
Navolas2 ยท 1 points ยท Posted at 16:15:10 on May 25, 2016 ยท (Permalink)
I at least want the US to use 8 x 12. It would be useful for measurement. Every single piece of paper could be used for measurement. 1 foot? whole paper. 6"? fold it height wise. 4"? fold it width wise. To get the odd numbers you'd need two pieces, but it still works none the less.
KitAndKat ยท 1 points ยท Posted at 16:17:32 on May 25, 2016 ยท (Permalink)
American exceptionalism strikes again.
radome9 ยท 1 points ยท Posted at 17:12:44 on May 25, 2016 ยท (Permalink)
American exceptionalism?
thezachneumann ยท 1 points ยท Posted at 17:13:58 on May 25, 2016 ยท (Permalink)
What size does everybody else use?
iIsMe95 ยท 1 points ยท Posted at 17:15:13 on May 25, 2016 ยท (Permalink)
We're told not to give in to peer pressure all the time and just took it to heart.
RickHalkyon ยท 1 points ยท Posted at 17:16:47 on May 25, 2016 ยท (Permalink)
I had no idea, TIL.
What the fuck, America, we don't have to be special in every fucking way!
CardonaC09 ยท 1 points ยท Posted at 17:19:46 on May 25, 2016 ยท (Permalink)
Because we don't settle with average ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐บ๐ธ๐ฅ๐ฅ๐ฅ๐ฅ
MakeItSick ยท 1 points ยท Posted at 17:29:58 on May 25, 2016 ยท (Permalink)
Because we do things our own way and it works
moby__dick ยท 1 points ยท Posted at 17:39:18 on May 25, 2016 ยท (Permalink)
Freedom, that's why.
DanFreedse ยท 1 points ยท Posted at 17:45:20 on May 25, 2016 ยท (Permalink)
There was a time you had to apply to the US Green Card Lottery on Letter size paper. Not being a 'rest-of-the-world-standard' this made it more difficult in some countries.
Although this was not the reason for Letter-size I guess it didn't hurt the INS at the time
[deleted] ยท 1 points ยท Posted at 17:53:04 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 18:20:44 on May 25, 2016 ยท (Permalink)
Uhhh because it's an American company?
[deleted] ยท 1 points ยท Posted at 20:26:18 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 01:09:34 on May 26, 2016 ยท (Permalink)
I've never even been to Europe so I don't really know what I'm talking about. I agree it should default now based on language preference or something I just think its silly that you are surprised an american product defaults to american standards.
[deleted] ยท 1 points ยท Posted at 11:55:06 on May 26, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 18:07:07 on May 26, 2016 ยท (Permalink)
Provided I could easily change it to English I wouldn't be like "WOAAHHH WHY DID DEY DO DIS????? HOW DARE THEY!". So... yeah.
joelomite11 ยท 1 points ยท Posted at 17:58:16 on May 25, 2016 ยท (Permalink)
Because freedom.
avolodin ยท 1 points ยท Posted at 18:00:11 on May 25, 2016 ยท (Permalink)
This is actually a problem at my company. We're in Russia and the HQ is in the US, so a majority of documents we receive from there look wrong when printed out.
evenstevens280 ยท 1 points ยท Posted at 18:00:40 on May 25, 2016 ยท (Permalink)
Because Freedom.
IntaglioSnow ยท 1 points ยท Posted at 18:03:30 on May 25, 2016 ยท (Permalink)
Canada too! (though I don't know why)
tantan35 ยท 1 points ยท Posted at 18:12:17 on May 25, 2016 ยท (Permalink)
Because your system just makes too much sense. It's too easy. We're fans of overcomplicating simple issues.
SkullDC ยท 1 points ยท Posted at 18:12:54 on May 25, 2016 ยท (Permalink)
Oh, we're happy to do what everyone else does, as long as that is what we're already doing, anyway!
sdremsw ยท 1 points ยท Posted at 18:32:46 on May 25, 2016 ยท (Permalink)
because 'Merica
When I moved to the states from Australia this was one of the most confusing things to understand
4567898761 ยท 1 points ยท Posted at 18:38:48 on May 25, 2016 ยท (Permalink)
Hey the rest of the world needs to fall in line.. We'll never change
Gropah ยท 1 points ยท Posted at 18:45:53 on May 25, 2016 ยท (Permalink)
Because reasons, and history combined with seperate development
Incognitogamer ยท 1 points ยท Posted at 19:08:55 on May 25, 2016 ยท (Permalink)
We're too busy setting our own standards... Namely:
jay314271 ยท 1 points ยท Posted at 19:27:26 on May 25, 2016 ยท (Permalink)*
Well we say "math" in the usa but also say "mathematicS". (I'm saying maths is consistent / logical)
Then again we don't have that extra letter in aluminum.
A lot of the usa differences came from intentionally sticking finger at the UK after the divorce. (you'll have to trust me on that because I am god)
silentclowd ยท 1 points ยท Posted at 20:01:57 on May 25, 2016 ยท (Permalink)
8.5x11 is nice because you can measure it out exactly with a ruler. A4 paper doesn't line up with centimeters.
[deleted] ยท 1 points ยท Posted at 20:10:44 on May 25, 2016 ยท (Permalink)
to be honest US paper size is much more functional than the obscenely long paper sizes in the EU
SupriseGinger ยท 1 points ยท Posted at 20:10:51 on May 25, 2016 ยท (Permalink)
The US paper sizes are setup such that folding in half will result in a sheet that is the same size as the next step down. So a 11x17 folded in half becomes an 8.5x11.
leshake ยท 1 points ยท Posted at 20:13:39 on May 25, 2016 ยท (Permalink)
Ergonomics.
clever_unique_name ยท 1 points ยท Posted at 20:37:22 on May 25, 2016 ยท (Permalink)
We do have ANSI paper sizes that are similar.
ANSI A - 8.5"x11" ANSI B - 11"x17" (8.5x2) ANSI C - 17"x22" (11x2) ANSI D - 22x34" (17x2)
Nicorhy ยท 1 points ยท Posted at 20:46:37 on May 25, 2016 ยท (Permalink)
Unfortunately, Canada's with them on this. :(
Avoidingsnail ยท 1 points ยท Posted at 20:51:30 on May 25, 2016 ยท (Permalink)
What size do you use?
Gejakiat ยท 1 points ยท Posted at 21:06:40 on May 25, 2016 ยท (Permalink)
TIfuckingL, that's insane to me
mangamaster03 ยท 1 points ยท Posted at 21:11:46 on May 25, 2016 ยท (Permalink)
Because every lobbyist in the country would rush to Washington to save the publishing industry, the paper industry, the educational industry, and whoever else is set on the 8.5x11. I use Rhodia A4, but everyone else is content with whatever is lying in the printer tray.
Mefic_vest ยท 1 points ยท Posted at 21:13:41 on May 25, 2016 ยท (Permalink)
Canada is right up there with the States. They also use Legal and Letter, no A sizes in sight.
SF1034 ยท 1 points ยท Posted at 21:33:17 on May 25, 2016 ยท (Permalink)
You mean why isn't the rest of the world standard with us?
Humpa ยท 1 points ยท Posted at 21:52:30 on May 25, 2016 ยท (Permalink)
W-Wait what? They don't use A1, A2 etc? Please tell me it's at least a proper ratio?
MargotFenring ยท 1 points ยท Posted at 21:56:27 on May 25, 2016 ยท (Permalink)
There are plenty of Americans who think it's ridiculous too. At some point "special" becomes "stupid" and the USA seems to have trouble distinguishing the two.
docbauies ยท 1 points ยท Posted at 22:02:46 on May 25, 2016 ยท (Permalink)
you can apparently blame the dutch, who started with a sheet that was 44x17. so that's 8 sheets of 8.5x11. it was done to minimize paper waste. https://www.davidberman.com/why-is-us-letter-paper-8-5-x-11-was-hoover-a-tree-hugger/
DishwasherTwig ยท 1 points ยท Posted at 22:14:10 on May 25, 2016 ยท (Permalink)
If we weren't such a superpower when these things were being developed, it would be far more likely that we would have followed the forms of the rest of the world. But since we not only had the resources but also the patriotic spirit, we developed our own systems for a lot of things rather than fit in with the rest of the world. It really came down to "AMERICA!".
bippetyboppety ยท 1 points ยท Posted at 22:49:10 on May 25, 2016 ยท (Permalink)
When I was a girl we had quarto and foolscap.
I can't believe I'm reading a thread about maths. I can barely do arithmetic. My favourite maths fact is that in the times table, multiples of 9 add up to 9. So 9x3=27 and 2+7=9. That's all I've got.
hazeleyedninja ยท 1 points ยท Posted at 04:36:25 on May 26, 2016 ยท (Permalink)
You are confusing Americans in general with American business. Many Americans are very nice and helpful. Texas for example. American business however is anything but nice and helpful. American business is all about separating people from their money in any legal way possible. And sometimes those limits get tested. We have also had many problems with monopolies throughout our history. We have a lot of stupid laws, because of how much big business gets into politics. The real reason is probably something to do with making more money. Thats how all things end up the way they do in the US. It's all about the money.
TheInternetHivemind ยท 1 points ยท Posted at 08:09:17 on May 26, 2016 ยท (Permalink)
Because by the time the world has a standard for something, we've been using our's for 20 years and we don't feel like changing.
Multai ยท 1 points ยท Posted at 14:59:57 on May 25, 2016 ยท (Permalink)
At least they know which side of the road to drive on...
Taokan ยท 1 points ยท Posted at 15:05:59 on May 25, 2016 ยท (Permalink)
Freedom!
(Yes, that's supposed to be a factorial joke. No, it's not good.)
behnow5 ยท 1 points ยท Posted at 15:12:42 on May 25, 2016 ยท (Permalink)
I see what you did there
weezyheff ยท 9 points ยท Posted at 15:30:35 on May 25, 2016 ยท (Permalink)
Had this "a-ha!" Moment where it all made sense... Then looked at the image and saw how our "standard letter" paper doesn't meet the rule... Classic America move
zapa8731 ยท 6 points ยท Posted at 14:57:49 on May 25, 2016 ยท (Permalink)
During freshman year as an engineering student we had a class that just covered drafting. This was the only thing I remember from that class.
gmtime ยท 7 points ยท Posted at 15:19:07 on May 25, 2016 ยท (Permalink)
Also, A0 has an effective area of exactly one square meter. Since every A size up is half the size, A4 is exactly 1/16th of a square meter in area. Also, sizes are rounded to the nearest millimeter.
occamrazor ยท 1 points ยท Posted at 23:11:37 on May 25, 2016 ยท (Permalink)
Actually sizes are rounded down, so one can always fit two A(n+1) sheets in an A(n) sheet
tokyorockz ยท 6 points ยท Posted at 15:16:06 on May 25, 2016 ยท (Permalink)
Does that mean it's a 30/60/90 triangle if you cut it diagonally?
[deleted] ยท 2 points ยท Posted at 17:09:44 on May 25, 2016 ยท (Permalink)
Not quite. If you draw a rectangle with side lengths 1 and sqrt(2) then draw a diagonal, you'd get a right triangle of sides 1, sqrt(2) and sqrt(3) (which is found with the Pythagorean theorem).
The side lengths for a 30-60-90 triangle are(some multiple of) 1, sqrt(3), and 2, whichis close but not the same as the triangle from the paper.
Also, one of the angles of the triangle from the paper is arctan(sqrt(2)) (approximately 55 degrees), which is not 30 or 60 degrees.
It is, however, one of the triangles in the Pythagorean spiral.
KingDarkBlaze ยท 2 points ยท Posted at 19:06:59 on May 25, 2016 ยท (Permalink)
No, that'd be 1-root3-2
minimim ยท 1 points ยท Posted at 15:39:40 on May 25, 2016 ยท (Permalink)
3/6 is 1/2, but the ratio is 1/โ2, so no. If one side measured 30, the other would measure 30โ2 (approx. 42.4).
tokyorockz ยท 3 points ยท Posted at 15:43:07 on May 25, 2016 ยท (Permalink)
A 30/60/90 triangle is the angles, not the sides. If a triangle has angles of 30ยฐ 60ยฐ and 90ยฐ then the sides are a ratio of X to 2X to Xโ2
minimim ยท 3 points ยท Posted at 15:44:24 on May 25, 2016 ยท (Permalink)
Oh, ok. I confused it with a Pythagorean triangle, but that is 3/4/5. Sorry for the confusion.
guglicap ยท 5 points ยท Posted at 15:33:51 on May 25, 2016 ยท (Permalink)
There's a Numberphile video about it
Powdercum ยท 3 points ยท Posted at 15:22:44 on May 25, 2016 ยท (Permalink)
Not only that, paper size A0 has a surface area of exactly 1m2 . When you know the paper weight, say 80 g/m2 then you know an A4 is 1/16th of that so 5 grams.
jfb1337 ยท 3 points ยท Posted at 15:29:53 on May 25, 2016 ยท (Permalink)
Also either A1 or A0 (can't remember which) is 1m2 in area
sionnach ยท 5 points ยท Posted at 15:40:01 on May 25, 2016 ยท (Permalink)
A0
smmck ยท 5 points ยท Posted at 17:35:48 on May 25, 2016 ยท (Permalink)
And here I was thinking that defaulting to A4 was just annoying. My wife is going to be so ticked when I replace our printer paper at home with the mathematically beautiful A4 paper.
ohitsasnaake ยท 3 points ยท Posted at 15:26:09 on May 25, 2016 ยท (Permalink)
Great fact, but cutting a 210mmร297mm A4 would give two 105mmร297mm long, thin halves. You would cut across to get two A5s.
elee0228 ยท 2 points ยท Posted at 15:31:24 on May 25, 2016 ยท (Permalink)
Ah thanks, I'll fix that.
gdub695 ยท 3 points ยท Posted at 15:59:49 on May 25, 2016 ยท (Permalink)*
I don't know about our other funky sized paper, but ANSI standard sizes follow the same convention. Double the short side, keep the long side the same when you go up. A is 8.5x11 B is 11x17 C is 17x22 D is 22x34 And so forth. I don't think I've ever used larger than those though
Edited: ANSI, not arch.
NumbZebra ยท 3 points ยท Posted at 18:34:23 on May 25, 2016 ยท (Permalink)
Negative. Those are ANSI engineering paper sizes not architectural sizes. Architectural sizes are 9x12, 12x18, 18x24, 24x36, 36x48.
gdub695 ยท 1 points ยท Posted at 18:50:35 on May 25, 2016 ยท (Permalink)
My bad. I forgot it was ANSI, all I could remember is architectural, since that's the class where I was introduced to it
NumbZebra ยท 2 points ยท Posted at 19:41:16 on May 25, 2016 ยท (Permalink)
No worries, Just have to deal with this silliness all the time trying to print 34" prints on 36" roll paper or worse, vise versa. The fun of large format plotters, and a purchasing department that can't be arsed to learn the different sizes.
King_of_Avalon ยท 2 points ยท Posted at 18:34:40 on May 25, 2016 ยท (Permalink)
Yeah, but the whole point is that the ratios keep alternating, whereas with A-series paper, it is always 1:sqrt2 which means you can scale up and down with no distortions or blank spaces
BananaSplit2 ยท 3 points ยท Posted at 16:58:42 on May 25, 2016 ยท (Permalink)
And it's awesome. Cut an A3 in half and you get A4. Cut an A4 in half and you get A5.
quintinn ยท 3 points ยท Posted at 18:11:48 on May 25, 2016 ยท (Permalink)
So the rest of the world uses a standard paper size and the US has decided to use some other strange thing. Why does this sound familiar?
[deleted] ยท 2 points ยท Posted at 15:26:20 on May 25, 2016 ยท (Permalink)
[deleted]
elee0228 ยท 2 points ยท Posted at 15:31:01 on May 25, 2016 ยท (Permalink)
No, that's a different thing.
djdadi ยท 2 points ยท Posted at 15:47:28 on May 25, 2016 ยท (Permalink)
Doesn't this have something to do with the Golden Ratio?
alexmojaki ยท 1 points ยท Posted at 18:12:27 on May 25, 2016 ยท (Permalink)
No.
tcfjr ยท 2 points ยท Posted at 19:10:26 on May 25, 2016 ยท (Permalink)
The Golden Ratio is 1 :: (1 + sqrt(5)) / 2, which is about 1 :: 1.618. The side ratios for International paper sizes is 1 :: sqrt(2), or 1 :: 1.414.
desiredpseudonym ยท 2 points ยท Posted at 17:01:06 on May 25, 2016 ยท (Permalink)
When i first started my degree, one of the first problem solving tasks they gave us on the first day was to work out the ratio given the fact that if you fold A3 in half you get A4 and so on. Quite interesting how stuff like this always seems to come up
SuchCoolBrandon ยท 2 points ยท Posted at 17:23:31 on May 25, 2016 ยท (Permalink)
Oh! This is why a greeting card made from folded A4 paper fits so well into an A5 envelope!
navinohradech ยท 2 points ยท Posted at 17:58:27 on May 25, 2016 ยท (Permalink)
IMHO this is a stupid way to design sizes. Why do we need a magic ratio? Pick sizes that are ergonomic for common tasks. I'm thinking in particular of index cards : 3x5 cards cut in halves or fourths are great for language flashcards. DIN sized cards are terrible
upstateman ยท 2 points ยท Posted at 18:13:58 on May 25, 2016 ยท (Permalink)
I so wish it was easier to get international paper sizes in the U.S.
elee0228 ยท 1 points ยท Posted at 18:47:41 on May 25, 2016 ยท (Permalink)
You can get international sizes on Amazon. Just search A4 or whatever size you are looking for.
upstateman ยท 2 points ยท Posted at 18:56:05 on May 25, 2016 ยท (Permalink)
Just more expensive.
alexmojaki ยท 2 points ยท Posted at 18:17:40 on May 25, 2016 ยท (Permalink)
A cool consequence of this is that if you fold the paper diagonally so that the short side meets up with the long side like this then the 'diagonal side' will be exactly the same length as the long side. It's easy to show this using Pythagoras: โ(12 + 12) = โ2.
01is ยท 2 points ยท Posted at 18:39:40 on May 25, 2016 ยท (Permalink)
For legal size they should use the golden ratio.
[deleted] ยท 2 points ยท Posted at 18:39:50 on May 25, 2016 ยท (Permalink)
I have layman's math skills, but I worked in a paper factory once and had to manage shipping. I'd like to add to this, if you multiply the sheet x and y in metres by the weight of the paper, that's how much it weighs. So for a ream of A4 (500 sheets) printer paper: .210m x .297m x 80gsm x 500 sheets, the weight of that ream is in grams, about 2.5kg. Typically boxed in 5's, that box of printer paper is then 12.5kg. Good for office workouts if the plastic shipping strap wasn't so lethal.
Sorry Reddit, it's all I got.
narwhals_narwhals ยท 2 points ยท Posted at 18:42:51 on May 25, 2016 ยท (Permalink)*
American paper sizes do follow a pattern:
Above that, the pattern stops. Wikipedia has a nice illustration of this here.
ver-say-see ยท 2 points ยท Posted at 18:47:18 on May 25, 2016 ยท (Permalink)
So would us Americans fold the paper hamburger or hotdog style?
elee0228 ยท 2 points ยท Posted at 18:48:24 on May 25, 2016 ยท (Permalink)
Hamburger.
NoRodent ยท 2 points ยท Posted at 18:58:57 on May 25, 2016 ยท (Permalink)
No one has linked this great video yet?
ferna182 ยท 2 points ยท Posted at 18:59:08 on May 25, 2016 ยท (Permalink)
also, it ONLY works for 1:โ2 ratio. It's very easy to prove.
CKtheFourth ยท 2 points ยท Posted at 19:10:04 on May 25, 2016 ยท (Permalink)
I wish the US would switch to this. So much easier
GroovingPict ยท 2 points ยท Posted at 21:15:54 on May 25, 2016 ยท (Permalink)
And it is the only ratio it works for.
DrewMcDrew ยท 2 points ยท Posted at 21:27:13 on May 25, 2016 ยท (Permalink)
I also personally love that the B series. It is the same ratio, but the B0 sheet has a longer side that is 1m. It makes more sense to me than something with the area of a square meter.
Zelpa ยท 1 points ยท Posted at 21:49:50 on May 25, 2016 ยท (Permalink)
I'm on that B5 shit
DrewMcDrew ยท 2 points ยท Posted at 21:27:14 on May 25, 2016 ยท (Permalink)
I also personally love that the B series. It is the same ratio, but the B0 sheet has a longer side that is 1m. It makes more sense to me than something with the area of a square meter.
J-thorne ยท 2 points ยท Posted at 21:32:04 on May 25, 2016 ยท (Permalink)
So root(2)/2? Seems like circles really ARE involved in everything.
mikeawsome ยท 2 points ยท Posted at 23:44:45 on May 25, 2016 ยท (Permalink)
Crosswise is that the paper folded hamburger or hotdog?
elee0228 ยท 2 points ยท Posted at 02:53:31 on May 26, 2016 ยท (Permalink)
hamburger
mikeawsome ยท 2 points ยท Posted at 02:55:52 on May 26, 2016 ยท (Permalink)
Thank you
JustRiedy ยท 2 points ยท Posted at 07:28:17 on May 26, 2016 ยท (Permalink)
I feel sorry for Americans, the A paper sizing is the best thing ever.
hoxem ยท 3 points ยท Posted at 15:27:08 on May 25, 2016 ยท (Permalink)
Yeah I went to England recently and all the paper was really tall. Like wtf England.
iamzombus ยท 2 points ยท Posted at 15:31:50 on May 25, 2016 ยท (Permalink)
ANSI paper sizes:
8.5" x 11" = A size.
11" x 17" = B size.
17" x 22" = C size.
22" x 34" = D size.
NumbZebra ยท 2 points ยท Posted at 16:26:45 on May 25, 2016 ยท (Permalink)
You missed Ansi E = 34" x 44". These follows the same fold in half rule as international paper sizes. Makes folding large drawing to fit into binders and folders much easier. Any size drawing can be folded to 8.5" x 11".
Sampsonite_Way_Off ยท 1 points ยท Posted at 17:40:29 on May 25, 2016 ยท (Permalink)
ARCH paper sizes:
9" x 12" = A size.
12" x 18" = B size.
18" x 24" = C size.
24" x 36" = D size.
36" x 48" = E size
In my fields it's maddening. We use ANSI A/B for small prints but then switch to ARCH C/D/E for large format. Scales always are getting screwed up.
iamzombus ยท 1 points ยท Posted at 17:44:40 on May 25, 2016 ยท (Permalink)
Guessing it's probably cheaper to buy ANSI A/B than ARCH A/B?
KarlKastor ยท 1 points ยท Posted at 18:27:08 on May 25, 2016 ยท (Permalink)
In fact, this is the only ratio for which this works:
Proof: Lets call the longer side a and the shorter one b. Same ratio if you half it on the longer side means:
multiply both sides by a/b:
SoftandChewy ยท 1 points ยท Posted at 18:32:33 on May 25, 2016 ยท (Permalink)
They talk about it in this Numberphile episode.
x_Sinister_x ยท 1 points ยท Posted at 19:26:13 on May 25, 2016 ยท (Permalink)
In other words, America fails again cough cough metric system cough cough
johnq-pubic ยท 1 points ยท Posted at 16:21:11 on May 25, 2016 ยท (Permalink)
Scumbag U.K. exports shitty Imperial measurement system and paper sizes to North America, then switches to more sensible Metric and 'A' system of paper sizes.
King_of_Avalon ยท 3 points ยท Posted at 18:32:52 on May 25, 2016 ยท (Permalink)
The UK never used Letter. 8.5x11 was standardised by Reagan in the 1980s. Britain had its own imperial paper sizes like Quarto and Foolscalp, but the UK switched to the ISO sizes back in the early '60s like most countries. 8.5x11 is all American
johnq-pubic ยท 1 points ยท Posted at 19:24:04 on May 25, 2016 ยท (Permalink)
TIL
[deleted] ยท 1 points ยท Posted at 17:30:50 on May 25, 2016 ยท (Permalink)
Is crosswise hamburger or hot dog?
elee0228 ยท 1 points ยท Posted at 17:38:54 on May 25, 2016 ยท (Permalink)
Hamburger, I think...
ksiyoto ยท 383 points ยท Posted at 14:58:47 on May 25, 2016 ยท (Permalink)
If you want to find a fraction between two fractions, you can just add the numerators together and the denominators together.
SillyFlyGuy ยท 202 points ยท Posted at 19:48:08 on May 25, 2016 ยท (Permalink)
1/3
1/2
2/5 ?
0.333 < 0.4 < 0.5
ok..
867/5309
868/5309
1735/10618 ?
0.1633075908834055 < 0.1634017705782633 < 0.1634959502731211
Well damn, it works.
ustainbolt ยท 6 points ยท Posted at 19:49:17 on May 25, 2016 ยท (Permalink)
Now prove it!
DustyLenz ยท 46 points ยท Posted at 20:43:36 on May 25, 2016 ยท (Permalink)
Not too bad. It was a cool problem to work on!
[deleted] ยท 10 points ยท Posted at 03:38:36 on May 26, 2016 ยท (Permalink)
[deleted]
DustyLenz ยท 3 points ยท Posted at 06:19:21 on May 26, 2016 ยท (Permalink)
Much cleaner proof than mine. Good work!
[deleted] ยท 6 points ยท Posted at 06:46:18 on May 26, 2016 ยท (Permalink)
[deleted]
DustyLenz ยท 5 points ยท Posted at 06:51:11 on May 26, 2016 ยท (Permalink)
Wow, thanks for taking time to give me feedback! I finished my undergrad in math, but I still have a lot to learn :)
[deleted] ยท 2 points ยท Posted at 10:09:03 on May 26, 2016 ยท (Permalink)
Here is another (slightly messier) proof, but I like it because it sort of follows the logic of why this intuitively makes sense - that the ratio you multiply the smaller fraction by will be greater than 1 and vice versa.
[deleted] ยท 2 points ยท Posted at 17:31:50 on May 26, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 18:40:21 on May 26, 2016 ยท (Permalink)
Thanks! I'd never used the website before and tbh don't exactly set things out formally. This was pretty much just scribbling on scrap paper before I decided to type it up.
graaahh ยท 1 points ยท Posted at 12:51:16 on September 26, 2016 ยท (Permalink)
I know this is an old comment but I just ran across it and I don't understand your proof. I can follow it line by line and see that the steps you take are true, but I don't understand how it proves that (p+r)/(q+s) is between p/q and r/s.
DustyLenz ยท 1 points ยท Posted at 16:52:37 on September 26, 2016 ยท (Permalink)
I got pretty lazy towards the end. In the second to last equation, you can multiply by q(q+s) on both sides, then subtract pq from both sides, to get ps < qr. We're given that a < b, which is the same as p/q < r/s. That statement justifies why ps < qr, so we've shown that a < (p+r)/(q+s). I didn't show that (p+r)/(q+s) < b, but you can use the same trick by manipulating fractions. Does that help?
graaahh ยท 1 points ยท Posted at 17:06:38 on September 26, 2016 ยท (Permalink)
I think so. It seems like most of the proof you worked out just wound up proving cross-multiplication (i.e. that p/q<r/s is the same as ps<qr.) But I think I see where you're coming from - the unstated part being that it proves a<(p+r)/(q+s). I'm wondering now whether this would work with negative numbers or not.
DustyLenz ยท 1 points ยท Posted at 17:16:41 on September 26, 2016 ยท (Permalink)
Nono, I used cross multiplication to prove that a < (p+r)/(q+s) is equivalent to p/q<r/s. That should also answer the question about negative numbers; as long as a < b, I believe my proof should still hold up? It gets a little weird when you mix positive and negative numbers, so a more careful proof is needed for that.
graaahh ยท 1 points ยท Posted at 17:17:32 on September 26, 2016 ยท (Permalink)
Thanks for the help! I'm normally fine with this kind of stuff but it's been awhile since I had to read through a proof.
Seraphaestus ยท 10 points ยท Posted at 20:18:36 on May 25, 2016 ยท (Permalink)*
Let m, n, and c be positive integers edit: c should in fact be a positive rational number
Let a be the fraction m/n and b the fraction m/n + c.
b = (m+cn)/n
[Top(a)+Top(b)]/[Bottom(a)+Bottom(b)] = (m+m+cn)/(n + n)
= (2m+cn)/2n
= [m + 1/2(cn)] / n
As the denominators are the same, we can compare the size with the numerators.
m + 1/2(cn) > m
m + 1/2(cn) < m + cn
Therefore the resultant fraction is between fractions a and b.
[deleted] ยท 0 points ยท Posted at 21:40:41 on May 25, 2016 ยท (Permalink)
[deleted]
Seraphaestus ยท 8 points ยท Posted at 22:04:13 on May 25, 2016 ยท (Permalink)
Maybe you could tell me what's wrong with it and make a constructive comment instead of making me feel stupid
[deleted] ยท 3 points ยท Posted at 22:11:03 on May 25, 2016 ยท (Permalink)
You assume a and b start with the same numerator. Sorry for being mean.
Seraphaestus ยท 1 points ยท Posted at 05:49:03 on May 26, 2016 ยท (Permalink)
It's ok! It was pointed out that I'd said c should be an integer by mistake when in fact I was using it as a rational number in the proof.
DustyLenz ยท 1 points ยท Posted at 22:49:58 on May 25, 2016 ยท (Permalink)
The assumption that b can be written as m/n + c, c an integer is incorrect. For example, let a = 1/3 and b = 1/2. There's no integer c such that 1/3 + c = 1/2. I think the proof will work without that assumption though. c will just be some funky fraction. Good work!
Seraphaestus ยท 2 points ยท Posted at 05:47:55 on May 26, 2016 ยท (Permalink)*
Good point, I meant c to be rational but I accidently lumped it in with m and n without thinking.
[deleted] ยท -2 points ยท Posted at 22:11:24 on May 25, 2016 ยท (Permalink)*
[removed]
Seraphaestus ยท 1 points ยท Posted at 05:47:14 on May 26, 2016 ยท (Permalink)
Obviously, I wrote it that way to make it as clear as possible what was going on.
[deleted] ยท 2 points ยท Posted at 21:59:51 on May 25, 2016 ยท (Permalink)
:(
lendluke ยท 1 points ยท Posted at 03:39:25 on May 26, 2016 ยท (Permalink)
This is only for simplified fractions correct?
SillyFlyGuy ยท 5 points ยท Posted at 03:59:57 on May 26, 2016 ยท (Permalink)
I don't think it has that limitation. If you use two of the same fraction un simplified, it spits out another fraction with the same value.
2/6
10/30
=
12/36
All of those equal 1/3, which just kinda blew my mind.
lendluke ยท 1 points ยท Posted at 19:48:47 on May 26, 2016 ยท (Permalink)
I was thinking 2/101 is not halfway between 1/1 and 1/100.
SillyFlyGuy ยท 3 points ยท Posted at 20:43:13 on May 26, 2016 ยท (Permalink)
Not exactly halfway, just technically between.
mrfreshmint ยท 1 points ยท Posted at 21:11:49 on May 27, 2016 ยท (Permalink)
what this guy said. doesnt have to be halfway, just has to lie between, somewhere, and it does!
lendluke ยท 1 points ยท Posted at 04:09:12 on May 28, 2016 ยท (Permalink)
Oh, sorry I didn't read it carefully.
[deleted] ยท 5 points ยท Posted at 00:55:46 on May 26, 2016 ยท (Permalink)
this is a super under-appreciated comment. a part of my brain already knew this but i never really understood it. it has actual life application too, as interesting as the Fibonacci sequence is, i will never use it. this is sort of great when picking something like a socket size for a bolt.
totallymanlytears ยท 1 points ยท Posted at 06:26:21 on May 26, 2016 ยท (Permalink)
socket sets are what came to mind for me as well
davidgro ยท 6 points ยท Posted at 09:15:58 on May 26, 2016 ยท (Permalink)
1/2 + 1/-2 = 2/Uh oh
snitchnipple ยท 8 points ยท Posted at 10:32:51 on May 26, 2016 ยท (Permalink)
The minus sign can be in front of the numerator or denominator, it's interchangeable. So it would be 1/2 + (-1)/2 = 0/2 = 0, which is the right answer :)
thefloydpink ยท 3 points ยท Posted at 14:51:53 on May 26, 2016 ยท (Permalink)
For anyone interested in a proof:
If we take two fractions, without loss of generality we can assume p/q <= r/s. From here we can derive the following relation: ps <= rq.
By adding pq to either side we get ps+pq <= rq + pq, which is the same as p(s+q) <= (r+p)q. Now divide everything by q(q+s) and you get p(s+q)/q(s+q) <= (r+p)q/q(q+s), which is the same as p/q <= (r+p)/(q+s). The right hand side of this equation is the sum of the the numerators divided by the sum of the denominators.
If you add rs to either side of the first relation (instead of pq) you prove that (r+p)/(q+s)<=r/s.
Therefore p/q<=(r+p)/(q+s)<=r/s.
hadtoupvotethat ยท 2 points ยท Posted at 10:18:30 on May 29, 2016 ยท (Permalink)
I was interested in a proof. Thank you.
crvc ยท 2 points ยท Posted at 22:31:22 on May 25, 2016 ยท (Permalink)
this has good application in generating the Farey sequence I believe
Snaperkids ยท 1 points ยท Posted at 02:13:44 on May 26, 2016 ยท (Permalink)
Look up the Stern-Brocot Tree. It is a tree that gives you all the the fractions only once.
Obscu ยท 1 points ยท Posted at 23:36:07 on May 25, 2016 ยท (Permalink)
1/3 < x < 2/3
(1+2)/(3+3) = 3/6 = 1/2
1/3 < 1/2 < 2/3
Checks out
ronnknee ยท -5 points ยท Posted at 06:46:39 on May 26, 2016 ยท (Permalink)
Or you can actually do it properly and get the exact answer.
lurker7087 ยท 2372 points ยท Posted at 11:20:40 on May 25, 2016 ยท (Permalink)
The Fibonacci sequence is encoded in the number 1/89
ktkps ยท 1042 points ยท Posted at 11:38:52 on May 25, 2016 ยท (Permalink)
1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034...
redditsoaddicting ยท 723 points ยท Posted at 12:42:24 on May 25, 2016 ยท (Permalink)*
Where this comes from:
1/(1 - x - x2) = 1 + x + 2x2 + 3x3 + ... (-1 < x < 1)
Let x = 1/10. Then 100(1/89) = 1 + 0.1 + 0.02 + 0.003 + ...
kman601 ยท 630 points ยท Posted at 14:41:14 on May 25, 2016 ยท (Permalink)
Is that.... A Taylor polynomial?
fapstar206587 ยท 1309 points ยท Posted at 14:59:25 on May 25, 2016 ยท (Permalink)
After just finishing calculus 2, that surfaced my PTSD.
BluntTruthGentleman ยท 2147 points ยท Posted at 16:02:29 on May 25, 2016 ยท (Permalink)*
TRIGGONOMETERED
edit: I try guys
[deleted] ยท 157 points ยท Posted at 18:14:29 on May 25, 2016 ยท (Permalink)
[deleted]
DeusXEqualsOne ยท 25 points ยท Posted at 19:16:38 on May 25, 2016 ยท (Permalink)
I guess you could say, he's within the radius of punvergence!
fapstar206587 ยท 3 points ยท Posted at 01:59:30 on May 26, 2016 ยท (Permalink)
An infinitesimally small point
sirius4778 ยท 2 points ยท Posted at 02:57:30 on May 26, 2016 ยท (Permalink)
Evert point is infinitesimally small, right?
LastStar007 ยท 2 points ยท Posted at 23:39:18 on May 25, 2016 ยท (Permalink)
Approximate up to O(x4)
sirius4778 ยท 2 points ยท Posted at 02:57:03 on May 26, 2016 ยท (Permalink)
But just approximately.
scienceofviolin ยท 74 points ยท Posted at 18:58:01 on May 25, 2016 ยท (Permalink)
You trigonometried.
BluntTruthGentleman ยท 3 points ยท Posted at 06:05:52 on May 26, 2016 ยท (Permalink)
God damnit this is such a perfect and eclipsing followup. And thank you.
Kiemebar ยท 2 points ยท Posted at 00:12:08 on May 26, 2016 ยท (Permalink)
You need more credit for this, made me laugh more than the origional!
scienceofviolin ยท 2 points ยท Posted at 00:15:34 on May 26, 2016 ยท (Permalink)
I actually laughed at yours as well cause I misread it as "orthogonal" rather than "original" and thought you were making another math pun.
TheHamCaptain ยท 6 points ยท Posted at 18:57:06 on May 25, 2016 ยท (Permalink)
Hahahaha this made me laugh.
mankstar ยท 3 points ยท Posted at 18:33:38 on May 25, 2016 ยท (Permalink)
I appreciate the effort
NedryOS ยท 5 points ยท Posted at 21:00:15 on May 25, 2016 ยท (Permalink)
I think triggeredometry works better, but I'm no tumblrista
deusset ยท 2 points ยท Posted at 20:15:58 on May 25, 2016 ยท (Permalink)*
I'm embarrassed by how much I laughed at that. Also, I'm in public.
BluntTruthGentleman ยท 2 points ยท Posted at 06:06:46 on May 26, 2016 ยท (Permalink)
Glad I could add to your day!
tiedyechicken ยท 2 points ยท Posted at 20:25:11 on May 25, 2016 ยท (Permalink)
What's funny is that it would have been better had you just used triggered
BluntTruthGentleman ยท 2 points ยท Posted at 05:58:18 on May 26, 2016 ยท (Permalink)
doh
doggmatic ยท 2 points ยท Posted at 07:46:25 on May 26, 2016 ยท (Permalink)
i thought this thread was gonna be terrible but it's genius and hilarious at the same time
xkna21 ยท 2 points ยท Posted at 08:16:30 on May 26, 2016 ยท (Permalink)
OK. hey, wait just a second...
G3Otherm ยท 204 points ยท Posted at 16:33:58 on May 25, 2016 ยท (Permalink)
Ahhh, Post Taylor Series Disorder. You should see a doctor about that friend.
SellMeAllYourKarma ยท 10 points ยท Posted at 17:28:11 on May 25, 2016 ยท (Permalink)
That was pretty clever
Coffee-Anon ยท 8 points ยท Posted at 17:56:36 on May 25, 2016 ยท (Permalink)
To be clear, he means a doctor with a PhD in mathematics, not an MD in a hospital
I_am_a_socialist ยท 10 points ยท Posted at 17:23:06 on May 25, 2016 ยท (Permalink)
If you are in physics or engineering, you will learn to love the Taylor series.
Alkalilee ยท 15 points ยท Posted at 17:43:00 on May 25, 2016 ยท (Permalink)
In Engineering. Taylor and I are on complex terms.
fapstar206587 ยท 2 points ยท Posted at 21:53:49 on May 25, 2016 ยท (Permalink)
That bitch toys with me but she knows I love her...
Coffee-Anon ยท 10 points ยท Posted at 15:41:37 on May 25, 2016 ยท (Permalink)
I hated calc 2
[deleted] ยท 1 points ยท Posted at 17:32:05 on May 25, 2016 ยท (Permalink)
Which one was Calc 2? Are you in high school? While we had algebra 1 and 2, in my high school, we just had AP calculus for calculus. In college there were separate classes for differential, integral, vector, and series calculus. None of them were ever called "Calc 2".
powermad80 ยท 10 points ยท Posted at 17:42:19 on May 25, 2016 ยท (Permalink)
I just finished calc 2 at uni and it was a grab bag of series/sequences, vectors & planes, parametric equations, and trig integrals that make death appealing.
[deleted] ยท 4 points ยท Posted at 17:49:12 on May 25, 2016 ยท (Permalink)
LOL
BorisAcornKing ยท 3 points ยท Posted at 01:35:39 on May 26, 2016 ยท (Permalink)
When I first took it 7 years ago, calc 2 was integrals, reimann sums, areas, volumes, volumes on xy and on periods, and surface areas.
When I took if this last semester, they threw out all of the complicated volume and area questions and made us do sequences and series instead. I think the latter one as easier.
[deleted] ยท 2 points ยท Posted at 17:46:13 on May 25, 2016 ยท (Permalink)
At my university, we had cal 1-4...
I'm somewhat assuming for those first two, since I took them in high school, but even at my high school that's how the designations for calculus 1 and 2 were.
Coffee-Anon ยท 2 points ยท Posted at 17:53:03 on May 25, 2016 ยท (Permalink)
Hmm, mine went: Calc 1-3, then Linear Algebra, then Differential Equations 1 and 2
[deleted] ยท 1 points ยท Posted at 17:57:53 on May 25, 2016 ยท (Permalink)
Even with AP calc, I took the basic ones in college because I knew I'd need it as an engineer. Anyway, my differential equations class was separate from the regular calculus sequence, just like numerical methods, discrete math, and linear algebra. You must have been on a semester system instead of quarters.
[deleted] ยท 1 points ยท Posted at 17:59:46 on May 25, 2016 ยท (Permalink)
Yep, in my opinion a quarter wouldn't have been enough time for most of these courses.
[deleted] ยท 1 points ยท Posted at 18:14:36 on May 25, 2016 ยท (Permalink)
It probably depends on you, the professor, and the classes you're taking at the same time. Did I say it depends on you? If you're anything like my students when I taught, a semester probably isn't enough for any given topic. The reasoning behind prerequisites was lost on them. Reading was a problem too. They would have done much better if they'd just read carefully. They couldn't read the assigned material, the homework problems, or the exam problems. Many will literally kill people after they graduate.
Coffee-Anon ยท 2 points ยท Posted at 17:49:39 on May 25, 2016 ยท (Permalink)
Your series calculus was probably similar to my calc 2. The calculus class I took in high school and Calc 1 in college were both differential and integral calculus together (the same class, in retrospect I should have clepped out of Calc 1). Then Calc 3 was 3d calculus.
Also, I really liked my Calc 1 and Calc 3 profs, and wasn't too thrilled with my calc 2 prof so that could be part of it too
tiajuanat ยท 4 points ยท Posted at 16:22:18 on May 25, 2016 ยท (Permalink)
I haven't had calc II for eight and a half years, and it gave me conniptions.
Alkalilee ยท -1 points ยท Posted at 17:46:00 on May 25, 2016 ยท (Permalink)
Not sure if Dark Souls 3 reference
Cosmic_Pigeon ยท 1 points ยท Posted at 15:32:39 on May 25, 2016 ยท (Permalink)
rip
alexsmithfanning ยท 1 points ยท Posted at 16:43:06 on May 25, 2016 ยท (Permalink)
Is it really as bad as they say? I have to take Calculus 1 next year.
[deleted] ยท 3 points ยท Posted at 17:43:40 on May 25, 2016 ยท (Permalink)
No. Learning it for the sake of learning it might suck though. I took AP calculus while I took trig based physics in high school because we didn't have AP physics. I saw how it was applicable and made everything easier... Differential calculus is essentially division and integral calculus is essentially multiplication. They're just in multiple dimensions and/or for curves. Vector calculus helps extended it into even more dimensions. My best advice is to find a good reason for it. Apply it. Don't let it just be abstract.
Alkalilee ยท 2 points ยท Posted at 17:46:59 on May 25, 2016 ยท (Permalink)
Calc 1 is a breeze. I went to one lecture all semester and still finished with a 79. Calc 2 is where the issues start.
BeardyMcNeckbeard ยท 1 points ยท Posted at 18:12:26 on May 25, 2016 ยท (Permalink)*
If you're solid in algebra and trigonometry, then you will be just fine.
[deleted] ยท 1 points ยท Posted at 19:50:49 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 21:19:12 on May 25, 2016 ยท (Permalink)
I'm pretty sure very few people will agree that Calc 1 was harder than Calc 3. I'm not sure what you learned exactly in those classes but Calc 3 was definitely far tougher.
GladiatorGary ยท 1 points ยท Posted at 16:52:43 on May 25, 2016 ยท (Permalink)
Same. I need help.
danhakimi ยท 1 points ยท Posted at 17:21:58 on May 25, 2016 ยท (Permalink)
Eight years later: Same. I'm happy I know what they are, and I never want to go near them again.
Alkalilee ยท 1 points ยท Posted at 17:40:43 on May 25, 2016 ยท (Permalink)
I just got my 60 in Calc 2, I understood approximately a third of the course. Praise the curve.
graciegray ยท 1 points ยท Posted at 18:06:29 on May 25, 2016 ยท (Permalink)
Using a third degree Taylor polynomial, find the error bound for e<.01 God damn.
jijibs ยท 1 points ยท Posted at 18:59:09 on May 25, 2016 ยท (Permalink)
wish me luck for next year. I'm going in!
Hanta3 ยท 1 points ยท Posted at 19:14:31 on May 25, 2016 ยท (Permalink)
Huh, I never learned that in calc 2. Go figure.
Goku_Uzamaki ยท 1 points ยท Posted at 19:54:23 on May 25, 2016 ยท (Permalink)
have fun in diff eq. even more sequences and way harder lol
BlindManBaldwin ยท 1 points ยท Posted at 20:27:05 on May 25, 2016 ยท (Permalink)
Taylor Series are the best though
Player8 ยท 1 points ยท Posted at 21:07:58 on May 25, 2016 ยท (Permalink)
As someone who switched to business major after Calc 2, what's a Taylor polynomial?
Mister1911 ยท 2 points ยท Posted at 04:25:52 on May 26, 2016 ยท (Permalink)
A Taylor Series that doesn't go on forever. You stop the Taylor Series at the nth derivative, where it's now a polynomial of the nth degree.
Odd-One ยท 1 points ยท Posted at 21:57:01 on May 25, 2016 ยท (Permalink)
I wouldn't reccomend Complex Variables then..
jesset77 ยท 1 points ยท Posted at 23:10:23 on May 25, 2016 ยท (Permalink)
Looks quizzical.
I learnt about Taylor polynomials in middle school due to my TI-81 graphing calculator supporting that natively (up to 6 degrees or so) in it's version of Basic.
How do they get used in Calc 2 that's so traumatizing? :o
Dovah1443 ยท 1 points ยท Posted at 02:15:07 on May 26, 2016 ยท (Permalink)
Just finished AP Calculus and Taylor Polynomials are why I won't have made a 4 on my AP Exam
fapstar206587 ยท 1 points ยท Posted at 02:22:18 on May 26, 2016 ยท (Permalink)
I hate them man. Those and power series fucked me on my final but I ended up with a B so I can't complain.
Dovah1443 ยท 1 points ยท Posted at 02:30:57 on May 26, 2016 ยท (Permalink)
I ended up with an A but I'll probably have to retake it in college though
fapstar206587 ยท 1 points ยท Posted at 02:34:34 on May 26, 2016 ยท (Permalink)
It depends on your major but I don't think it'll be a bad idea to do that. You just don't get the same rigor that you do in high school that you do in college.
sirius4778 ยท 1 points ยท Posted at 02:56:29 on May 26, 2016 ยท (Permalink)
You know I just finished calculus ll and can't make sense of anything on this page. Don't tell my professor. I'm ashamed.
PotHead96 ยท 1 points ยท Posted at 04:05:54 on May 26, 2016 ยท (Permalink)
I'm solving 6hs of differential equations and recurrence relations a day for the class I'm taking.
ImS0hungry ยท 1 points ยท Posted at 06:24:58 on May 26, 2016 ยท (Permalink)
I'm going to taking Calc2 in a 5 week summer session....did i just sign my own death warrant?
fapstar206587 ยท 1 points ยท Posted at 06:32:41 on May 26, 2016 ยท (Permalink)
Nah bro, you got it. It's hard but you have to hang in there. Don't skip class though, that's a big mistake.
ImS0hungry ยท 1 points ยท Posted at 07:18:06 on May 26, 2016 ยท (Permalink)
its 5 hours a day, 4 days a week, for 5 weeks. I absolutely rocked calc 1, so i'm feeling confident, but I've been hearing a lot of bad things about calc 2 from my STEM buddies. I'm setting myself up for Linear this fall.
fapstar206587 ยท 1 points ยท Posted at 14:47:11 on May 26, 2016 ยท (Permalink)
It all depends on your professor. Calc 2 is definitely more difficult to understand than calc 1 though.
[deleted] ยท -5 points ยท Posted at 15:14:18 on May 25, 2016 ยท (Permalink)
[deleted]
andinuad ยท 9 points ยท Posted at 15:46:28 on May 25, 2016 ยท (Permalink)*
That's good since taylor expansions is one of the most widely used mathematical tools in physics.
dny6 ยท 10 points ยท Posted at 15:17:09 on May 25, 2016 ยท (Permalink)
ok. take an algorithm class then.
Pm_me_any_dragon ยท 1 points ยท Posted at 17:01:53 on May 25, 2016 ยท (Permalink)
Algorythms are pretty awesome.
And then there is fast inverse square root. Which just blows my mind each time i see it. (Because how could anyone figure that out)
[deleted] ยท 1 points ยท Posted at 15:58:16 on May 25, 2016 ยท (Permalink)*
[deleted]
Bioman312 ยท 3 points ยท Posted at 16:09:08 on May 25, 2016 ยท (Permalink)
/r/ihaveanibdiploma
Yurika_BLADE ยท 5 points ยท Posted at 16:03:48 on May 25, 2016 ยท (Permalink)
Every physicist, engineer, and mathematician should find the level of Taylor Polynomials taught in Calc 2 easy. It has useful applications in linear algebra, modeling, circuits, and so on.
ATownStomp ยท 2 points ยท Posted at 17:20:18 on May 25, 2016 ยท (Permalink)
It might be simple but it isn't easy.
[deleted] ยท 0 points ยท Posted at 16:19:04 on May 25, 2016 ยท (Permalink)
"Every."
Either I can't handle mathemagics, or it wasn't tought to me well enough because I look at that shit and I just. don't. get it.
tiajuanat ยท 1 points ยท Posted at 16:27:37 on May 25, 2016 ยท (Permalink)
Going from open form to closed form Taylor series is nontrivial, and anyone who says otherwise is a liar, or inexperienced.
andinuad ยท 1 points ยท Posted at 18:15:12 on May 25, 2016 ยท (Permalink)
I haven't heard that terminology before. By "open" and "closed" form, do you refer to what's written on the 2nd page in http://people.math.sc.edu/girardi/m142/handouts/06FTaylorPolySeries.pdf?
tiajuanat ยท 1 points ยท Posted at 18:47:41 on May 25, 2016 ยท (Permalink)
I can't open the PDF for whatever reason, but open form is generally prefaced with a sigma or pi, for summation and product series respectively.
Closed form is like cos, sin, tan.
It starts out easy, but ramps up in difficulty.
andinuad ยท 1 points ยท Posted at 18:54:43 on May 25, 2016 ยท (Permalink)
Ok, so I am guessing you mean that given an explicit open form, it can sometimes be hard to write down it in a closed form where one has explicitly stated the n'th coefficient in the sum/product?
That I can agree with. If I find it too hard to find the explicit expression for the n'th coefficient, I'll just refer to an equation that yields it implicitly.
godnah ยท 1 points ยท Posted at 16:42:01 on May 25, 2016 ยท (Permalink)
don't be so hyperbolic, it's just a saddle point
SkeetOnYaBish4Head ยท 1 points ยท Posted at 17:27:49 on May 25, 2016 ยท (Permalink)
I believe you mean parabolic.
[deleted] ยท 1 points ยท Posted at 16:57:25 on May 25, 2016 ยท (Permalink)
Took Calc 2 4 years ago. The PTSD doesn't go away.
Ancient_hacker ยท 14 points ยท Posted at 15:59:15 on May 25, 2016 ยท (Permalink)
You can think of it as one. When they encode sequences in this way they're known as generating functions.
lagerbaer ยท 13 points ยท Posted at 16:32:40 on May 25, 2016 ยท (Permalink)
It's related, but not the same. 1/(1 - x - x2) is the generating function of the Fibonacci sequence. For any sequence An (n = 1, 2, 3, ...) you can define a polynomial whose n-th coefficient is the n-th element of the series, so A_0 + A_1 x + A_2 x2 + ...
Using the recurrence relation of the Fibonacci numbers, you can then show that this polynomial sums to the function 1/(1 - x - x2).
Generating functions have a lot of uses. For example, it can give you a closed form for the Fibonacci numbers. Use the partial fraction expansion on the form 1/(1 - x - x2), obtain two terms that can be expanded as a geometric series, whose coefficients have simple closed forms.
needuhLee ยท 6 points ยท Posted at 16:36:12 on May 25, 2016 ยท (Permalink)
It's a generating function, but is a similar idea!
snuffleupagus_Rx ยท 3 points ยท Posted at 19:20:48 on May 25, 2016 ยท (Permalink)
It's also a Taylor series (though in this context we're using it as a generating function).
Bobshayd ยท 4 points ยท Posted at 15:55:11 on May 25, 2016 ยท (Permalink)
It's actually a formal power series.
vimsical ยท 1 points ยท Posted at 19:50:11 on May 25, 2016 ยท (Permalink)
In this case, it is called a "Generating Function". Function whose Taylor expansion has coefficients corresponding to the sequence.
This can be done for any sequence. https://en.wikipedia.org/wiki/Generating_function
nnitro ยท 1 points ยท Posted at 20:24:45 on May 25, 2016 ยท (Permalink)
No. A generating function
udbluehens ยท 1 points ยท Posted at 02:07:05 on May 26, 2016 ยท (Permalink)
Isn't everything?
r1p4c3 ยท 1 points ยท Posted at 07:04:39 on May 26, 2016 ยท (Permalink)
Technically it's a generating function.
DRHARNESS ยท -2 points ยท Posted at 14:48:24 on May 25, 2016 ยท (Permalink)
Yep!
ThereOnceWasAMan ยท 17 points ยท Posted at 15:09:13 on May 25, 2016 ยท (Permalink)
No it isn't. It's a generating function. Not all power series are Taylor polynomials.
snuffleupagus_Rx ยท 4 points ยท Posted at 15:13:41 on May 25, 2016 ยท (Permalink)
It is a Taylor series centered at x=0 though.
ninjalink84 ยท 3 points ยท Posted at 16:29:55 on May 25, 2016 ยท (Permalink)*
Nah, in order to be a Taylor series, it would have to converge to a function in some neighborhood of 0. This is a generating function, which is a similar looking formal construct, but is different in all practical uses.
Edit: Ignore this hasty, completely false statement that I made. /u/YoungIgnorant below me has the right idea.
YoungIgnorant ยท 7 points ยท Posted at 16:50:34 on May 25, 2016 ยท (Permalink)
It converges for x within 1/phi of 0 to 1/(1 - x - x2 ) (just do the root test)
snuffleupagus_Rx ยท 2 points ยท Posted at 19:01:40 on May 25, 2016 ยท (Permalink)*
We may be working with different definitions of Taylor Series, but if you look at the definition here you see that the series in /u/redditsoaddicting comment is what you obtain by plugging in f(x)=1/(1-x-x2 ) with a=0.
Convergence of Taylor series is a separate issue. Every Taylor series converges at its center, though for some Taylor series this is the only place it converges (we say that those functions have radius of convergence equal to 0). There are even some Taylor series which do converge everywhere, but to a different function (see the example of the piecewise function f(x) given in here).
Functions f(x) for which the Taylor series at every point converges to f(x) in a neighborhood of that point are called analytic, a property which gives complex analysis much of it's flavor.
ThereOnceWasAMan ยท 0 points ยท Posted at 17:45:04 on May 25, 2016 ยท (Permalink)*
A Taylor series has a very specific definition. The coefficients of a Taylor series are generated from successively higher derivatives of some differentiable function (along with some factorials). What differentiable function has derivatives such that you get the coefficients described in the top parent comment?
edit: I was wrong, as /u/snuffleupagus_Rx pointed out
snuffleupagus_Rx ยท 2 points ยท Posted at 19:09:06 on May 25, 2016 ยท (Permalink)*
I explained this in a comment above (including the subtleties of convergence), but if you look at the definition here you see that the series in /u/redditsoaddicting comment is what you obtain by plugging in f(x)=1/(1-x-x2 ) with a=0.
In other words, it's a Taylor series for the function f(x) = 1/(1-x-x2 ) centered at 0. In fact, any time you can express a function as a series of the form
f(x) = c_0 + c_1 (x-a) + c_2 (x-a)2 + ...
the series on the right-hand-side will be THE Taylor series for f(x) centered at x=a (which you can verify by taking derivatives on both sides to see that the coefficients match the form of the coefficients from the Taylor series).
ThereOnceWasAMan ยท 2 points ยท Posted at 22:45:16 on May 25, 2016 ยท (Permalink)
You are right and I am wrong. Thanks for enlightening me.
KrishaCZ ยท 0 points ยท Posted at 16:40:57 on May 25, 2016 ยท (Permalink)
Taywhat?
jelloey ยท 15 points ยท Posted at 15:42:24 on May 25, 2016 ยท (Permalink)
You chose a poor place for the ..., it seems like the next terms in the power series will be 4x4 + 5x5 instead of 5x4 + 8x5
redditsoaddicting ยท 1 points ยท Posted at 15:56:09 on May 25, 2016 ยท (Permalink)
Yeah, I was debating it, but I was short on time.
derangerd ยท 2 points ยท Posted at 20:22:12 on May 25, 2016 ยท (Permalink)
Is x =1/10 because base 10?
redditsoaddicting ยท 3 points ยท Posted at 21:41:09 on May 25, 2016 ยท (Permalink)
Yeah, I could see this working the same way in other bases. That is, sub in 1/b and expand the polynomial all in terms of that base b. It would be interesting to see if it truly does.
Detritovore ยท 2 points ยท Posted at 17:24:13 on May 26, 2016 ยท (Permalink)*
To immediately see this, let's define formally
f(x) = 1 + x + 2x2 + 3x3 + 5x4 + 8x5 + ...
x f(x) = 0 + x + x2 + 2x3 + 3x4 + 5x5 + ...
x2 f(x) = 0 + 0 + x2 + x3 + 2x4 + 3x5 + ...
The defining property of the Fibonacci sequence is that every number in the sequence is the sum of the previous two numbers. So, if you look at coefficients in the above generating functions, you see that f(x) = 1 + x f(x) + x2 f(x), which can be rearranged to give f(x) = 1/(1 - x - x2 ).
FertilePosition ยท 1 points ยท Posted at 17:04:11 on May 25, 2016 ยท (Permalink)
This is similar to a cool blog post I saw this year: https://mathwithbaddrawings.com/2016/03/14/the-pi-day-recipe-book/. I thought it had something about the Fibonacci sequence in it because I also remember looking at something rehashed to it this semester as well. This is a lot if cool things about pi!!!
richardathome ยท 1 points ยท Posted at 20:31:26 on May 25, 2016 ยท (Permalink)
THAT'S NUMBERWANG!
How_Suspicious ยท 7 points ยท Posted at 15:00:50 on May 25, 2016 ยท (Permalink)
How the FUCK did they figure this out?
Terracot ยท 8 points ยท Posted at 15:39:52 on May 25, 2016 ยท (Permalink)
Using math
columbus8myhw ยท 1 points ยท Posted at 12:44:34 on May 26, 2016 ยท (Permalink)*
Hint: 1+x+10x=100x, where x is that infinite series.
calvangri ยท 3 points ยท Posted at 20:36:48 on May 25, 2016 ยท (Permalink)
I keep getting the number 0.011235955056180. I don't think this is correct.
Edit: Never mind. I see how it's done. I'm a derp.
columbus8myhw ยท 0 points ยท Posted at 12:43:22 on May 26, 2016 ยท (Permalink)*
You can prove this by showing 1+x+10x=100x. I can write the details later if you want, but this essentially boils down to the fact that the sum of consecutive Fibonacci numbers is the next one.
whebzy ยท 1 points ยท Posted at 13:18:29 on May 26, 2016 ยท (Permalink)
That doesn't make sense, you end up at:
columbus8myhw ยท 1 points ยท Posted at 17:03:27 on May 26, 2016 ยท (Permalink)
Whoops. Fixed. We have 1+x+10x=100x.
Aj16ay ยท -1 points ยท Posted at 17:12:20 on May 25, 2016 ยท (Permalink)
This is false
[deleted] ยท 74 points ยท Posted at 11:50:29 on May 25, 2016 ยท (Permalink)
[deleted]
Umbrall ยท 15 points ยท Posted at 14:49:24 on May 25, 2016 ยท (Permalink)
I would just cut it to 8/5 and be done with it. If I'm doing it in my head I'm not doing 13/8
heeb ยท 8 points ยท Posted at 16:31:02 on May 25, 2016 ยท (Permalink)
Indeed. I'm from mainland Europe but live in the UK.
Whenever I see 20 mph, I think 30 km/h.
Whenever I see 30 mph, I think 50 km/h.
Whenever I see 50 mph, I think 80 km/h.
Thanks, Fibonacci! :)
FrenchyFungus ยท 2 points ยท Posted at 16:44:25 on May 25, 2016 ยท (Permalink)
The point is that, since 13 follows 8 in the Fibonacci sequence, you already know that 13/8 is roughly 1.61, and therefore 8 miles is roughly 13km - no calculations are necessary.
elyisgreat ยท 6 points ยท Posted at 14:27:41 on May 25, 2016 ยท (Permalink)
I made up separate units for this, because it's not quite the golden ratio...
dalr3th1n ยท 3 points ยท Posted at 15:24:38 on May 25, 2016 ยท (Permalink)
For those who didn't follow what this means: you can (approximately) convert from miles to kilometers by taking your number of miles, (say 5) and just getting the next Fibonacci number (in this case 8).
This is of course a bit harder to do if you want to convert 6 miles to kilometers.
DrAgonit3 ยท 1 points ยท Posted at 16:22:50 on May 25, 2016 ยท (Permalink)
Or just ditch murica and use metric all the way.
karlexceed ยท 1 points ยท Posted at 16:50:21 on May 25, 2016 ยท (Permalink)
Now, to get the Brits to stop using miles as well...
thephotoman ยท 1 points ยท Posted at 19:33:55 on May 25, 2016 ยท (Permalink)
Not just that, but any sequence f defined by fixing f(1) and f(2), then defining all other numbers in the sequence as f(n) = f(n-1) + f(n-2) will have the ratio f(n)/f(n-1) approach the golden ratio as n goes to infinity.
rubelmj ยท 3 points ยท Posted at 16:28:52 on May 25, 2016 ยท (Permalink)
Another fun related math/biology fact: because it's the product of haplodiploid sexual reproduction, the number of ancestors a drone (male) bee has follows the Fibonacci sequence as you move along the family tree.
kroxigor01 ยท 2 points ยท Posted at 16:10:44 on May 25, 2016 ยท (Permalink)
I'm fucking freaking out man
KypDurron ยท 2 points ยท Posted at 23:12:04 on May 25, 2016 ยท (Permalink)
Every sequence is encoded in every transcendental number. At some point in pi, there exists a string of ones and zeroes that would, when converted into alphanumeric text, spell out the entire written works of mankind, in chronological order, from the beginning of the invention of writing.
And then in another spot, there will be a string of ones and zeroes that spell out the exact chemical composition for a drug that can kill cancer cells without killing healthy ones.
In another place, a string for code that creates a strong AI that follows Asimov's Three Laws. And another string that makes a strong AI that will kill all humans.
Infinite length means everything will eventually be found in it.
53504 ยท 1 points ยท Posted at 15:58:48 on May 25, 2016 ยท (Permalink)
Why is this your favorite? I'm not attacking. Just wondering. If you encode it like you say it's going to add up to something. Am I missing why it's particularly interesting?
[deleted] ยท 1 points ยท Posted at 16:05:21 on May 25, 2016 ยท (Permalink)
The guy from prison break?
actual_factual_bear ยท 1 points ยท Posted at 16:31:55 on May 25, 2016 ยท (Permalink)
Can you generalize that for other recurrence relations?
quatrevingtneuf ยท 1 points ยท Posted at 16:46:42 on May 25, 2016 ยท (Permalink)
this is my #1 reason for 89 being my favourite number
Treeflower ยท 1 points ยท Posted at 19:15:12 on May 25, 2016 ยท (Permalink)
1/81 is also pretty cool :D
Aj16ay ยท 0 points ยท Posted at 17:11:48 on May 25, 2016 ยท (Permalink)
Not true
godnah ยท -1 points ยท Posted at 16:41:07 on May 25, 2016 ยท (Permalink)
Whoa of all of these this is one I've never heard, time to pull out a notebook and a joint and figure this shit out...
[deleted] ยท 8339 points ยท Posted at 11:34:25 on May 25, 2016 ยท (Permalink)
[deleted]
ktkps ยท 3593 points ยท Posted at 11:40:39 on May 25, 2016 ยท (Permalink)
You forgot to mention the best part: These numerical values stays true for Mercury, Mars, Jupiter, even the Sun (if you could stand on all of these)!
sorry /u/jerkandletjerk
jack_brew ยท 3093 points ยท Posted at 14:15:17 on May 25, 2016 ยท (Permalink)
So you're saying increasing the circumference of a circle by 6.3m will increase its radius by 1 meter regardless of its initial size?
kDubya ยท 1905 points ยท Posted at 14:22:05 on May 25, 2016 ยท (Permalink)*
Yup, exactly.
*edit:
Ok everybody, here are some common responses, and below each is my response:
No, it doesn't. pi doesn't equal 3.14159265, either, but it's good enough for the vast majority of cases and is plenty accurate. For a simple thought experiment like this, 6.3 is close enough to 2*pi and results in an extra 2.7 mm radius over the 1 m stated.
It works at any scale. Wrap a carbon nanotube rope around a speck of dust. It still works, because it's a simple mathematical relationship between radius and circumference. For any change in radius, there will be a corresponding change in circumference that will be 2 * pi (roughly 6.3) times the change in radius.
jack_brew ยท 1183 points ยท Posted at 14:26:46 on May 25, 2016 ยท (Permalink)
Neat
fghjconner ยท 558 points ยท Posted at 14:58:45 on May 25, 2016 ยท (Permalink)
Since circumference is equal to 2 * pi * r, it makes sense. If you increase the radius by 1 it's equal to 2 * pi * (r+1) which equals (2 * pi * r) + 2 * pi.
[deleted] ยท 301 points ยท Posted at 15:21:56 on May 25, 2016 ยท (Permalink)*
[removed]
willyolio ยท 729 points ยท Posted at 15:58:20 on May 25, 2016 ยท (Permalink)*
For those of you who still don't get it:
โซโ((r+1)2 cos2 [t]+ (r+1)2 sin2 [t])dt - โซโ(r2 cos2 [t]+ r2 sin2 [t])dt = ~6.28 for t = [0,2ฯ]
edit: damnit reddit, 7 hours in and nobody commented on the error in the equation. Y'all failed me. it's fixed now... probably
CyborgSlunk ยท 133 points ยท Posted at 16:07:56 on May 25, 2016 ยท (Permalink)
ELI maths major.
downbeataura ยท 184 points ยท Posted at 18:07:07 on May 25, 2016 ยท (Permalink)
The proof is left as an exercise for the reader.
[deleted] ยท 4 points ยท Posted at 21:00:57 on May 25, 2016 ยท (Permalink)
Most perfect reply ever.
UraniumSpoon ยท 2 points ยท Posted at 23:39:21 on May 25, 2016 ยท (Permalink)
This triggers my PTSD from my discrete mathematics class.
expateli ยท 1 points ยท Posted at 23:53:03 on May 25, 2016 ยท (Permalink)
This sentence is giving me flashbacks to Calc 3 at Uni... shudder.
Testas86 ยท 1 points ยท Posted at 02:09:27 on May 26, 2016 ยท (Permalink)
Lol after just finishing teaching my self linear algebra this is the best comment!
PolioKitty ยท 60 points ยท Posted at 16:13:13 on May 25, 2016 ยท (Permalink)
I'll have a truly remarkable proof of this, which Reddit comments are too small to contain.
PaulJAsimov ยท 11 points ยท Posted at 17:56:26 on May 25, 2016 ยท (Permalink)
ELI Fermat
mountaincyclops ยท 2 points ยท Posted at 19:08:41 on May 25, 2016 ยท (Permalink)
Imgur or it didn't happen?
GeeJo ยท 2 points ยท Posted at 19:43:55 on May 25, 2016 ยท (Permalink)
You don't fool me. I know that you co-wrote the definitive paper on this.
CyborgSlunk ยท 1 points ยท Posted at 21:47:41 on May 25, 2016 ยท (Permalink)
You caught me, I definitely prefer minimal compactness in my curves if you know what I'm sayin
[deleted] ยท 1 points ยท Posted at 20:59:54 on May 25, 2016 ยท (Permalink)
When did math become maths?
DemonicMandrill ยท 5 points ยท Posted at 17:59:06 on May 25, 2016 ยท (Permalink)
for fucks sake mate I'm studying for an integer (integrals? not really sure how it translates) test tomorrow, and I can't make a single one of them I was trying to escape to reddit but nooooooo, you just had to press my face in it huh?
Steel_Shield ยท 5 points ยท Posted at 19:34:12 on May 25, 2016 ยท (Permalink)
An integer is a whole number (1, 2, 3.... n). An integral is what you mean here and is the opposite of a differential/derivative.
The branch of maths about differentials and integrals is commonly called Calculus.
DemonicMandrill ยท 2 points ยท Posted at 19:35:47 on May 25, 2016 ยท (Permalink)
....help me. I see k's and x's and square roots and /'s floating in front of me, they're laughing at me, mocking me, I should burn them, I should burn them all.....
Steel_Shield ยท 2 points ยท Posted at 19:40:35 on May 25, 2016 ยท (Permalink)
Well. Good luck tomorrow!
DemonicMandrill ยท 1 points ยท Posted at 11:02:25 on May 29, 2016 ยท (Permalink)
it went fucking horrible, but thanks anyway.
[deleted] ยท 1 points ยท Posted at 22:11:20 on May 25, 2016 ยท (Permalink)
Yeah based on your response, you probably haven't learned how to integrate by parts yet and so you cant compute the integrals above yet.
I wouldn't worry about seeing stuff like that above on your test, but if you do there is a super easy way to evaluate the riemenn integral of the product of a function which is finitely differentiable and something like cos(x) or ex, which are infinitely differentiable. Look up 'integration by parts using table' if you're concerned.
slickasducks ยท 8 points ยท Posted at 16:25:04 on May 25, 2016 ยท (Permalink)
Finally a ELIF!
PhysicalStuff ยท 16 points ยท Posted at 17:24:48 on May 25, 2016 ยท (Permalink)
Explain Like I'm Frobenius
Astrobliss ยท 5 points ยท Posted at 18:51:24 on May 25, 2016 ยท (Permalink)
Explain Like I'm Feynman
Fletch_Lives_ ยท 1 points ยท Posted at 21:20:08 on May 25, 2016 ยท (Permalink)
Explain Like I'm Fry.
I asked a cop once. It means "Up yours, kid".
film_composer ยท 9 points ยท Posted at 16:53:51 on May 25, 2016 ยท (Permalink)
ohhh
cascer1 ยท 8 points ยท Posted at 17:39:29 on May 25, 2016 ยท (Permalink)
For those who still don't get it: just accept this is a fact and let it go.
corobo ยท 4 points ยท Posted at 18:09:23 on May 25, 2016 ยท (Permalink)
Finally someone in this message chain gets me
Jurby ยท 3 points ยท Posted at 17:56:59 on May 25, 2016 ยท (Permalink)
Oh thanks, that cleared it all up
GuitarRunner ยท 6 points ยท Posted at 16:56:23 on May 25, 2016 ยท (Permalink)
For those who still don't get it: just nod your head and say yes
FlexGunship ยท 2 points ยท Posted at 17:41:33 on May 25, 2016 ยท (Permalink)
This was worth it.
InsiderT ยท 2 points ยท Posted at 17:49:32 on May 25, 2016 ยท (Permalink)
Oh FFS /u/fghjconner and /u/ph0t0shop, why didn't you just say that!!
BuyThisVacuum1 ยท 3 points ยท Posted at 16:52:09 on May 25, 2016 ยท (Permalink)
Rdrr?
JebbeK ยท 2 points ยท Posted at 17:42:39 on May 25, 2016 ยท (Permalink)
For those of you who still dont get it
+68ยฅ&#hร รฆล7%รทโยฅ{ยฅ
Wildwoodywoodpecker ยท 1 points ยท Posted at 17:42:02 on May 25, 2016 ยท (Permalink)
You da real mvp
reddit_orangeit ยท 1 points ยท Posted at 17:52:48 on May 25, 2016 ยท (Permalink)
Oh, now I get it!
obscurecolours ยท 1 points ยท Posted at 18:00:00 on May 25, 2016 ยท (Permalink)
okay that was less than not helpful
Kaldricus ยท 1 points ยท Posted at 18:14:09 on May 25, 2016 ยท (Permalink)
NOW it makes sense
FromTheFieldOfJay ยท 1 points ยท Posted at 18:15:19 on May 25, 2016 ยท (Permalink)
Well now you put that that way...
JimTheActuary ยท 1 points ยท Posted at 18:15:40 on May 25, 2016 ยท (Permalink)
For those of you who still don't get it:
I've got nothing for ya, head back to camp.
Panda_Bowl ยท 1 points ยท Posted at 18:21:54 on May 25, 2016 ยท (Permalink)
For those who still don't get it:
Make rope longer, rope gets longer.
Pettycash80 ยท 1 points ยท Posted at 18:41:21 on May 25, 2016 ยท (Permalink)
Oh ok
clusterlove ยท 1 points ยท Posted at 18:55:36 on May 25, 2016 ยท (Permalink)
....thanks for clearing that up.
NettleFrog ยท 1 points ยท Posted at 18:59:07 on May 25, 2016 ยท (Permalink)
Thank you. Finally someone speaking English here.
Hegiman ยท 1 points ยท Posted at 19:03:08 on May 25, 2016 ยท (Permalink)
Ah yes I was totally flummoxed by the previous equation, now that you've simplified it I completely get it. /s
food_bag ยท 1 points ยท Posted at 19:08:57 on May 25, 2016 ยท (Permalink)
For those who still don't get it, 6.3 is double pi.
TheCreepUnderYourBed ยท 1 points ยท Posted at 19:36:04 on May 25, 2016 ยท (Permalink)
Finally a simple explanation
tim_jam ยท 1 points ยท Posted at 20:03:06 on May 25, 2016 ยท (Permalink)
I mean, yeah if you're gonna simplify it...
Shootypatootie ยท 1 points ยท Posted at 20:13:58 on May 25, 2016 ยท (Permalink)
I want to gold this
Calbomb98 ยท 1 points ยท Posted at 20:38:31 on May 25, 2016 ยท (Permalink)
And if you still still don't get it: x% of y = y% of x
trogers1995 ยท 1 points ยท Posted at 21:56:38 on May 25, 2016 ยท (Permalink)
Thanks now it's super clear.
JC1112 ยท 1 points ยท Posted at 22:03:15 on May 25, 2016 ยท (Permalink)
Oooookay, that makes much more sense, thank you.
nanotubes ยท 1 points ยท Posted at 23:34:55 on May 25, 2016 ยท (Permalink)*
Just saw this. Should be Pi*n, technically not part of the equation.
Edit: Also not too sure that the integrals gives the circumference either...you are integrating radius. (Also my calc/trig is pretty rusty, haven't had the need to use it in a long time haha)
MauPow ยท 1 points ยท Posted at 23:38:42 on May 25, 2016 ยท (Permalink)
Clear as mud, thanks
_lukey___ ยท 1 points ยท Posted at 23:41:23 on May 25, 2016 ยท (Permalink)
Okay but I can't even read that let alone find the error...
Tm1337 ยท 1 points ยท Posted at 12:31:26 on May 26, 2016 ยท (Permalink)
Now in latex
[deleted] ยท 1 points ยท Posted at 08:05:04 on June 2, 2016 ยท (Permalink)
that makes me get it even less.
Anouther ยท 52 points ยท Posted at 15:24:31 on May 25, 2016 ยท (Permalink)
As someone who didn't initially still didn't get it, thank you, I, a non-mathematician, totally understand your much longer equation like 2nd-grade English.
spidaminida ยท 3 points ยท Posted at 15:34:28 on May 25, 2016 ยท (Permalink)
If you take the Earth, moon, sun variable out the equation, and imagine there is a single point with no radius, the rope makes a circle with a radius of 1m.
Put that into the 2ฯr equation to find how much rope you need, and it's about 6.3m.
The radius of the circle (Earth, sun, moon) is ADDED to this number, which means that the extra amount of rope you need is always the same.
Anouther ยท 2 points ยท Posted at 15:38:37 on May 25, 2016 ยท (Permalink)
But why not just one nanometer to make it rise from the ground? Why sex and some change?
spidaminida ยท 2 points ยท Posted at 15:40:30 on May 25, 2016 ยท (Permalink)
Because fickle fillies fly frequently.
DJDomTom ยท 2 points ยท Posted at 16:27:08 on May 25, 2016 ยท (Permalink)
Never question sex. Just let it happen.
Anouther ยท 1 points ยท Posted at 19:59:20 on May 25, 2016 ยท (Permalink)
Right, but why also some change? I mean, thanks, but I already had bus fare.
UltimateDracoMeteor ยท 2 points ยท Posted at 16:44:05 on May 25, 2016 ยท (Permalink)
Oh, because THAT helps.
steppe5 ยท 1 points ยท Posted at 16:24:47 on May 25, 2016 ยท (Permalink)
RDRR?
h83r ยท 1 points ยท Posted at 16:40:00 on May 25, 2016 ยท (Permalink)
Ahh yes, I know some of these variables
lickylicky_69 ยท 1 points ยท Posted at 16:49:31 on May 25, 2016 ยท (Permalink)
Okay as some who got the equation but didn't quite understand it yet here's what my presumption was - the length of the rope which goes around the equator.
The length of the equator changes causing the length of the rope to change.
Hopefully those who didn't get it now get it
IsNotAPipe ยท 1 points ยท Posted at 16:59:00 on May 25, 2016 ยท (Permalink)
For those who still don't get it:
2 * ฯ * (r+1) = 2((ฯr) + (ฯ*1)) = 2ฯr + 2ฯ = the original length + ยฑ6.3
buck9000 ยท 1 points ยท Posted at 17:01:57 on May 25, 2016 ยท (Permalink)
do what now?
SneakyRocket ยท 1 points ยท Posted at 18:30:14 on May 25, 2016 ยท (Permalink)
If I didn't get it before asshole, I sure can't get it now.
aduar ยท 1 points ยท Posted at 18:57:29 on May 25, 2016 ยท (Permalink)
Google: the chicken from minsk
needsmoresteel ยท 1 points ยท Posted at 19:02:44 on May 25, 2016 ยท (Permalink)
The very second I see a formula like this my brain begins having an out of body experience.
guninmouth ยท 1 points ยท Posted at 19:02:55 on May 25, 2016 ยท (Permalink)
Ok. Got it.
DaxNagtegaal ยท 1 points ยท Posted at 16:20:33 on May 25, 2016 ยท (Permalink)
Yes
DJGiblets ยท 1 points ยท Posted at 17:47:02 on May 25, 2016 ยท (Permalink)
The math makes perfect sense, but would someone be able to explain it in a more physical way? Intuitively, it just seems like such a big sphere would need more than 6.3m to lift up the rope by 1m on all sides.
fghjconner ยท 2 points ยท Posted at 18:00:45 on May 25, 2016 ยท (Permalink)
Imagine if the earth was a cube. The rope around the equator would then be a square. Obviously if you want to lift up one side of that square by one meter, you need to add two meters of rope (lengthen both adjacent sides by one meter). So to move the whole rope up a meter, you have to add 8 meters of rope, no matter how big the original square was. From there, it's not that surprising it works similarly with a circle.
DJGiblets ยท 1 points ยท Posted at 19:22:31 on May 25, 2016 ยท (Permalink)
Ya that helped, thanks! Still feels weird to think about, but pretty undeniably true.
jk01 ยท -1 points ยท Posted at 16:20:37 on May 25, 2016 ยท (Permalink)
This shows why pi is stupid and tau is much more useful
mojomagic66 ยท 7 points ยท Posted at 14:54:27 on May 25, 2016 ยท (Permalink)
How neat is that!
JordHardwell ยท 2 points ยท Posted at 17:34:22 on May 25, 2016 ยท (Permalink)
How can you tell its neat?
Funski33 ยท 3 points ยท Posted at 17:38:59 on May 25, 2016 ยท (Permalink)
By the way it is!
Chucky332 ยท 1 points ยท Posted at 15:19:35 on May 25, 2016 ยท (Permalink)
neature
nusigf ยท 1 points ยท Posted at 15:38:18 on May 25, 2016 ยท (Permalink)
Sigh... Unzips
pnasmaster ยท 1 points ยท Posted at 15:44:16 on May 25, 2016 ยท (Permalink)
That's right, it's a linear equation y=K x.
MisterPT ยท 1 points ยท Posted at 00:56:52 on May 26, 2016 ยท (Permalink)
I hope you always remember that one of your top comments was "Neat"
DiabloConQueso ยท 58 points ยท Posted at 14:58:49 on May 25, 2016 ยท (Permalink)
Is it simply a coincidence that 6.3 is roughly pi * 2? Or is there something more sinister going on?
kDubya ยท 67 points ยท Posted at 15:05:10 on May 25, 2016 ยท (Permalink)
Yeah, that's it.
ohitsasnaake ยท 9 points ยท Posted at 15:06:18 on May 25, 2016 ยท (Permalink)
Well, not a coincidence, but algebra. See the answers that have shown the math.
bhrgunatha ยท 15 points ยท Posted at 15:51:32 on May 25, 2016 ยท (Permalink)
... sinister algebra.
Ceilibeag ยท -1 points ยท Posted at 17:06:16 on May 25, 2016 ยท (Permalink)
NO IT'S NOT; IT'S THE ILLUM...
<dart shot from the shadows, hits exposed neck>
URK!
MAADcitykid ยท 2 points ยท Posted at 15:25:36 on May 25, 2016 ยท (Permalink)
Illuminaty
DiabloConQueso ยท 2 points ยท Posted at 15:30:44 on May 25, 2016 ยท (Permalink)
CONFIRMED
[deleted] ยท 1 points ยท Posted at 17:02:01 on May 25, 2016 ยท (Permalink)
Not a coincidence, somebody else already showed the full solution but I'll rewrite it more simply:
2ฯr is the circumference of a circle. You want to increase the radius by 1 meter, so you want 2ฯ(r+1)
You can then distribute: (2ฯ*r) + (2ฯ*1)
So to increase the radius by 1, it's simply adding 2ฯ*1 = ~6.3.
buzzkill_aldrin ยท 1 points ยท Posted at 17:13:37 on May 25, 2016 ยท (Permalink)
6.3 is because OP rounded.
glexarn ยท 1 points ยท Posted at 17:45:35 on May 25, 2016 ยท (Permalink)
6.3 is an approximation of tau (tau = 2 pi)
PoisonousPlatypus ยท 1 points ยท Posted at 18:46:06 on May 25, 2016 ยท (Permalink)
The actual term is Tau.
JalopyPilot ยท 1 points ยท Posted at 16:34:48 on May 25, 2016 ยท (Permalink)
Now if we just used ฯ it would be more obvious.
Sy27 ยท 2 points ยท Posted at 15:11:20 on May 25, 2016 ยท (Permalink)
What if the initial circumference is 1mm?
Oddtail ยท 4 points ยท Posted at 15:20:20 on May 25, 2016 ยท (Permalink)
Exactly the same thing would happen.
kDubya ยท 1 points ยท Posted at 15:21:22 on May 25, 2016 ยท (Permalink)
Still works.
Malacalypse_theElder ยท 2 points ยท Posted at 15:01:49 on May 25, 2016 ยท (Permalink)
well, not exactly. To be exact, the circumference will increase 2ฯm.
kDubya ยท 10 points ยท Posted at 15:08:34 on May 25, 2016 ยท (Permalink)
What? Not sure if you're trying to be pedantic or what... 6.3 isn't exactly 2 * pi, but it's off by more than .000000002
Malacalypse_theElder ยท -1 points ยท Posted at 15:48:54 on May 25, 2016 ยท (Permalink)
Naw, sarcastically pedantic. Nothing wrong with what ya said.
nickins ยท -5 points ยท Posted at 15:12:31 on May 25, 2016 ยท (Permalink)
OMG ALL OF YOU MATH NERDS STOP!!!!!!!!!!!!!!!!!
BlindTiger86 ยท 1 points ยท Posted at 15:12:19 on May 25, 2016 ยท (Permalink)
How does that work? The 6.3:1 ratio is a constant for all spheres?
kDubya ยท 2 points ยท Posted at 15:20:42 on May 25, 2016 ยท (Permalink)
Circumference = 2 x pi x radius, 2 x pi is roughly 6.3
BlindTiger86 ยท 1 points ยท Posted at 15:21:41 on May 25, 2016 ยท (Permalink)
Thank ya kindly
CatsLeMatts ยท 1 points ยท Posted at 15:14:53 on May 25, 2016 ยท (Permalink)
Is that because 6.2 is approximately Pi x 2?
kDubya ยท 2 points ยท Posted at 15:19:16 on May 25, 2016 ยท (Permalink)
Yup.
ectish ยท 1 points ยท Posted at 15:15:33 on May 25, 2016 ยท (Permalink)
What's the lower limit of this? How small of a sphere would this work with.
kDubya ยท 3 points ยท Posted at 15:19:07 on May 25, 2016 ยท (Permalink)
It works for any size circle.
reltd ยท 1 points ยท Posted at 15:45:33 on May 25, 2016 ยท (Permalink)
where did you learn that?
kDubya ยท 1 points ยท Posted at 15:54:01 on May 25, 2016 ยท (Permalink)
High school geometry class, I guess.
droodic ยท 1 points ยท Posted at 16:00:45 on May 25, 2016 ยท (Permalink)
What about smaller things, say a soccer ball. What would be the length for that? At what point does the meters formula stop working
kDubya ยท 1 points ยท Posted at 16:05:34 on May 25, 2016 ยท (Permalink)
It works for anything.
Olclops ยท 1 points ยท Posted at 16:42:51 on May 25, 2016 ยท (Permalink)
Wait. The top rated comment above is about the specialness of .63. Now 6.3? What the hell?
greenfly ยท 1 points ยท Posted at 16:56:34 on May 25, 2016 ยท (Permalink)
But what if the initial lengh was just like 1m and we are talking about a ball. The 6,3 m have to change at some point.
kDubya ยท 2 points ยท Posted at 18:11:20 on May 25, 2016 ยท (Permalink)
Nope, it works at any scale.
greenfly ยท 1 points ยท Posted at 08:51:58 on May 26, 2016 ยท (Permalink)
Fascinating!
darksingularity1 ยท 1 points ยท Posted at 17:14:17 on May 25, 2016 ยท (Permalink)
Every 1 m rise will have another 2*pi increase
ChrispyK ยท 1 points ยท Posted at 17:27:49 on May 25, 2016 ยท (Permalink)
I'm confused, that doesn't seem to hold up on small scale. If I have enough rope to wrap around a tennis ball, I won't need 6.3m of additional rope to make a 1m halo around it.
kDubya ยท 1 points ยท Posted at 17:53:05 on May 25, 2016 ยท (Permalink)
It holds up at any scale.
Tennis ball - 6.86 cm diameter, 3.43 cm radius circumference = 21.55 cm
add 1 meter to radius
1.0343 m radius, 2.0686 m diameter 6.499 m circumference
6.499 - 0.2155 = 6.283 (2*pi = 6.238, not 6.3, that's just an approximation).
haircutbob ยท 1 points ยท Posted at 17:28:36 on May 25, 2016 ยท (Permalink)
So if I wrap a string around a marble, adding 6.3 meters of string will give me exactly enough to create a ring around it that hovers one meter out? That is so crazy to think about.
[deleted] ยท 1 points ยท Posted at 18:08:03 on May 25, 2016 ยท (Permalink)
Would this hold true for something as small as a ping pong ball?
Gstreetshit ยท 1 points ยท Posted at 18:11:00 on May 25, 2016 ยท (Permalink)
What if its on something like a marble?
Uberbooberluber ยท 1 points ยท Posted at 18:54:21 on May 25, 2016 ยท (Permalink)
Is this at all related to the current top comment about 63% probability ratios?
kDubya ยท 1 points ยท Posted at 19:08:31 on May 25, 2016 ยท (Permalink)
Nope.
Grunflachenamt ยท 1 points ยท Posted at 18:56:51 on May 25, 2016 ยท (Permalink)
This is a good point about sig figs and tolerances
The earth is around 6,353 kilometers, to keep sig figs you only need Pi out to 3.141
Do you want to calculate earth to the meter? add three sig figs! 3.141592
Do you want to calculate it to the millimeter? add Three sig figs! 3.141592653
So on and so forth, atomic length is on the length of a picometer, ergo to calculate the circumference of the earth to an atomic length the value of pi you need is 3.141592653589793238462643383279502884197
ManualNarwhal ยท 1 points ยท Posted at 19:01:10 on May 25, 2016 ยท (Permalink)
What is the relation between this and the 63% example in another part of this thread?
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j1hc1
kDubya ยท 2 points ยท Posted at 19:08:22 on May 25, 2016 ยท (Permalink)
No relationship at all. It isn't actually 6.3, it's pi * 2, so 6.2831...
ManualNarwhal ยท 1 points ยท Posted at 20:22:01 on May 25, 2016 ยท (Permalink)
Thanks for answering!
Waniou ยท 1 points ยท Posted at 20:32:23 on May 25, 2016 ยท (Permalink)
Well of course not, you can't do a factorial on a decimal. </badjoke>
PhantomLord666 ยท 1 points ยท Posted at 22:01:45 on May 25, 2016 ยท (Permalink)
Exactly. FWIW, I think knowing Pi to 30 something decimal places lets you calculate the circumference of the visible universe to within half the width of a hydrogen atom? And you need 60-something decimal places to calculate to within 1 Planck length.
deth1262 ยท 1 points ยท Posted at 23:25:07 on May 25, 2016 ยท (Permalink)
You can tell this is right because of the way that it is
ToTouchAnEmu ยท 1 points ยท Posted at 23:35:24 on May 25, 2016 ยท (Permalink)
Fun fact.... Pi calculated to 39 digits is accurate enough for a circle the size of the observable universe down to the size of single hydrogen atom.
Trevita17 ยท 1 points ยท Posted at 12:04:30 on May 26, 2016 ยท (Permalink)
Meaning that, not only does it work in meters, but increasing the circumference by 6.3 of any unit of measure will increase the radius by 1 of that unit of measure.
Wyand1337 ยท 1 points ยท Posted at 16:20:18 on May 26, 2016 ยท (Permalink)
Linear functions being linear.
kDubya ยท 1 points ยท Posted at 16:53:35 on May 26, 2016 ยท (Permalink)
If only everyone knew what that meant.
PhysicalStuff ยท 1 points ยท Posted at 17:20:33 on May 25, 2016 ยท (Permalink)
"Exactly" insofar as pi is exactly 3.15.
kDubya ยท 1 points ยท Posted at 18:00:00 on May 25, 2016 ยท (Permalink)
Well aren't you so smart. How dare we use 6.3 instead of 6.28318530717958. Increasing the circumference by 6.3 would cause the rope to hover 2.7 mm higher than exactly 1 meter. That ruins the entire thought experiment.
DunceOfSpades ยท 1 points ยท Posted at 20:26:22 on May 25, 2016 ยท (Permalink)
(minor elaboration: 3.15 is around 0.2676% larger than the actual value of pi, or roughly 1/370th larger. If a piece of paper money that was supposed to be 16cm long were 0.2676% longer than intended, it would be 16cm and 0.416 millimeters long)
Zhortsy ยท 0 points ยท Posted at 15:07:02 on May 25, 2016 ยท (Permalink)
Well, technically not exactly (6.3 m that is)... :P 2*pi :)
ShadeofIcarus ยท 0 points ยท Posted at 15:30:47 on May 25, 2016 ยท (Permalink)
Inaccurate!!
Increasing it by 6.3m wouldn't be 1meter.
Increasing it by 2*pi would give you 1 meter!!
/s of course, these are rough estimates obviously.
yahtzeeshots ยท 0 points ยท Posted at 15:44:00 on May 25, 2016 ยท (Permalink)
I don't buy it
[deleted] ยท 0 points ยท Posted at 16:47:31 on May 25, 2016 ยท (Permalink)
not exactly tho, exactly would be 2pi meters ;)
bruisedunderpenis ยท 0 points ยท Posted at 21:12:53 on May 25, 2016 ยท (Permalink)
Well pi doesn't equal 3.14159268 for a different reason though. Mostly because the last digit of your estimation is wrong. It should be 3.14159265 (rounding or truncating doesn't matter it's the same either way).
kDubya ยท 1 points ยท Posted at 21:43:42 on May 25, 2016 ยท (Permalink)
Whoops, I misremembered it.
Multai ยท 174 points ยท Posted at 14:41:09 on May 25, 2016 ยท (Permalink)
Since circumference is 2ฯ*r adding 1 to r will just add 2ฯ to the answer, which is about 6,3 of whatever r was (meters for example).
manondorf ยท 14 points ยท Posted at 17:09:04 on May 25, 2016 ยท (Permalink)
jesus fuck thank you. All those entirely-too-complicated "ELI5"s up there, each making less sense than the last.
backwardsups ยท 1 points ยท Posted at 21:53:52 on May 25, 2016 ยท (Permalink)
simplest explanation right here lol
CT2169 ยท 1 points ยท Posted at 10:59:30 on May 26, 2016 ยท (Permalink)
But the planets aren't completely spherical.
Multai ยท 1 points ยท Posted at 11:50:36 on May 26, 2016 ยท (Permalink)
Nothing is.
BanginNLeavin ยท 1 points ยท Posted at 14:58:26 on May 25, 2016 ยท (Permalink)
What if the circle is less than 1 meter at radius to begin with?
ohitsasnaake ยท 3 points ยท Posted at 15:11:24 on May 25, 2016 ยท (Permalink)
The algebraic calculations shown in a couple of the other answers pretty much prove it for any circle (r>0 at least), but for a concrete example, a circle of r = 0.5m would have a circumference of 2 ร pi ร 0.5 m = pi m or about 3.14 m, and for r = 1.5m you get 2 ร pi ร 1.5 m = 3 ร pi m, i.e. pi m + 2 pi m i.e. 3.14 m + 6.3 m.
WRONGFUL_BONER ยท 1 points ยท Posted at 15:13:10 on May 25, 2016 ยท (Permalink)
Yup. Because 2*3.14.
MystyrNile ยท 1 points ยท Posted at 15:17:57 on May 25, 2016 ยท (Permalink)
In other words, the circumference of a circle is proportional to its radius.
FierceDeity_ ยท 1 points ยท Posted at 15:21:36 on May 25, 2016 ยท (Permalink)
Somehow if you increase the radius by 0.5 meters instead you get a circumference increase be 3.15... which is close to pi. Is the 6.3m number wrong or is it just a coincidence?
[deleted] ยท 1 points ยท Posted at 16:18:55 on May 25, 2016 ยท (Permalink)
If you increase it by 0.5m your answer will be exactly pi. Not a coincidence.
sr71Girthbird ยท 1 points ยท Posted at 17:27:25 on May 25, 2016 ยท (Permalink)
No coincidence. He's just using 6.3m for 2pi.
UwasaWaya ยท 1 points ยท Posted at 15:22:39 on May 25, 2016 ยท (Permalink)
That... actually blew my mind.
sup3rdr01d ยท 1 points ยท Posted at 15:23:47 on May 25, 2016 ยท (Permalink)
Yeah. 2ฯr.
[deleted] ยท 1 points ยท Posted at 15:26:47 on May 25, 2016 ยท (Permalink)
2pi(r+1)-2pi(r)=2pi
JoelMahon ยท 1 points ยท Posted at 15:48:32 on May 25, 2016 ยท (Permalink)
So I'm guessing a circle of 1 meter radius has 2pi meter circumference, yup 6.3m, makes sense fam.
Crivens1 ยท 1 points ยท Posted at 15:53:36 on May 25, 2016 ยท (Permalink)
So, 20 feet would lead to a yard? ish?
Mathea666 ยท 1 points ยท Posted at 16:20:02 on May 25, 2016 ยท (Permalink)
What if the circle is only 10cm in the beginning?
PM_ME_BOOB_PICTURES_ ยท 1 points ยท Posted at 16:20:47 on May 25, 2016 ยท (Permalink)
I feel like testing this, but nah.
IDoThingsOnWhims ยท 1 points ยท Posted at 16:27:34 on May 25, 2016 ยท (Permalink)
No, he's saying the key to anti-gravity is a bunch of circles of rope of circumference n+6.3m.
Liftylym ยท 1 points ยท Posted at 16:38:59 on May 25, 2016 ยท (Permalink)
it's true even for an atom!
aalambis ยท 1 points ยท Posted at 16:52:53 on May 25, 2016 ยท (Permalink)
Which is really really close to 2 pi
Bmandk ยท 1 points ยท Posted at 17:18:14 on May 25, 2016 ยท (Permalink)
Yes. It's actually Pi*2, which explains why it's the same. It's just a circle, and circles have strong ties to Pi.
Purplociraptor ยท 1 points ยท Posted at 17:24:31 on May 25, 2016 ยท (Permalink)
This makes losing 2 or 3 inches off you waistline feel like less of an ahievement, but also gaining an inch or two not so bad.
TheOneTrueTrench ยท 1 points ยท Posted at 17:27:14 on May 25, 2016 ยท (Permalink)
Including circles with a radius of 0!
Worm_Whomper ยท 1 points ยท Posted at 17:33:14 on May 25, 2016 ยท (Permalink)
The same whether for a planet or a marble.
frothface ยท 1 points ยท Posted at 17:34:39 on May 25, 2016 ยท (Permalink)
Now think about how much water it would take to flood a perfectly smooth earth with 1m of water and you understand why they push to make things like planes, tanks, pipelines, dams, etc bigger and bigger.
Domin1c ยท 1 points ยท Posted at 17:50:06 on May 25, 2016 ยท (Permalink)
It's almost as if 6.3 = 2*Pi.
ThePr1d3 ยท 1 points ยท Posted at 17:55:12 on May 25, 2016 ยท (Permalink)
well you only have to increase by 2*pi right ?
Annoyed_ME ยท 1 points ยท Posted at 18:03:27 on May 25, 2016 ยท (Permalink)
This fun math fact is extremely useful for designing bends in sheet metal structures.
Stupid_Man_Suit ยท 1 points ยท Posted at 18:14:46 on May 25, 2016 ยท (Permalink)
The other way to see this:
For a circle, C = 2ฯr
dC/dr = 2ฯ
dC = 2ฯ(dr)
for dr = 1m, dC = 2ฯm โ 6.3m, without specifying any values of r or C.
doofinator ยท 1 points ยท Posted at 18:18:23 on May 25, 2016 ยท (Permalink)
2pi*r = C
So let's set up our problem: Let Ci be the circumference of the earth, and let r be the radius of the earth (or ball, or anything) PLUS the new amount that comes from the added circumference.
Then, solving for r,
QED.
green_meklar ยท 1 points ยท Posted at 18:19:10 on May 25, 2016 ยท (Permalink)
pi = 3.14
pi*2 = 6.28
Conclusion: Yes. (Well, close enough.)
Goons_Forever ยท 1 points ยท Posted at 20:39:21 on May 25, 2016 ยท (Permalink)
Wouldn't it be two meters if it hovers one meter over the ground? One meter on each side right?
Bluesander ยท 1 points ยท Posted at 21:03:21 on May 25, 2016 ยท (Permalink)
I'm confused. Then don't you need to increase the radius by 2m for it to hover above the ground by 1m?
[deleted] ยท 1 points ยท Posted at 21:41:55 on May 25, 2016 ยท (Permalink)
Circumference=Radius times 2 timespi
C+x = (R+1) times 2 times pi => x=2 times pi with is rougthly 6.3m
Poggystyle ยท 1 points ยท Posted at 02:52:10 on May 26, 2016 ยท (Permalink)
2pir
2*3.14= 6.28
Math checks out.
I_cut_my_own_jib ยท 1 points ยท Posted at 15:21:04 on May 25, 2016 ยท (Permalink)
I'm guessing this 6.3 is really 2 pi, right?
DisRuptive1 ยท 0 points ยท Posted at 17:00:40 on May 25, 2016 ยท (Permalink)
Technically two * pi but 6.3 is close enough to that.
bluesam3 ยท 816 points ยท Posted at 12:42:08 on May 25, 2016 ยท (Permalink)
I've a strong feeling that for the sun you'd have to replace the whole rope.
Lee1138 ยท 2912 points ยท Posted at 14:41:38 on May 25, 2016 ยท (Permalink)
Nah, just do it at night.
Neo_Unidan ยท 412 points ยท Posted at 14:51:24 on May 25, 2016 ยท (Permalink)
I always go to the sun in winter, when it's cold.
km559 ยท 4 points ยท Posted at 15:06:51 on May 25, 2016 ยท (Permalink)
and you gotta leave from the Antarctic
Neo_Unidan ยท 2 points ยท Posted at 15:19:09 on May 25, 2016 ยท (Permalink)
That goes without saying, I've heard of people trying to go from the arctic but it's just not the same.
[deleted] ยท 3 points ยท Posted at 15:10:03 on May 25, 2016 ยท (Permalink)
When there is no fire on the sun, it makes for a great vacation spot.
Neo_Unidan ยท 1 points ยท Posted at 15:18:36 on May 25, 2016 ยท (Permalink)
Yeah, I'm really surprised people don't visit more often. It's definitely one of the universe's best kept secrets.
aviddivad ยท 1 points ยท Posted at 20:43:22 on May 25, 2016 ยท (Permalink)
it's one of the univere's best hotspots
_apocalypse_meow ยท 1 points ยท Posted at 15:18:24 on May 25, 2016 ยท (Permalink)
Low Winter Sun?
HerpDerpImARedditor ยท 2 points ยท Posted at 18:02:22 on May 25, 2016 ยท (Permalink)
Better in high Winter, the snow is lazier.
ComradeStrange ยท 1 points ยท Posted at 17:42:38 on May 25, 2016 ยท (Permalink)
Just stay on the dark side.
jaydiz ยท 1 points ยท Posted at 17:49:37 on May 25, 2016 ยท (Permalink)
Respek
turnpikenorth ยท 1 points ยท Posted at 18:50:59 on May 25, 2016 ยท (Permalink)
I go at night.
dewhashish ยท 5 points ยท Posted at 15:39:36 on May 25, 2016 ยท (Permalink)
Thank you /r/kenm
Colonel_of_Wisdom ยท 4 points ยท Posted at 15:48:20 on May 25, 2016 ยท (Permalink)
/r/shittyaskscience needs you
lordtuts ยท 2 points ยท Posted at 15:57:12 on May 25, 2016 ยท (Permalink)
r/KenM is leaking
Solkre ยท 2 points ยท Posted at 18:28:18 on May 25, 2016 ยท (Permalink)
Dumbass. The whole sun isn't night at once, what about the day side?
Abaddon33 ยท 1 points ยท Posted at 14:52:37 on May 25, 2016 ยท (Permalink)
DasValdez fan? =D
saltywings ยท 1 points ยท Posted at 15:06:56 on May 25, 2016 ยท (Permalink)
You could just take a few steps back.
Sample_Name ยท 1 points ยท Posted at 15:13:55 on May 25, 2016 ยท (Permalink)
That's exactly what the North Koreans did in order to land on the sun.
[deleted] ยท 1 points ยท Posted at 15:16:46 on May 25, 2016 ยท (Permalink)
This made me lol. If I wasn't poor you would have gold rn
HEYdontIknowU ยท 1 points ยท Posted at 15:30:26 on May 25, 2016 ยท (Permalink)
How did no one ever think of this?
Alexanderspants ยท 1 points ยท Posted at 16:08:43 on May 25, 2016 ยท (Permalink)
Just wear your sunglasses at night
Bibbster94 ยท 1 points ยท Posted at 17:30:39 on May 25, 2016 ยท (Permalink)
Genius
dr_dijj ยท 1 points ยท Posted at 18:55:14 on May 25, 2016 ยท (Permalink)
Douglas Reynholm?
[deleted] ยท 1 points ยท Posted at 19:05:32 on May 25, 2016 ยท (Permalink)
We need you at /r/shittyaskscience
BuddhasPalm ยท 1 points ยท Posted at 20:20:22 on May 25, 2016 ยท (Permalink)
Well, according to Fox, the sun is on fire, so doing it at night changes nothing.
canadianleroy ยท 1 points ยท Posted at 20:44:43 on May 25, 2016 ยท (Permalink)
Found the Fox News Science correspondent
Sw4rmlord ยท 1 points ยท Posted at 23:28:55 on May 25, 2016 ยท (Permalink)
Half the people read your comment and face palmed because you said that.
The other half face palmed because they didn't.
[deleted] ยท 1 points ยท Posted at 23:49:53 on May 25, 2016 ยท (Permalink)
But when it's night on one side it's day on the other side, and you need to wrap the rope all around the Sun.
ktkps ยท 1 points ยท Posted at 04:57:32 on May 26, 2016 ยท (Permalink)
I have a son
Vaethyr ยท 1 points ยท Posted at 14:55:53 on May 25, 2016 ยท (Permalink)
that's not how the sun works
the sun has to cool down and it would still be too hot for the rope
lern 2 science, casual scrub
ExcaliburTheBiscuit ยท 0 points ยท Posted at 14:44:27 on May 25, 2016 ยท (Permalink)
Yeah, when the sun turns off.
nobody2000 ยท 18 points ยท Posted at 14:47:22 on May 25, 2016 ยท (Permalink)
Turns off? What the hell are you talking about. The sun doesn't turn off at night. That's the most ridiculous thing I've read in a thread full of ridiculous shit.
The sun becomes the moon at night.
you_got_fragged ยท 2 points ยท Posted at 15:01:40 on May 25, 2016 ยท (Permalink)
Then how do I see the sun and the moon at the same time? Does the sun have a twin brother?
nobody2000 ยท 6 points ยท Posted at 15:19:57 on May 25, 2016 ยท (Permalink)
Science time.
So as you pointed out, there are times, usually in the morning, evening, or during a "solar eclipse" where we can see both the sun and the moon.
The first two examples are an example of "solar photon dilation" essentially, photons from the sun are accelerated so rapidly around the earth that you are actually seeing the future sun (the moon) at the same time. This, coupled with the earth's rotation, distance from the sun, and everything actually results in a rather seamless transition from the double-sun to the moon.
If the earth was even a meter away from where it is now in relation to the sun, then we would see a lag or a jump (depending on the season) during the day-to-night transition.
As for an eclipse, this one's easy. It's the sun taking a quick nap. It has a circular blanket to keep it warm.
LeavesCat ยท 2 points ยท Posted at 15:05:40 on May 25, 2016 ยท (Permalink)
...Yes.
VikingCoder ยท 3 points ยท Posted at 14:48:13 on May 25, 2016 ยท (Permalink)
This reminds me of a moment of sportcaster glory.
This basketball star pulled off this amazing slam-dunk. So one sportscaster yells out, "I think he was in the air for like five seconds!" The other sportscaster, trying to be diplomatic but factual chided him, "I think it was more like two seconds."
Even that would be a 16 foot jump...
ohitsasnaake ยท 1 points ยท Posted at 15:15:32 on May 25, 2016 ยท (Permalink)
16 feet high? That's a heck of a jump, it would smash olympic high jump records to pieces.
It's not a maths fact but rather a physics fact that IIRC the air time of a jump/thrown ball etc. (ballistic trajectory, without any aerodynamic effects such as aeroplanes and birds have) doesn't depend on the horizontal velocity but only on the initial vertical velocity, or optionally on the consequence of the latter, the height of a jump.
VikingCoder ยท 1 points ยท Posted at 15:29:22 on May 25, 2016 ยท (Permalink)
...almost true...
If your horizontal velocity is fast enough.... You enter into orbit around the Earth. =)
Of course, your orbit will decay rapidly due to friction with the atmosphere (or buildings, or trees, or mountains)...
ohitsasnaake ยท 1 points ยท Posted at 18:03:40 on May 25, 2016 ยท (Permalink)
I guessed that there was some other restriction I forgot to mention...
RedditConsciousness ยท 1 points ยท Posted at 20:14:58 on May 25, 2016 ยท (Permalink)
Lasso the moon and impress a girl.
tael89 ยท -1 points ยท Posted at 15:49:17 on May 25, 2016 ยท (Permalink)
In this hypothetical situation where you get a rope on the surface of the sun, remember that the surface is not actually the hottest part of the sun.
bluesam3 ยท 2 points ยท Posted at 15:51:16 on May 25, 2016 ยท (Permalink)
No, but it's plenty hot enough.
tael89 ยท -1 points ยท Posted at 18:30:50 on May 25, 2016 ยท (Permalink)
Yes, but the rope that is somehow on the surface, the materials designed that it is just barely surviving, may not survive 1 m above the surface where temperature is hotter.
Eulerich ยท 201 points ยท Posted at 12:02:56 on May 25, 2016 ยท (Permalink)
Also a golfball, a basketball and OP's mum.
jallenrt ยท 276 points ยท Posted at 14:21:13 on May 25, 2016 ยท (Permalink)
I grabbed a rope that is 6.3 meters long plus the c of a golf ball. Put it around the golf ball but it's not hovering. Therefore you are all full of shit.
DrAbra ยท 9 points ยท Posted at 16:46:39 on May 25, 2016 ยท (Permalink)
It's probably caught in OP's moms gravitational field, she's probably on the other side of the planet.
JBHedgehog ยท 3 points ยท Posted at 15:21:18 on May 25, 2016 ยท (Permalink)
'Cause golf balls have pits...freakin' duh.
It's all about the math...
chickenthinkseggwas ยท 2 points ยท Posted at 18:28:13 on May 25, 2016 ยท (Permalink)
Yeah, maths... and asapartame. It collects in the pits and goes all fizzy. That's what makes the rope hover.
JBHedgehog ยท 2 points ยท Posted at 18:50:06 on May 25, 2016 ยท (Permalink)
I am happy to read that you are indeed a man of science.
IPoopInYourInbox ยท 36 points ยท Posted at 13:31:12 on May 25, 2016 ยท (Permalink)
Nope. OP's mum is so big that she defies the laws of spacetime.
[deleted] ยท 6 points ยท Posted at 15:14:15 on May 25, 2016 ยท (Permalink)
But she will need to be thinner than her Schwarschild radius to do so. Not possible.
SexyVoldemort ยท 1 points ยท Posted at 20:31:59 on May 25, 2016 ยท (Permalink)
Are you sure there's enough rope for his mom? :O
Ahdilable ยท 0 points ยท Posted at 14:56:20 on May 25, 2016 ยท (Permalink)
It does nothing on OP's mom, it just opens up more space.
Flutemouth ยท 0 points ยท Posted at 18:08:56 on May 25, 2016 ยท (Permalink)
But OP's mom is egg shaped.
SGrumpy ยท 0 points ยท Posted at 18:58:55 on May 25, 2016 ยท (Permalink)
But there isn't a rope long enough to go around OPs mum.
[deleted] ยท 50 points ยท Posted at 12:39:43 on May 25, 2016 ยท (Permalink)
2 pi * r it's first grade spongebob
Project2r ยท 2 points ยท Posted at 15:12:48 on May 25, 2016 ยท (Permalink)
Impressive schooling. I think my first introduction into geometry was closer to 6th grade.
1st grade i was trying to add and subtract i think.
[deleted] ยท 1 points ยท Posted at 16:40:06 on May 25, 2016 ยท (Permalink)
I'm just trying to fit it in the wumbology quote as best as possible
edp1123 ยท 4 points ยท Posted at 14:55:19 on May 25, 2016 ยท (Permalink)
What's with the random apology?
[deleted] ยท 1 points ยท Posted at 18:29:11 on May 25, 2016 ยท (Permalink)
[deleted]
ktkps ยท 2 points ยท Posted at 05:28:12 on May 26, 2016 ยท (Permalink)
thnx for doing this
MrMeltJr ยท 3 points ยท Posted at 16:43:02 on May 25, 2016 ยท (Permalink)
It's almost as if there's some kind of constant relationship between the radius and the circumference of a circle...
ktkps ยท 1 points ยท Posted at 04:39:17 on May 26, 2016 ยท (Permalink)
I see what you did there....so correct answer is never 6.3 then...approaching 6.3, but never quite getting there
Lucoda ยท 3 points ยท Posted at 17:39:33 on May 25, 2016 ยท (Permalink)
It's to do with 2Pi right?
ktkps ยท 1 points ยท Posted at 05:21:08 on May 26, 2016 ยท (Permalink)
yes
I_got_nothin_ ยท 2 points ยท Posted at 16:19:25 on May 25, 2016 ยท (Permalink)
Wait wait wait wait wait. 6.3 meters...for everything. Does this somehow go along with the top comment. The one talking about 63% chance of something happening?
ktkps ยท 3 points ยท Posted at 04:53:34 on May 26, 2016 ยท (Permalink)
We did it Reddit!
New answer to life the universe and everything = 63 or 6.3 or 63% etc
SOwED ยท 1 points ยท Posted at 18:34:47 on May 25, 2016 ยท (Permalink)
No. It's actually not exactly 6.3 but rather 2ฯ.
jerkandletjerk ยท 2 points ยท Posted at 18:00:43 on May 25, 2016 ยท (Permalink)
Aww man, I too saw it on TV, so go ahead, spread the word freely!
Prof_G ยท 1 points ยท Posted at 15:06:59 on May 25, 2016 ยท (Permalink)
That's easy, just do it at night.
[deleted] ยท 1 points ยท Posted at 16:15:54 on May 25, 2016 ยท (Permalink)
What about smaller spheres, like a marble?
SOwED ยท 1 points ยท Posted at 18:35:43 on May 25, 2016 ยท (Permalink)
Here is my comment from elsewhere in this thread. It works for any sphere.
2ฯr = x where r is the radius of your sphere and x is the length of rope. Add 1 to the radius.
2ฯ(r+1) = 2ฯr+2ฯ
From before, we have 2ฯr = x, so
2ฯ(r+1) = x+2ฯ
2ฯ is approximately 6.3.
actual_factual_bear ยท 1 points ยท Posted at 16:28:11 on May 25, 2016 ยท (Permalink)
I feel like it should be possible to use this fact to violate some kind of conservation law...
SOwED ยท 2 points ยท Posted at 18:34:20 on May 25, 2016 ยท (Permalink)
2ฯr = x where r is the radius of your sphere and x is the length of rope. Add 1 to the radius.
2ฯ(r+1) = 2ฯr+2ฯ
From before, we have 2ฯr = x, so
2ฯ(r+1) = x+2ฯ
2ฯ is approximately 6.3.
ktkps ยท 1 points ยท Posted at 04:51:16 on May 26, 2016 ยท (Permalink)
more accurately: Wolfram
SOwED ยท 1 points ยท Posted at 05:23:44 on May 26, 2016 ยท (Permalink)
I think 6.28 is as far as anyone would care about this.
pitchingataint ยท 1 points ยท Posted at 16:53:28 on May 25, 2016 ยท (Permalink)
What about earth's topography? Wouldn't it be different since it isn't perfectly round?
SOwED ยท 1 points ยท Posted at 18:29:43 on May 25, 2016 ยท (Permalink)
It only works if you assume a sphere.
ktkps ยท 1 points ยท Posted at 04:39:55 on May 26, 2016 ยท (Permalink)
science works in a lot of ways - when we first assume certain things
SOwED ยท 1 points ยท Posted at 05:26:08 on May 26, 2016 ยท (Permalink)
Well, the whole planet thing is just a useful way to explain the concept, but it's not realistic on any planet that you can't circle around without maintaining constant radius. I'm not sure if the gas giants have this property or not, do you know? I feel like they don't exactly have a border on the meter scale.
PM_me_ur_DIYpics ยท 1 points ยท Posted at 18:33:42 on May 25, 2016 ยท (Permalink)
and for a bowling ball, a tennis ball, your head, etc!
axelAcc ยท 1 points ยท Posted at 20:20:07 on May 25, 2016 ยท (Permalink)
and even a golf ball :)
a_zoldyck ยท 1 points ยท Posted at 21:57:21 on May 25, 2016 ยท (Permalink)*
Also true for waists apparently, this is why one hole in the belt is always too tight and the next one is too loose.
ubspirit ยท 1 points ยท Posted at 00:04:09 on May 26, 2016 ยท (Permalink)
Except it won't because of the variations of equatorial elevation.
Not only are planets not perfect circles, they aren't uniform perfect circles.
Fenor ยท 1 points ยท Posted at 14:13:28 on May 26, 2016 ยท (Permalink)
i don't think that my rope can float on the sun. it will probably burn before i end up running the sun's equator
onfire9123 ยท 0 points ยท Posted at 15:39:01 on May 25, 2016 ยท (Permalink)*
If the value 6.3 remains constant for all of those, then it is independent of the circumference, yes? So it works for literally every round object.
But there must be a minimum, because obviously this theorem is false for the case of a tennis ball.
Or there is a discrete, finite set of circumference lengths that this holds true. In which case, where do we define the surface of the sun to be? Because there is no point of change of mass. It fades into the next phase of matter over many kilometers.
edit: raising it up a meter is the same as adding 1m to the radius. 2 * radius = diameter. pi * diameter = circumerence. you're adding 2 to the diameter, and 6.3 is nearly exactly 2 * pi. It makes sense. But is much less impressive now. :(
Bosck ยท 2 points ยท Posted at 16:23:54 on May 25, 2016 ยท (Permalink)
It doesn't depend of the radius. It is really strange, but it is true. Take a rope and try with a tennis ball. You will see that it is true even if it seems impossible
onfire9123 ยท 1 points ยท Posted at 18:08:20 on May 25, 2016 ยท (Permalink)
Now that I think about it further, you're adding 2 to the diameter. 6.3 is nearly exactly twice the value of pi. Now it makes sense.
But its much less impressive now that I understand it.
Bosck ยท 1 points ยท Posted at 18:30:49 on May 25, 2016 ยท (Permalink)
Actually the real value is 2*pi. 6.3 is just and approximation
formative_informer ยท 241 points ยท Posted at 14:00:20 on May 25, 2016 ยท (Permalink)
Well, ignoring gravity. Dammit physics! The math works out!
Quuantix ยท 148 points ยท Posted at 14:51:16 on May 25, 2016 ยท (Permalink)
Just adding length allows the rope to float. So if you grow 6.3 meters taller you will hover 1 meter over the ground.
apparaatti ยท 23 points ยท Posted at 15:52:18 on May 25, 2016 ยท (Permalink)
/r/shittyaskscience
vesomortex ยท 12 points ยท Posted at 16:58:03 on May 25, 2016 ยท (Permalink)
Nope. If my circumference becomes 6.3 meters then I can float 1 meter off the ground. I better start eating more.
Quuantix ยท 8 points ยท Posted at 17:41:59 on May 25, 2016 ยท (Permalink)
This is more logical.
Sanguinetemper ยท 1 points ยท Posted at 00:20:10 on May 26, 2016 ยท (Permalink)
Lets use some /r/shittyaskscience Being simply taller would not make you float, but if the rope was perfectly disributed around the world, the gravitational pull of the earth would force it to hold form (the reason the world is round in the first place) so surely as a result, if the rope was the right length and had perfect distribution of the force of gravity it would force the rope to be the exact same distance from the ground the whole way round.
GodzillaLikesBoobs ยท 19 points ยท Posted at 15:29:41 on May 25, 2016 ยท (Permalink)
What. If it's solid like a pipe? How can it fall when on the other side it's also falling?
Pun-Master-General ยท 6 points ยท Posted at 15:51:17 on May 25, 2016 ยท (Permalink)
Checkmate, gravity!
RadicalDog ยท 2 points ยท Posted at 16:31:51 on May 25, 2016 ยท (Permalink)
Or, if it is orbiting ridiculously fast?
Time_on_my_hands ยท 1 points ยท Posted at 18:29:55 on May 25, 2016 ยท (Permalink)
Holy fuck this is confusing.
miter01 ยท 1 points ยท Posted at 19:05:07 on May 25, 2016 ยท (Permalink)
So called Dyson ring.
Buntschatten ยท 1 points ยท Posted at 20:26:43 on May 25, 2016 ยท (Permalink)
Even a bendy rope could hover in obviously idealized cricumstances. After releasing the rope, its movement can't break rotational symmetry, therefore it cant fold and fall. It could compress and fall down though, becoming slightly thicker.
Amp3r ยท 1 points ยท Posted at 01:30:31 on May 26, 2016 ยท (Permalink)
Are the ideal circumstances that it won't bend to the sides and fall on the ground as a snake shape?
Buntschatten ยท 1 points ยท Posted at 10:21:21 on May 26, 2016 ยท (Permalink)
No. The ideal circumstances would be that gravity is perfectly even everywhere. To make the rope bend to the sides there would have to be a sideways force. But gravity only pulls downwards. So unless the rope gets perturbed, it will hover.
Amp3r ยท 1 points ยท Posted at 23:53:35 on May 26, 2016 ยท (Permalink)
I don't think that is the case. Ropes aren't good at longitudinal compression forces which is what would be needed to keep it hovering. Something like a steel cable might work
orcscorper ยท 3 points ยท Posted at 17:11:58 on May 25, 2016 ยท (Permalink)
You could just spin the rope really fast, ignoring friction and topology. Frictionless surfaces in a vacuum always make physics calculations easier.
AND_MY_HAX ยท 2 points ยท Posted at 18:27:01 on May 25, 2016 ยท (Permalink)
Relevant XKCD
platinum001 ยท 2 points ยท Posted at 20:42:35 on May 25, 2016 ยท (Permalink)
I was so confused for a sec. I was thinking how does 6.3m of extra rope cause it to defy gravity.
Dobako ยท 2 points ยท Posted at 21:12:53 on May 25, 2016 ยท (Permalink)
You just have to teach the rope to miss the ground
fairysdad ยท 1 points ยท Posted at 22:57:58 on May 25, 2016 ยท (Permalink)
Happy Towel Day :)
Dobako ยท 1 points ยท Posted at 23:29:29 on May 25, 2016 ยท (Permalink)
You seem like a hoopy frood
linehan23 ยท 4 points ยท Posted at 17:01:02 on May 25, 2016 ยท (Permalink)
No not ignoring gravity... If you set it up just exactly right it will hover, it will be super unstable and easy to knock down though
[deleted] ยท 3 points ยท Posted at 17:12:41 on May 25, 2016 ยท (Permalink)*
[deleted]
Buntschatten ยท 0 points ยท Posted at 20:29:05 on May 25, 2016 ยท (Permalink)
Nope. If we assume the rope is perfectly round and can't just compress to a ring with smaller radius. (Idealized) gravity can't break rotational symmetry, therefore the rope would hover. It doesn't even nead to be spinning.
Banzai51 ยท 1 points ยท Posted at 16:05:08 on May 25, 2016 ยท (Permalink)
Then you just say at the event horizon of a black hole. Fixed!
mishagale ยท 1 points ยท Posted at 19:55:57 on May 25, 2016 ยท (Permalink)
It'd work on a planet with zero atmosphere, if you spun the rope fast enough.
computeraddict ยท 1 points ยท Posted at 20:40:34 on May 25, 2016 ยท (Permalink)
Spin the rope very, very quickly.
mangamaster03 ยท 1 points ยท Posted at 21:20:52 on May 25, 2016 ยท (Permalink)
Math and physics both ignore physics in the beginning.
Study kinematics? Infinite plane of zero friction. In a vacuum. With spherical chickens.
raddaya ยท 0 points ยท Posted at 14:24:55 on May 25, 2016 ยท (Permalink)
If Earth were a perfect sphere, there wouldn't be any such problem.
[deleted] ยท 9 points ยท Posted at 15:26:56 on May 25, 2016 ยท (Permalink)*
[deleted]
muttyfut ยท 3 points ยท Posted at 15:33:59 on May 25, 2016 ยท (Permalink)
A regular, non-rigid rope would work fine if you spin it at sufficient (angular)velocity.
raddaya ยท 2 points ยท Posted at 15:28:10 on May 25, 2016 ยท (Permalink)
Ah, yes, I was mentioning lower down that the rope would need to be taut, though I was wondering about whether if it was needed or not. I suppose a physical definition of "taut" would be "rigid".
Buntschatten ยท 1 points ยท Posted at 20:33:25 on May 25, 2016 ยท (Permalink)
Let's assume the rope is a one-dimensional massive string. For a real rope, you're right, you can't separate bendiness and compressibility. But in that ideal case, where it is bendy but not compressibly, it would still hover, because the gravity cannot induce a movement that does not have rotational symmetry.
MariachiDesperado ยท 3 points ยท Posted at 14:44:50 on May 25, 2016 ยท (Permalink)
and the rope was solid?
AadeeMoien ยท 3 points ยท Posted at 17:38:20 on May 25, 2016 ยท (Permalink)
Then it would be a shitty rope.
raddaya ยท 1 points ยท Posted at 14:47:00 on May 25, 2016 ยท (Permalink)
Well, if it was pulled perfectly taut, there shouldn't be any problem due to the Shell Theorem.
Wetbung ยท 4 points ยท Posted at 14:54:29 on May 25, 2016 ยท (Permalink)
And what would be pulling the rope taut?
raddaya ยท 1 points ยท Posted at 14:58:20 on May 25, 2016 ยท (Permalink)
Hmm, I actually don't think the rope would need to be taut, just even.
Wetbung ยท 2 points ยท Posted at 15:33:43 on May 25, 2016 ยท (Permalink)
It would pull toward the center of the Earth. What would make it levitate?
raddaya ยท 6 points ยท Posted at 15:35:55 on May 25, 2016 ยท (Permalink)
No, you're right, as a guy said in another reply to my original post- the rope would need to be rigid to prevent it from collapsing into the Earth.
Chalkmans ยท 277 points ยท Posted at 13:52:02 on May 25, 2016 ยท (Permalink)
How
You_Have_Nice_Hair ยท 1628 points ยท Posted at 14:12:33 on May 25, 2016 ยท (Permalink)
The answer is independent of the earth's circumference, because circumference increases linearly with radius.
In fact, replace earth's circumference with your waist. You will still need an additional 6.3 meters of rope to have the rope hover a meter from your body.
Axleboy57 ยท 1093 points ยท Posted at 14:22:35 on May 25, 2016 ยท (Permalink)
This realization blew my mind more than the original fact.
InfyTurtle ยท 37 points ยท Posted at 15:22:08 on May 25, 2016 ยท (Permalink)
The pyramids and woolly mammoths coexisted.
2rapey4you ยท 25 points ยท Posted at 15:27:08 on May 25, 2016 ยท (Permalink)
I can rub my belly and pat my head at the same time.
Kaptain_Oblivious ยท 30 points ยท Posted at 16:27:13 on May 25, 2016 ยท (Permalink)
I can believe it's not butter
tarantula13 ยท 2 points ยท Posted at 17:27:05 on May 25, 2016 ยท (Permalink)
Gonna need proof on this claim.
2rapey4you ยท 8 points ยท Posted at 17:46:29 on May 25, 2016 ยท (Permalink)
I lost my belly and head in the war, sorry
drakoslayr ยท 1 points ยท Posted at 18:12:47 on May 25, 2016 ยท (Permalink)
You pour soul
troll_right_above_me ยท 1 points ยท Posted at 22:27:01 on May 25, 2016 ยท (Permalink)
Duh, how else would they build them? People? Hah!
[deleted] ยท 6 points ยท Posted at 15:27:04 on May 25, 2016 ยท (Permalink)
[deleted]
MintClassic ยท 4 points ยท Posted at 17:09:03 on May 25, 2016 ยท (Permalink)
2ฯr
Aloysius7 ยท 5 points ยท Posted at 17:42:17 on May 25, 2016 ยท (Permalink)
I can't comprehend it. I understand it, but it is hard to believe for big objects like planets.
The_Revolutionary ยท 3 points ยท Posted at 15:39:29 on May 25, 2016 ยท (Permalink)
This realization blew out my pants more than the original fat.
dtn1496 ยท 2 points ยท Posted at 17:13:55 on May 25, 2016 ยท (Permalink)
The thing that gets me is that is sounds crazy but it's actually really simple math. A circle's circumference is 2piradius so increasing the radius by 1 increases the circumference by 2*pi (which is roughly 6.3)
FindingLooking ยท 2 points ยท Posted at 21:16:03 on May 25, 2016 ยท (Permalink)
Your Mom, on the other hand, would require 7 meters of rope.
fireatx ยท 1 points ยท Posted at 06:57:07 on May 26, 2016 ยท (Permalink)
c = 2ฯr? not that crazy
Gold_Ret1911 ยท 0 points ยท Posted at 17:47:03 on May 25, 2016 ยท (Permalink)
Yeah but did you know that steve buscemi was a firefighter during 9/11?
ecoliz ยท 719 points ยท Posted at 14:37:03 on May 25, 2016 ยท (Permalink)
Are you calling me fat?
BloodFartTheQueefer ยท 44 points ยท Posted at 14:52:34 on May 25, 2016 ยท (Permalink)
No, he's saying it's independent of how fat you are
ecoliz ยท 9 points ยท Posted at 14:54:58 on May 25, 2016 ยท (Permalink)
Sorry mate, I'll explain my joke - the circumference of a circle is 2ฯ*R and only a really fat person's waist would resemble a circle
BloodFartTheQueefer ยท 3 points ยท Posted at 15:11:19 on May 25, 2016 ยท (Permalink)
h, my comment was also a joke but yours is better :p
bradn ยท 2 points ยท Posted at 16:24:51 on May 25, 2016 ยท (Permalink)
Most underrated joke I've seen in a while here!
3lbFlax ยท 6 points ยท Posted at 17:32:27 on May 25, 2016 ยท (Permalink)
Your momma is so fat one would have to add an additional 7m to the circumference of a rope around her waist in order to increase the radius of said rope by 1m.
88gavinm ยท 1 points ยท Posted at 20:49:26 on May 25, 2016 ยท (Permalink)
Brilliant
GenericEvilDude ยท 7 points ยท Posted at 14:47:49 on May 25, 2016 ยท (Permalink)
I believe he was referring to your mother
Project2r ยท 1 points ยท Posted at 15:14:01 on May 25, 2016 ยท (Permalink)
only if you gain 1 meter to the radius of your waist. but know that it only took 6.3 meters more of fabric to make your belt.
WattledPenguin ยท 1 points ยท Posted at 15:49:48 on May 25, 2016 ยท (Permalink)
Fat by 6.3 meters to be precise.
miked4o7 ยท 1 points ยท Posted at 17:38:49 on May 25, 2016 ยท (Permalink)
Fact: You're so fat that it would take the same extra amount of rope to hover a meter away from your body as opposed to wrap around it, as it would to do the same with the entire Earth.
NinjaRobotPilot ยท 1 points ยท Posted at 21:51:25 on May 25, 2016 ยท (Permalink)
Statistically fat.
Th3Element05 ยท 11 points ยท Posted at 15:36:25 on May 25, 2016 ยท (Permalink)
I'm no maths genius, but I'm assuming that it's not a coincidence that 6.3 is, roughly, (3.14 * 2)?
stillusesAOL ยท 6 points ยท Posted at 17:15:33 on May 25, 2016 ยท (Permalink)
You ARE A GENIUS
You_Have_Nice_Hair ยท 2 points ยท Posted at 15:48:04 on May 25, 2016 ยท (Permalink)
The additional radius = 1m
The additional diameter = 2 * additional radius
The additional circumference = PI * additional diameter
Phototropically ยท 2 points ยท Posted at 14:43:04 on May 25, 2016 ยท (Permalink)
Whoa, math.
ICanHomerToo ยท 2 points ยท Posted at 14:43:58 on May 25, 2016 ยท (Permalink)
Is it exactly 6.3? And is it just a coincidence that it happens to be approximately 2pi?
Edit: someone answer my question below....woops!
Towerss ยท 2 points ยท Posted at 17:11:37 on May 25, 2016 ยท (Permalink)*
I don't even want a math answer for this, I need a way to visualize it. It makes no sense to me
lukesvader ยท 1 points ยท Posted at 20:11:46 on May 25, 2016 ยท (Permalink)
Yeah, someone make a gif
fuckitimatwork ยท 2 points ยท Posted at 17:13:16 on May 25, 2016 ยท (Permalink)
wtf
[deleted] ยท 2 points ยท Posted at 17:28:05 on May 25, 2016 ยท (Permalink)
Your mom would need 7.3
Etonet ยท 2 points ยท Posted at 17:47:32 on May 25, 2016 ยท (Permalink)
Why though?
You_Have_Nice_Hair ยท 1 points ยท Posted at 17:49:58 on May 25, 2016 ยท (Permalink)
Why does circumference increase linearly with radius? Geometry.
butwhatsmyname ยท 1 points ยท Posted at 14:49:55 on May 25, 2016 ยท (Permalink)
But... it... I...
0_0
JuanDeLasNieves_ ยท 1 points ยท Posted at 15:03:27 on May 25, 2016 ยท (Permalink)
There's a yo mamma joke hiding somewhere in this comment
imp3r10 ยท 1 points ยท Posted at 15:37:35 on May 25, 2016 ยท (Permalink)
While maintaining a perfect circle shape
[deleted] ยท 1 points ยท Posted at 15:44:08 on May 25, 2016 ยท (Permalink)*
Wow... holy crap. So counterintuitive.
josephdevon ยท 1 points ยท Posted at 15:46:53 on May 25, 2016 ยท (Permalink)
I don't care how much more rope you add, I still can't make it hover.
OM3N1R ยท 1 points ยท Posted at 16:29:17 on May 25, 2016 ยท (Permalink)
Finally, it made sense. All them fancy equations gettin' me confused like.
d3adbor3d2 ยท 1 points ยท Posted at 17:12:22 on May 25, 2016 ยท (Permalink)
you'll need more rope for your momsorrymybro
merelyadoptedthedark ยท 1 points ยท Posted at 17:36:02 on May 25, 2016 ยท (Permalink)
That makes no sense to me, if I am ~ 1m around, I would need a 1m rope to go around me. If I make the rope 7.3 metres long, it will be 1m away from me at all points...that sounds like it would be way further away from me than just 1m...and then taking a 40,075km rope, and making it 40,075.0063km, it would then be long enough to still float 1m about the earth?
You_Have_Nice_Hair ยท 1 points ยท Posted at 17:38:47 on May 25, 2016 ยท (Permalink)
1m from belly button to the centre of your mass (middle of your stomach? [radius]), resulting in a 6.3m rope. With the extension, that would be 12.6m rope.
Filobel ยท 1 points ยท Posted at 17:52:12 on May 25, 2016 ยท (Permalink)
Why are we not using this to make hover crafts?
wasirapd ยท 1 points ยท Posted at 18:36:56 on May 25, 2016 ยท (Permalink)
Okay I added the extra meters, now how do I make it hover?
Esleeezy ยท 1 points ยท Posted at 19:32:04 on May 25, 2016 ยท (Permalink)
This is true when dealing with the circumference of planets and large object but does it still hold true when dealing with even larger objects? Ex: Ya fat ass mamma
FindingLooking ยท 1 points ยท Posted at 21:15:40 on May 25, 2016 ยท (Permalink)
Your Mom, on the other hand, would require 7 meters of rope.
igginator77 ยท 1 points ยท Posted at 13:18:52 on May 26, 2016 ยท (Permalink)
I still don't understand
ERJ21 ยท 1 points ยท Posted at 19:54:24 on May 26, 2016 ยท (Permalink)
6.3 is about 2pi, which is how many radians (radii) are in the circumference
CyberDonkey ยท 0 points ยท Posted at 16:51:02 on May 25, 2016 ยท (Permalink)
What is meant by hover a meter from your body? Does it mean that the rope's circumference will always be a meter away from the body or will it somehow gain anti-gravitational properties?
ATownStomp ยท 0 points ยท Posted at 17:11:25 on May 25, 2016 ยท (Permalink)
Totally ineffective use of language! Tailor the response to the question.
You_Have_Nice_Hair ยท 3 points ยท Posted at 17:19:32 on May 25, 2016 ยท (Permalink)
That is a perfect use of language. Each word belongs in the vocabulary of a high school freshman.
ATownStomp ยท 1 points ยท Posted at 17:51:57 on May 25, 2016 ยท (Permalink)
And so is the formula for the circumference of a circle but if they don't recall that then it's unlikely that your response will have any meaning to them. Your response was concise but it won't help someone who doesn't already understand.
You_Have_Nice_Hair ยท 2 points ยท Posted at 17:56:31 on May 25, 2016 ยท (Permalink)
I'm pretty content with my response. I broke it down to a level I thought was suitable. If you don't like it, why not post a better description?
If someone cared for an in depth answer, they could google the question. I don't exist solely to provide answers for the plebs.
ATownStomp ยท 1 points ยท Posted at 18:19:55 on May 25, 2016 ยท (Permalink)
Here is the response from /u/brockers24 which the original commenter responded to.
And another comment chain which demonstrates an attempt at accommodating in a response for the person who is being taught.
I'm sure you're content with the anonymous validation you've received but that's an immature attitude and it isn't characteristic of an intelligent person. Pragmatism is important. Don't act like a mediocre person with a decent education and a big ego.
You_Have_Nice_Hair ยท 2 points ยท Posted at 18:29:39 on May 25, 2016 ยท (Permalink)
And here is an excerpt one of mine to a different user:
There is no need for you to be policing this board.
juangamboa ยท 0 points ยท Posted at 00:58:28 on May 26, 2016 ยท (Permalink)
I still don't get it :(
[deleted] ยท 169 points ยท Posted at 14:06:50 on May 25, 2016 ยท (Permalink)
[deleted]
Douche_Kayak ยท 5 points ยท Posted at 16:18:27 on May 25, 2016 ยท (Permalink)
That's what I was looking for. Thanks
[deleted] ยท 5 points ยท Posted at 17:32:59 on May 25, 2016 ยท (Permalink)
Can you explain it purely in words?
[deleted] ยท 6 points ยท Posted at 17:52:40 on May 25, 2016 ยท (Permalink)*
[deleted]
[deleted] ยท 2 points ยท Posted at 17:54:13 on May 25, 2016 ยท (Permalink)
OH I GET IT. Thanks man :D
youdubdub ยท 2 points ยท Posted at 15:55:40 on May 25, 2016 ยท (Permalink)
6.3/2 = ~3.141529
brockers24 ยท 31 points ยท Posted at 14:11:07 on May 25, 2016 ยท (Permalink)
Circumference of a circle = 2 * pi * radius
You are increasing the radius by 1m, so you are increasing it by 2 * pi * 1 = 6.3m
Chalkmans ยท 5 points ยท Posted at 14:15:57 on May 25, 2016 ยท (Permalink)
Ahh, this one makes the most sense, thanks!
BritTorrent ยท 1 points ยท Posted at 16:02:55 on May 25, 2016 ยท (Permalink)
This is the simplest explanation yet. Thank you for this.
Sadgasm0 ยท 5 points ยท Posted at 14:13:26 on May 25, 2016 ยท (Permalink)
Think of two circles one of which has a radius 1m larger than the other. Then just subtract their circumferences.
2*pi*(r+1)-2*pi*r= 2*pi+(2*pi*r - 2*pi*r) = 2*pi = 6.28... ~= 6.3m
This is true for all circles. You can use any radii, it doesn't matter.
adruven ยท 2 points ยท Posted at 14:07:59 on May 25, 2016 ยท (Permalink)
Cirumference=2ฯr, so if we increase the radius by 1 meter, we get 2ฯ(r+1)=2ฯr+2ฯ.
ErsatzCats ยท 1 points ยท Posted at 15:45:02 on May 25, 2016 ยท (Permalink)
C = 2pir
C' = 2pi(r+1) = 2pir + 6.28
Jouglet ยท 1 points ยท Posted at 16:07:02 on May 25, 2016 ยท (Permalink)
Circumference of a circle is 2ฯr
Extra rope needed = 2ฯ(r+1) - 2ฯr
crow1170 ยท 1 points ยท Posted at 17:06:44 on May 25, 2016 ยท (Permalink)
setofskills ยท 1 points ยท Posted at 17:27:07 on May 25, 2016 ยท (Permalink)
Others have given the longer form answer, but if we use implicit differentiation, we simply get:
Makes no difference if we're talking about a marble or the world.
Edit: Formatting
mperklin ยท 1 points ยท Posted at 19:02:27 on May 25, 2016 ยท (Permalink)
pi * 2 ~= 6.3
KyleHooks ยท 37 points ยท Posted at 14:02:26 on May 25, 2016 ยท (Permalink)
So...you need 2pi meters of rope to make anything hover 1 meter?
(past the circumference, of course)
290077 ยท 6 points ยท Posted at 14:34:28 on May 25, 2016 ยท (Permalink)
Yup
imp3r10 ยท -1 points ยท Posted at 15:38:22 on May 25, 2016 ยท (Permalink)*
It's only for 1 side though. The other side would still touch the groundKalsion ยท 2 points ยท Posted at 16:03:17 on May 25, 2016 ยท (Permalink)
This is wrong. Adding 2pi meters increases the radius by 1 meter. That means the circle expands by 1 meter in all directions.
imp3r10 ยท 1 points ยท Posted at 16:10:21 on May 25, 2016 ยท (Permalink)
Whoops. You are right
archworker ยท -5 points ยท Posted at 14:40:11 on May 25, 2016 ยท (Permalink)
What is this meter thing you guys are discussing? We speak English in the US.
KyleHooks ยท 5 points ยท Posted at 14:49:10 on May 25, 2016 ยท (Permalink)
About 3 large feet.
KyleHooks ยท 1 points ยท Posted at 14:49:25 on May 25, 2016 ยท (Permalink)
or a yard+
ohitsasnaake ยท -2 points ยท Posted at 15:18:29 on May 25, 2016 ยท (Permalink)
Ironically, the official spelling is metre everywhere except in the US.
myredditlogintoo ยท 2 points ยท Posted at 15:20:36 on May 25, 2016 ยท (Permalink)
Because US is freedomER than other countries.
Poteten01 ยท 2 points ยท Posted at 16:16:34 on May 25, 2016 ยท (Permalink)
Actually not true.
In the Scandinavian it's spelled meter:/
ohitsasnaake ยท 1 points ยท Posted at 18:10:47 on May 25, 2016 ยท (Permalink)
I meant in English, of course. In Finnish the unit is spelled "metri", and there are probably a few other variations in other languages too.
el_loco_avs ยท 1 points ยท Posted at 15:46:35 on May 25, 2016 ยท (Permalink)
er. No it's not?
ohitsasnaake ยท 1 points ยท Posted at 18:09:38 on May 25, 2016 ยท (Permalink)
I'm on mobile, so https://en.m.wikipedia.org/wiki/Metre, section spelling, and/or citation #3. What's your source?
el_loco_avs ยท 1 points ยท Posted at 05:41:58 on May 26, 2016 ยท (Permalink)
https://nl.m.wikipedia.org/wiki/Meter https://de.m.wikipedia.org/wiki/Meter
etc etc etc
ohitsasnaake ยท 1 points ยท Posted at 08:10:30 on May 27, 2016 ยท (Permalink)
As I forgot to mention in my previous post with the links (but did mention in another post in this sub-thread), I was talking about the English-language spelling, which as pointed out in my source, was most recently defined as metre, with only the US measurements authority specifically deviating from that. Hence you get the irony of an American (presumably) complaining to people to speak English and write meter, when the current spelling (and I think this has always been the case for British spelling, compare theatre, centre) in English i.e. British English is defined as metre and only the Americans have officially declared otherwise.
Furthermore, official spelling may of course be different from common usage, which is pretty clearly meter in most international usage as well as obviously Americans.
Morall_tach ยท 5 points ยท Posted at 17:05:21 on May 25, 2016 ยท (Permalink)
Here's a good way to picture this. Imagine that instead of a circle of rope around the Earth, it's a square frame (figure 1). This square frame will only contact the Earth at four points, in the middle of each side. Now, imagine you want to get each point a meter off the ground. All you have to do is add a meter at each end of each of the edges (the yellow segments in figure 2) and the clearance of the square frame is increased from 0m to 1m. The total in this case would be 8m, but since it takes less rope (or frame) to make a circle, a circle would only need 6.3m.
The craziest thing about this is that the original size of the circle doesn't matter. Whether you're wrapping a rope around a car tire or the Moon, if you want to increase clearance by 1m, you need 6.3m of extra rope.
GateauBaker ยท 8 points ยท Posted at 15:25:09 on May 25, 2016 ยท (Permalink)
I don't understand the physics behind this. How does adding rope allow it to defy gravity?
[deleted] ยท 4 points ยท Posted at 16:22:33 on May 25, 2016 ยท (Permalink)
It doesn't. Increasing the length won't cause it to hover. OP is worded stupidly/suggestively.
Schnectadyslim ยท 4 points ยท Posted at 14:46:05 on May 25, 2016 ยท (Permalink)
Bullshit! You'd also need some sort of device to make the rope hover! (Seriously though, this one blows my mind)
WooshJ ยท 4 points ยท Posted at 15:09:00 on May 25, 2016 ยท (Permalink)
Was expecting you to say "you only need to add 6.3 meters of rope to be able to wrap it around your mom."
arsenale ยท 2 points ยท Posted at 14:44:46 on May 25, 2016 ยท (Permalink)
You can cut the earth in half and cause death and destruction by shortening the rope by the same length.
Oncey ยท 2 points ยท Posted at 15:07:49 on May 25, 2016 ยท (Permalink)
If you think about it, it becomes a bit intuitive. If you add 2m rope in 2 opposite places, then the rope in both middles is hovering 1m above the surface. If you add 2m rope in those middle places, then the places where you added the original rope are now 1m above the earth. That's 8m rope.
nnyx ยท 1 points ยท Posted at 19:02:11 on May 25, 2016 ยท (Permalink)
Holy shit thank you.
This makes it so much easier to wrap your head around.
RagingNerdaholic ยท 2 points ยท Posted at 15:23:40 on May 25, 2016 ยท (Permalink)
I need some pie to console myself after that mindfuck.
Andythegriffin ยท 4 points ยท Posted at 15:13:23 on May 25, 2016 ยท (Permalink)
what makes it hover?
SOwED ยท 2 points ยท Posted at 18:49:49 on May 25, 2016 ยท (Permalink)
That's not really the point.
[deleted] ยท 1 points ยท Posted at 19:01:55 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 19:14:32 on May 25, 2016 ยท (Permalink)
No, the point is that adding 2ฯ (~6.3) units to the circumference will increase the radius by one unit, regardless of the sizes of the radius or circumference.
It was an imperfect analogy to explain this consequence of the relationship between radius and circumference.
[deleted] ยท 1 points ยท Posted at 20:15:44 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 20:35:53 on May 25, 2016 ยท (Permalink)
I understand your question, but as I said, it's an analogy. Analogies are, by nature, imperfect.
If you actually did this on a perfect sphere the size of the earth (so no mountains or anything to convolute things), the rope would not hover.
The original comment just used that analogy as a short way to explain that the radius of the circle made by the rope would increase by 1 unit if the rope length were increased by 2ฯ units. It does not matter the scale. This is true of a marble and it's true of a sphere larger than the Milky Way.
[deleted] ยท 1 points ยท Posted at 20:45:15 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 20:55:09 on May 25, 2016 ยท (Permalink)
No, because gravity would pull the rope down. I suppose there is a size at which you could send the rope into a spin and it would orbit.
[deleted] ยท 1 points ยท Posted at 21:35:15 on May 25, 2016 ยท (Permalink)
[deleted]
SOwED ยท 1 points ยท Posted at 21:59:16 on May 25, 2016 ยท (Permalink)
That depends on the mass of the sphere and velocity of the spin. So, actually, given a high enough velocity, the rope could hover one meter above a perfectly spherical earth. Now that I've refreshed my memory on the orbit equation, the size of the sphere doesn't matter as long as the mass of the sphere is compensated for by the velocity of the rope. The limit of this would probably be the speed of light, assuming you could magically have the rope already spinning evenly.
YourmomgoestocolIege ยท 3 points ยท Posted at 16:26:36 on May 25, 2016 ยท (Permalink)
Does this 6.3 have any relation to the 63% from that statistics comment?
chrisTHEayers ยท 1 points ยท Posted at 18:40:38 on May 25, 2016 ยท (Permalink)
Yeah they both have to do with pi
jojoblogs ยท 2 points ยท Posted at 14:43:06 on May 25, 2016 ยท (Permalink)*
In other words, for there is a 1:6.3 ratio between radius and circumference.
Edit: And to be more of a party pooper, I'm fairly certain a rope would crumple. Unless (this is pure conjecture) the rope in question was perfectly aligned across the equator, was arranged into a perfect Circle, had no momentum, and was completely physically uniform, with no defects. If this is all true than the G force of the rope would push inwards into itself, thus being supported. However, it come under the same issues as "trying to play pull with a rope". Or driving a truck in reverse, with more than 1 trailer. Every trailer you add makes the task of steering exponentially harder.
PoisonMind ยท 1 points ยท Posted at 15:05:18 on May 25, 2016 ยท (Permalink)
Why is nobody working on this? What are the engineering limitations on building a 25,000-mile long rope?
ShutUpTodd ยท 1 points ยท Posted at 15:12:13 on May 25, 2016 ยท (Permalink)
Holy crap. I just did the math and it worked out. Mind blown.
heap42 ยท 1 points ยท Posted at 15:15:22 on May 25, 2016 ยท (Permalink)
For anyone wondering yes... 6.4 is 2pi... and that's why it always the same ... cus the circumference is 2rpi
[deleted] ยท 1 points ยท Posted at 15:18:36 on May 25, 2016 ยท (Permalink)
Oh my gosh I always wondered what would happen if this happened. So weird seeing an answer to a hypothetical question I've always had here.
Grumpy_Kong ยท 1 points ยท Posted at 15:22:16 on May 25, 2016 ยท (Permalink)
Circles are so certifiably weird in so many ways that they sometimes literally cause me to doubt the validity of external reality...
And I have a hard time explaining this to anyone.
I mean, how can simple ratios get so crazy? It is as if there is a literal flaw in spacetime when dealing with curves...
Though, in all likelihood, the flaw is in my own understanding...
But, DAMN pi, you weird...
HipHomelessHomie ยท 1 points ยท Posted at 15:24:08 on May 25, 2016 ยท (Permalink)
The size of the earth makes the linear dependency very unintuitive.
meeyowastaken ยท 1 points ยท Posted at 15:24:37 on May 25, 2016 ยท (Permalink)
I find this hard to believe in real time as the earth rotates. Maybe if the earth was frozen in time.
[deleted] ยท 1 points ยท Posted at 15:28:03 on May 25, 2016 ยท (Permalink)
What's holding the rope up?
AcclimateToMind ยท 1 points ยท Posted at 15:34:17 on May 25, 2016 ยท (Permalink)
Neat.
kikenazz ยท 1 points ยท Posted at 15:50:09 on May 25, 2016 ยท (Permalink)
I would have guessed it was closer to 6.28 meters
lkraider ยท 1 points ยท Posted at 16:00:50 on May 25, 2016 ยท (Permalink)
Assuming it's a perfect circle.
cartmancakes ยท 1 points ยท Posted at 16:07:04 on May 25, 2016 ยท (Permalink)
But would it hover?
WhysEveryoneSoPissed ยท 1 points ยท Posted at 16:13:18 on May 25, 2016 ยท (Permalink)
Is this related to the 63% probability mentioned in the top post?
Yamatjac ยท 1 points ยท Posted at 16:18:46 on May 25, 2016 ยท (Permalink)
This is only impressive because it's talking about earth which we can't really understand the scale of, and a meter which we view as large.
A meter is actually REALLY REALLY REALLY REALLY REALLY REALLY REALLY small compared to the earth.
Steinberg1 ยท 1 points ยท Posted at 16:23:06 on May 25, 2016 ยท (Permalink)
So the 2 most interesting responses so far in this thread are 63% and 6.3 meters. Coincidence???
Yes.
ifimhereimnotworking ยท 1 points ยท Posted at 16:29:39 on May 25, 2016 ยท (Permalink)
Ah!!! 2pi! I seeee!!
XavierSimmons ยท 1 points ยท Posted at 16:32:09 on May 25, 2016 ยท (Permalink)
6.3m
63% (another highly rated question here)
Any relationship here?
[deleted] ยท 1 points ยท Posted at 16:33:44 on May 25, 2016 ยท (Permalink)
If it were a solid hoop, would it actually hover?
RoosterBurncog ยท 1 points ยท Posted at 16:44:53 on May 25, 2016 ยท (Permalink)
But, how do you get the rope to hover? (I'm assuming with more math...)
Bandin03 ยท 1 points ยท Posted at 16:51:27 on May 25, 2016 ยท (Permalink)
But, assuming perfect uniformity of the ground beneath the rope, how fast would you have to spin the rope to make it actually hover?
randomguy186 ยท 1 points ยท Posted at 16:54:20 on May 25, 2016 ยท (Permalink)
Nah, lengthening the rope won't make it hover.
vesomortex ยท 1 points ยท Posted at 16:56:51 on May 25, 2016 ยท (Permalink)
Well you'd need to add an anti-grav device of some kind too.
erdmanatee ยท 1 points ยท Posted at 16:58:57 on May 25, 2016 ยท (Permalink)
we really need that rope..
synthabusion ยท 1 points ยท Posted at 17:00:27 on May 25, 2016 ยท (Permalink)
I've always enjoyed the fact that if you lined all the people around the earth holding hands a significant portion of them would drown.
nachofiend ยท 1 points ยท Posted at 17:03:12 on May 25, 2016 ยท (Permalink)
could you or someone draw this out? I'm having a hard time picturing it
3kindsofsalt ยท 1 points ยท Posted at 17:06:56 on May 25, 2016 ยท (Permalink)
tau, baby, tau.
cujoslim ยท 1 points ยท Posted at 17:15:11 on May 25, 2016 ยท (Permalink)
How.
danhakimi ยท 1 points ยท Posted at 17:16:59 on May 25, 2016 ยท (Permalink)
or 6.28.....
2 pi.
humanracedisgrace ยท 1 points ยท Posted at 17:20:42 on May 25, 2016 ยท (Permalink)
Yeah, but what if you want it to hover 2m off the ground. Work that one out, Einstein!
sluggles ยท 1 points ยท Posted at 17:24:13 on May 25, 2016 ยท (Permalink)
For people that don't understand, it might be helpful to think of squares as well. If you have a square with side length s, then the perimeter is 4s by adding up all the sides. If you want a square (with the diagonals lined up) that is at least 1 m away from the edge at every point, then you'd need to add a meter in length to the left, right, top, and bottom of the square. The new square would have side length s+2, and so the perimeter would be 4s+8. So no matter what side length you have, you'll get an increase in perimeter of 8 if you want to make a new square that encloses the old one at a minimum distance of 1 away (with the diagonals lined up) from the old square.
typhoon_2099 ยท 1 points ยท Posted at 17:25:30 on May 25, 2016 ยท (Permalink)
Just heard something similar on House of Lies last night
asaspades1138 ยท 1 points ยท Posted at 17:27:54 on May 25, 2016 ยท (Permalink)
is there a connection between the 6.3 meters here and the 63% odds in the top comment? is there a relationship between 63 and 1? or circles?
poop-trap ยท 1 points ยท Posted at 17:29:02 on May 25, 2016 ยท (Permalink)
A little more than 6.3, let's not round pi too much.
imGnarly ยท 1 points ยท Posted at 17:36:08 on May 25, 2016 ยท (Permalink)
It bothers me that you say 6.3 metres and not 2ฯ metres.
[deleted] ยท 1 points ยท Posted at 17:39:21 on May 25, 2016 ยท (Permalink)
Note: You do have to spin the rope for this to work. If you don't it will just have a bulge somewhere.
Caterwaulingcavalier ยท 1 points ยท Posted at 17:39:49 on May 25, 2016 ยท (Permalink)
For this to be perfectly accurate for all diameters, you'd have to assume the rope has a diameter of 0.
fermesomme ยท 1 points ยท Posted at 17:41:48 on May 25, 2016 ยท (Permalink)
Assuming that the equator is a perfect circle.
luluandthecrick ยท 1 points ยท Posted at 17:47:14 on May 25, 2016 ยท (Permalink)
Imagine an infinitely long rope that is 6.3 m long...
dogfish83 ยท 1 points ยท Posted at 17:47:55 on May 25, 2016 ยท (Permalink)
This one always boggles (but not blows) my mind.
198jazzy349 ยท 1 points ยท Posted at 17:50:57 on May 25, 2016 ยท (Permalink)
Pretty sure you'd need more than just additional length to cause a rope to hover...
[deleted] ยท 1 points ยท Posted at 07:32:36 on May 26, 2016 ยท (Permalink)
[deleted]
198jazzy349 ยท 1 points ยท Posted at 14:08:29 on May 26, 2016 ยท (Permalink)
You are magic!
SkaTSee ยท 1 points ยท Posted at 17:53:24 on May 25, 2016 ยท (Permalink)
is this assuming that where the rope touches the earth is flat all the way around? Or does that not need to factor in?
[deleted] ยท 1 points ยท Posted at 07:32:15 on May 26, 2016 ยท (Permalink)
[deleted]
SkaTSee ยท 1 points ยท Posted at 18:46:07 on May 26, 2016 ยท (Permalink)
I can't tell if you're being sarcastic or not, but to clarify I mean smooth? Like if you were to go around a mountain range would that fuck things up?
IGotSkills ยท 1 points ยท Posted at 17:53:50 on May 25, 2016 ยท (Permalink)
Aye, but how to ye get the rope ter hover harry?
[deleted] ยท 1 points ยท Posted at 18:05:55 on May 25, 2016 ยท (Permalink)
That makes absolutely no sense, but I believe you.
[deleted] ยท 1 points ยท Posted at 18:06:24 on May 25, 2016 ยท (Permalink)
Is this regardless of units? Like, if I'm trying to impress my American friends, can I use 6.3 feet?
rondosfinger ยท 1 points ยท Posted at 18:09:18 on May 25, 2016 ยท (Permalink)
2ฯ
c010rb1indusa ยท 1 points ยท Posted at 18:11:48 on May 25, 2016 ยท (Permalink)
I need to rethink how I do my cable runs.
michael1026 ยท 1 points ยท Posted at 18:12:17 on May 25, 2016 ยท (Permalink)
I'm an idiot. I was sitting here trying to figure out why it would hover off the ground.
[deleted] ยท 1 points ยท Posted at 18:27:53 on May 25, 2016 ยท (Permalink)
I understand why this is true, but it still hurts my brain to think about.
NightFire19 ยท 1 points ยท Posted at 18:31:55 on May 25, 2016 ยท (Permalink)
Assuming the Earth is a perfect sphere, which it isn't :/
kip256 ยท 1 points ยท Posted at 18:43:07 on May 25, 2016 ยท (Permalink)
Is it 6.3 because this is related to Pi in some fashion?
maz-o ยท 1 points ยท Posted at 19:00:40 on May 25, 2016 ยท (Permalink)
that's considering the world is a perfectly round sphere?
diemunkiesdie ยท 1 points ยท Posted at 19:27:47 on May 25, 2016 ยท (Permalink)
OH you mean for the ENTIRE rope to hover. I've been picturing just the end hovering and not understanding what the fuck you were talking about.
[deleted] ยท 1 points ยท Posted at 19:40:40 on May 25, 2016 ยท (Permalink)
I..don't..understand.
bluegender03 ยท 1 points ยท Posted at 19:41:20 on May 25, 2016 ยท (Permalink)
Neat!
naptakerr ยท 1 points ยท Posted at 19:41:53 on May 25, 2016 ยท (Permalink)
HOW
HillaryBot9000 ยท 1 points ยท Posted at 19:57:17 on May 25, 2016 ยท (Permalink)
Hover? Like Saturn?
ThirdRook ยท 1 points ยท Posted at 21:01:21 on May 25, 2016 ยท (Permalink)
If you have a rope as long as the circumference of the earth you can sell it and create a rope business.
scotscott ยท 1 points ยท Posted at 21:01:57 on May 25, 2016 ยท (Permalink)
Similarly, if everyone in China formed a line and stood shoulder to shoulder, lots of them would be hit by cars and most of them would drown.
zuquack ยท 1 points ยท Posted at 21:02:25 on May 25, 2016 ยท (Permalink)
How much would you need to add to get the rope to orbit the earth in one big ring?
siliconloser ยท 1 points ยท Posted at 21:10:59 on May 25, 2016 ยท (Permalink)
You did a copy and paste of my answer the last time this was asked and got much more karma. I don't really mind, but dang at least write it in your own words.
oblioguzzi ยท 1 points ยท Posted at 21:20:00 on May 25, 2016 ยท (Permalink)
The same as a basketball!
tendeuchen ยท 1 points ยท Posted at 21:24:27 on May 25, 2016 ยท (Permalink)
Don't you need to add some sort of hover capability too or is it just HoverRopeโข?
SenorBeef ยท 1 points ยท Posted at 21:34:08 on May 25, 2016 ยท (Permalink)
This may be a dumb question, but why is it 6.3 instead of 3.15? Doesn't adding 1 unit to the length add 3.15 units to the circumference? C=D*pi ?
seeteethree ยท 1 points ยท Posted at 21:38:08 on May 25, 2016 ยท (Permalink)
If you wrap a rope around a billiard ball, you need only add 6.3 meters of rope for it to hover 1 meter away from the billiard ball!
erveek ยท 1 points ยท Posted at 21:41:43 on May 25, 2016 ยท (Permalink)
Antigravity rope?
Styrak ยท 1 points ยท Posted at 21:43:12 on May 25, 2016 ยท (Permalink)
You also need it to be magical rope that can hover.
trogers1995 ยท 1 points ยท Posted at 21:55:43 on May 25, 2016 ยท (Permalink)
Does also work on small objects like an atom? It seems like it would.
timmydunlop ยท 1 points ยท Posted at 22:02:51 on May 25, 2016 ยท (Permalink)
Assuming earth is round at the equator
spartanburt ยท 1 points ยท Posted at 22:36:59 on May 25, 2016 ยท (Permalink)
I bet you could just stretch it that extra bit.
OSU09 ยท 1 points ยท Posted at 22:40:51 on May 25, 2016 ยท (Permalink)
If De = earth's diameter,
(Rope length initial) = ฯ*De
To make it hover 1 meter off the ground, the diameter is essentially 2 meters longer (1 meter off the ground on each side of the earth),
(Rope length 1m) = ฯ*(De+2)
(Rope length 1m) = ฯDe+ฯ2
(Rope length 1m) = (Rope length initial) + ฯ*2
2*ฯ rounds to 6.3
realitytvexec ยท 1 points ยท Posted at 22:53:56 on May 25, 2016 ยท (Permalink)
Wait - is this somehow related to the top comment in this thread:
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j1hc1
kthxtyler ยท 1 points ยท Posted at 22:57:48 on May 25, 2016 ยท (Permalink)
This works for anything that has a circumference doesn't it?
dug99 ยท 1 points ยท Posted at 23:04:33 on May 25, 2016 ยท (Permalink)
I know it's true... but it seems so counterintuitive!
benargee ยท 1 points ยท Posted at 23:45:38 on May 25, 2016 ยท (Permalink)
Or 2pi meters of diameter for every 1 meter off the ground
[deleted] ยท 1 points ยท Posted at 23:52:06 on May 25, 2016 ยท (Permalink)
C = 2*pi*R
dC/dR = 2*pi
cuestix56 ยท 1 points ยท Posted at 00:47:57 on May 26, 2016 ยท (Permalink)
I will believe the math all day long. I just can't visualize how actually adding that amount of rope really does it.
I'm having a hard time thinking that for even 1 mile of the original length that 1.56585540E-7 meters of rope can raise that segment 1 meter.
gvsteve ยท 1 points ยท Posted at 00:53:01 on May 26, 2016 ยท (Permalink)
Earth diameter is 12,742,000 meters.
Earth's circumference is approx 3.14 times that, 40,009,880 meters
Add 6.3 to the length of the circumference, 40,009,886.3
Divide by 3.14 and you get 12,742,002. A diameter of two meters more! It works!
(I remember hearing this factoid years ago and I tried the math and it didn't work, so I guess I did my math wrong back then. )
BeaverCleaver69 ยท 1 points ยท Posted at 01:10:28 on May 26, 2016 ยท (Permalink)
Makes sense. If the circumference of earth is 2 * pi * the radius of earth, adding one meter to the radius is just adding 2pi to the circumference.
C1 = 2 * pi * r
C2 = 2 * pi * (r + 1)
C2 = 2 * pi * r + 2 * pi
C2 = C1 + 2 * pi
C2 = C1 + 6.28
ktkps ยท 7558 points ยท Posted at 11:42:11 on May 25, 2016 ยท (Permalink)*
Hairy Ball Theorem: The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres.
English: It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick.
Edit: found a funny version :
More here : http://uncyclopedia.wikia.com/wiki/Hairy_ball_theorem
Gr1pp717 ยท 3665 points ยท Posted at 13:46:02 on May 25, 2016 ยท (Permalink)
This proves that there is always a spot on earth where there is no wind. (I believe it's 2 spots, but I can't recall)
PointyBagels ยท 2157 points ยท Posted at 14:00:00 on May 25, 2016 ยท (Permalink)
Nope, only one. The obvious attempt leaves 2 spots but it is possible to create a situation with one as well.
kangaroooooo ยท 621 points ยท Posted at 14:33:22 on May 25, 2016 ยท (Permalink)
How?
jamese1313 ยท 1028 points ยท Posted at 16:05:58 on May 25, 2016 ยท (Permalink)
Actual answer here...
Imagine all the air is moving east to west, like it's a spinning top. This creates two points, one at each the north and south pole. Now, on a straight line between the poles (a meridian), move the poles toward eachother a little bit. The lines the wind follows look kind of like the lines on a croissant if the poles were the points. Keep moving the poles together until they reach eachother at the equator, and you only have one point where there's a cowlick.
pennypinball ยท 127 points ยท Posted at 16:38:12 on May 25, 2016 ยท (Permalink)
this is a really good explanation, especially with the croissant thing
AirbornElephant ยท 38 points ยท Posted at 18:49:09 on May 25, 2016 ยท (Permalink)
I got distracted after that part.
[deleted] ยท 14 points ยท Posted at 19:25:37 on May 25, 2016 ยท (Permalink)
[deleted]
SpaceClef ยท 1 points ยท Posted at 00:51:42 on May 26, 2016 ยท (Permalink)
Calm down, Kanye.
EnglishThor ยท 5 points ยท Posted at 20:15:00 on May 25, 2016 ยท (Permalink)
I got hungry
Kjellvis ยท 3 points ยท Posted at 22:16:24 on May 25, 2016 ยท (Permalink)
Croissants are always the answer
Dr_Zorand ยท 15 points ยท Posted at 18:21:29 on May 25, 2016 ยท (Permalink)
I don't understand how you would merge the two. Just before they move, when they are very close, there is wind blowing between them. How do you eliminate that wind?
Thraol ยท 16 points ยท Posted at 20:16:21 on May 25, 2016 ยท (Permalink)
This gif might help visualise the final result.
Dr_Zorand ยท 5 points ยท Posted at 20:29:49 on May 25, 2016 ยท (Permalink)
Is there a picture of just the snarl part? It spins away before I can get a good look at it.
thebestdaysofmyflerm ยท 2 points ยท Posted at 22:00:56 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Hairy_ball_theorem
Dr_Zorand ยท 3 points ยท Posted at 22:04:38 on May 25, 2016 ยท (Permalink)
Thanks. Although it still looks like 2 poles to me. The vectors coming in from the south don't diminish as they approach the center, so they must be going through and out the other side, which would cut the 1 pole in half to make 2.
MaloWlol ยท 1 points ยท Posted at 21:02:08 on May 25, 2016 ยท (Permalink)
Just press your printscreen button and paste it into paint or something to look at it.
TibsChris ยท 2 points ยท Posted at 04:25:52 on May 26, 2016 ยท (Permalink)
It doesn't. It still looks like two poles arbitrarily close. There has to be one stream flowing between the two points, and bringing the poles together concentrates the vectors.
Bringing the poles together concentrates these vectors infinitely across that pole, yet that pole's vector is supposed to be zero.
DiabloTerrorGF ยท 1 points ยท Posted at 00:18:22 on May 26, 2016 ยท (Permalink)
Risky click.
davomyster ยท 9 points ยท Posted at 16:53:15 on May 25, 2016 ยท (Permalink)
That croissant analogy is a great way of visualizing the movement you described. I'm just learning about this now, after reading the Wikipedia article, so I'm definitely not an expert but your explanation seems to make a lot of sense.
baconshake8 ยท 3 points ยท Posted at 19:42:08 on May 25, 2016 ยท (Permalink)
Would it really work with wind though? I thought it only applies to 2 dimensional surface areas, but with wind there air currents that are closer to the surface of the earth and others that are higher up in the sky
BlackholeZ32 ยท 2 points ยท Posted at 17:49:03 on May 25, 2016 ยท (Permalink)
When I first learned limits, my eyes were truly opened on how simple things could be broken down.
[deleted] ยท 3 points ยท Posted at 17:54:03 on May 25, 2016 ยท (Permalink)*
[deleted]
[deleted] ยท 2 points ยท Posted at 21:20:38 on May 25, 2016 ยท (Permalink)
hm i think the way i imagine hurricane winds, i would worry that there's a second stationary spot opposite the eye.
are hurricane wins like concentric circles around the eye? or does it like spiral into the eye?
Bruggie ยท 1 points ยท Posted at 17:18:56 on May 25, 2016 ยท (Permalink)
Like a giant tornado that focuses on one spot?
jamese1313 ยท 1 points ยท Posted at 17:22:42 on May 25, 2016 ยท (Permalink)
Like 2 giant tornadoes, on opposite sides of the earth, spinning in opposite directions that eventually merge with one another.
stratys3 ยท 4 points ยท Posted at 17:53:00 on May 25, 2016 ยท (Permalink)
So... one tornado then?
oighen ยท 2 points ยท Posted at 18:42:04 on May 25, 2016 ยท (Permalink)
Two tornadoes, they spin in different directions.
kevindlv ยท 1 points ยท Posted at 18:00:42 on May 25, 2016 ยท (Permalink)
neat
Triingtoohard ยท 1 points ยท Posted at 18:10:02 on May 25, 2016 ยท (Permalink)
The wind directions would change in this scenario though right? Or is there some way of getting the lines to stay pointed in the same direction and still end up with one point?
chrisTHEayers ยท 1 points ยท Posted at 18:30:53 on May 25, 2016 ยท (Permalink)
It ends up as a dipole, though. How is this considered one point rather than 2 just really close together?
PaintItPurple ยท 1 points ยท Posted at 20:03:56 on May 25, 2016 ยท (Permalink)
Because it's one physical area with no wind, I'd imagine.
DrWobstaCwaw ยท 1 points ยท Posted at 20:50:49 on May 25, 2016 ยท (Permalink)
When the meet at the equator, another cowlick will have sprouted on the opposite side of the earth. Like having two poles again.
jamese1313 ยท 1 points ยท Posted at 22:11:15 on May 25, 2016 ยท (Permalink)
Not at all. If you pull two points on a croissant to touch, does a third pop up out of nowhere?
DrWobstaCwaw ยท 1 points ยท Posted at 00:44:18 on May 26, 2016 ยท (Permalink)
The Earth stays a sphere though. It's shape doesn't change. Your croissant becomes a bagel when the ends touch. The Earth doesn't do that.
aqf ยท 1 points ยท Posted at 20:51:58 on May 25, 2016 ยท (Permalink)
Except doesn't that also mean there's no wind on the other side, but you basically have a bald spot?
jamese1313 ยท 1 points ยท Posted at 22:11:46 on May 25, 2016 ยท (Permalink)
There is wind on the other side. Like the lines on a croissant, where there are lines, there is wind.
bakugandrago18 ยท 1 points ยท Posted at 22:16:03 on May 25, 2016 ยท (Permalink)
I really wish someone animated this, as I'm having trouble visualizing it.
MrClamhammer ยท 1 points ยท Posted at 22:32:23 on May 25, 2016 ยท (Permalink)
You had me at croissant.
DanishWonder ยท 1 points ยท Posted at 22:32:59 on May 25, 2016 ยท (Permalink)
Or, just look at a picture of Donald Trump's hair.
spartanburt ยท 1 points ยท Posted at 22:39:49 on May 25, 2016 ยท (Permalink)
Thats pretty wild. And crazy that I actually somewhat get it.
Paladia ยท -2 points ยท Posted at 18:01:49 on May 25, 2016 ยท (Permalink)
As the wind can blow in different directions at different altitudes, you can't imagine it as a 2 dimensional sphere but rather a 3 dimensional one without a core, if you want an actual answer.
oighen ยท 1 points ยท Posted at 18:44:30 on May 25, 2016 ยท (Permalink)
It's all about the hairy ball theorem and that is about a two dimensional sphere, not a "3 dimensional one without a core".
Paladia ยท 1 points ยท Posted at 19:43:04 on May 25, 2016 ยท (Permalink)
Except we are talking about wind. And wind doesn't move two dimensionally and thus the hairy ball theorem doesn't apply.
oighen ยท 2 points ยท Posted at 19:58:46 on May 25, 2016 ยท (Permalink)
The wind was an analogy. The statement of the hairy ball theorem is about the two dimensional sphere. It's nice and helpful to visualize it using a ball with hair or the wind. You have to implicitly assume to be in the right conditions for the theorem to hold. If, as a first approximation, you think Earth's surface as a sphere and imagine to be able to talk about the wind's direction and intensity at every point then you are bound to have tornadoes. It's math, not physics, don't be a pedantic ass for the sake of it.
Paladia ยท 1 points ยท Posted at 20:28:38 on May 25, 2016 ยท (Permalink)
Don't go berserk and start throwing insults left and right just because someone points out the flaw in using the wrong theorem.
jamese1313 ยท 1 points ยท Posted at 20:07:00 on May 25, 2016 ยท (Permalink)
The wind stands for the 2-D vector field visualization.
JoeFalchetto ยท 4896 points ยท Posted at 14:39:30 on May 25, 2016 ยท (Permalink)
Trying real hard.
Pork-A ยท 596 points ยท Posted at 15:12:57 on May 25, 2016 ยท (Permalink)
Believing in yourself.
DrNoodles247 ยท 22 points ยท Posted at 16:04:53 on May 25, 2016 ยท (Permalink)
Well that's the place to start.
[deleted] ยท 19 points ยท Posted at 16:19:50 on May 25, 2016 ยท (Permalink)
And I say, hey! What a wonderful kind of day!
hellABunk ยท 3 points ยท Posted at 16:35:27 on May 25, 2016 ยท (Permalink)
:Damn.
someone2639 ยท 3 points ยท Posted at 16:53:37 on May 25, 2016 ยท (Permalink)
Just DOING it!
ThebocaJ ยท 3 points ยท Posted at 17:40:01 on May 25, 2016 ยท (Permalink)
Or for the lazy https://en.m.wikipedia.org/wiki/File:Hairy_ball_one_pole_animated.gif
apercots ยท 2 points ยท Posted at 16:04:05 on May 25, 2016 ยท (Permalink)
giving it your best for once
[deleted] ยท 2 points ยท Posted at 16:30:12 on May 25, 2016 ยท (Permalink)
Wanting it hard enough and being pure of heart.
[deleted] ยท 2 points ยท Posted at 18:34:35 on May 25, 2016 ยท (Permalink)
Your honor must be unbesmirched.
[deleted] ยท 2 points ยท Posted at 16:37:10 on May 25, 2016 ยท (Permalink)
[deleted]
misterpickles69 ยท 2 points ยท Posted at 18:05:34 on May 25, 2016 ยท (Permalink)
Have a dream.
greyghost6 ยท 2 points ยท Posted at 17:44:50 on May 25, 2016 ยท (Permalink)
And that wind's name? Albert Einstein.
Edgecloser ยท 1 points ยท Posted at 16:41:38 on May 25, 2016 ยท (Permalink)
You need to believe in yourself!
throwaway10241988 ยท 1 points ยท Posted at 16:42:43 on May 25, 2016 ยท (Permalink)
Believing in your SMELF
ticktockaudemars ยท 1 points ยท Posted at 16:47:15 on May 25, 2016 ยท (Permalink)
YOU CAN DOO IT!
frozenturkey ยท 1 points ยท Posted at 16:54:38 on May 25, 2016 ยท (Permalink)
Being filled with...DETERMINATION.
Ceilibeag ยท 1 points ยท Posted at 16:57:58 on May 25, 2016 ยท (Permalink)
Trust in Dog.
Littlewigum ยท 1 points ยท Posted at 16:58:00 on May 25, 2016 ยท (Permalink)
Using drugs.
Sardonnicus ยท 1 points ยท Posted at 17:07:36 on May 25, 2016 ยท (Permalink)
Believe in your smelf
banksyb00mb00m ยท 1 points ยท Posted at 17:47:02 on May 25, 2016 ยท (Permalink)
may the force be with you.
johnnyrd ยท 1 points ยท Posted at 18:27:07 on May 25, 2016 ยท (Permalink)
Not playing your self!
Mr-Marshmallow ยท 1 points ยท Posted at 18:49:09 on May 25, 2016 ยท (Permalink)
Pixie dust.
betterhappier ยท 1 points ยท Posted at 18:51:11 on May 25, 2016 ยท (Permalink)
Don't give up.
Alarid ยท 1 points ยท Posted at 19:01:14 on May 25, 2016 ยท (Permalink)
That's my ninja way
krelin ยท 1 points ยท Posted at 19:24:21 on May 25, 2016 ยท (Permalink)
And your hairy balls...
HiMyNameIsAri ยท 1 points ยท Posted at 20:37:18 on May 25, 2016 ยท (Permalink)*
This comment has been deleted...
adamrcarmack ยท 1 points ยท Posted at 21:47:40 on May 25, 2016 ยท (Permalink)
Si se puede
mister11th ยท 1 points ยท Posted at 22:05:56 on May 25, 2016 ยท (Permalink)
be a man
Cheerzy ยท 1 points ยท Posted at 23:55:55 on May 25, 2016 ยท (Permalink)
UninvitedGhost ยท 0 points ยท Posted at 18:15:30 on May 25, 2016 ยท (Permalink)
You gotta do what?
StormRider2407 ยท 4 points ยท Posted at 14:58:15 on May 25, 2016 ยท (Permalink)
Well that blows.
DangerBrewin ยท 7 points ยท Posted at 16:44:16 on May 25, 2016 ยท (Permalink)
Not in that one spot it doesn't.
jmgf ยท 1 points ยท Posted at 15:54:53 on May 25, 2016 ยท (Permalink)
What does my boner have to do with solving a math problem?
JoeFalchetto ยท 2 points ยท Posted at 15:59:17 on May 25, 2016 ยท (Permalink)
Usually that's when you're called at the board.
jameskcubed ยท 1 points ยท Posted at 16:00:39 on May 25, 2016 ยท (Permalink)
Every accomplishment starts with the decision to try.
JardyB10 ยท 1 points ยท Posted at 16:23:19 on May 25, 2016 ยท (Permalink)
Giving it 110%.
jorge1213 ยท 1 points ยท Posted at 17:04:17 on May 25, 2016 ยท (Permalink)
JUST DO IT!!
audacias ยท 1 points ยท Posted at 17:21:42 on May 25, 2016 ยท (Permalink)
Ah, the real math
thugnastyanal ยท 1 points ยท Posted at 17:23:42 on May 25, 2016 ยท (Permalink)
Don't let your winds be dreams
dogfish83 ยท 1 points ยท Posted at 17:43:54 on May 25, 2016 ยท (Permalink)
coworker now knows I'm not doing work. Thanks.
morvis ยท 1 points ยท Posted at 23:56:02 on May 25, 2016 ยท (Permalink)
You'll know when you've done it by how it is.
lol_and_behold ยท 1 points ยท Posted at 15:07:54 on May 25, 2016 ยท (Permalink)
That joke blows.
JoeFalchetto ยท 2 points ยท Posted at 15:09:02 on May 25, 2016 ยท (Permalink)
You can't make everyone happy!
lol_and_behold ยท 5 points ยท Posted at 15:16:31 on May 25, 2016 ยท (Permalink)
Nono dude, I tried to be funny with a pun about wind (blows), just sucked at it. I liked your joke really!
Fillipe ยท 3 points ยท Posted at 15:18:41 on May 25, 2016 ยท (Permalink)
Can't believe /u/JoeFalchetto didn't catch wind of that.
Shovelbum26 ยท 2 points ยท Posted at 16:00:07 on May 25, 2016 ยท (Permalink)
It definitely blew right past him.
aboxacaraflatafan ยท 1 points ยท Posted at 16:23:24 on May 25, 2016 ยท (Permalink)
It's impossible to make everyone in the world happy and not leave a cowlick.
yougottasliceitright ยท -1 points ยท Posted at 14:52:34 on May 25, 2016 ยท (Permalink)
Fuck that
itCompiledThrsNoBugs ยท -2 points ยท Posted at 14:46:03 on May 25, 2016 ยท (Permalink)
Very carefully.
JamesTheJerk ยท 1 points ยท Posted at 14:53:51 on May 25, 2016 ยท (Permalink)
You'll need two teabags and a sheet of wax paper.
[deleted] ยท 2 points ยท Posted at 14:54:37 on May 25, 2016 ยท (Permalink)
Wax on Wax off.
PointyBagels ยท 92 points ยท Posted at 14:37:17 on May 25, 2016 ยท (Permalink)
The picture of one such solution is on the wikipedia page (posted by someone else here)
DoctorOctagonapus ยท 23 points ยท Posted at 17:14:33 on May 25, 2016 ยท (Permalink)
https://upload.wikimedia.org/wikipedia/commons/6/6e/Hairy_ball_one_pole_animated.gif
This one here
Yodamanjaro ยท 3 points ยท Posted at 15:10:14 on May 25, 2016 ยท (Permalink)
What I can't remember is how I have you on here as a friend. Do we know each other?
PointyBagels ยท 22 points ยท Posted at 15:48:57 on May 25, 2016 ยท (Permalink)
Forgive me for stalking your post history but I think I may have found a clue. Were you the guy I met on Omegle (like 4+ years ago) who got me into trance music?
Yodamanjaro ยท 16 points ยท Posted at 16:16:12 on May 25, 2016 ยท (Permalink)
Ohhhh yeah! How's things been?
pennypinball ยท 12 points ยท Posted at 16:37:04 on May 25, 2016 ยท (Permalink)
holy shit that is some insane chance
nonowords ยท 13 points ยท Posted at 16:59:55 on May 25, 2016 ยท (Permalink)
probably about 63%
Yodamanjaro ยท 8 points ยท Posted at 17:00:12 on May 25, 2016 ยท (Permalink)
Nah, I've seen people on here that merely recognize me by my username and ask me if I used to post music to Newgrounds...in like 2007.
Axis73 ยท 2 points ยท Posted at 17:26:05 on May 25, 2016 ยท (Permalink)
Actually 50/50... Either it happened, or it didn't.
locke1718 ยท 4 points ยท Posted at 17:11:24 on May 25, 2016 ยท (Permalink)
Reddit... Bringing people together since 2005.
holybrohunter ยท 3 points ยท Posted at 16:28:17 on May 25, 2016 ยท (Permalink)
We did it Reddit!
PointyBagels ยท 1 points ยท Posted at 19:17:39 on May 25, 2016 ยท (Permalink)
I've been alright haha. Sad to say I don't listen to trance all that much anymore though. More of a progressive house guy now.
Though it's possible you started me on that too haha. I vaguely recall something along those lines.
Yodamanjaro ยท 1 points ยท Posted at 19:20:12 on May 25, 2016 ยท (Permalink)
Knowing me, I probably showed you all I knew about EDM. Glad to hear things have been good!
[deleted] ยท 15 points ยท Posted at 15:22:06 on May 25, 2016 ยท (Permalink)
How can you just forget your friends like that /u/Yodamanjaro?
GoTaW ยท 5 points ยท Posted at 15:33:25 on May 25, 2016 ยท (Permalink)
Trying real hard.
Yodamanjaro ยท 1 points ยท Posted at 16:29:46 on May 25, 2016 ยท (Permalink)
I've been on here long enough that it all seems like a big blur.
YouAreInAComaWakeUp ยท 1 points ยท Posted at 17:25:24 on May 25, 2016 ยท (Permalink)
Thanks for clarifying. Now let me search through all 4,600+ comments to find that link.
PointyBagels ยท 1 points ยท Posted at 18:56:05 on May 25, 2016 ยท (Permalink)
There were only like 5 in the subthread when I replied.
https://en.wikipedia.org/wiki/Hairy_ball_theorem
MemeHunter421x ยท 13 points ยท Posted at 14:50:23 on May 25, 2016 ยท (Permalink)
FIRMLY GRASP IT
mcmcc ยท 3 points ยท Posted at 15:31:41 on May 25, 2016 ยท (Permalink)
Go to one of the spots and breathe really hard. Obviously you can't be in two places at once so... QED.
muttyfut ยท 2 points ยท Posted at 15:31:19 on May 25, 2016 ยท (Permalink)
IIRC, you can move the spots whilst still satisfying the conditions. By 'pushing' both of these spots together it's possible to only have one point of zero.
zombie_girraffe ยท 2 points ยท Posted at 15:38:07 on May 25, 2016 ยท (Permalink)
You just put a fan blowing in the opposite direction at one of the spots.
DisRuptive1 ยท 2 points ยท Posted at 16:58:12 on May 25, 2016 ยท (Permalink)
Spirals.
Redbiertje ยท 1 points ยท Posted at 15:40:11 on May 25, 2016 ยท (Permalink)
Imagine you have the obvious solution, and then shift one point to the other, till they are the same.
Glitch29 ยท 1 points ยท Posted at 15:56:52 on May 25, 2016 ยท (Permalink)
Basically by dragging both of the discontinuities to the same location.
rager123 ยท 1 points ยท Posted at 15:59:12 on May 25, 2016 ยท (Permalink)
Get a rebids ball and comb all the hair uniformly away from one single point in all direction.
[deleted] ยท 1 points ยท Posted at 16:18:16 on May 25, 2016 ยท (Permalink)
I'm assuming combing all hairs clockwise or counterclockwise around the ball as if it were a vertical cylinder. Two spots would be on the top and bottom (ends of the "cylinder").
MeOfAllTrades ยท 1 points ยท Posted at 17:17:55 on May 25, 2016 ยท (Permalink)
More wind
Waydizzle ยท 1 points ยท Posted at 17:30:39 on May 25, 2016 ยท (Permalink)
Basically if you started at the South Pole and combed all the hairs toward the North Pole, you would end up with only one cowlick.
Spingolly ยท 1 points ยท Posted at 18:08:13 on May 25, 2016 ยท (Permalink)
Boot straps, baby!
jeffseadot ยท 1 points ยท Posted at 18:49:20 on May 25, 2016 ยท (Permalink)
Globe-spanning hurricane
NotGloomp ยท 1 points ยท Posted at 20:40:49 on May 25, 2016 ยท (Permalink)
The two empty bits merge into one bigger empty bit.
edrudathec ยท 1 points ยท Posted at 21:11:12 on May 25, 2016 ยท (Permalink)
Put the two spots in the same spot.
spidaminida ยท 1 points ยท Posted at 05:20:54 on May 26, 2016 ยท (Permalink)
Imagine covering a sphere with a piece of stretchy fabric and gathering the edges in your fist. Now imagine that material as perfectly stretchy and thin, and you have it converging only at one spot!
Willch4000 ยท 0 points ยท Posted at 14:50:00 on May 25, 2016 ยท (Permalink)*
Imagine a tennis ball. Pick any single spot on it and imagine a ripple going outwards from that spot, flattening the hairs it goes across. The ripple will go around the ball and come back together, closing on the other side and causing a single cowlick there.Now, replace the tennis ball with the Earth and replace the hair flattening ripple with wind and presumably you get a single spot where there is no wind.Now, I have exactly zero experience on this and don't fully understand it, however, that is how I imagine it might work./u/PointyBagels, thoughts?Edit: Nevermind, I'm not going to try explaining something I don't understand...
nazzyc ยท 8 points ยท Posted at 15:04:05 on May 25, 2016 ยท (Permalink)
With that method, you've created 2 spots. The one you start on, and the one that you end on.
[deleted] ยท 1 points ยท Posted at 15:32:37 on May 25, 2016 ยท (Permalink)
The one he started on is not a cowlick.
PointyBagels ยท 2 points ยท Posted at 15:34:17 on May 25, 2016 ยท (Permalink)
As the others have said, that creates two spots. I think it's a common misunderstanding because of the name of the theorem. Obviously if you're working with an actual hairy ball, your solution creates a situation where the hair stands up in only one place. However, the theorem itself, simply stated as
does not distinguish between the two points. In your case, there is one point which all nearby vectors point towards (the end of the ripple), and another point which all nearby vectors point away from (the start of the ripple). There's also a third kind of point possible, a point which all nearby vectors circle around (for example, the eye of a hurricane).
However, even though all of these situations act differently, the only thing that matters to the theorem is whether a single zero-vector (or point) exists, not the behavior of the vectors around it.
Nloveladyallen ยท 1 points ยท Posted at 15:04:29 on May 25, 2016 ยท (Permalink)
Then you have the origin of the wind and the opposite point.
fro-doh ยท 0 points ยท Posted at 14:50:45 on May 25, 2016 ยท (Permalink)
A fan
HaywoodJablomie2512 ยท 0 points ยท Posted at 14:52:26 on May 25, 2016 ยท (Permalink)
Only if you really believe in it.
firematt422 ยท 0 points ยท Posted at 15:18:53 on May 25, 2016 ยท (Permalink)
There is nothing so useless as doing efficiently that which should not be done at all.
Poerflip23 ยท 0 points ยท Posted at 16:29:23 on May 25, 2016 ยท (Permalink)
By trusting the heart of the cards
Tomerg91 ยท 0 points ยท Posted at 16:48:17 on May 25, 2016 ยท (Permalink)
Love, Tars, Love.
manondorf ยท 0 points ยท Posted at 17:02:41 on May 25, 2016 ยท (Permalink)
just gotta lick your thumb first
AlmightyNeckbeardo ยท -1 points ยท Posted at 14:44:40 on May 25, 2016 ยท (Permalink)
Magic.
nothingremarkable ยท 3 points ยท Posted at 14:31:46 on May 25, 2016 ยท (Permalink)
Is there a picture of the single spot case somewhere?
gazaleon ยท 9 points ยท Posted at 16:55:21 on May 25, 2016 ยท (Permalink)
Animated GIF of a 2D sphere with a single pole: https://en.wikipedia.org/wiki/File:Hairy_ball_one_pole_animated.gif
kazneus ยท 2 points ยท Posted at 18:27:23 on May 25, 2016 ยท (Permalink)
This is assuming we are talking about the surface of a sphere. However, that isn't true; there is depth to the atmosphere of Earth and therefore you have an extra dimension to deal with. So vectors that can't cross on the surface of a sphere can cross in the extra dimension...
but now I'm thinking that it might end up with at least one spot of zero wind by symmetry of vectors around it. Or not because you could define a vector within that field..
So you squish a torus around the earth such that the center of the torus becomes two columns of vectors at each poll - one pointing all up and one pointing all down. But that leaves the inside of the torus, which you could just define as a ring of vectors pointing clockwise or counter-clockwise in sort of an equatorial sense.
Anyways, yay for hairy balls!
PointyBagels ยท 3 points ยท Posted at 19:01:26 on May 25, 2016 ยท (Permalink)*
For any arbitrarily thin surface surrounding the Earth (but inside its atmosphere), there must always be at least one point on this surface where the component of the wind's velocity tangent to the surface is zero.
Better?
kazneus ยท 3 points ยท Posted at 19:26:47 on May 25, 2016 ยท (Permalink)
Yes.
For the record I wasn't trying to give you shit I was just extemporizing on the idea
PointyBagels ยท 3 points ยท Posted at 19:32:19 on May 25, 2016 ยท (Permalink)
No worries, and no sass was intended. I wasn't trying to give you shit either, if that's how it came across.
Just applying the theorem to the atmosphere in a way that it actually does work.
ElvishJerricco ยท 1 points ยท Posted at 15:14:49 on May 25, 2016 ยท (Permalink)
Is this necessarily true, considering that Earth isn't a perfect sphere?
PointyBagels ยท 9 points ยท Posted at 15:23:14 on May 25, 2016 ยท (Permalink)
As far as I know, that does not make a difference. In a topological sense, the Earth can be treated like a sphere.
What does, however, make a difference, is the fact that the atmosphere is not a 2 dimensional surface, but a 3 dimensional "shell".
ElvishJerricco ยท 1 points ยท Posted at 15:27:50 on May 25, 2016 ยท (Permalink)
Ah. Well then does that mean it isn't necessarily true?
TurkeyPits ยท 6 points ยท Posted at 15:33:46 on May 25, 2016 ยท (Permalink)
It means that it's true at any given "layer" of the atmosphere. Every layer will have at least one cyclone (point of zero wind) at all times. These spots in each layer don't have to line up vertically, though, so in a macro sense it does indeed mean it's not true
PointyBagels ยท 3 points ยท Posted at 15:40:17 on May 25, 2016 ยท (Permalink)
And to clarify one point, "zero wind" in this case means "zero horizontal wind". Vertical wind is still completely possible, as the theorem would only concern the component of the wind that is tangent to the surface.
/u/ElvishJerricco
Fenring ยท 3 points ยท Posted at 15:25:30 on May 25, 2016 ยท (Permalink)
Yes. It's a theorem of topology, which means that it's true of things that can be bent or stretched into spheres without tearing. It would still be true if the Earth were extremely lumpy, like an asteroid, but not if the Earth were donut-shaped.
Gr1pp717 ยท 1 points ยท Posted at 15:54:04 on May 25, 2016 ยท (Permalink)
IIRC it's true on any "closed" shape. Topology classifies things in a really weird, and unintuitive way, so I'd be hard pressed to explain what that means in an ELI5 way. But here's the wiki on the topic, if you care to dig in.
SpiffAZ ยท 1 points ยท Posted at 15:24:43 on May 25, 2016 ยท (Permalink)
Something something "only if you don't blow it" something... It's too early.
ubergorp ยท 1 points ยท Posted at 16:46:59 on May 25, 2016 ยท (Permalink)
Couldn't we just do no spots? I hate wind :(
ryan4588 ยท 1 points ยท Posted at 17:17:10 on May 25, 2016 ยท (Permalink)
define "spot" in this case? How big is this location?
PointyBagels ยท 1 points ยท Posted at 19:06:03 on May 25, 2016 ยท (Permalink)*
A spot in this case would be a single point.
But as has been pointed out, this doesn't actually apply to the Earth's atmosphere as a whole, since the atmosphere has thickness and is not a 2d surface. It could apply to a surface drawn inside the atmosphere though.
ryan4588 ยท 1 points ยท Posted at 19:07:40 on May 25, 2016 ยท (Permalink)
Ahhh I see. Thanks!(:
yolafaml ยท 1 points ยท Posted at 18:40:54 on May 26, 2016 ยท (Permalink)
Dumb question- what if you have this pattern where there is one spot with no wind, then make the pattern move offer the surface without distorting? Would that just perfectly sync with another area and so stop wind there too, or is there some long-winded maths explanation?
PointyBagels ยท 1 points ยท Posted at 18:50:59 on May 26, 2016 ยท (Permalink)
Yes, it would always cause another point to have no wind. At least if we make the simplifying but false assumption that the atmosphere has 0 thickness so the theorem applies.
As for the reason, that is a long winded maths explanation. The actual proof deals with transformations of vector fields (a example of which you actually just described),so if you can understand it, I'd take a look at the real proof. Otherwise, suffice to say that no transformation can be applied that leaves the vector field both continuous and without a zero vector.
yolafaml ยท 1 points ยท Posted at 19:03:46 on May 26, 2016 ยท (Permalink)
I'll check it out! I enjoy maths, but at the moment I haven't learned much of it (currently doing my gcse...)
BrahmsAllDay ยท 259 points ยท Posted at 14:18:46 on May 25, 2016 ยท (Permalink)
Isn't this only true if you assume winds operate in two dimensions? If winds move other than parallel to the surface, you can have winds everywhere, I would have thought.
alandbeforetime ยท 271 points ยท Posted at 14:24:59 on May 25, 2016 ยท (Permalink)*
For a small enough measurement point, there will always be a zero-point for wind at every layer. This means that a human would still experience wind if he/she stood anywhere though (the body is way larger than the required measurement point).
Source: Hairy Ball Theorem
EDIT: I am wrong if you account for vertical vectors in three dimensions (which you should in the case of wind)
BrahmsAllDay ยท 24 points ยท Posted at 14:50:10 on May 25, 2016 ยท (Permalink)
I'm not sure if this is true if you add in a third dimension - the "cowlick" can just be rising air. When you say "every layer" you're saying the layers are arbitrarily thin, i.e. have two dimensions. But if the vector at any given point in the layer can point "up" (which would only make sense if you have a third dimension), then you can avoid having zero points.
alandbeforetime ยท 5 points ยท Posted at 15:00:38 on May 25, 2016 ยท (Permalink)
Oh. Huh. You may be right. I don't know why I was assuming measurement wouldn't count up/down winds.
Alternative_Reality ยท 6 points ยท Posted at 18:07:14 on May 25, 2016 ยท (Permalink)
It doesn't because the Hairy Ball Theorem only concerns tangent vectors
[deleted] ยท 4 points ยท Posted at 18:18:44 on May 25, 2016 ยท (Permalink)*
[deleted]
Alternative_Reality ยท 3 points ยท Posted at 18:27:53 on May 25, 2016 ยท (Permalink)
Vertical movement of wind is not a tangent vector though.
[deleted] ยท 3 points ยท Posted at 19:09:51 on May 25, 2016 ยท (Permalink)*
[deleted]
Alternative_Reality ยท 3 points ยท Posted at 19:59:18 on May 25, 2016 ยท (Permalink)
This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere.
And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite.
The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object.
harmlesspotato ยท 2 points ยท Posted at 19:47:06 on May 25, 2016 ยท (Permalink)
Doesn't hairy ball theorem only apply to even dimensional n-spheres?
LSeww ยท 1 points ยท Posted at 22:32:35 on May 25, 2016 ยท (Permalink)
It says that among all only even cannot have this fancy property.
2weirdy ยท 2 points ยท Posted at 15:32:49 on May 25, 2016 ยท (Permalink)*
Even if it counted up and down winds, you'd still have a limit to the distance you can go.
Edit2: My reasoning was wrong.ยจ
Edit3: New reasoning: The Hairy Ball theorem is actually a result of the PoincarรฉโHopf Theorem, which states that with finitely (zero included) many zero points in a vector field, the sum of the indices of the vector field is equal to the Euler characteristic of the space.
An index of a vector field only has a defined value at a zero point.
The Euler characteristic of a ball is 1. I checked on wolfram alpha, and honestly can't be bothered to learn more about it at the moment.
Therefore, there must be a nonzero amount of zero points in a vector field, in order for the indices to add up to 1.
BrahmsAllDay ยท 3 points ยท Posted at 16:16:29 on May 25, 2016 ยท (Permalink)
I'm not sure what "limited" means in this context. In the classic example, the cowlick is not a zero point when you extend into a third dimension: the vector points "up", away from the surface. You have a zero point in two dimensions, but not in three (this is kind of the whole point of HBT - the cowlick is the non-zero point projection into the third dimension). Note that I'm calling the surface of a sphere a two-dimensional object.
2weirdy ยท 1 points ยท Posted at 17:13:58 on May 25, 2016 ยท (Permalink)
Limited effetively means finite sized space. Even if you extend into the third dimension, a 3-dimensional sphere is effectively the surface of half of a 4-dimensional sphere, like a circle(2d sphere) is the surface of half of a 3-dimensional sphere, and a line(1d sphere) is the surface of half of a 2d sphere. The hairy ball theorem applies to ALL of those, and therefore also to the 4d sphere surface, and thus also to a filled 3d sphere (ball).
Think about it this way. if you have air moving "up", you'll reach the edge of the atmossphere eventually. Unless you have an infinitely large OR looping space (such as a torus or donut), there will always be a zero point somewhere in that space.
Essentially, you can only have no zero points if you allow circulation into a dimension you're not using, in other words having circulation into nowhere.
Slime0 ยท 1 points ยท Posted at 18:43:32 on May 25, 2016 ยท (Permalink)
The theorem doesn't hold for a sphere in 4D space (a 3-sphere).
2weirdy ยท 1 points ยท Posted at 21:29:28 on May 25, 2016 ยท (Permalink)*
Right, missread that. Still, I can't imagine a non-vanishing continuous vector-field in a finite ball in 3 dimensional space. I can neither find proof against nor for whether or not it is possible so far. Might come back when I do so.
Edit: Alright. The Hairy Ball theorem is actually a result of the PoincarรฉโHopf Theorem, which states that with finitely (zero included) many zero points in a vector field, the sum of the indices of the vector field is equal to the Euler characteristic of the space.
An index of a vector field only has a defined value at a zero point.
The Euler characteristic of a ball is 1. I checked on wolfram alpha, and honestly can't be bothered to learn more about it at the moment.
Therefore, there must be a nonzero amount of zero points in a vector field, in order for the indices to add up to 1.
I've updated my previous post to reflect this new proof. So while my argumentation was wrong, my initial statement based on a hunch was right. Considering this is a reddit comment and thus not that important, I'd say good enough in this case.
Random832 ยท 1 points ยท Posted at 21:11:00 on May 25, 2016 ยท (Permalink)
Well, what's at the top of that rising air? Wouldn't it have to go up forever for your argument to work?
TonkaTuf ยท 1 points ยท Posted at 15:55:58 on May 25, 2016 ยท (Permalink)
But an infinitesimal layer can still have a vertical component of wind velocity...
billndotnet ยท 0 points ยท Posted at 15:19:10 on May 25, 2016 ยท (Permalink)
That's assuming a form of two dimensional space on the surface of the sphere, though. The earth isn't a closed system, the energy that drives wind comes from an external source. The zero point for terrestrial wind could be miles above the surface. Imagine a blow dryer pointed at your tennis ball.
Ugbrog ยท 5 points ยท Posted at 15:07:26 on May 25, 2016 ยท (Permalink)
from wikipedia: This is not strictly true as the air above the earth has multiple layers, but for each layer there must be a point with zero horizontal windspeed.
BrahmsAllDay ยท -4 points ยท Posted at 15:14:38 on May 25, 2016 ยท (Permalink)
But how thick are those layers? If they're arbitrarily thin, that's just another way of saying they only have two dimensions. If at a point, however, the vector points "up" (i.e. you recognise an extra dimension), it is not a zero point.
Ugbrog ยท 4 points ยท Posted at 15:19:19 on May 25, 2016 ยท (Permalink)
You do realize that you're arguing the premise, right? The point of the HAIRY BALL theorem is that you can't comb the hairs of the ball in the same direction. You end up with hairs pointing STRAIGHT UP. No one cares about the third dimension because IT WAS NEVER PART OF THE PROBLEM.
BrahmsAllDay ยท -2 points ยท Posted at 16:03:40 on May 25, 2016 ยท (Permalink)
No, I'm not.
I'm addressing a very specific claim, made above: "there is always a spot on earth where there is no wind".
My point is that this would only be true if you assume two dimensions. In three, it's not true.
Ugbrog ยท -2 points ยท Posted at 16:22:09 on May 25, 2016 ยท (Permalink)
Which is a pointless argument, since we are only discussing horizontal windspeed as described by the mathematical theorem that this entire discussion is about. But yes, he was incorrect in how he oversimplified the phenomenon. Good job.
BrahmsAllDay ยท 0 points ยท Posted at 16:31:40 on May 25, 2016 ยท (Permalink)
It's not pointless, it's precise. What's pointless is your incorrect and oddly aggressive assertion that I was arguing the premise. And I mean it is literally pointless - you have contributed exactly nothing of value to this discussion.
Ugbrog ยท -1 points ยท Posted at 17:19:37 on May 25, 2016 ยท (Permalink)
Goddamnit, I'm being trolled. Fuck off.
BrahmsAllDay ยท 0 points ยท Posted at 17:30:29 on May 25, 2016 ยท (Permalink)
..What? Are you actually autistic or something?
Negotiator1225 ยท 3 points ยท Posted at 16:03:32 on May 25, 2016 ยท (Permalink)
The hairy ball theorem would then imply that there is at least one point on earth where the wind is entirely vertical or non-existent.
BrahmsAllDay ยท -1 points ยท Posted at 16:08:43 on May 25, 2016 ยท (Permalink)
It doesn't have to be "entirely vertical" - only not parallel to the surface.
Negotiator1225 ยท 3 points ยท Posted at 19:08:19 on May 25, 2016 ยท (Permalink)
It would have to be vertical. Suppose that, for every point on the surface of the earth, x, we have a 3D wind vector w(x), where w(x) is not orthogonal (entirely vertical) to the surface. We of course assume w is continuous. Now suppose for each vector w(x), we take the projection of w(x) onto the tangent plane to the earth at x. Call that projection p. Projections are continuous, so p is continuous. Then p(w(x)) is continuous. Since no w(x) is orthogonal to the earth, p(w(x)) is nonzero for every x.
So, we would have a function p(w(x)) which is continuous, nonzero, and tangent to the surface at every x. This is a contradiction to the Hairy Ball Theorem.
about372people ยท 2 points ยท Posted at 14:27:16 on May 25, 2016 ยท (Permalink)
Well, sure, but for the most part the wind on earth moves parallel to the ground. The up drafts and downdrafts are either too small to be considered, or they are moving along the ground as well.
BrahmsAllDay ยท 3 points ยท Posted at 14:51:28 on May 25, 2016 ยท (Permalink)
Right but at the hypothetical zero point you could just have rising air - the "cowlick" and so even theoretically, there won't be a zero point for wind.
Navyguy330 ยท 1 points ยท Posted at 14:42:29 on May 25, 2016 ยท (Permalink)
that and there are nothing but flat topology on earth, but since there are mountains its dynamic enough that theoretically you can have ZERO places on earth without wind moving.
Eric_the_Barbarian ยท 1 points ยท Posted at 15:18:55 on May 25, 2016 ยท (Permalink)
The cowlick is that vertical component where the vectors become non-tangental.
BrahmsAllDay ยท 1 points ยท Posted at 15:59:59 on May 25, 2016 ยท (Permalink)
Right. So it isn't true that "there is always a spot on earth where there is no wind".
Eric_the_Barbarian ยท 1 points ยท Posted at 17:19:22 on May 25, 2016 ยท (Permalink)
More accurately, if there is wind anywhere on Earth, there must be an updraft or downdraft (and probably both.)
frostbird ยท 1 points ยท Posted at 16:24:10 on May 25, 2016 ยท (Permalink)
"continuous tangent vector field"
Yes, you are exactly correct.
ydubs ยท 0 points ยท Posted at 16:13:10 on May 25, 2016 ยท (Permalink)
Well, don't forget that the second dimension is really a function of the third and fourth dimensions! 2= (34 )(34) - (43 )(43) And that's my favorite math fact
[deleted] ยท 3 points ยท Posted at 15:03:16 on May 25, 2016 ยท (Permalink)
Amphidromes! I just learned about these. Where the tide barely moves.
milkand24601 ยท 2 points ยท Posted at 15:16:35 on May 25, 2016 ยท (Permalink)
Which coincidentally would be the best spot for a tennis match!
ArtichokeHeartAttack ยท 2 points ยท Posted at 15:50:26 on May 25, 2016 ยท (Permalink)
The two point thing you may be thinking of is that there exist two points on the exact opposite end of the Earth with identical temperature and humidity (or any other pair of measurements like 2d wind direction and magnitude). It comes from the Borsuk-Ulam Theorem.
Gr1pp717 ยท 1 points ยท Posted at 15:59:19 on May 25, 2016 ยท (Permalink)
I want to say that it's more that the solutions for a single point is so special that they just don't really happen. And the poles don't have to be opposite to each other.
But it's been like 12 years since or so since I was into math, so things area bit fuzzy (pun intended).
c3534l ยท 2 points ยท Posted at 16:24:14 on May 25, 2016 ยท (Permalink)
There's also always two spots where the temperature is exactly the same.
potatan ยท 2 points ยท Posted at 18:39:55 on May 25, 2016 ยท (Permalink)
I think I found it
https://earth.nullschool.net/#current/wind/isobaric/1000hPa/orthographic=-48.03,42.50,812
shaggorama ยท 1 points ยท Posted at 15:28:08 on May 25, 2016 ยท (Permalink)
I think you mean there is always at least one vortex. I don't think it's accurate to describe the center of a vortex as "no wind"
rathat ยท 1 points ยท Posted at 15:34:10 on May 25, 2016 ยท (Permalink)
But how small of a spot?
Infinity_Farts ยท 1 points ยท Posted at 15:40:43 on May 25, 2016 ยท (Permalink)
Do farts count as wind?
WeaponsGradeHumanity ยท 1 points ยท Posted at 15:49:20 on May 25, 2016 ยท (Permalink)
And that spot is where you'll find the fractal butterfly.
AltoidNerd ยท 1 points ยท Posted at 16:02:24 on May 25, 2016 ยท (Permalink)
I've always heard this but since we have a radial direction I'm not sure if it's even true.
bassinastor ยท 1 points ยท Posted at 16:16:37 on May 25, 2016 ยท (Permalink)
Correct me if I'm wrong, but that's only true for an instant in time. The thing is that wind is about movement, so it requires time to really mean anything. Like if you took a snapshot of the earth right now, at least one spot would have no wind. However, if you were watching a video of the wind on earth then that one spot could be moving around constantly which means it wouldn't be a stationary point.
Gr1pp717 ยท 1 points ยท Posted at 17:25:19 on May 25, 2016 ยท (Permalink)
Yes. Just for some instant, and the spot shifts anywhere. As other's have pointed out there's likely still updraft at this location, but that's not how wind speed is measured.
notsurewhatimlookin4 ยท 1 points ยท Posted at 16:27:07 on May 25, 2016 ยท (Permalink)
FTFY: This proves that there is AT LEAST ONE spot on earth where there is no wind.
Camjw1123 ยท 1 points ยท Posted at 16:27:36 on May 25, 2016 ยท (Permalink)
It actually doesn't. The earth isn't topologically equivalent to a sphere, it has a really really high genus (all the tunnels through mountains and even natural rock formations give the earth holes) so the theorem doesn't necessarily apply to the earth. It might do for the surface of Jupiter though!
Randomredditacnt ยท 1 points ยท Posted at 16:30:06 on May 25, 2016 ยท (Permalink)
This brings back bad memories of dealing with streamlines and stagnation points in my aerodynamics class.
[deleted] ยท 1 points ยท Posted at 16:35:33 on May 25, 2016 ยท (Permalink)
This assumes far too much about the earth, that wind is measured with large vectors for example (they are just approximations, each instantaneous location is too small to measure). Wind is movement of nitrogen molecules - there are at any given time almost uncountable numbers with common velocity values imaginable.
In other words, it is purely a hypothetical that is true of a mathematical model, but on Earth has no practical meaning.
1Daverham ยท 1 points ยท Posted at 16:55:55 on May 25, 2016 ยท (Permalink)
this place?
TheTallGuy0 ยท 1 points ยท Posted at 17:00:20 on May 25, 2016 ยท (Permalink)
I found it. It was at last weeks regatta.
krkirch ยท 1 points ยท Posted at 17:02:28 on May 25, 2016 ยท (Permalink)
I'm picturing two hemisphere-sized hurricanes. Frightening
MCCornflake1 ยท 1 points ยท Posted at 17:08:45 on May 25, 2016 ยท (Permalink)
Is it just one location all the time? Or does it like move around?
candybomberz ยท 1 points ยท Posted at 17:09:09 on May 25, 2016 ยท (Permalink)
Problem is that earths atmosphere isn't a flat surface, so the theorem does not apply to atmospheric movement.
nomadish ยท 1 points ยท Posted at 17:09:53 on May 25, 2016 ยท (Permalink)
So you're saying it's impossible for the entire world to suck at once thanks to hairy ball?
AntarcticanJam ยท 1 points ยท Posted at 17:15:53 on May 25, 2016 ยท (Permalink)
Doldrums? I learned something like this in elementary school but at the time it all went way over my head.
LogicFish ยท 1 points ยท Posted at 17:20:15 on May 25, 2016 ยท (Permalink)
It is possible to "comb" a torus (donut), so any tunnel being windy would make it possible?
[deleted] ยท 1 points ยท Posted at 17:28:59 on May 25, 2016 ยท (Permalink)
No, wind is not continuous or in the same direction
mormotomyia ยท 1 points ยท Posted at 17:39:36 on May 25, 2016 ยท (Permalink)
this also means that there are two spots on the earth that have the same temperature.
KuntaStillSingle ยท 1 points ยท Posted at 17:54:15 on May 25, 2016 ยท (Permalink)
This is not true, there need only be one spot with no wind tangential to the earth 's surface, it can and probably will blow upwards and downwards at that point.
Paladia ยท 1 points ยท Posted at 18:05:05 on May 25, 2016 ยท (Permalink)
No it doesn't as the Hairy ball theorem only applies to a two dimensional sphere. Wind blows in the third dimension as it can also change altitude, as well as blow in different directions depending on altitude.
Alternative_Reality ยท 1 points ยท Posted at 18:05:41 on May 25, 2016 ยท (Permalink)
It only proves there is no horizontal wind at one point, since we are only looking at tangent vectors in the Hairy Ball Theorem
anonymousWizard ยท 1 points ยท Posted at 18:11:25 on May 25, 2016 ยท (Permalink)
How? All the wind on earth doesn't simultaneously travel in the same direction right? Isn't it in like 'pockets'? (me trying to remember 7th grade science class)
simuse ยท 1 points ยท Posted at 18:28:06 on May 25, 2016 ยท (Permalink)
I'm in my bathroom right now, and I can confirm : no wind.
yaosio ยท 1 points ยท Posted at 18:37:32 on May 25, 2016 ยท (Permalink)
What if I have a fan going in the spot where's there's no wind?
mcbinladen ยท 1 points ยท Posted at 18:50:19 on May 25, 2016 ยท (Permalink)
But with so many high and low altitude spots, can you really consider Earth just an upscale of a tennis ball?
MartinLoofah ยท 1 points ยท Posted at 19:24:13 on May 25, 2016 ยท (Permalink)
Also, it can be used to show that at any given moment, there are two points on the earth exactly opposite of each other which have exactly the same temperature and barometric pressure.
Herooftme ยท 1 points ยท Posted at 19:37:40 on May 25, 2016 ยท (Permalink)
Houston ?
IAmBlakeM ยท 1 points ยท Posted at 19:51:38 on May 25, 2016 ยท (Permalink)
The extension is that the spot with no wind is the eye of a cyclone/anticyclone, implying there's always at least one of those on earth all the time.
Probable_Foreigner ยท 1 points ยท Posted at 21:05:06 on May 25, 2016 ยท (Permalink)
But what if the wind is going up?
InsaneLazyGamer ยท 1 points ยท Posted at 21:29:30 on May 25, 2016 ยท (Permalink)
Where is this place? I feel bad for the local Kite Flying Club
brownshoesdontmakeit ยท 1 points ยท Posted at 22:24:31 on May 25, 2016 ยท (Permalink)
It's not in Scotland, I can tell you that.
Nemox ยท 1 points ยท Posted at 22:52:06 on May 25, 2016 ยท (Permalink)
Obviously not realistic, but mathematically speaking couldn't wind=0 on all spots?
Gr1pp717 ยท 1 points ยท Posted at 22:56:50 on May 25, 2016 ยท (Permalink)
If we're talking a dead planet floating light years away from any heat or gravity source, I suppose.
Dharmasabitch ยท 1 points ยท Posted at 23:16:40 on May 25, 2016 ยท (Permalink)
There's an analogous theorem in chaos theory: every iterated map that maps over itself must have a fixed point. When you make a smoothie, there's always some point that didn't move at all.
LukeInDenver ยท 1 points ยท Posted at 02:30:57 on May 26, 2016 ยท (Permalink)
Crazy. Does this mean there is ONLY one spot with no wind? or that there is always at least one?
Gr1pp717 ยท 1 points ยท Posted at 11:31:08 on May 26, 2016 ยท (Permalink)
At least one. Usually many more than that.
bathrobehero ยท 1 points ยท Posted at 14:36:05 on May 25, 2016 ยท (Permalink)
This is just dumb. Wind have different speeds and can move in 3 dimensions. It's flowing more like water. And then there's the size of the "spot" you're talking about.
[deleted] ยท 2 points ยท Posted at 15:50:11 on May 25, 2016 ยท (Permalink)
That it has different speeds and flows like water is irrelevant. That wind can blow up or down is true, so, interpret the statement as 'there is at least one spot on the earth where the wind is not blowing east/west or north/south (but possibly up/down).'
It's not dumb at all! It's both true and not at all obvious!
Seldon314 ยท 1 points ยท Posted at 15:58:41 on May 25, 2016 ยท (Permalink)
You can try to apply it to wind, but in a mathematical sense it doesn't prove that at all because the earth is (as far as I know) 3-dimensional which clearly doesn't meet the requirements of "even-dimensional n-spheres". I guess such details don't stop people from upvoting false facts though.
AlekRivard ยท 1974 points ยท Posted at 12:50:56 on May 25, 2016 ยท (Permalink)*
What if the tennis ball has alopecia?
Edit: what have I done
humma__kavula ยท 1406 points ยท Posted at 14:04:29 on May 25, 2016 ยท (Permalink)
How did llama's get involved in this ?
flashnet ยท 1334 points ยท Posted at 14:26:35 on May 25, 2016 ยท (Permalink)
You're thinking of alpaca. Alopecia is another name for northern lights.
I_PET_KITTIES ยท 1205 points ยท Posted at 14:42:18 on May 25, 2016 ยท (Permalink)
You're thinking of aurora. Alpaca is a prison in San Francisco Bay.
Throtex ยท 1102 points ยท Posted at 14:50:21 on May 25, 2016 ยท (Permalink)
You're thinking of Alcatraz. Aurora is Honda's luxury car brand.
NeonTankTop ยท 1001 points ยท Posted at 14:56:54 on May 25, 2016 ยท (Permalink)
You're thinking of Acura. Aurora is the circle on a breast surrounding the nipple.
Camping_is_intense ยท 933 points ยท Posted at 14:59:39 on May 25, 2016 ยท (Permalink)
You're thinking of an Areola. Aurora is a spicy sauce for pasta made from garlic, tomatoes, and red chili peppers cooked in olive oil.
manly_lumberjack ยท 839 points ยท Posted at 15:05:33 on May 25, 2016 ยท (Permalink)
You're thinking of Arrubiatta. Areola is a fancy cheese
bcdm ยท 789 points ยท Posted at 15:13:12 on May 25, 2016 ยท (Permalink)
You're thinking of Asiago. Arrubiatta is a popular German board game that uses building tiles.
kovr ยท 205 points ยท Posted at 15:17:56 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a former name for the Middle East.
shef78 ยท 203 points ยท Posted at 15:24:42 on May 25, 2016 ยท (Permalink)
You're thinking of Assyria. Alhambra is a south-eastern state in the US
tinkerpunk ยท 183 points ยท Posted at 15:27:09 on May 25, 2016 ยท (Permalink)
Your thinking of Alabama. Alhambra is petrified tree sap often containing small insects.
eddie_koala ยท 178 points ยท Posted at 15:35:28 on May 25, 2016 ยท (Permalink)
You're thinking Amber. Alabama is a word, phrase, or name formed by rearranging the letters of another.
D_dark0 ยท 170 points ยท Posted at 15:39:59 on May 25, 2016 ยท (Permalink)
You're thinking of anagram. Amber is the capital and most populous city of theย Kingdom of the Netherlands.
intangiblesniper_ ยท 162 points ยท Posted at 15:47:57 on May 25, 2016 ยท (Permalink)
You're thinking of Amsterdam. Anagram is the French word for "stop"
[deleted] ยท 156 points ยท Posted at 15:50:03 on May 25, 2016 ยท (Permalink)
You're thinking of Arrรชtez. Amsterdam is a orange giant star located about 65 light years away.
79037662 ยท 134 points ยท Posted at 15:52:57 on May 25, 2016 ยท (Permalink)
You're thinking of Antares. Amsterdam is a mountain range in South America.
arnielsAdumbration ยท 129 points ยท Posted at 15:56:29 on May 25, 2016 ยท (Permalink)
You're thinking of the Andes. Amsterdam is a type of small banded mammal that lives in the desert.
3kindsofsalt ยท 101 points ยท Posted at 15:59:45 on May 25, 2016 ยท (Permalink)
You're thinking of Armadillo. Andes is a Dreamworks movie from 1998.
masterjmp ยท 93 points ยท Posted at 16:14:43 on May 25, 2016 ยท (Permalink)
You're thinking of Antz. An armadillo is a Swedish heavy metal band known for having three lead singers.
3kindsofsalt ยท 93 points ยท Posted at 16:24:42 on May 25, 2016 ยท (Permalink)
You're thinking of Amaranthe. Antz is an imperial unit of land area.
[deleted] ยท 91 points ยท Posted at 16:26:42 on May 25, 2016 ยท (Permalink)
You're thinking of acres. Amaranthe is the guy we named America after.
3kindsofsalt ยท 85 points ยท Posted at 16:32:25 on May 25, 2016 ยท (Permalink)
You're thinking of Amerigo. An acre is a collection of beehives.
howl_44 ยท 82 points ยท Posted at 16:36:59 on May 25, 2016 ยท (Permalink)
You're thinking of apiary. An amerigo is a line approaching another line but not touching it.
Philip_J_Frylock ยท 82 points ยท Posted at 16:38:50 on May 25, 2016 ยท (Permalink)
You're thinking of asymptote. An apiary is the killing of a prominent political leader.
milanhuh ยท 81 points ยท Posted at 16:41:20 on May 25, 2016 ยท (Permalink)
You're thinking of assassination. An asymptote is globular or cup-shaped structure in some rust fungi in which aeciospores are produced.
Philip_J_Frylock ยท 77 points ยท Posted at 16:43:50 on May 25, 2016 ยท (Permalink)
You're think of an aecium. Assassination is an Australian heavy metal band who had hits like Highway to Hell and Thunderstruck.
BoundForMexico ยท 71 points ยท Posted at 16:53:07 on May 25, 2016 ยท (Permalink)
You're thinking of AC/DC. Aecium is the fictional asylum in the Batman universe.
grimly59 ยท 68 points ยท Posted at 17:01:35 on May 25, 2016 ยท (Permalink)
You're thinking of Arkham. AC/DC is what people use to condition the air in their homes.
Yohanaten ยท 66 points ยท Posted at 17:03:44 on May 25, 2016 ยท (Permalink)
Youre thinking of AC. Arkham is the name of the scientist who discovered the theory of relativity.
ElectroBoof ยท 65 points ยท Posted at 17:06:15 on May 25, 2016 ยท (Permalink)
You're thinking of Albert. Arkham is the name of an ancient calculating tool.
Philip_J_Frylock ยท 62 points ยท Posted at 17:12:54 on May 25, 2016 ยท (Permalink)
You're thinking of an abacus. Albert was the headmaster at Hogwarts.
StrawberrySheikh ยท 59 points ยท Posted at 17:27:56 on May 25, 2016 ยท (Permalink)
You're thinking of Albus. Albert is a Pokรฉmon that evolves into Kadabra.
[deleted] ยท 55 points ยท Posted at 17:34:14 on May 25, 2016 ยท (Permalink)*
[deleted]
pubeINyourSOUP ยท 52 points ยท Posted at 17:38:45 on May 25, 2016 ยท (Permalink)
You're thinking of albatross. Abra is the ancient fortress located in Granada, Spain.
Maikerudono ยท 54 points ยท Posted at 17:44:46 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Albatross is a Slavic state in Southern Europe.
Philip_J_Frylock ยท 50 points ยท Posted at 17:50:24 on May 25, 2016 ยท (Permalink)
You're thinking of Albania. Alhambra is a character from 1001 Nights.
pubeINyourSOUP ยท 48 points ยท Posted at 17:54:17 on May 25, 2016 ยท (Permalink)
You're thinking of Ali Baba. Albania is a neurological disease that effects memory, typically in older folks.
reedkeeper ยท 64 points ยท Posted at 18:00:02 on May 25, 2016 ยท (Permalink)
You're thinking of Alzheimer. Albania is . . . wait, what were we talking about again.
canier ยท 67 points ยท Posted at 18:14:21 on May 25, 2016 ยท (Permalink)*
you're thinking of ADD. Alzheimer is a German word for 'home for the elderly'
EDIT: WOO HOO! My first Reddit Gold! Thanks /u/reedkeeper
JRHelgeson ยท 43 points ยท Posted at 18:21:20 on May 25, 2016 ยท (Permalink)*
You're thinking of Altenheim. ADD was a Turkish army officer.
EDIT: Thanks /u/reedkeeper for the Gold!
firedrake242 ยท 44 points ยท Posted at 18:28:37 on May 25, 2016 ยท (Permalink)
You're thinking of Atatรผrk. ADD is the continent south of Europe.
ByzantineStarfish ยท 38 points ยท Posted at 18:33:25 on May 25, 2016 ยท (Permalink)
You're thinking of Africa. Atatรผrk is a city in Belgium.
spikebrennan ยท 40 points ยท Posted at 18:35:31 on May 25, 2016 ยท (Permalink)
You're thinking of Antwerp. Africa is an insurance company whose spokesman is a goose.
Noswad92002 ยท 37 points ยท Posted at 18:39:06 on May 25, 2016 ยท (Permalink)
You're thinking of Aflac. Antwerp is a weird topping that people sometimes put on pizzas.
Gwthrowaway80 ยท 33 points ยท Posted at 18:43:19 on May 25, 2016 ยท (Permalink)
You're thinking of Anchovies. Antwerp is a brand of lubricant that contains a numbing agent for those that want to try butt love.
Kandorr ยท 35 points ยท Posted at 18:45:29 on May 25, 2016 ยท (Permalink)
You're thinking of Astroglide. Anchovies are the planet that was destroyed in A New Hope.
NexEstVox ยท 35 points ยท Posted at 18:48:47 on May 25, 2016 ยท (Permalink)
You're thinking of Alderaan. Astroglide is the stuff on the ground in a football stadium.
browntown92 ยท 34 points ยท Posted at 18:57:11 on May 25, 2016 ยท (Permalink)
You're thinking of AstroTurf. Alderaan is the fruit that fell on Newton's head, to discover gravity.
PhillBerry ยท 33 points ยท Posted at 18:58:07 on May 25, 2016 ยท (Permalink)
You're thinking of Apple, Alderaan is a subphylum of echinoderms comprising of starfishes.
Elvahkiin ยท 31 points ยท Posted at 19:07:06 on May 25, 2016 ยท (Permalink)
You're thinking of Asteroidea, Apple is a device used for measuring windspeed
Philip_J_Frylock ยท 29 points ยท Posted at 19:12:48 on May 25, 2016 ยท (Permalink)
You're thinking of an anemometer. Asteroidea is a character from Soul Calibur.
AlecYouALot ยท 27 points ยท Posted at 19:21:05 on May 25, 2016 ยท (Permalink)
You're thinking of Astaroth. Anemometer is a flowering plant native to temperate zones.
Nueraman1997 ยท 25 points ยท Posted at 19:49:09 on May 25, 2016 ยท (Permalink)
You're thinking of Acacia pycnantha. Anemometer is the food of the Greek Gods.
frohedadrine ยท 24 points ยท Posted at 19:59:40 on May 25, 2016 ยท (Permalink)
You're thinking of ambrosia. Acacia pycnantha is a brain disorder that affects speech.
SayingTheSameThing ยท 26 points ยท Posted at 20:04:46 on May 25, 2016 ยท (Permalink)
You're thinking of Apraxia. Ambrosia was the name of the family dog on The Jetsons.
FiveFourThreeNoseOne ยท 27 points ยท Posted at 20:26:12 on May 25, 2016 ยท (Permalink)
You're thinking of Astro. Apraxia was a person who prepared and sold medicines and drugs.
mmoffitt15 ยท 25 points ยท Posted at 20:35:48 on May 25, 2016 ยท (Permalink)
I think you are referring to an apothecary. Astro is the largest element in the halogen family on the periodic table.
I don't mean to interrupt but is this a subreddit yet?
If not, it needs to become a thing now.
GetDeadKid ยท 20 points ยท Posted at 20:46:56 on May 25, 2016 ยท (Permalink)
You're thinking of Astatine. Apothecary is a distilled, highly alcoholic beverage which is an anise-flavoured spirit derived from botanicals.
iflythewafflecopter ยท 19 points ยท Posted at 20:53:55 on May 25, 2016 ยท (Permalink)
You're thinking of Anisette. Astatine is a large cage or building that's used to keep birds in.
delongpre ยท 18 points ยท Posted at 21:00:11 on May 25, 2016 ยท (Permalink)
You're thinking of Aviary. Anisette is the name for the list of letters used in a given language.
astheriae ยท 18 points ยท Posted at 21:03:07 on May 25, 2016 ยท (Permalink)
You're thinking of Alphabet. Aviary is the mad scientist from South Park.
Philip_J_Frylock ยท 15 points ยท Posted at 21:09:17 on May 25, 2016 ยท (Permalink)
You're thinking of Alphonse. Alphabet is a small South American llama.
Pieisguud ยท 17 points ยท Posted at 21:17:00 on May 25, 2016 ยท (Permalink)
You're thinking of Alpaca. Alfonse is a thick, creamy cheese sauce usually poured over fettuccini.
Philip_J_Frylock ยท 15 points ยท Posted at 21:18:28 on May 25, 2016 ยท (Permalink)
No, you're thinking of alfredo. Alpaca is a hair loss disease.
Pieisguud ยท 14 points ยท Posted at 21:24:10 on May 25, 2016 ยท (Permalink)
You're thinking of Alopecia. Alfredo is the name of Batman's butler.
Anton2181 ยท 14 points ยท Posted at 21:28:45 on May 25, 2016 ยท (Permalink)
You're thinking of Alfred. Alfredo are a fictional team of superheroes created by Stan Lee.
Pieisguud ยท 15 points ยท Posted at 21:33:20 on May 25, 2016 ยท (Permalink)
You're thinking of the avengers. Alfred is Sansa Stark's sister.
_JPG97_ ยท 13 points ยท Posted at 21:36:35 on May 25, 2016 ยท (Permalink)
You're thinking of Anya. Alfred is a term used to describe the height of something relative to land or sea.
Pieisguud ยท 14 points ยท Posted at 21:58:24 on May 25, 2016 ยท (Permalink)
You're thinking of altitude. Arya is what we breathe.
Verily_Amazing ยท 15 points ยท Posted at 22:05:52 on May 25, 2016 ยท (Permalink)*
You're thinking of Air. Altitude is a speech disorder.
Edit: A word.
Aking1998 ยท 15 points ยท Posted at 22:11:38 on May 25, 2016 ยท (Permalink)
You're thinking of Apraxia. Air is an organ with an unknown function.
Indubitably_DLish ยท 14 points ยท Posted at 22:29:07 on May 25, 2016 ยท (Permalink)
Your thinking of Appendix. Air is a type of chest pain caused by reduced blood flow to the heart.
dnteatyellwsnw ยท 14 points ยท Posted at 22:36:22 on May 25, 2016 ยท (Permalink)
You're thinking of angina. An appendix is the Hawaiian word for hello.
graffplaysgod ยท 13 points ยท Posted at 22:47:34 on May 25, 2016 ยท (Permalink)
You're thinking of aloha. An appendix is a mixture or blend
ScurvyRobot ยท 13 points ยท Posted at 22:50:57 on May 25, 2016 ยท (Permalink)
You're thinking of an alloy. Aloha is a word opposite in meaning to another.
xerox13ster ยท 11 points ยท Posted at 22:53:56 on May 25, 2016 ยท (Permalink)
You're thinking of antonym. Aloha is how you say goodbye in Italy.
jaketheyak ยท 12 points ยท Posted at 23:17:43 on May 25, 2016 ยท (Permalink)
You're thinking of arrivederci. Antonym is a region of France bordering Germany and Switzerland.
xerox13ster ยท 14 points ยท Posted at 00:00:15 on May 26, 2016 ยท (Permalink)
You're thinking of Alsace. Arrivederci is region of the Eastern United States that stretches from New York to Alabama.
jaketheyak ยท 14 points ยท Posted at 00:04:23 on May 26, 2016 ยท (Permalink)
You're thinking of Appalachia. Alsace is the German word for "nightmare".
rhynoplaz ยท 15 points ยท Posted at 00:28:02 on May 26, 2016 ยท (Permalink)
You're thinking of Alptraum, Appalachia is the Greek God of War.
SurprisedPotato ยท 13 points ยท Posted at 01:21:36 on May 26, 2016 ยท (Permalink)
You're thinking of Ares. Alptraum is a country on the border of France and Spain.
GenreBless ยท 14 points ยท Posted at 01:30:32 on May 26, 2016 ยท (Permalink)
You're thinking of Algeria. Ares is the name for air sacs found in mammalian lungs.
gordura ยท 12 points ยท Posted at 01:42:58 on May 26, 2016 ยท (Permalink)
You're thinking of alveoli. Algeria is the spanish word for mild happiness.
jaketheyak ยท 12 points ยท Posted at 01:51:05 on May 26, 2016 ยท (Permalink)
You're thinking of alegrรญa. Alveoli is a critically acclaimed Spanish film director.
2dayoldbread ยท 11 points ยท Posted at 02:03:24 on May 26, 2016 ยท (Permalink)
You're thinking of Alvin. Alveoli is a term to describe payment to an ex-spouse after divorce.
rhynoplaz ยท 12 points ยท Posted at 02:30:43 on May 26, 2016 ยท (Permalink)
You're thinking of alimony, alveoli is a brand name for an arthritis pain reliever.
Breedwell ยท 12 points ยท Posted at 02:34:08 on May 26, 2016 ยท (Permalink)
You're thinking of Aleve. Alimony is the name of the Indian comedian known for starring in the show Parks and Recreation.
fantabularistical ยท 10 points ยท Posted at 02:39:23 on May 26, 2016 ยท (Permalink)
You're thinking of Aziz Ansari. Aleve is a Star Wars character known for his line "It's a trap!"
legrac ยท 9 points ยท Posted at 02:54:08 on May 26, 2016 ยท (Permalink)
You're thinking of Admiral Ackbar. Aleve is medicine made from a plant to help deal with sunburns.
jaketheyak ยท 8 points ยท Posted at 03:02:03 on May 26, 2016 ยท (Permalink)
You're thinking of aloe vera gel. Ackbar is an adjective to describe a situation that's embarassing or troublesome.
Segfault_Inside ยท 11 points ยท Posted at 03:09:06 on May 26, 2016 ยท (Permalink)
You're thinking of awkward. Aloe vera gel is a tool which measures electrical current.
RoadieRich ยท 11 points ยท Posted at 03:48:50 on May 26, 2016 ยท (Permalink)
You're thinking of ammeter. Aloe vera gel is a licensed radio communication system.
canier ยท 9 points ยท Posted at 04:21:39 on May 26, 2016 ยท (Permalink)
You're thinking Amateur Radio. Ammeter is an animal with a long snout that eats ants.
halofreakrun ยท 10 points ยท Posted at 04:32:21 on May 26, 2016 ยท (Permalink)
You're thinking of an anteater. Amateur Radio is a radical that smells awful.
rhynoplaz ยท 8 points ยท Posted at 08:22:04 on May 26, 2016 ยท (Permalink)
You're thinking of an anarchist. An anteater is a series of words that all start with the same letter.
jaketheyak ยท 9 points ยท Posted at 10:20:15 on May 26, 2016 ยท (Permalink)
You're thinking of alliteration. An anarchist is the great deceiver foretold of in the book of Revelations.
rhynoplaz ยท 8 points ยท Posted at 10:51:02 on May 26, 2016 ยท (Permalink)
You're thinking of the antichrist. Alliteration is the surgical removal of a limb.
kubuzetto ยท 9 points ยท Posted at 10:53:59 on May 26, 2016 ยท (Permalink)
You're thinking of amputation. Antichrist is a state or condition markedly different from the norm.
Edible_Pie ยท 7 points ยท Posted at 11:24:39 on May 26, 2016 ยท (Permalink)
You're thinking of
deviationabnormality. Amputation is a strong dislike or disinclination.rhynoplaz ยท 9 points ยท Posted at 12:55:18 on May 26, 2016 ยท (Permalink)
You're thinking of abhorrence. Abnormality is the termination of a system or practice.
ScurvyRobot ยท 9 points ยท Posted at 13:58:59 on May 26, 2016 ยท (Permalink)
You're thinking of abortion. Abhorrence is a comparison between two things.
AshtarB ยท 9 points ยท Posted at 16:33:33 on May 26, 2016 ยท (Permalink)
You're thinking of analogy. Abortion is when a substance takes up another through the gaps between its molecules.
Solaer ยท 6 points ยท Posted at 17:08:05 on May 26, 2016 ยท (Permalink)
You're thinking of absorption. Analogy is a literary device marked by the repetition of vowel sounds in close succession.
JRHelgeson ยท 7 points ยท Posted at 18:33:05 on May 26, 2016 ยท (Permalink)
You're thinking of Assonance. Absorption is the practice of not doing or having something that is wanted or enjoyable.
Nueraman1997 ยท 7 points ยท Posted at 21:11:21 on May 26, 2016 ยท (Permalink)
You're thinking of austerity. Absorption is a person or thing accursed or consigned to damnation or destruction.
kidinacandirustore ยท 7 points ยท Posted at 23:50:39 on May 26, 2016 ยท (Permalink)
You're thinking of anathema. Absorption is a young adult fantasy novel by Garth Nix.
jaketheyak ยท 6 points ยท Posted at 04:22:03 on May 27, 2016 ยท (Permalink)
You're thinking of Abhorsen. Anathema is the 10th highest mountain in the world.
kittydancer ยท 6 points ยท Posted at 05:17:42 on May 27, 2016 ยท (Permalink)
You're thinking of Annapurna. Abhorsen is a large snake found in tropical South America.
legrac ยท 6 points ยท Posted at 06:12:42 on May 27, 2016 ยท (Permalink)
You're thinking of an anaconda. Abhorsen is a generic term for a small, usually stoneless, juicy fruit.
jaketheyak ยท 4 points ยท Posted at 08:30:09 on May 27, 2016 ยท (Permalink)
You're thinking of acerola. Abhorsen is an ecclesiastical title given to the head of a monastery.
VibraphoneFuckup ยท 3 points ยท Posted at 16:15:39 on May 29, 2016 ยท (Permalink)
You're thinking of an abbott. Abhorsen is a way of measuring the diffuse reflectivity of a surface.
[deleted] ยท 3 points ยท Posted at 14:46:23 on September 12, 2016 ยท (Permalink)
How does it feel to be the last in the meme chain?
EstusFiend ยท 2 points ยท Posted at 08:16:22 on May 27, 2016 ยท (Permalink)
You're thinking of a . . . . . well, a berry. Great, you broke it. Okay folks, pack it up. We're done here.
Indubitably_DLish ยท 1 points ยท Posted at 04:19:13 on May 26, 2016 ยท (Permalink)
Your thinking of Admiral Ackbar. Aziz Ansari is a Macrolide Antibiotic.
drumaffe ยท 2 points ยท Posted at 23:18:51 on May 25, 2016 ยท (Permalink)
Please let it end!!!
drummer11x ยท 5 points ยท Posted at 23:03:14 on May 25, 2016 ยท (Permalink)
I think this is a good stopping point.
RampanToast ยท 5 points ยท Posted at 23:14:54 on May 25, 2016 ยท (Permalink)
That was a trip.
wanderingalice ยท 1 points ยท Posted at 22:38:03 on May 25, 2016 ยท (Permalink)
You are thinking of Angina. Appendix is painful infammation of joints.
Pieisguud ยท 2 points ยท Posted at 22:08:50 on May 25, 2016 ยท (Permalink)
You're thinking of Apraxia. Air is who inherits your stuff.
Pieisguud ยท 0 points ยท Posted at 21:24:32 on May 25, 2016 ยท (Permalink)
You're thinking of Alopecia. Alfredo is the name of Batman's butler.
misterspokes ยท 0 points ยท Posted at 21:17:19 on May 25, 2016 ยท (Permalink)
You're thinking of Alpaca, Alphonse is a german card buying worker placement farming game.
GetDeadKid ยท 1 points ยท Posted at 22:37:11 on May 25, 2016 ยท (Permalink)
Bro. Absinthe.
GiovanniMoffs ยท 5 points ยท Posted at 20:52:17 on May 25, 2016 ยท (Permalink)
You're thinking of Absynthe. Astatine is the french word for Pinapples.
Philip_J_Frylock ยท 2 points ยท Posted at 20:52:42 on May 25, 2016 ยท (Permalink)
You're thinking of absinthe. Astatine is a mild form of autism.
GMY0da ยท 0 points ยท Posted at 20:51:12 on May 25, 2016 ยท (Permalink)
You're thinking of apothecary. Astro is a part of the brain that controls fear.
Firelordbob ยท 3 points ยท Posted at 20:05:29 on May 25, 2016 ยท (Permalink)
You're thinking of Aphasia. Ambrosia is a waxlike substance that originates as a secretion in the intestines of the sperm whale.
VibraphoneFuckup ยท 1 points ยท Posted at 20:14:09 on May 25, 2016 ยท (Permalink)
You're thinking of ambergris. Aphasia is a thing that gets set to stun in startrek.
desopez ยท -2 points ยท Posted at 20:11:38 on May 25, 2016 ยท (Permalink)
Your thinking of ambergris. Aphasia is a combination of a speech and language disorder caused by damage to the brain that affects about one million individuals within the US.
[deleted] ยท 2 points ยท Posted at 19:09:29 on May 25, 2016 ยท (Permalink)
You're thinking of Asteroidea. Apple is a mass of snow, ice, and rocks falling rapidly down a mountainside.
big_cheddars ยท 0 points ยท Posted at 19:34:31 on May 25, 2016 ยท (Permalink)
You're thinking of avalanche. Achilles is the fictional evil organisation from the Assassin's Creed series.
16tonweight ยท -1 points ยท Posted at 19:51:17 on May 25, 2016 ยท (Permalink)
You're thinking of Abstergo, an Avalanche is the German term Georg Hegel used to describe the dialectic process of sublimation.
semester5 ยท 2 points ยท Posted at 18:55:16 on May 25, 2016 ยท (Permalink)
You're thinking of AstroTurf. Astroglide is a person who has been to space.
[deleted] ยท 1 points ยท Posted at 18:58:58 on May 25, 2016 ยท (Permalink)
[deleted]
DrFoxbard ยท 1 points ยท Posted at 19:00:22 on May 25, 2016 ยท (Permalink)
You're thinking of Atlantis. Astronaut is the study of movements and relative positions of celestial bodies having an influence on human affairs and the natural world.
crathera ยท 2 points ยท Posted at 18:50:16 on May 25, 2016 ยท (Permalink)
You're thinking of Alderaan. Anchovies is an heavy metal object used by ships to stay still while out in the ocean.
Philip_J_Frylock ยท 1 points ยท Posted at 18:39:59 on May 25, 2016 ยท (Permalink)
You're thinking of Aflac. Antwerp is a St. Louis-based brewing company that owns Budweiser.
JBL15TX ยท -2 points ยท Posted at 18:40:42 on May 25, 2016 ยท (Permalink)
You're thinking of Aflac. Antwerp is a classification of cold-blooded vertebrate animals that sometimes reside in water.
masterjmp ยท -2 points ยท Posted at 18:41:00 on May 25, 2016 ยท (Permalink)
You're thinking of Aflac. Antwerp is a mathematical study of symbols and the rules for manipulating those symbols.
Zapfaced ยท -1 points ยท Posted at 18:35:23 on May 25, 2016 ยท (Permalink)
You're thinking of Antwerp. Africa is the surname of a Pakistani cricketer.
firedrake242 ยท -1 points ยท Posted at 18:56:59 on May 25, 2016 ยท (Permalink)
You're thinking of Antwerp. Atatรผrk is a positively charged particle composed of quarks.
VibraphoneFuckup ยท 2 points ยท Posted at 20:10:33 on May 25, 2016 ยท (Permalink)
Nice recovery
canier ยท 1 points ยท Posted at 21:20:11 on May 25, 2016 ยท (Permalink)
I try!
catapulp ยท -1 points ยท Posted at 18:02:15 on May 25, 2016 ยท (Permalink)
You're thinking of Alzheimer. Albania is a type of medicinal plant.
[deleted] ยท -1 points ยท Posted at 18:04:28 on May 25, 2016 ยท (Permalink)
You're thinking of Alzheimers. Ali Baba is a line of collectible toys created by notable Japanese company Nintendo.
[deleted] ยท -2 points ยท Posted at 17:54:35 on May 25, 2016 ยท (Permalink)
You're thinking of Aladdin. Alhambra is an emotion used to describe disinterest in something.
StringJohnson ยท -2 points ยท Posted at 17:54:31 on May 25, 2016 ยท (Permalink)
You're thinking of Ali Baba. Alhambra is the scientific name for a particular point in your nether region.
JRHelgeson ยท 0 points ยท Posted at 17:51:08 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Albatross is a defective development or congenital absence of an organ or tissue.
kudeikis ยท -2 points ยท Posted at 17:28:04 on May 25, 2016 ยท (Permalink)
You're thinking of Albus. Alveolus was a Greek hero in the Trojan War.
dickskittles ยท 2 points ยท Posted at 17:12:03 on May 25, 2016 ยท (Permalink)
You're thinking of the abacus. Arkham is the guy that said the simplest explanation is usually the correct one.
Dask1124 ยท -1 points ยท Posted at 17:33:22 on May 25, 2016 ยท (Permalink)
You're thinking of William of Ockham. Arkham is the Latin word for spider.
gustywinds ยท -2 points ยท Posted at 17:01:27 on May 25, 2016 ยท (Permalink)
You're thinking of Arkham. AC/DC is the name of the voice actor whose name also contains the word "Arkham" in it.
AskMeToDoodle ยท 4 points ยท Posted at 16:55:13 on May 25, 2016 ยท (Permalink)
You're thinking of ACDC. Aecium is Earth's southernmost continent, containing the geographic South Pole.
MidnightDBA ยท 9 points ยท Posted at 16:02:23 on May 25, 2016 ยท (Permalink)
You're thinking of Antz, the fifteenth brightest star in the night sky.
montse246 ยท 8 points ยท Posted at 16:14:40 on May 25, 2016 ยท (Permalink)
You're thinking of Aldebaran, arrรชtez is the scientific class that contains spiders, scorpions, and ticks.
beleg_tal ยท 4 points ยท Posted at 16:19:07 on May 25, 2016 ยท (Permalink)
You're thinking of Arthropoda, Aldebaran is Princess Leia's home planet.
ivanvzm ยท 4 points ยท Posted at 16:20:55 on May 25, 2016 ยท (Permalink)
You're thinking of Alderaan. Aldebaran is a popular Disney film from 1992.
baaliam ยท 4 points ยท Posted at 16:23:35 on May 25, 2016 ยท (Permalink)
You're thinking of Aladdin. Alderaan is ascribing human form or attributes to a being or thing not human.
IceColt21 ยท 0 points ยท Posted at 16:27:24 on May 25, 2016 ยท (Permalink)
You're thinking of Anthropomorphic. Aladdin is the lintel or beam that rests on the capitals of the columns.
ivanvzm ยท -1 points ยท Posted at 17:18:31 on May 25, 2016 ยท (Permalink)
You're thinking of Architrave. Anthropomorphic is the name given to the opposition that faces against a protagonist in a story.
D_dark0 ยท -1 points ยท Posted at 16:23:10 on May 25, 2016 ยท (Permalink)
You're thinking Alderaan. Arthropoda is a specific phobia of spiders and other arachnids such as scorpions.
chickenthinkseggwas ยท -3 points ยท Posted at 16:23:22 on May 25, 2016 ยท (Permalink)*
You're thinking of arachnids. Aldebaran is the last word of this sentence.
Edit: -1 downvoted, eh? We're 20 posts deep in this exhausted joke, but there are still people who think it's mandatory to stick to the formula.
[deleted] ยท 1 points ยท Posted at 17:56:41 on May 25, 2016 ยท (Permalink)
You're thinking armadillo. Antares is an old school video game console.
falconpunch5 ยท 4 points ยท Posted at 16:48:26 on May 25, 2016 ยท (Permalink)*
You're thinking of Aldebaran. Antares is 550 ly away. ;)
Edit: Quick, someone calculate the apparent magnitude of Antares if it was at Aldebaran's distance! Antares' absolute magnitude is โ5.28.
[deleted] ยท -3 points ยท Posted at 15:54:49 on May 25, 2016 ยท (Permalink)
[deleted]
kinless33 ยท 0 points ยท Posted at 15:57:21 on May 25, 2016 ยท (Permalink)
You're thinking of Aristotle. Appalachian is a type of horse with a spotted coat.
[deleted] ยท -1 points ยท Posted at 16:00:00 on May 25, 2016 ยท (Permalink)
You're thinking of Appaloosa, Aristotle is one of the star signs.
montse246 ยท -2 points ยท Posted at 16:05:45 on May 25, 2016 ยท (Permalink)
You're thinking of Aries, Andes is the first letter of the alphabet.
[deleted] ยท 1 points ยท Posted at 04:13:09 on May 26, 2016 ยท (Permalink)
You're thinking of A, you fucking imbecile.
whydoesntmyusernamef ยท -1 points ยท Posted at 15:58:20 on May 25, 2016 ยท (Permalink)
You're thinking of Archimedes. Appalachian are the large dogs commonly used as police dogs.
Ayit_Sevi ยท -2 points ยท Posted at 16:02:09 on May 25, 2016 ยท (Permalink)
You'ring think of the Andes Mountain Range. Antares is a landlocked country to the west of Iran and to the North of Pakistan.
dickskittles ยท 0 points ยท Posted at 15:56:00 on May 25, 2016 ยท (Permalink)
You're thinking of Aldebaran. Amsterdam was a hilarious website from the 90's featuring rotating rodents and a sped-up Roger Miller vocal on loop.
tinkerpunk ยท 3 points ยท Posted at 17:15:58 on May 25, 2016 ยท (Permalink)
I don't know what you're thinking of, but Aldebaran was blown up by Grand Moff Tarkin.
Drachefly ยท 0 points ยท Posted at 17:25:35 on May 25, 2016 ยท (Permalink)
You're thinking of Alderaan. Occultation is the magic of preventing your mind from being read in Harry Potter.
_Neoshade_ ยท 1 points ยท Posted at 22:09:03 on May 25, 2016 ยท (Permalink)
You're thinking of arrรชt. Amsterdam is the easternmost French province with Germanic origins and annexed early in the second Great War.
Emperor_Triceratops ยท -2 points ยท Posted at 15:53:55 on May 25, 2016 ยท (Permalink)
You're thinking of Amsterdam. Anagram is any organism does not require oxygen to live.
THSSFC ยท 4 points ยท Posted at 15:33:08 on May 25, 2016 ยท (Permalink)
You're thinking of Amber. Alabama is a god-forsaken shithole. No, wait, that's Mississippi.
dickskittles ยท 4 points ยท Posted at 15:37:17 on May 25, 2016 ยท (Permalink)
You're thinking of Detroit. Alabama is a type of stone, used to make chess pieces in The Shawshank Redemption.
dbm5 ยท 6 points ยท Posted at 15:44:27 on May 25, 2016 ยท (Permalink)
You're thinking of Alabaster. Alabama is a god-forsaken shithole.
TenthSpeedWriter ยท 0 points ยท Posted at 16:06:31 on May 25, 2016 ยท (Permalink)
Mississippi is the means by which Alabama reassures itself that "at least things ain't total shit 'round here"
Kwazimoto169 ยท 1 points ยท Posted at 15:35:41 on May 25, 2016 ยท (Permalink)
You're thinking of Amber. Alhambra is music played at a lively or brisk tempo.
[deleted] ยท -5 points ยท Posted at 15:34:18 on May 25, 2016 ยท (Permalink)
[deleted]
jdovew ยท 3 points ยท Posted at 16:05:47 on May 25, 2016 ยท (Permalink)
You tried.
barbarr ยท 0 points ยท Posted at 15:27:33 on May 25, 2016 ยท (Permalink)
You're thinking of Alabama. Assyria is the colloquial word for a donkey.
6chan ยท -1 points ยท Posted at 15:25:20 on May 25, 2016 ยท (Permalink)
You're thinking of Alaska. Alhambra is a French-persian ham carrying harness.
aggleflaggle ยท 3 points ยท Posted at 21:41:53 on May 25, 2016 ยท (Permalink)
You're thinking of settlers of catan. For some reason.
extraordinary15 ยท 2 points ยท Posted at 21:44:21 on May 25, 2016 ยท (Permalink)
I don't know what you're talking about, Asiago is a condition that makes you lose all your hair
MrTThompson ยท 2 points ยท Posted at 02:21:53 on May 26, 2016 ยท (Permalink)
Who the eff is Hank?
shrubs311 ยท 1 points ยท Posted at 23:19:03 on May 25, 2016 ยท (Permalink)
Carcassonne doesn't even start with an A though.
916ian ยท 1 points ยท Posted at 23:31:32 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is the dried latex exuded from the tap root of the ferula herb
MauPow ยท 1 points ยท Posted at 23:37:05 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Arrubiatta is a small island country off the coast of Venezuela.
onacloverifalive ยท 1 points ยท Posted at 01:01:47 on May 26, 2016 ยท (Permalink)*
You're thinking Alhambra, Arubiatta is a rhythmic sequence of notes.
[deleted] ยท 1 points ยท Posted at 04:02:07 on May 26, 2016 ยท (Permalink)
Not sure what you're thinking of...
Tm1337 ยท 1 points ยท Posted at 12:11:15 on May 26, 2016 ยท (Permalink)
It bothers me that there are no rules in this comment chain
Bristal ยท 1 points ยท Posted at 18:24:26 on May 25, 2016 ยท (Permalink)
And it took me 10 minutes of trying to frame the next step to figure out bcdm fucked it up. Thanks, Obama.
thatwasnotkawaii ยท 1 points ยท Posted at 20:36:21 on May 25, 2016 ยท (Permalink)
You're thinking of Apricots. Asiago is a type of cement
A-IAH-HDE-CDF0 ยท 0 points ยท Posted at 17:48:06 on May 25, 2016 ยท (Permalink)
Man you guys are terrible at this game.
Rift-Raft ยท -1 points ยท Posted at 16:06:21 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a tribe of Native Americans that used to live in the Colorado and Wyoming regions.
bangjurmom ยท 0 points ยท Posted at 19:25:29 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Stupid
Sheepocalypse ยท 0 points ยท Posted at 20:21:28 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a condiment made from eggs that goes well on burgers and fries and the like.
kaiju-taxi ยท -1 points ยท Posted at 18:52:19 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is an Italian phrase meaning "goodbye".
iplaypokerforaliving ยท -1 points ยท Posted at 19:56:21 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a Mediterranean sauce made of garlic, olive oil, and in some regions egg.
C0812 ยท -2 points ยท Posted at 15:56:30 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. David Arubiatta was that guy on American Idol.
Ragnorok3141 ยท -2 points ยท Posted at 16:20:19 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is the sea seperating Italy from the Balkan peninsula.
rpm4real ยท -2 points ยท Posted at 16:20:51 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Arrubiatta is the food or drink of the gods in Greek mythology.
clapham1983 ยท -2 points ยท Posted at 17:01:40 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a mission in San Antonio Texas that was used as a fort during the Texas Revolution. "Remember the Asiago".
halfwayhanks ยท -2 points ยท Posted at 17:05:41 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is the name of the dog from the popular cartoon "The Jetsons".
Letsallgotothebar ยท -2 points ยท Posted at 17:06:59 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a group of small to large edible sea snails.
ben_on_reddit ยท -2 points ยท Posted at 17:25:13 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Arulca is the fictional banana republic that the computer game Jagged Alliance 2 takes place in.
ARealSlimBrady ยท -2 points ยท Posted at 17:41:47 on May 25, 2016 ยท (Permalink)
You're thinking of Alhambra. Asiago is a highly trained wizard specializing in investigating the Dark Arts and apprehending bad witches and wizards.
Apmaddock ยท -2 points ยท Posted at 17:51:10 on May 25, 2016 ยท (Permalink)
You're thinking of Agricola. Arrubiatta is a word that sounds like the thing it describes.
DirkFroyd ยท 5 points ยท Posted at 17:59:00 on May 25, 2016 ยท (Permalink)
You fucked it up.
ProtoHawk ยท 1 points ยท Posted at 22:30:28 on May 25, 2016 ยท (Permalink)
I think it was the guy before them that fucked up
DirkFroyd ยท 1 points ยท Posted at 01:23:18 on May 26, 2016 ยท (Permalink)
Oh yeah, it was fucked up a few comments up.
jetpacksforall ยท 6 points ยท Posted at 16:43:35 on May 25, 2016 ยท (Permalink)
Arrabbiata godfuckingdammit. (It means "angry" in Italian.)
JohnGillnitz ยท 0 points ยท Posted at 15:34:38 on May 25, 2016 ยท (Permalink)
I thought "tomatoes" were a name for unusually perky nipples.
anomalous_cowherd ยท 2 points ยท Posted at 18:25:24 on May 25, 2016 ยท (Permalink)
I was about to Google for ridiculously swollen nipples to illustrate your point.
Then I thought twice. Nobody needs to see that.
[deleted] ยท 0 points ยท Posted at 14:58:35 on May 25, 2016 ยท (Permalink)
You're thinking of Ariola. Acura is the plural form for correct.
Gullex ยท 3 points ยท Posted at 15:00:22 on May 25, 2016 ยท (Permalink)
You're thinking of accurate. Ariola is the external part of the ear.
[deleted] ยท 3 points ยท Posted at 15:10:16 on May 25, 2016 ยท (Permalink)
You're thinking of Ravioli, the Italian word for a small rave.
3asin3speech ยท 1 points ยท Posted at 15:09:48 on May 25, 2016 ยท (Permalink)
You're thinking of auricle. Accurate is an angle smaller than 90 degrees.
mechabeast ยท 0 points ยท Posted at 15:00:49 on May 25, 2016 ยท (Permalink)*
You're thinking of areola. Aorta is a farming game focusing on worker placement.
Nick6281 ยท -2 points ยท Posted at 15:14:28 on May 25, 2016 ยท (Permalink)
You're thinking of areola. Acura is a medical condition where the patient has trouble remembering things.
tinkerpunk ยท 0 points ยท Posted at 15:28:12 on May 25, 2016 ยท (Permalink)
You're thinking of... Wait I forgot what we were doing.
icanhe ยท 1 points ยท Posted at 17:29:52 on May 26, 2016 ยท (Permalink)
You're thinking of Oldsmobile. Auroras were made by Oldsmobile.
Source: owned one
Throtex ยท 2 points ยท Posted at 17:55:18 on May 26, 2016 ยท (Permalink)
lol I was waiting for this response after I realized the actual car connection
icanhe ยท 1 points ยท Posted at 17:58:50 on May 26, 2016 ยท (Permalink)
I don't know if you've ever seen/been in an Oldsmobile Aurora, but they were a joke of a luxury car. I was the 3rd owner of mine, a broke college student, and that thing handled like a spaceship.
Hysterical looking car, sometimes I miss its ridiculousness.
[deleted] ยท -1 points ยท Posted at 14:59:14 on May 25, 2016 ยท (Permalink)
You're thinking of Accord. Aurora is the main artery of the body.
ninjashroom ยท -2 points ยท Posted at 14:56:42 on May 25, 2016 ยท (Permalink)*
You're thinking of an
AccordAcura. Alcatraz is a type of math where you find x.*Edit: Oops, guess I don't know my Hondas from each other... oh well.
Hahlia ยท 1 points ยท Posted at 15:05:20 on May 25, 2016 ยท (Permalink)
You're thinking of Algebra. Accord is a box shaped musical instrument.
3asin3speech ยท 1 points ยท Posted at 15:10:58 on May 25, 2016 ยท (Permalink)
You're thinking of accordian. Accords fall from oak trees.
oaknutjohn ยท -1 points ยท Posted at 15:53:54 on May 25, 2016 ยท (Permalink)
You're thinking of Acura. Alcatraz is an award winning actor best known for his leading role in Scarface.
Say-It-Aloud ยท 1 points ยท Posted at 22:23:16 on May 25, 2016 ยท (Permalink)
Congrats on the karma everyone, you all tried real hard
[deleted] ยท 1 points ยท Posted at 01:21:59 on May 26, 2016 ยท (Permalink)
You're thinking about Skinners kitchen. Steamed hams is another name for Krutsy burgers
ktkps ยท 1 points ยท Posted at 04:58:31 on May 26, 2016 ยท (Permalink)
pinging /u/psycho_alpaca
mitchmatch1 ยท 1 points ยท Posted at 16:48:43 on May 25, 2016 ยท (Permalink)
/r/yourethinkingof
It had to be done
AlekRivard ยท 0 points ยท Posted at 16:54:30 on May 25, 2016 ยท (Permalink)
<3
DeprestedDevelopment ยท -1 points ยท Posted at 15:05:46 on May 25, 2016 ยท (Permalink)
You're thinking of aurora. Alopecia is a plant we put on burn wounds.
3asin3speech ยท -1 points ยท Posted at 15:12:16 on May 25, 2016 ยท (Permalink)
You're thinking of aloe vera. Alopecia is a branch of medicine.
pv46 ยท -1 points ยท Posted at 15:09:12 on May 25, 2016 ยท (Permalink)
You're thinking of Aurora. Alopecia is a series of symbols that make up a written language.
GilesDMT ยท 0 points ยท Posted at 18:20:07 on May 25, 2016 ยท (Permalink)
Look what you've started.
jacksonstew ยท -1 points ยท Posted at 18:00:05 on May 25, 2016 ยท (Permalink)
"Northern Lights, Cannabis Sativa"
"No. It's marijuana :("
Eric_the_Barbarian ยท 4 points ยท Posted at 15:22:26 on May 25, 2016 ยท (Permalink)
Then the hairy ball theorem obviously does not apply and the hairless ball theorem comes into play which states that on any surface devoid of vectors, a cowlick becomes impossible and that Nair can cause irritation in sensitive areas.
AlekRivard ยท 2 points ยท Posted at 15:35:32 on May 25, 2016 ยท (Permalink)
So you're saying I should use Nair on my asshole?
Velvet_Hustler ยท 1 points ยท Posted at 02:09:24 on May 26, 2016 ยท (Permalink)
Make to post the video.
valeyard89 ยท 3 points ยท Posted at 14:32:48 on May 25, 2016 ยท (Permalink)
Then it's a squash ball
AlekRivard ยท 2 points ยท Posted at 14:46:34 on May 25, 2016 ยท (Permalink)
Who squashed it though?
DerringerHK ยท 4 points ยท Posted at 15:18:41 on May 25, 2016 ยท (Permalink)
What has Al Pacino got to do with this?
CoolLordL21 ยท 5 points ยท Posted at 15:37:33 on May 25, 2016 ยท (Permalink)
Then it's a tennis "bald."
FirstWaveMasculinist ยท 1 points ยท Posted at 18:54:07 on May 25, 2016 ยท (Permalink)
ba dumph tss
omniscientonus ยท 4 points ยท Posted at 16:19:06 on May 25, 2016 ยท (Permalink)
You have started something beautiful my friend. The larger the group of people who manage to continue this correctly, the more I love it. This is why I reddit!
AlekRivard ยท 1 points ยท Posted at 16:36:10 on May 25, 2016 ยท (Permalink)
I reddit so I have some form of socialization in my daily life
scarymonkey11622 ยท 3 points ยท Posted at 16:54:36 on May 25, 2016 ยท (Permalink)
nods silently
checkmate3001 ยท 3 points ยท Posted at 16:51:22 on May 25, 2016 ยท (Permalink)
I have no idea what you have done, but it is glorious! I wish I had gold to give you.
JustALuckyShot ยท 8 points ยท Posted at 15:35:29 on May 25, 2016 ยท (Permalink)
That comment chain you created is amazing, congrats on that!
xerox13ster ยท 1 points ยท Posted at 22:57:23 on May 25, 2016 ยท (Permalink)
It's still going.
EddieTheJedi ยท 2 points ยท Posted at 14:46:43 on May 25, 2016 ยท (Permalink)
I think the adjective "nonvanishing" excludes that case.
HectorTheOwl ยท 2 points ยท Posted at 18:24:22 on May 25, 2016 ยท (Permalink)
Something beautiful. That's what.
Illsonmedia ยท 2 points ยท Posted at 18:27:06 on May 25, 2016 ยท (Permalink)
LOL
NNJAxKira ยท 2 points ยท Posted at 18:58:55 on May 25, 2016 ยท (Permalink)
You've killed us all
EchoesinthekeyofbluE ยท 2 points ยท Posted at 20:15:32 on May 25, 2016 ยท (Permalink)
You did a bad thing.
carBoard ยท 2 points ยท Posted at 07:45:22 on May 26, 2016 ยท (Permalink)
woah what the hell did you cuase to happen! it goes on forever!
popedarren ยท 1 points ยท Posted at 15:44:01 on May 25, 2016 ยท (Permalink)
Or trichotillomania. That was the first thing I thought of when I googled alopecia and saw those pictures.
ExtinctForYourSins ยท 1 points ยท Posted at 16:46:38 on May 25, 2016 ยท (Permalink)
Cheeri-e, cheeri-oh!
Headozed ยท 1 points ยท Posted at 18:06:02 on May 25, 2016 ยท (Permalink)
I think that's called a racquetball :)
GilesDMT ยท 1 points ยท Posted at 18:19:32 on May 25, 2016 ยท (Permalink)
This is all your fault.
AlekRivard ยท 1 points ยท Posted at 18:21:24 on May 25, 2016 ยท (Permalink)
Pls no I cri
horsepie ยท 1 points ยท Posted at 18:19:32 on May 25, 2016 ยท (Permalink)
For a brief moment, you brought back memories of 2009 reddit.
2010 reddit ran this exact style of comment chains into the ground, though.
geneparm333 ยท 1 points ยท Posted at 18:39:20 on May 25, 2016 ยท (Permalink)
stick it to her
ParisGreenGretsch ยท 1 points ยท Posted at 20:01:15 on May 25, 2016 ยท (Permalink)
Is that like albino?
BAMFMF ยท 1 points ยท Posted at 22:48:16 on May 25, 2016 ยท (Permalink)
upvote for the edit.
[deleted] ยท 286 points ยท Posted at 13:17:53 on May 25, 2016 ยท (Permalink)
It's one of those ones that if you think about it, it intuitively seems almost certainly to be true. But I wouldn't even know where to start on the maths of proving this
Crandom ยท 168 points ยท Posted at 15:08:34 on May 25, 2016 ยท (Permalink)
I would recommend "Proof by Handwaving"
Aman_Fasil ยท 11 points ยท Posted at 18:30:16 on May 25, 2016 ยท (Permalink)
Proof by reference to inaccessible literature was always my favorite.
Crandom ยท 6 points ยท Posted at 19:01:13 on May 25, 2016 ยท (Permalink)
Proof by Intimidation was the favourite of my scariest lecturer.
Let_It_Sano ยท 2 points ยท Posted at 18:25:00 on May 25, 2016 ยท (Permalink)
Ah yes, half of my proof techniques in my Analysis homework. Mention a few definitions, a proof result from class, somehow connect the dots, and we're done!
[deleted] ยท 2 points ยท Posted at 19:05:36 on May 25, 2016 ยท (Permalink)
I recall my differential equations professor was very fond of that technique
Spogito ยท 1 points ยท Posted at 15:30:52 on May 25, 2016 ยท (Permalink)
As a lab monkey would use emiprical evidence from 30 different tennis balls and 30 different combs AND novelty sized versions too.
pnasmaster ยท 1 points ยท Posted at 15:39:50 on May 25, 2016 ยท (Permalink)
Is that book by Bell and Howell?
northrupthebandgeek ยท 1 points ยท Posted at 22:29:02 on May 25, 2016 ยท (Permalink)
Then it'd be a postulate, not a theorem.
Source: my few memories of middle school geometry class.
c3534l ยท 39 points ยท Posted at 16:26:04 on May 25, 2016 ยท (Permalink)
From math exchange:
So I imagine you'd have to first start by looking up what homotopy means.
QuigleyQ ยท 7 points ยท Posted at 18:16:50 on May 25, 2016 ยท (Permalink)
Basically, a homotopy is a smooth deformation of one function to another. It's somewhat similar to the "squish a donut into a coffee mug" concept.
Here's an ELI5 of the proof:
We'll do a proof by contradiction. Assume such a vector field exists. We'll use this field to deform the identity map into the "antipodal map" (which is just f(x) = -x). There's many ways to show this, but it turns out that no such deformation can exist. So if we can build one using this vector field, that vector field can't exist.
Given a point x, there's a non-zero vector v_x attached to it. Imagine you're an ant at point x, and you walk in the direction of v_x. You'll trace out an arc on the sphere, eventually making it back to where you started. Let F(x,t) be the location of an ant starting at x and walking for time t.
Note: we can pick whatever speed we want for our ants. Let's pick ants that walk halfway around the sphere by the time t = 1. This only works because v_x is non-zero for all x. If some v_x were zero, the ant starting at x would just stand there like an idiot, and never make it to the other side.
Now we can define the deformation we wanted. For each time t between 0 and 1, let f_t be the function that sends x to F(x,t). So f_0(x) = F(x,0) = x (because the ants haven't moved yet), and f_1(x) = F(x,1) = -x (because the ants made it halfway around). So as t slides from 0 to 1, our function f_t smoothly changes from the identity map to the antipodal map. That's the deformation we were looking for!
c3534l ยท 1 points ยท Posted at 18:31:08 on May 25, 2016 ยท (Permalink)
Sorry if this is a stupid rephrasing, but would that mean if such a hairy ball existed, our ant might wander in some direction and wind up facing the wrong way?
QuigleyQ ยท 2 points ยท Posted at 19:27:33 on May 25, 2016 ยท (Permalink)
Not quite. The ants are points, so there's not really a notion of them facing the wrong way. The real issue is that if such a hairy ball existed, we'd have ants that could walk to the other side of the sphere in a continuous fashion (nearby ants take similar paths). It's a little surprising, but that can't exist; you must have ants that behave very differently no matter how close they start out.
For example, if every ant except at the poles walks to the right latitude, then walks through 180 degrees of longitude, you still have to figure out what to do with the polar ants. No matter which way you start them moving, they'll move discontinuously from their neighbors.
This boils down to the "there's no deformation from the identity to the antipodal map". If you want more intuition for that, note that the antipodal map can be deformed to a reflection across the equator (just rotate the ball). So it suffices to show that there's no deformation from the identity to a reflection, which is a little less surprising.
c3534l ยท 1 points ยท Posted at 19:39:39 on May 25, 2016 ยท (Permalink)
I'm learning topology right now, so that's quite helpful. I'm still building my intuiton about this sort of thing.
Magical_Gravy ยท 5 points ยท Posted at 16:36:11 on May 25, 2016 ยท (Permalink)
Apparently this is true on a surprisingly common basis.
fb5a1199 ยท 3 points ยท Posted at 14:46:16 on May 25, 2016 ยท (Permalink)
I solved the problem by going bald. Take THAT Einstein...
lordalch ยท 1 points ยท Posted at 00:36:57 on May 26, 2016 ยท (Permalink)
HTTP://Www.Theproofistrivial.com
_TheRooseIsLoose_ ยท 1 points ยท Posted at 03:25:17 on May 26, 2016 ยท (Permalink)
A new proof technique that a lot of my students come in with and use throughout the year is "I tried for like 3 minutes to find a counterexample, QED"
Detritovore ยท 1 points ยท Posted at 17:07:11 on May 26, 2016 ยท (Permalink)
Imagine that you are walking in a loop on a flat surface with a wind vane pointing the direction of the wind at every point. Call the number of complete rotations the wind vane makes the winding number of the loop.
Cut the Earth into two halves along the equator and flatten the two hemispheres into discs without disturbing the wind pattern. Note that because of the way the two hemispheres were attached, the winding number along the loops forming the boundaries of the two discs always have a difference of two, which means in particular that they both can't vanish at the same time. Try making a picture to convince yourself of this.
If a loop on a flat plane doesn't enclose any point at which there is no wind, its winding number of the loop has to vanish. Because if it didn't, we could continuously shrink the loop to a point, which has winding number zero, and the winding number being an integer can't suddenly jump as the loop is deformed. (For the case when the wind at some point vanishes, the wind has no well-defined direction at that time and the above argument doesn't apply.)
It follows that at least one of the two hemispheres must contain a point at which the wind vanishes.
Cynical_Walrus ยท -4 points ยท Posted at 15:53:07 on May 25, 2016 ยท (Permalink)
Lots and lots of multivariable calculus. Terrible, terrible stuff
[deleted] ยท 23 points ยท Posted at 14:40:18 on May 25, 2016 ยท (Permalink)
The English doesn't help. Let's try German this time.
Chypsylon ยท 34 points ยท Posted at 14:49:44 on May 25, 2016 ยท (Permalink)
Auf einer Sphรคre Sn gibt es genau dann ein tangentiales, stetiges, nirgends verschwindendes Vektorfeld, wenn n ungerade ist.
unreadable_captcha ยท 28 points ยท Posted at 14:53:16 on May 25, 2016 ยท (Permalink)
Thanks I get it now
Chypsylon ยท 10 points ยท Posted at 15:00:04 on May 25, 2016 ยท (Permalink)
Bitte, gern geschehen!
[deleted] ยท 1 points ยท Posted at 11:53:26 on May 29, 2016 ยท (Permalink)
Scheiรe!
NoxWild ยท 47 points ยท Posted at 12:56:05 on May 25, 2016 ยท (Permalink)
This is worth memorizing for small talk at parties.
CHE6yp ยท 133 points ยท Posted at 14:58:15 on May 25, 2016 ยท (Permalink)
"Hey let me tell you something about hairy balls!"
GokuMoto ยท 3 points ยท Posted at 17:41:40 on May 25, 2016 ยท (Permalink)
well it's not exactly brain surgery
Linfinity8 ยท 2 points ยท Posted at 17:50:18 on May 25, 2016 ยท (Permalink)
Jesus, I can't take you anywhere...
RigbyThePower ยท 1 points ยท Posted at 15:28:41 on May 25, 2016 ยท (Permalink)
Have you stheen my basthhball??
puheenix ยท 1 points ยท Posted at 15:44:29 on May 25, 2016 ยท (Permalink)
This is probably what I'd say before clamming up and playing on my phone.
succulentlysimple ยท 11 points ยท Posted at 15:19:55 on May 25, 2016 ยท (Permalink)
I don't want to go to your parties.
Telespaulocaster ยท 8 points ยท Posted at 15:24:00 on May 25, 2016 ยท (Permalink)
"Would you like to hear my hairy ball theorem?"
BonScoppinger ยท 2 points ยท Posted at 16:48:43 on May 25, 2016 ยท (Permalink)
In algebraic topology there is also a ham sandwich theorem
Deacon_Steel ยท 2 points ยท Posted at 14:46:38 on May 25, 2016 ยท (Permalink)
Also remember that it is totally cool to comb a hairy donut.
[deleted] ยท 1 points ยท Posted at 16:14:18 on May 25, 2016 ยท (Permalink)
Please don't be that guy
MAADcitykid ยท -2 points ยท Posted at 15:24:40 on May 25, 2016 ยท (Permalink)
No it's not. I'd punch you in the face at a party if you said this
[deleted] ยท 21 points ยท Posted at 13:31:16 on May 25, 2016 ยท (Permalink)*
Isn't this also used to show that there has to be a tornado somewhere on earth at all times?
E: Or maybe that there is always somewhere on earth with no wind?
acejohn ยท 75 points ยท Posted at 13:44:39 on May 25, 2016 ยท (Permalink)
I believe it implies the existence of an "eye" where there is no wind at all.
C_IsForCookie ยท 1 points ยท Posted at 00:35:59 on May 26, 2016 ยท (Permalink)
Could the eye theoretically be the size of a marble, thus making this more or less practically useless? Or does the eye have to be a few miles wide?
Also, is it possible to determine where the eye is based on... numbers n stuff?
acejohn ยท 1 points ยท Posted at 00:45:10 on May 26, 2016 ยท (Permalink)
I have no idea.
[deleted] ยท 1 points ยท Posted at 14:22:04 on May 25, 2016 ยท (Permalink)
Thanks. I knew it had something to do with wind/lack there of.
magicsonar ยท 12 points ยท Posted at 14:45:02 on May 25, 2016 ยท (Permalink)
At first i read that as "Hairy Balls Theorem" and i thought to myself, wow, math has an explanation for everything!
[deleted] ยท 3 points ยท Posted at 15:14:22 on May 25, 2016 ยท (Permalink)
aka "the one theorem you don't want to google"
everyday847 ยท 3 points ยท Posted at 14:56:04 on May 25, 2016 ยท (Permalink)
For those uninitiated, an n-sphere refers to the dimension of the sphere surface, not the dimension of the space that contains it. So a tennis ball is a 2-sphere, as it's a surface, not a 3-sphere. A circle is a 1-sphere, which is why you can define a nonvanishing continuous tangent vector field quite easily thereon.
abig7nakedx ยท 1 points ยท Posted at 16:21:45 on May 25, 2016 ยท (Permalink)
Thanks! I was about to get really confused about how 3 was even...lol
MrXian ยท 2 points ยท Posted at 14:57:51 on May 25, 2016 ยท (Permalink)
featherfooted ยท 1 points ยท Posted at 18:24:15 on May 25, 2016 ยท (Permalink)
"Hairs" in this sense refer to vectors tangential to the surface of the tennis ball.
English: wind has a direction, North/South/East/West and the wind pushes air along the surface of the Earth. Imagine hairs on the tennis ball as individual gusts of wind, the direction each hair is facing is the direction of said wind, and the length of the hair is how strong the wind is.
Consequence: the phrase "no non vanishing continuous tangent field" translates to meaning that there is no magic configuration of hairs (in terms of spirals along the surface of the tennis ball) in which everybody lays flat. There has to be a break somewhere, and in terms of wind (since the Earth is a closed system of wind-tangents) there must always be some point on Earth where there is no wind right now.
ScoopOKarma ยท 2 points ยท Posted at 18:01:16 on May 25, 2016 ยท (Permalink)
The Hairy Ball Theorem is what I use to prove out that it's time to buy my husband new razors
poizan42 ยท 5 points ยท Posted at 14:28:20 on May 25, 2016 ยท (Permalink)
Though an actual tennis ball has a finite number of hairs and each hair has a non-infinitesimal width. I would kinda like to know if the details for the actual physical case have been worked out, and if it has any real connection to the Hairy Ball Theorem besides the superfluous similarity.
davvblack ยท 1 points ยท Posted at 15:14:18 on May 25, 2016 ยท (Permalink)
Two cowlicks, in fact. Or more.
HowDeepisYourLearnin ยท 1 points ยท Posted at 15:15:46 on May 25, 2016 ยท (Permalink)
What does same direction mean here? If I have a tennisball in 3d-space, all the hairs point towards a single point in space? Or same direction along the 2d-surface of the ball?
featherfooted ยท 2 points ยท Posted at 18:26:51 on May 25, 2016 ยท (Permalink)
"Tangent field" means direction along the surface of the tennis ball.
Erstezeitwar ยท 1 points ยท Posted at 15:16:18 on May 25, 2016 ยท (Permalink)
This bothers my OCD.
banfromallsubreddits ยท 1 points ยท Posted at 15:17:11 on May 25, 2016 ยท (Permalink)
Come on guys...you're making this too easy.
cboski ยท 1 points ยท Posted at 15:19:38 on May 25, 2016 ยท (Permalink)
It's cool because if you remove the poles (make a Taurus) there will be no cowlicks and you can make the hairs perfectly put in one direction
PAxlFitz ยท 1 points ยท Posted at 15:21:46 on May 25, 2016 ยท (Permalink)
I upvoted just because you had 999 upvotes
Supersnazz ยท 1 points ยท Posted at 15:30:08 on May 25, 2016 ยท (Permalink)
Thats only if the hairs cant bend and also only if the hairs are dense enough to overlap.
CrazyKirby97 ยท 1 points ยท Posted at 15:31:26 on May 25, 2016 ยท (Permalink)
The limp dick theorem: you can name a theorem whatever you want if you discover it.
bravo_ragazzo ยท 1 points ยท Posted at 15:32:48 on May 25, 2016 ยท (Permalink)
does that mean there is some high probability or certainty that ever human head has a cowlick to some degree?
[deleted] ยท 1 points ยท Posted at 15:34:09 on May 25, 2016 ยท (Permalink)
Or in German: jeder stetig gekรคmmte Igel hat mindestens einen Glatzpunkt.
DJAllOut ยท 1 points ยท Posted at 15:43:06 on May 25, 2016 ยท (Permalink)
The more amazing fact is someone actually wasted their life to figure that out
ClawTheBeast ยท 1 points ยท Posted at 15:44:16 on May 25, 2016 ยท (Permalink)
Words
OneTrueKingOfOOO ยท 1 points ยท Posted at 15:44:24 on May 25, 2016 ยท (Permalink)
So you're saying we need to create a 5-dimensional tennis ball?
smixton ยท 1 points ยท Posted at 15:51:29 on May 25, 2016 ยท (Permalink)
I have my own hairy ball theorem. I theorize that if my balls are hairy my wife won't suck them.
etacarinaeblue ยท 1 points ยท Posted at 15:53:17 on May 25, 2016 ยท (Permalink)
This is quite possibly the most eloquent ELI5 I've ever read. Well done.
not-a-f-given ยท 1 points ยท Posted at 16:02:46 on May 25, 2016 ยท (Permalink)
Yeah but how do you explain Trump's hair?
ktkps ยท 2 points ยท Posted at 05:09:04 on May 26, 2016 ยท (Permalink)
That's some other kind of lick I guess
vizzmay ยท 1 points ยท Posted at 16:06:46 on May 25, 2016 ยท (Permalink)
TIL about cowlick.
Jono0259 ยท 1 points ยท Posted at 16:09:54 on May 25, 2016 ยท (Permalink)
i thought it was spelled something like "calic" =(
komali_2 ยท 1 points ยท Posted at 16:10:43 on May 25, 2016 ยท (Permalink)
When I first read about this was when I've realized we've let math come too far.
roh8880 ยท 1 points ยท Posted at 16:18:57 on May 25, 2016 ยท (Permalink)
Unless they are combed straight out. And essentially, they are all in the same direction of r-hat.
PaulieStreams ยท 1 points ยท Posted at 16:30:00 on May 25, 2016 ยท (Permalink)
Hairy Ball Theorem is now my all time favorite theory, solely due to the name.
ktkps ยท 2 points ยท Posted at 04:48:11 on May 26, 2016 ยท (Permalink)
If you liked that...then there is the Ham Sandwich Theorm:
English: You can cut a ham sandwich(any sandwich of n dimensions) in half and have with your friend.
PaulieStreams ยท 1 points ยท Posted at 20:56:39 on May 26, 2016 ยท (Permalink)
You have just blown my mind.
theCrono ยท 1 points ยท Posted at 16:39:23 on May 25, 2016 ยท (Permalink)
For the mayor of Fort Wayne, seeย Harry Baals. lol
ikilledtupac ยท 1 points ยท Posted at 16:39:34 on May 25, 2016 ยท (Permalink)
That's why I shave my tennis balls
CBo_Slayer ยท 1 points ยท Posted at 16:57:22 on May 25, 2016 ยท (Permalink)
Hairy ball... Heh
setfire3 ยท 1 points ยท Posted at 16:58:48 on May 25, 2016 ยท (Permalink)
can you also give French version?
President_of_Space ยท 1 points ยท Posted at 16:59:10 on May 25, 2016 ยท (Permalink)
This also proves the theory that you can in fact comb a hairy donut ... not sure why this is significant, but there you have it.
Pragmataraxia ยท 1 points ยท Posted at 17:07:46 on May 25, 2016 ยท (Permalink)
Does it bother anyone else that an n-sphere exists in n-plus-one-space?
ktkps ยท 1 points ยท Posted at 06:17:55 on May 26, 2016 ยท (Permalink)
like how we exist in 4 dimensional space, perceiving only 3 dimensions?
Pragmataraxia ยท 1 points ยท Posted at 14:29:36 on May 26, 2016 ยท (Permalink)
Thinking about how 2D creatures would observe the passing of 3D objects, I don't believe this is true. I would expect a 4D object passing through 3D space to manifest as a pretty serious violation of the laws of thermodynamics (e.g. a planet growing out of nothing, and returning to nothing). Of course, the absence of evidence is not evidence of absence, but it's pretty compelling in this case.
It is true that time is a dimension, but it is not considered a spacial dimension as far as I know.
sudzone89 ยท 1 points ยท Posted at 17:11:08 on May 25, 2016 ยท (Permalink)
At first I was interested, thinking Halle Berry made a theorem
cpt_drumstik ยท 1 points ยท Posted at 17:14:35 on May 25, 2016 ยท (Permalink)
from that title, I thought we were going in a complete different direction
BelongingsintheYard ยท 1 points ยท Posted at 17:19:59 on May 25, 2016 ยท (Permalink)
Why didn't you say it in English the first time?
StabbyPants ยท 1 points ยท Posted at 17:22:23 on May 25, 2016 ยท (Permalink)
do you mean odd? because i can do it on a 2 sphere.
Wolfeman0101 ยท 1 points ยท Posted at 17:23:40 on May 25, 2016 ยท (Permalink)
Are we not doing phrasing anymore?
merelyadoptedthedark ยท 1 points ยท Posted at 17:31:18 on May 25, 2016 ยท (Permalink)
Does this have any real world application or usefulness?
Etonet ยท 1 points ยท Posted at 17:46:04 on May 25, 2016 ยท (Permalink)
?
juicyt8 ยท 1 points ยท Posted at 17:52:23 on May 25, 2016 ยท (Permalink)
I was doing a project on chaos theory.. but this sounds so much better.
Kimihro ยท 1 points ยท Posted at 17:57:55 on May 25, 2016 ยท (Permalink)
The basic logic to this is that you have to take off the comb at some point.
ktkps ยท 1 points ยท Posted at 05:19:30 on May 26, 2016 ยท (Permalink)
are you talking about the soothing itch in the balls that you try to comb out?
Corrosivelol ยท 1 points ยท Posted at 18:07:36 on May 25, 2016 ยท (Permalink)
I'm gonna need pictures of hairy balls for proof
ktkps ยท 1 points ยท Posted at 05:18:36 on May 26, 2016 ยท (Permalink)
Here you go
upstateman ยท 1 points ยท Posted at 18:12:09 on May 25, 2016 ยท (Permalink)
Or the Earth will always have at least one cyclone/tornado.
po8 ยท 1 points ยท Posted at 18:18:04 on May 25, 2016 ยท (Permalink)
I would have thought a tennis ball would be a 3D sphere, and therefore of odd dimension?
chequilla ยท 1 points ยท Posted at 18:20:52 on May 25, 2016 ยท (Permalink)
I've got a hairy ball theorem for ya
anomalous_cowherd ยท 1 points ยท Posted at 18:23:50 on May 25, 2016 ยท (Permalink)
Can't I comb them straight outwards?
like this maybe
ktkps ยท 1 points ยท Posted at 05:14:42 on May 26, 2016 ยท (Permalink)
Yeah, and probably this too
thistadpole ยท 1 points ยท Posted at 18:57:23 on May 25, 2016 ยท (Permalink)
Is this true for any object homeomprphic to the sphere?
StereotypeLumberjack ยท 1 points ยท Posted at 19:28:05 on May 25, 2016 ยท (Permalink)
A tennis ball is not the first thing I thought of when I read Hairy Ball.
ktkps ยท 2 points ยท Posted at 05:12:11 on May 26, 2016 ยท (Permalink)
Hairy with a chance of meat balls starring Stereotype Lumberjack. Coming this Christmas.
sardu1 ยท 1 points ยท Posted at 19:41:32 on May 25, 2016 ยท (Permalink)
or a part
ywecur ยท 1 points ยท Posted at 19:52:39 on May 25, 2016 ยท (Permalink)
Next time your math teacher gives you a hard time, tell him to try comb a hairy banana.
[deleted] ยท 1 points ยท Posted at 20:00:32 on May 25, 2016 ยท (Permalink)
No shit? Cool!
Bertrejend ยท 1 points ยท Posted at 20:08:14 on May 25, 2016 ยท (Permalink)
Also the reason why coconuts have a tuft!
ryguy2503 ยท 1 points ยท Posted at 20:20:23 on May 25, 2016 ยท (Permalink)
Just from the name of the theorem alone I was expecting something completely different than what it turned out to be...
gregnuttle ยท 1 points ยท Posted at 20:28:57 on May 25, 2016 ยท (Permalink)
The mayor of my hometown (Fort Wayne, Indiana) in the 1930-1950s was named Harry Baals!
cadrianzen23 ยท 1 points ยท Posted at 20:40:03 on May 25, 2016 ยท (Permalink)
What is a cowlick? Dare I ask?
eoghanf ยท 1 points ยท Posted at 21:03:24 on May 25, 2016 ยท (Permalink)
Why even-dimensional?
ktkps ยท 1 points ยท Posted at 02:37:54 on May 26, 2016 ยท (Permalink)
You know how theorems state things considering a perfect backdrop? Thats the reason... You never question Pythagoras theorm asking what if one of the side is slightly bent...
eoghanf ยท 1 points ยท Posted at 06:27:25 on May 26, 2016 ยท (Permalink)
No. This is not the reason. Even-dimensional means "of dimension 2,4,6,8...".
Frostywood ยท 1 points ยท Posted at 21:17:16 on May 25, 2016 ยท (Permalink)
What about if you get all the hairs standing perfectly perpendicular to the surface
SodaCanSuperman ยท 1 points ยท Posted at 21:20:37 on May 25, 2016 ยท (Permalink)
The heck is a cowlick?
ktkps ยท 1 points ยท Posted at 02:26:13 on May 26, 2016 ยท (Permalink)
Glad you asked. Cowlicks aka hair whorls
adelie42 ยท 1 points ยท Posted at 22:04:44 on May 25, 2016 ยท (Permalink)
Is the "comb" thing a simple way of illustrating the point, despite the fact that the teeth are parallel?
I imagine from any hair root as the center, the polar vector of each hair could be relatively identical. But you (obviously?) can't accomplish that with a comb because parallel teeth cause parallel hairs to have identical absolute Euclidean vectors over the curve created by the vector of the comb, not identical relativistic polar vectors (which definitively can't be equal).
Or is there more to it than that?
Jayboman66 ยท 1 points ยท Posted at 22:58:11 on May 25, 2016 ยท (Permalink)
This doesn't explain how when I shave my balls there is always a hair left. Disappointed.
ktkps ยท 1 points ยท Posted at 02:20:03 on May 26, 2016 ยท (Permalink)
Already someone is trying that experiment tonight. Go cheer him up.
expateli ยท 1 points ยท Posted at 00:00:20 on May 26, 2016 ยท (Permalink)
This animation on wikipedia was immensely helpful for understanding this concept.
MooseCockSandwich ยท 1 points ยท Posted at 01:15:24 on May 26, 2016 ยท (Permalink)
What about all the hairs on my hairy balls? Will run experiment and update later tonight
ktkps ยท 1 points ยท Posted at 02:14:05 on May 26, 2016 ยท (Permalink)
Hope you deliver
superalienhyphy ยท 1 points ยท Posted at 01:30:50 on May 26, 2016 ยท (Permalink)
No matter how good you think you shaved your balls, there will always be at least one long ass pube
fi-lover ยท 1 points ยท Posted at 03:06:24 on May 26, 2016 ยท (Permalink)
Works for tides too.
SonOfaFlynn ยท 1 points ยท Posted at 04:15:32 on May 26, 2016 ยท (Permalink)
That's fucking sweet
xmastreee ยท 5141 points ยท Posted at 11:59:49 on May 25, 2016 ยท (Permalink)*
If you divide any number by 7, and the answer isn't an integer, you end up with the sequence 142857 recurring.
1/7 = .142857142857
3/7 = .428571428571
2/7 = .285714285714
6/7 = .857142857142
4/7 = .571428571428
5/7 = .714285714285
Edit: formatting, with thanks to /u/Kirushi
mathidiot ยท 2266 points ยท Posted at 14:02:59 on May 25, 2016 ยท (Permalink)*
These are called cyclic numbers. Part of my undergrad research were on these types of numbers. 7, 17, 19, and
2123 are the first numbers that form cyclics. They are formed by n/p, where p is the full repetend prime used to form the cyclic (say 7) and n are all numbers p-1 (1, 2, 3, 4, 5, 6).Some other properties include if you split the number into two separate halves, for instance split 142857 into 142 and 857, and add the two halves together you will get a number containing only 9's (142 + 857 = 999). If you split the number into thirds you will achieve the same result: 14 + 28 + 57 = 99.
If you multiply the base cyclic (142857) by the prime that produced it (7), you will get a number containing only 9's (142857 x 7 = 999999). Multiplying by a number greater than p, for instance 8, will give you the following: 1142856. You can then get back to the original cyclic by taking the right most p-1 numbers and adding the left over numbers: 1 + 142856 = 142857.
If we again break the number into two halves, square each half, and then subtract the resulting numbers, you will receive a permutation of the cyclic. Example: 8572 - 1422 = 734449 - 20164 = 714285.
There are even more facts to cyclics, but this Numberphile video can explain more!
Edit: Made a mistake on the squaring each half, you are suppose to subtract them not add them, thanks for pointing that out /u/DoubleFuckingRainbow
Edit 2: 23, not 21! Thanks /u/jcarlson08
weird_witha_beard ยท 354 points ยท Posted at 14:15:32 on May 25, 2016 ยท (Permalink)
Holy crap. I'm going to talk about cyclic numbers at the water cooler today
Cerberus73 ยท 617 points ยท Posted at 15:44:47 on May 25, 2016 ยท (Permalink)
With any luck someone will pass by to hear you talk about it
Spotlight0xff ยท 75 points ยท Posted at 17:39:16 on May 25, 2016 ยท (Permalink)
with a probability of 63%?
hkap ยท 12 points ยท Posted at 18:44:17 on May 25, 2016 ยท (Permalink)
Now we're learning!
iwillnotgetaddicted ยท 3 points ยท Posted at 20:25:16 on May 25, 2016 ยท (Permalink)
Only if he keeps at it long enough!
tree_jayy ยท 3 points ยท Posted at 03:03:34 on May 26, 2016 ยท (Permalink)
2meta63%me
Yippie-kay-yae ยท 1 points ยท Posted at 22:17:33 on June 6, 2016 ยท (Permalink)
or 1 in X times
Ceilibeag ยท 3 points ยท Posted at 17:08:39 on May 25, 2016 ยท (Permalink)
Not for them... <rim shot>
blakeinalake ยท 3 points ยท Posted at 19:16:59 on May 25, 2016 ยท (Permalink)
"I think that weird guy with the beard that always stands next to the water cooler finally snapped. He's going on about cycling numbers and repeating 9's."
rallick_nom ยท 1 points ยท Posted at 04:58:55 on May 26, 2016 ยท (Permalink)
Today at work, one of my coworkers was explaining cyclic number to the water cooler. We asked him to go see a psychiatrist.
dustyceilingfan ยท 5 points ยท Posted at 15:09:57 on May 25, 2016 ยท (Permalink)
I'm sure the office will love you for it.
do_you_smoke_paul ยท 16 points ยท Posted at 14:20:20 on May 25, 2016 ยท (Permalink)
Man that's some interesting shit. It always amazes me that these patterns exist. It seems to me like maths is something that just IS rather than our own attempts to describe the world we live in.
But then again I'm from a biology field so my understanding of maths has always been embarrassingly limited to simple statistical analysis!
chickenthinkseggwas ยท 3 points ยท Posted at 19:06:09 on May 25, 2016 ยท (Permalink)*
And the stuff you're reading here is only the tip of the iceberg. The patterns just keep getting more profound and amazing the deeper you go.
But it's still a tough call to say whether maths is "something that just IS", because you could observe that the patterns of maths are just a product of the logic we use, which is, in fact, merely the logic we choose. Logic and maths are the same thing, really. And they're man made. The logic/maths we choose certainly seems to reflect reality, but perhaps they just approximate it. There's no way to say for sure. There are many logics that might accurately describe reality. Or the universe may even be inherently illogical. Maths/logic could just be a tale told by a race of idiots, full of sound and fury, signifying nothing.
trumplord ยท 11 points ยท Posted at 14:30:31 on May 25, 2016 ยท (Permalink)
What happens if we use any ther basis than 10? What numbers are cyclic? Are some numbers cyclic for many basis? If n is cyclic for basis a, is it cyclic for a*b or something?
mathidiot ยท 16 points ยท Posted at 14:38:40 on May 25, 2016 ยท (Permalink)
Yes there are cyclics in other bases. I don't have my research available right now, but just pulling some information from Wikipedia you can construct the cyclics in other bases using the following method:
[deleted] ยท 1 points ยท Posted at 17:02:27 on May 25, 2016 ยท (Permalink)*
[deleted]
mathidiot ยท 2 points ยท Posted at 17:30:06 on May 25, 2016 ยท (Permalink)
This is not true, as it fails in base 6.
OrganicFlu ยท 1 points ยท Posted at 18:04:04 on May 25, 2016 ยท (Permalink)
But for math idiots, it's true except for base 6?
au_travail ยท 1 points ยท Posted at 18:53:33 on May 25, 2016 ยท (Permalink)
It's not true for bases 6, 9, 12, 15, 18, 21...
7, 11, 13, 17, 19, 23, 25, ...
[deleted] ยท 1 points ยท Posted at 17:02:12 on May 25, 2016 ยท (Permalink)*
[deleted]
au_travail ยท 1 points ยท Posted at 18:49:06 on May 25, 2016 ยท (Permalink)
Not true for 3, 6, 9, ...
How_Suspicious ยท 6 points ยท Posted at 14:57:23 on May 25, 2016 ยท (Permalink)
I'm so angry at the universe right now
log_out_and_crush_it ยท 60 points ยท Posted at 14:13:27 on May 25, 2016 ยท (Permalink)
I've known since I was about 10 about the sevenths-fractions thing.
I finally learned some new and weird stuff beyond the obvious. Thank you.
Redhavok ยท 7 points ยท Posted at 14:55:02 on May 25, 2016 ยท (Permalink)
I used to do this stuff in school too, it's like a little game, finding little patterns in stuff. It's like doing puzzles but without being sure there is actually an answer.
space_guy95 ยท 3 points ยท Posted at 01:55:43 on May 26, 2016 ยท (Permalink)
It's like searching for easter eggs in a game, apart from these easter eggs seem to be hard-coded into the very fabric of reality.
THIS_MSG_IS_A_LIE ยท 2 points ยท Posted at 02:51:37 on May 26, 2016 ยท (Permalink)
This. I wish this playing-with-numbers attitude would be taught at school instead of rote memorization. It practically killed my math skills at a very early age.
Redhavok ยท 3 points ยท Posted at 03:42:18 on May 26, 2016 ยท (Permalink)
Know what you mean, I hated school, but I actually loved the subjects in my own time
SpaceKittyHero ยท 6 points ยท Posted at 15:04:51 on May 25, 2016 ยท (Permalink)
you should do abstract algebra
BloodFartTheQueefer ยท 3 points ยท Posted at 16:47:35 on May 25, 2016 ยท (Permalink)
I figured out the n/7 fractions as well around 10 by realizing with long division in my head that the remainder kept doubling (14, 28, 57 (56 Cary over the one from 114))
secaedelcielo ยท 6 points ยท Posted at 14:15:37 on May 25, 2016 ยท (Permalink)
This is beyond cool. Thanks numbers guy!
jallenrt ยท 6 points ยท Posted at 14:17:14 on May 25, 2016 ยท (Permalink)
And they told me magic isn't real! Ha!
DoubleFuckingRainbow ยท 5 points ยท Posted at 15:08:11 on May 25, 2016 ยท (Permalink)
I dont get the same result as you? i get 754613
EDIT: Its 8572 - 1422 and you get the right result
mathidiot ยท 1 points ยท Posted at 15:13:46 on May 25, 2016 ยท (Permalink)
My mistake! I will fix it in the post.
eek_a_shark ยท 9 points ยท Posted at 14:14:38 on May 25, 2016 ยท (Permalink)
Coolest comment in here
donuthazard ยท 4 points ยท Posted at 14:41:09 on May 25, 2016 ยท (Permalink)
You win the internet today.
LambastingFrog ยท 4 points ยท Posted at 15:08:24 on May 25, 2016 ยท (Permalink)
I didn't know most of those other facts, but they feel true to me without checking them, due to other things I know more about. In my case, that's generators in a finite field using modular exponentiation.
Slivlan ยท 3 points ยท Posted at 15:08:55 on May 25, 2016 ยท (Permalink)
Any idea about what are the requisites (I'm not sure that's the word I need, sorry, am not English) for a number to be cyclic?
Obviously it must be a prime, but what else?
mathidiot ยท 1 points ยท Posted at 15:28:23 on May 25, 2016 ยท (Permalink)
The prime must be a full repetend prime. Which means it must fit the formula:
(bp-1 - 1)/p where b is the base and p is the prime.
prancingElephant ยท 2 points ยท Posted at 15:50:38 on May 25, 2016 ยท (Permalink)
But you listed 21, and 21 isn't a prime.
mathidiot ยท 2 points ยท Posted at 15:55:45 on May 25, 2016 ยท (Permalink)
My mistake, it was supposed to be 23. I have fixed it in the post.
prancingElephant ยท 1 points ยท Posted at 16:05:24 on May 25, 2016 ยท (Permalink)
Oh, okay!
Slivlan ยท 2 points ยท Posted at 16:12:48 on May 25, 2016 ยท (Permalink)
Bot now the number you get has to add up to bn -1 if you split it in half. And also all the other stuff. Is it that how you look for "new" cyclic numbers? Going through permutations that add up to 999...?
mathidiot ยท 1 points ยท Posted at 16:16:30 on May 25, 2016 ยท (Permalink)
Exactly. bp-1 - 1 must equal a number containing p-1 number of 9's, and only 9's, for b = 10
au_travail ยท 1 points ยท Posted at 18:48:31 on May 25, 2016 ยท (Permalink)
This is always true.
Slivlan ยท 1 points ยท Posted at 16:00:39 on May 25, 2016 ยท (Permalink)
I see, interesting.
[deleted] ยท 2 points ยท Posted at 14:54:55 on May 25, 2016 ยท (Permalink)
Havent seen this sort of thing in ages! Did a research project on the guptisaki (spelling may be wrong) p group during uni
manly_lumberjack ยท 2 points ยท Posted at 15:12:02 on May 25, 2016 ยท (Permalink)
Yea bro, but can you even calculate the terminal velocity of an unladen swallow?
jarrit0s ยท 2 points ยท Posted at 15:13:33 on May 25, 2016 ยท (Permalink)
Can cyclic numbers or their properties be used to solve a problem?
[deleted] ยท 3 points ยท Posted at 15:34:25 on May 25, 2016 ยท (Permalink)
You can look like a genius when you can figure out what 5/7 is in decimal form in a few seconds :)
mathidiot ยท 1 points ยท Posted at 15:29:25 on May 25, 2016 ยท (Permalink)
Cyclic numbers do not have any real world uses, but they do pop up in other mathematical studies such as Carmichael numbers.
gizzardgullet ยท 2 points ยท Posted at 15:15:11 on May 25, 2016 ยท (Permalink)*
Are cyclic numbers different for different number bases? For example, hexadecimal?
mathidiot ยท 1 points ยท Posted at 15:30:53 on May 25, 2016 ยท (Permalink)
There are different cyclic numbers in other bases, although there are none in hexadecimal.
lFailedTheTuringTest ยท 1 points ยท Posted at 15:18:58 on May 25, 2016 ยท (Permalink)*
Well the multiply by 7 or splitting of the elements to form a 9's number is kind of trivial. Since you cant divide 1 by 7, you are always approximating it as close as possible to 1 which will be a long string of 9's. So wherever you decide to taper the division when you multiply by 7 you will get a string of 9's.
cboski ยท 1 points ยท Posted at 15:22:29 on May 25, 2016 ยท (Permalink)
How exactly do you conduct your research? Do you just grab random numbers and attempt to apply properties to them or is there a pattern searching/testing algorithm somewhere?
jcarlson08 ยท 1 points ยท Posted at 15:34:41 on May 25, 2016 ยท (Permalink)
I think you made a mistake. In this post you say:
and in a lower post:
But you say the fourth cyclic is 21, which is not a prime number.
mathidiot ยท 1 points ยท Posted at 15:49:30 on May 25, 2016 ยท (Permalink)
You are correct! It should be 23! Thanks for catching that!
onfire9123 ยท 1 points ยท Posted at 15:42:25 on May 25, 2016 ยท (Permalink)
Forgive me, but did you really continue and study freakin' Number Theory at the masters/phd levels...?
mathidiot ยท 2 points ยท Posted at 15:52:31 on May 25, 2016 ยท (Permalink)
I did not unfortunately. I am now studying Nuclear Engineering. Friends of mine did go on to graduate school from Pure Mathematics though, which includes Number Theory and Abstract Algebra. They have told me that at this point they miss numbers!
ParanoidDrone ยท 1 points ยท Posted at 15:44:39 on May 25, 2016 ยท (Permalink)
This is just such a bizarre set of properties.
lightslightup ยท 1 points ยท Posted at 15:46:43 on May 25, 2016 ยท (Permalink)
Jesus fucking Christ. Math is spooky.
the_warmest_color ยท 1 points ยท Posted at 15:52:59 on May 25, 2016 ยท (Permalink)
Wew what a journey
puheenix ยท 1 points ยท Posted at 15:56:59 on May 25, 2016 ยท (Permalink)
I knew about the 7ths thing, but splitting and summing the string for an all-9's number just blew my mind. That kind of thing just feels too complex to work perfectly. Is there some elegant way to explain why this happens? Are there similar properties to numbers in other base systems? Would an analogous operation on cyclics in base N result in N-1 repeating?
mathidiot ยท 1 points ยท Posted at 16:03:35 on May 25, 2016 ยท (Permalink)
I don't have my research available at the moment, I will have to dig it out when I get off work, but I was able to prove the string of 9's and why it will always work.
There are cyclic numbers in other bases, for instance in ternary both primes 2 and 5 form cyclic numbers, 1 and 0121 respectively. They follow the form (bp-1 -1) / p, where b is the base and p is the full repetend prime.
ademnus ยท 1 points ยท Posted at 16:06:24 on May 25, 2016 ยท (Permalink)
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
Multiply any number made of ones by itself. This pattern seems to go on forever. Is this a "cyclic number" or something else? I find it so interesting how the results follow this pattern where the middle numeral of the answer equals the number of 1s in the number (let's call it X) in the equation and it's a sequence of numbers that incrementally rise from 1 to X and back down to 1.
mathidiot ยท 1 points ยท Posted at 16:14:26 on May 25, 2016 ยท (Permalink)
No this is some form of sequence. Cyclic numbers are formed from 1 prime number, such as 7. 11 would not be cyclic because:
1/11 = 0.09
2/11 = 0.18
3/11 = 0.27
4/11 = 0.36
5/11 = 0.45
...
These numbers would all have to be permutations of each other.
ademnus ยท 1 points ยท Posted at 16:18:05 on May 25, 2016 ยท (Permalink)
I've always found it so odd. Now to just wait for the day a gameshow host asks me "what's 111,111 times 111,111" so I can answer without doing math and collect my winnings! this will never happen
nodlezfodlez ยท 1 points ยท Posted at 16:18:47 on May 25, 2016 ยท (Permalink)
also 1 + 4 + 2 + 8 + 5 + 7 = 27
2 + 7 = 9
mathidiot ยท 1 points ยท Posted at 16:27:05 on May 25, 2016 ยท (Permalink)
You are correct! Forgot about this one! This works for all cyclic numbers as well.
1/17 = 0588235294117647 = 5+8+8+2+3+5+2+9+4+1+1+7+6+4+7 = 72 = 7+2 = 9
ydubs ยท 1 points ยท Posted at 16:24:18 on May 25, 2016 ยท (Permalink)
There's also a pattern tha does 49382716 and its reverse for example if you compute 1/2025
mathidiot ยท 1 points ยท Posted at 16:28:53 on May 25, 2016 ยท (Permalink)
You are forgetting a zero! But yes I never knew about this one. This isn't a cyclic though, as 2025 isn't prime.
godnah ยท 1 points ยท Posted at 16:39:03 on May 25, 2016 ยท (Permalink)
This is fucking mental!
wicked-dog ยท 1 points ยท Posted at 16:40:28 on May 25, 2016 ยท (Permalink)
Are these just an artifact of the base ten system we use for our numbers, or is there some meaning in all this?
Sardonnicus ยท 1 points ยท Posted at 17:17:38 on May 25, 2016 ยท (Permalink)
But can't any number be reached from another number by some kind of equation? Like if you want 22 and you are given the numbers 1000, 45, 56789033 and 39.876, you can get to 22 you can design an equation to get you to 22. I'm by no means fluent in maths, but I hear people talk alot about searching for repeating numbers and number sequences, but it seems that you can get to any number from any starting number by an equation. I'm not sure how to describe it, but it's like you can make the rules work in your favor to get the answer you are looking for.
mathidiot ยท 1 points ยท Posted at 17:32:13 on May 25, 2016 ยท (Permalink)
Yes, that is by using any form of equation. This holds true for a set equation for all cyclic numbers. You can take any cyclic and perform the difference of squared halves and still receive one of the cyclics. I'm not squaring one, cubing another, dividing and then adding. It is a set formula that will always work.
Sardonnicus ยท 1 points ยท Posted at 17:51:11 on May 25, 2016 ยท (Permalink)
I kind of don't understand your reply, or even my original comment to your comment, but what I was thinking of when I posted my original comment was the film "23." In that film, the main character became obsessed with the number "23" and went looking for it everywhere, and he seemed to find it everywhere and called it some grand conspiracy. But what I am trying to ask or talk about is... if you want to find a number, say 23, you can find it anywhere by using an equation tailored to that specific situation to get you to "23." So when people talk about number patterns and problems I have a hard time understanding or grasping the concept of there being things that haven't been solved yet, because you should be able to formulate an equation that gets you to your desired destination or "number." I am not even sure I am making sense at this point anymore.
Sampwnz ยท 1 points ยท Posted at 17:31:09 on May 25, 2016 ยท (Permalink)
Thanks, mathidiot
kato3399 ยท 1 points ยท Posted at 17:47:08 on May 25, 2016 ยท (Permalink)
Username doesn't check out.
[deleted] ยท 1 points ยท Posted at 17:56:56 on May 25, 2016 ยท (Permalink)
What's the definition of a cyclic number?
upstateman ยท 1 points ยท Posted at 18:17:27 on May 25, 2016 ยท (Permalink)
That's the repeating part.
notyou13 ยท 1 points ยท Posted at 18:22:20 on May 25, 2016 ยท (Permalink)
This is the type of thing I was hoping for in this thread. This one is really cool.
AND_MY_HAX ยท 1 points ยท Posted at 18:30:22 on May 25, 2016 ยท (Permalink)
Another fun fact - taking the Fibonacci sequence mod X always yields a cyclic sequence.
Birdyer ยท 1 points ยท Posted at 19:07:53 on May 25, 2016 ยท (Permalink)
Do these rules hold true in other bases?
BillDStrong ยท 1 points ยท Posted at 20:50:59 on May 25, 2016 ยท (Permalink)
In your specific example, if add all the individual numbers together, you get nine. Does this hold true for other?
If you add any number of 9s together, such as 999, and keep adding them together until you only have one digit, that digit will be 9.
sonicandfffan ยท 1 points ยท Posted at 20:53:40 on May 25, 2016 ยท (Permalink)
Intuitively the fact about nines is because if you multiply .142857 by 7 you will get .999~ (= 1)
MisterMan12 ยท 1 points ยท Posted at 22:00:35 on May 25, 2016 ยท (Permalink)
This is very cool/ interesting, but in what ways is this information useful/ applicable/ seen in nature?
jesset77 ยท 1 points ยท Posted at 23:13:05 on May 25, 2016 ยท (Permalink)
Cline Butte, Crooked River Ranch Rim Repeater, South Madras, and
Juniper ButteRound Butte.Sorry, I run a WISP and we assign area numbers to different sites for MPLS tagging, vlans, and private IP ranges based on odd numbers (Evens for the backhaul links) so when I see a bunch of small, odd numbers my brain instantly reads geographic locations instead now. x3
Quigz ยท 1 points ยท Posted at 23:49:22 on May 25, 2016 ยท (Permalink)
Holy shit thank you so much. Like, I knew that 0.9 repeating = 1, but I never understood that 0.142857 repeating was 1/7th of 0.999999 repeating. I think I finally understand fractions now.
Tasgall ยท 1 points ยท Posted at 00:29:45 on May 26, 2016 ยท (Permalink)
Ha - I figured this out, or a version of it, in high school: any number divided by a number of the same length consisting of only 9s gives you a cyclic version of that number. Ex:
142857 / 999999 = 0.142857142857...
or
123 / 999 = 0.123123123...
or single digits
7 / 9 = 0.7777...
The reason I figured that out of course was because arguing with the math teacher about the "fun math fact" that "0.9 repeating equals 1" was all the rage at the time, and being able to show that "x/9" = "0.xxxxxxx..." made it really easy to prove because the fractional form of 0.9999... would then have to be 9/9, which is 1.
Fun times, I didn't know it went deeper than that.
MJWood ยท 1 points ยท Posted at 12:55:24 on May 26, 2016 ยท (Permalink)
These are all just incidental features of using a decimal system, aren't they? There should be some sort of function of n, where n is your base number, that allows you to calculate cyclic features for any n - but I'm just speculating wildly here.
VikingCoder ยท 0 points ยท Posted at 14:52:14 on May 25, 2016 ยท (Permalink)
I feel like I just watched The Da Vinci Code, all over again, except this time it wasn't all mumbo jumbo!
Zopffware ยท 26 points ยท Posted at 14:48:02 on May 25, 2016 ยท (Permalink)
Another in the same vein: Any number divided by 9 is that number recurring.
1/9 = 0.111111...
2/9 = 0.222222...
9/9 = 0.999999... = 1
10/99 = 0.101010...
xnaas ยท 5 points ยท Posted at 15:45:01 on May 25, 2016 ยท (Permalink)
I always enjoy writing out the proof that 0.9 repeating is, in fact, 1. :D
bsievers ยท 8 points ยท Posted at 16:07:49 on May 25, 2016 ยท (Permalink)
There are so many people who just can't see it using the normal proof, I've added the proof-by-contradiction using adding 3 thirds as well.
i.e.:
1/3 = .333333
and
1/3+1/3+1/3 = 1
therefore
.333333+.333333+.333333 = .999999 = 1
xnaas ยท 2 points ยท Posted at 16:10:02 on May 25, 2016 ยท (Permalink)
Ah, I like that addition. I might need that in the future for some of those who need a little help grasping the concept. :)
Thank you!
bibbibob2 ยท 2 points ยท Posted at 17:18:12 on May 25, 2016 ยท (Permalink)
If i remember correctly it is not as simple as that, since we are dealing with infinity and such, but that it still showcases the logic quite well.
It can be shown in so many ways :^
bsievers ยท 1 points ยท Posted at 17:45:49 on May 25, 2016 ยท (Permalink)
The more rigorous way is using the 10x-x method showcased elsewhere, but this is a good (less rigorous) proof to help show.
bibbibob2 ยท 2 points ยท Posted at 18:03:58 on May 25, 2016 ยท (Permalink)
Also the pure definition that since nothing separates the two numbers they are equal :^
boohooboo_ ยท 2 points ยท Posted at 22:56:21 on May 25, 2016 ยท (Permalink)
Taking a risk diving into a maths thread. Wouldn't the 9/9 example just be 1 straight away anyway? And never 0.9999...?
Kirushi ยท 16 points ยท Posted at 18:18:18 on May 25, 2016 ยท (Permalink)
This really missed the opportunity to show it in the cool looking way:
1/7 = .142857142857
3/7 = .428571428571
2/7 = .285714285714
6/7 = .857142857142
4/7 = .571428571428
5/7 = .714285714285
xmastreee ยท 3 points ยท Posted at 18:38:04 on May 25, 2016 ยท (Permalink)
True, but I wrote it on my phone.
SonicMaster12 ยท 32 points ยท Posted at 14:05:31 on May 25, 2016 ยท (Permalink)
Nah. That can't be right.
*Checks calculator*
Holy Shit.
deusnefum ยท 1 points ยท Posted at 17:30:23 on May 25, 2016 ยท (Permalink)
9/9 = .99999... = 1
[deleted] ยท 10 points ยท Posted at 15:18:10 on May 25, 2016 ยท (Permalink)
Nope: pi / 7 = 0.448798950512827605494663340468500412...
Did you mean "divide any integer by 7"?
dustybizzle ยท 4 points ยท Posted at 15:57:30 on May 25, 2016 ยท (Permalink)
Username checks out
mathidiot ยท 2 points ยท Posted at 15:54:39 on May 25, 2016 ยท (Permalink)
Any integer in the set {1, p-1}, where p is the full repetend prime used to form the cyclic number.
Moj88 ยท 1 points ยท Posted at 16:01:31 on May 26, 2016 ยท (Permalink)
Technically, the sequence 142857 still reoccurs in pi/7.
CharlesDarwon ยท 4 points ยท Posted at 16:24:30 on May 25, 2016 ยท (Permalink)*
What about 7/7?
Edit: I swear he put that in there after... Or not who cares.
[deleted] ยท 3 points ยท Posted at 17:53:46 on May 25, 2016 ยท (Permalink)
GokuMoto ยท 5 points ยท Posted at 18:10:46 on May 25, 2016 ยท (Permalink)
what about reading comprehension
modernbenoni ยท 3 points ยท Posted at 14:51:57 on May 25, 2016 ยท (Permalink)
Wow I didn't know this. My interesting fact about sevenths is that you get this number .142857... by taking (7*2/100) + (7*22 /1002 ) + (7*23 /1003 ) etc...
I never realised that the result is cyclical though.
wabassoap ยท 3 points ยท Posted at 16:53:26 on May 25, 2016 ยท (Permalink)
This is something that has always freaked me out about the n/7 series in particular. Obviously the last two digits '57' are off by one (7*23 = 56) so I guess it could just be a big coincidence. But is it?
bobotheking ยท 3 points ยท Posted at 20:59:30 on May 25, 2016 ยท (Permalink)
If you haven't already done so, sneak a peek down to my post below where I explain that it isn't a coincidence at all and is a result of carrying. You can go a step further and sum the geometric series u/modernbenoni refers to and show directly that it is equal to 1/7.
modernbenoni ยท 2 points ยท Posted at 21:12:22 on May 25, 2016 ยท (Permalink)
The link you posted doesn't work for me, but I can see the comment in your post history... Weird.
modernbenoni ยท 2 points ยท Posted at 20:59:21 on May 25, 2016 ยท (Permalink)
If you continue on, the next number is 112, so the one carries over making it 57.
It's no coincidence, I saw it proved once using summations but I can't remember it and I'm not the mathematician I used to be sadly...
Wolfram knows it though:
http://www.wolframalpha.com/input/?i=sum((2%5En)*7%2F100%5En)+from+n%3D1
Mindless_Insanity ยท 2 points ยท Posted at 22:53:30 on May 25, 2016 ยท (Permalink)
It works because 7*24 is 112, so the 1 in the hundreds place carries and adds to 56. What I didn't know is that there were other numbers that produce this pattern too. I wonder if there are infinitely many? Are they all primes?
MoralisticCommunist ยท 3 points ยท Posted at 15:05:03 on May 25, 2016 ยท (Permalink)
That is actually really cool!
TheBoldManLaughsOnce ยท 3 points ยท Posted at 17:19:31 on May 25, 2016 ยท (Permalink)
I used to teach commodities options trading in a trading pit to grad students. On day 1 I would have them memorize all the decimal equivalents of fractions from 1/2 to 1/16 (skipping 1/13 and 1/15 because they end up being fairly useless if you know everything else. It's a lot of fun to see someone who's lived a lot of life and studied a lot of math realize how powerful knowing these simple fractions are for estimating quantities on the fly.
One thing to add: 1/14th is just 1/2 of 1/7th, and since it doubles with every pair... 1/14th = .072856(rounding down to make a point here)
Gelnef ยท 1 points ยท Posted at 20:59:55 on May 25, 2016 ยท (Permalink)
If I was to teach math in school I'd make the kids learn decimal approximations like this. I keep them memorized as approximate factors of 100 or 1000, with two digit accuracy. And no, don't skip 1/13 (roughly 77) and 1/15 (a third of a fifth, roughly 67)! So, the list goes:
1/2 50 1/3 33 1/4 25 1/5 20 1/6 17 1/7 14 1/8 125 1/9 11 1/10 10 1/11 91 1/12 83 1/13 77 1/14 73 1/15 67 1/16 63
lastpulley ยท 2 points ยท Posted at 17:52:14 on May 25, 2016 ยท (Permalink)
I'm pretty sure 5/7 = 100%
BCM_00 ยท 2 points ยท Posted at 18:58:03 on May 25, 2016 ยท (Permalink)
It bothers me that it's not .142856...
It would have been so convenient.
bison142857 ยท 2 points ยท Posted at 12:17:49 on May 26, 2016 ยท (Permalink)
cool. my username is based on this fact.
jorellh ยท 1 points ยท Posted at 15:02:44 on May 25, 2016 ยท (Permalink)
I don't like 1/7, it is the first "ugly" fraction to me in base 10
JJean1 ยท 1 points ยท Posted at 16:03:21 on May 25, 2016 ยท (Permalink)
But this fact should make it "not ugly". The first one I don't ever bother learning any decimal places for is 1/13. Even 1/11 has the nice form 0.09090909090909...
jorellh ยท 1 points ยท Posted at 16:47:18 on May 25, 2016 ยท (Permalink)
It gives the impression that nine of the numbers quite fit in so it keeps cycling the pattern. Almost ad if it would be nice in base 9
pnasmaster ยท 1 points ยท Posted at 15:46:40 on May 25, 2016 ยท (Permalink)
This won't be the same in other numbering systems.
deusnefum ยท 2 points ยท Posted at 17:32:12 on May 25, 2016 ยท (Permalink)
It is actually, the rule is just divide by n-1 where n is your base.
So in hexadecimal, 0xA / 0xF = 0.AAAAA...
dingboodle ยท 1 points ยท Posted at 15:58:47 on May 25, 2016 ยท (Permalink)
Holy cow! That's really cool, but how did anyone ever notice this in the first place? Was there just some guy dividing everything by 7 one day and was going over his answers and was like "waaaait a minute..."? I would never have spotted that.
NoRodent ยท 2 points ยท Posted at 19:16:57 on May 25, 2016 ยท (Permalink)
That's actually exactly how I noticed this. Probably when I was in high school or even in late elementary school. If you use a calculator a lot, it's not that hard to spot it.
JJean1 ยท 1 points ยท Posted at 16:00:30 on May 25, 2016 ยท (Permalink)
I am a math instructor and I love using this in the few instances it comes up. Students are always amazed that I can instantly write down a lot of decimal places, but, unfortunately, they do not seem to care when I try to show them what I did. They just ask "Can't we just use the calculator?".
Shotgun_squirtle ยท 1 points ยท Posted at 16:37:09 on May 25, 2016 ยท (Permalink)
Divide 7 or its multiples end up with an integer, actually if you divide any number by anything buts its multiples you end up without an integer. In fact the exact same fact happens of 3, 9, 11, but they just have a much shorter string (1 for 3 and 9, 2 for 11)
mitchmatch1 ยท 1 points ยท Posted at 16:52:12 on May 25, 2016 ยท (Permalink)
What the shit
Asking77 ยท 1 points ยท Posted at 16:55:01 on May 25, 2016 ยท (Permalink)
Weird, that number contains no single digit multiples of 3.
xmastreee ยท 1 points ยท Posted at 18:47:31 on May 25, 2016 ยท (Permalink)
3, 6, or 9. And they're related to each other.
NotAnotherBlackGuy ยท 1 points ยท Posted at 17:12:24 on May 25, 2016 ยท (Permalink)
I actually found this out myself when having sex because I do math to last longer in the sack. The harder the math the more you have to focus on it and the longer you last.
I started doing shit with sevens because I already got bored with primes, and powers of 2.
brianbrianbrian ยท 1 points ยท Posted at 17:19:40 on May 25, 2016 ยท (Permalink)
My brain just popped a boner. Neat.
knightcrusader ยท 1 points ยท Posted at 17:37:01 on May 25, 2016 ยท (Permalink)
I think this is my favorite one cause its so easy (for me) to remember to do in my head despite looking difficult to normal people.
PSi_Terran ยท 1 points ยท Posted at 17:38:56 on May 25, 2016 ยท (Permalink)
This is true for all decimals. Well, not quite. Rational decimals will either:
a) Stop. e.g. 1/10.
b) Repeat the same number for ever. e.g. 1/3 (which is basically a cycle of length 1).
c) Form a cycle. e.g. 1/7.
Think about doing long division. Either you end up with a perfect remainder and stop OR at some point you'll have to do a division you've done already and the pattern will repeat from there. The length of the repeating string cannot be more than the value of the number. I.e. 1/7 must have a repeating string of length 6 or less.
g_h_j ยท 1 points ยท Posted at 17:46:00 on May 25, 2016 ยท (Permalink)
Hey! Hush hush! Dividing things by 7 in my head is my party trick, you're ruining things. For me and my obviously cool parties...
Outstando ยท 1 points ยท Posted at 18:07:50 on May 25, 2016 ยท (Permalink)
I figured this out when I was 7, messing around with my dad's calculator. And the next year I was looking at a map and announced to my 3rd grade class that South America and Africa used to be joined.
It's all gone downhill from there.
Qscfr ยท 1 points ยท Posted at 18:28:33 on May 25, 2016 ยท (Permalink)
How does this not apply to 5 for example?
1/ 5 = .2 2 / 5 = .4
It's a cycle of .2
TheMusicArchivist ยท 1 points ยท Posted at 18:28:51 on May 25, 2016 ยท (Permalink)
I raced someone on a calculator to find 300/7 in my head once. I knew this fact, that 1/7 was .14285xxxx, and multiplied by 100 and then by 3. Was wrong on the 4th or 5th decimal point but got the approximate-enough answer in the same time. Had I known 3/7 was .428571 I would have been even quicker. So, TIL.
critic2029 ยท 1 points ยท Posted at 18:37:06 on May 25, 2016 ยท (Permalink)
This is a common thing tested on GMAT and GRE.
joeydee93 ยท 1 points ยท Posted at 18:50:46 on May 25, 2016 ยท (Permalink)
Only in base 10. Different bases have different cycle numbers
EAVBERBWF ยท 1 points ยท Posted at 20:01:37 on May 25, 2016 ยท (Permalink)*
not always true
pi/7=0.44879895051...
6.6/7=0.94285714285
maybe if you divide any integer by 7? though any rational divided by 7 does eventually produce the sequence
DalkerKD ยท 1 points ยท Posted at 20:02:20 on May 25, 2016 ยท (Permalink)
also 1/983 has a repeating cycle that is 982 digits long...
hot_exhaust ยท 1 points ยท Posted at 20:16:09 on May 25, 2016 ยท (Permalink)
So, 5/7 with rice?
KamiKagutsuchi ยท 1 points ยท Posted at 20:23:46 on May 25, 2016 ยท (Permalink)
The pedantic version:
If you divide any non-zero, natural number, that does not have 7 as a factor, in base 10, by 7, you end up with the sequence 142857 recurring.
ilambiquated ยท 1 points ยท Posted at 22:11:36 on May 25, 2016 ยท (Permalink)
also :
cynoclast ยท 1 points ยท Posted at 22:12:10 on May 25, 2016 ยท (Permalink)
This is an artifact of the base 10 number system more than anything.
SergeantGrumblz ยท 1 points ยท Posted at 23:06:04 on May 25, 2016 ยท (Permalink)
figured this out doodling on paper in high school, thought it was awesome.
prufrock2015 ยท 1 points ยท Posted at 23:17:55 on May 25, 2016 ยท (Permalink)
There're many other numbers like that. This is the premise of Project Euler #26, Reciprocal Cycles. https://projecteuler.net/problem=26
I still could only 66.67% it on Hackerrank https://www.hackerrank.com/contests/projecteuler/challenges/euler026/submissions because my Python solution keeps timing out...
agumonkey ยท 1 points ยท Posted at 23:25:25 on May 25, 2016 ยท (Permalink)
Nice zig zagging offset too.
ashessnow ยท 1 points ยท Posted at 00:41:37 on May 26, 2016 ยท (Permalink)
I remember noticing this as a kid!
santaliqueur ยท 1 points ยท Posted at 00:53:03 on May 26, 2016 ยท (Permalink)
I remember being a lonely 7 year old kid with a calculator and figuring that out myself. Tried to tell my friends and teacher. Whoever understood it wasn't impressed.
YLXV ยท 1 points ยท Posted at 03:46:07 on May 26, 2016 ยท (Permalink)
my grade 7 math teacher showed me this one time and it saved me on a university math exam a couple months back
usernumber36 ยท 1 points ยท Posted at 09:08:35 on May 26, 2016 ยท (Permalink)
this makes it REALLY easy to memorise results of dividing anything by 7.
paularkay ยท 1 points ยท Posted at 16:35:15 on May 25, 2016 ยท (Permalink)
7/7=1, he's full of shit, get him.
[deleted] ยท 1 points ยท Posted at 14:01:38 on May 25, 2016 ยท (Permalink)
[deleted]
Steam_MrMoo ยท 1 points ยท Posted at 14:04:28 on May 25, 2016 ยท (Permalink)
If it isn't an integer.
[deleted] ยท 0 points ยท Posted at 14:00:18 on May 25, 2016 ยท (Permalink)
Upvote. You cool. This best one.
herlihyboy ยท 0 points ยท Posted at 14:14:38 on May 25, 2016 ยท (Permalink)
What about 7?
jokul ยท 7 points ยท Posted at 14:31:47 on May 25, 2016 ยท (Permalink)
ultimation ยท 1 points ยท Posted at 14:36:32 on May 25, 2016 ยท (Permalink)
The answer is 1, and therefore an integer.
CupWalletTiger ยท 0 points ยท Posted at 14:32:41 on May 25, 2016 ยท (Permalink)
7/7 = 1
1 is an integer
klparrot ยท 0 points ยท Posted at 16:51:32 on May 25, 2016 ยท (Permalink)
If you divide any integer by 7.
xmastreee ยท 1 points ยท Posted at 18:41:35 on May 25, 2016 ยท (Permalink)*
Well, no. I said "you end up with" the sequence. If you divide a non integer, you get there eventually, after the requisite number of decimal places.
1.25/7 = 0.18142857142857142857
klparrot ยท 1 points ยท Posted at 08:27:10 on May 26, 2016 ยท (Permalink)
Beg to differ. Try it with โ รท 7.
Ekrank ยท -1 points ยท Posted at 15:17:33 on May 25, 2016 ยท (Permalink)
7/7=1
Source: math
magnue ยท -1 points ยท Posted at 15:31:51 on May 25, 2016 ยท (Permalink)
What about 7?
( อกยฐ อส อกยฐ)
brewster_the_rooster ยท -2 points ยท Posted at 15:14:17 on May 25, 2016 ยท (Permalink)
except 7, 14, 21, etc
flammablepenguins ยท 2452 points ยท Posted at 11:48:25 on May 25, 2016 ยท (Permalink)*
Using binary you can count to 31 on one hand 1023 on two. https://en.m.wikipedia.org/wiki/Finger_binary
Edit: Wasn't really expecting this post to get noticed but it pleases me greatly that so many people are holding their phones while putting their fingers in awkward positions, probably in public.
I 19 most of you, the rest can have a heaping helping of 132.
**edit 2: For those complaining about hurt fingers/difficult positions: Really it is just about representation. If you need to know binary 8 or 9, you can visualize it by going left to right and saying " 0 ouch 000 ok that is eight; 0 ouch 00 ouch ok that is nine. " Even if you can't physically make your fingers make the numbers you can easily visualize the values using your hands.
PiperArrow ยท 2170 points ยท Posted at 14:25:40 on May 25, 2016 ยท (Permalink)
Using binary you can count to 11111 on 1 hand and 1111111111 on 10
asparagus_pants ยท 89 points ยท Posted at 15:51:43 on May 25, 2016 ยท (Permalink)
We truely live in a... [puts on sunglasses]... digital world.
titty_pics_plz ยท 2 points ยท Posted at 03:38:41 on May 26, 2016 ยท (Permalink)
Kind of reminds me of the phrase "Digital Rectal Exam"... It sounds super high-tech as if it uses some awesome computer-machine to scan your bowels similar to an MRI or X-Ray...
... nope, not even close.
PM_ME_YOUR_MESMER ยท 1 points ยท Posted at 16:30:02 on May 25, 2016 ยท (Permalink)
Yeeaaaaahhhhhhhhh!
[deleted] ยท -1 points ยท Posted at 17:13:30 on May 25, 2016 ยท (Permalink)
[deleted]
wooq ยท 9 points ยท Posted at 18:27:21 on May 25, 2016 ยท (Permalink)
file:///c|/Users/wooq/Pictures/internet/not%20porn/thatsthejoke.jpg
caustic_kiwi ยท 2 points ยท Posted at 09:48:45 on May 26, 2016 ยท (Permalink)
sudo ./takemetotherealporn.exe
theFunkiestButtLovin ยท 6 points ยท Posted at 17:26:33 on May 25, 2016 ยท (Permalink)
I'm pretty sure /u/asparagus_pants already knows that.
[deleted] ยท 6 points ยท Posted at 18:26:17 on May 25, 2016 ยท (Permalink)
That was quite obviously the joke...
SkyKiwi ยท 59 points ยท Posted at 16:18:19 on May 25, 2016 ยท (Permalink)
There are 10 kinds of people in this world. Those who understand binary, and those who do not.
BubBidderskins ยท 84 points ยท Posted at 17:47:45 on May 25, 2016 ยท (Permalink)
There are 10 kinds of people in this world. Those who understand binary, those who don't, and those who didn't expect this to be a base 3 joke.
Letterpairs ยท 8 points ยท Posted at 18:24:14 on May 25, 2016 ยท (Permalink)
Probably the best version I've seen
jonpearse ยท 5 points ยท Posted at 20:27:54 on May 25, 2016 ยท (Permalink)
Iโm glad Iโm not the only one who loves this variantโฆ
uberguby ยท 1 points ยท Posted at 22:53:37 on May 25, 2016 ยท (Permalink)
This is actually a great joke to get people asking about base numbers, and it gives them a mnemonic if they get the aha moment
Plasma_000 ยท 5 points ยท Posted at 22:12:25 on May 25, 2016 ยท (Permalink)
But the 3rd group is not mutually exclusive :(
caustic_kiwi ยท 3 points ยท Posted at 09:51:38 on May 26, 2016 ยท (Permalink)
There are 10 kinds of people in the world. Those who understand binary, and those who understand ternary, and those who understand quaternary, and those who understand quinary, and those who understand senary, and those who understand octal, and...
Jutanium ยท 1 points ยท Posted at 21:40:00 on May 25, 2016 ยท (Permalink)
Balanced ternary, to be specific!
Pcc210 ยท 1 points ยท Posted at 03:11:12 on May 26, 2016 ยท (Permalink)
Sensible chuckle
PM_ME_BALD_BEAVERS ยท 116 points ยท Posted at 17:15:50 on May 25, 2016 ยท (Permalink)
There are two kinds of people in this world. Those who can extrapolate from incomplete data.
[deleted] ยท 19 points ยท Posted at 17:16:55 on May 25, 2016 ยท (Permalink)
[deleted]
yumyumgivemesome ยท 24 points ยท Posted at 17:45:24 on May 25, 2016 ยท (Permalink)
There are three kinds of people in this world. Those who can count and those who can't.
Thecharrer ยท 26 points ยท Posted at 17:53:50 on May 25, 2016 ยท (Permalink)
There are 10 kinds of people in this world. One group that can understand hexadecimal and F the rest.
uberguby ยท 1 points ยท Posted at 22:51:31 on May 25, 2016 ยท (Permalink)
Wait... Sorry, I know f is 16 but i don't get this
i mean i get "f the rest" but i mean i don't get the math
Icalasari ยท 2 points ยท Posted at 22:56:31 on May 25, 2016 ยท (Permalink)
123456789ABCDEF 10,11,12,13,14,15,16,17,18,19,1A, and so on
Qaysed ยท 2 points ยท Posted at 23:36:59 on May 25, 2016 ยท (Permalink)
Actually, F in hexadecimal is 15 in decimal.
uberguby ยท 1 points ยท Posted at 23:42:17 on May 25, 2016 ยท (Permalink)*
Yup! I learned a lot about hexadecimal today. I wonder if I'll retain it...
Edit: It's been 21 days, which is ancient in internet times on askreddit. I haven't thought about hexadecimal since I wrote this. I retained nothing. But if you found this then you're some kinda weirdo historian who goes through internet comments. Hi! I hope it excites you to be found like this. I hope it's like 120 years later (June 16, 2136 by my calendar) and you can't believe this letter I wrote, apparently to you.
ManPumpkin ยท 2 points ยท Posted at 01:01:06 on May 26, 2016 ยท (Permalink)
I learned it 3 years ago, and it's fucking lingering. Forever.
Obsolescent ยท 2 points ยท Posted at 19:50:12 on May 25, 2016 ยท (Permalink)
PM'd
Player8 ยท 1 points ยท Posted at 21:09:10 on May 25, 2016 ยท (Permalink)
I... I want to see.
Deliphin ยท 2 points ยท Posted at 02:40:25 on May 26, 2016 ยท (Permalink)
...and who else? /s
MacNugget ยท 1 points ยท Posted at 20:08:28 on May 25, 2016 ยท (Permalink)
people who understand hexadecimal are 1 in a
[deleted] ยท 1 points ยท Posted at 21:08:37 on May 25, 2016 ยท (Permalink)
There are 10 kinds of people in this world. Those who understand binary, and those who do not
and those who did not realise this was in base 3
magpie_army ยท 1 points ยท Posted at 11:37:05 on May 26, 2016 ยท (Permalink)
And those who didn't realise the joke was in base-3
noggin-scratcher ยท 5 points ยท Posted at 16:26:29 on May 25, 2016 ยท (Permalink)
To avoid ambiguity absolutely all numbers should be written using base 10, without exception.
(Now you just need to figure out which base I mean)
spartaboy ยท 7 points ยท Posted at 17:47:04 on May 25, 2016 ยท (Permalink)
You mean base 10 because bases are always written in denary, to avoid confusion.
wildcard5 ยท 18 points ยท Posted at 15:14:49 on May 25, 2016 ยท (Permalink)
But I have only two hands.
MarcelRED147 ยท 61 points ยท Posted at 15:33:52 on May 25, 2016 ยท (Permalink)
What's a 'two'?
barbarr ยท 15 points ยท Posted at 15:38:40 on May 25, 2016 ยท (Permalink)
In binary it's not like you're going to lose the word "two"...
bsievers ยท 15 points ยท Posted at 16:13:10 on May 25, 2016 ยท (Permalink)
Yeah, you do. 10 is read as 'ten'.
11111 is read as 'eleven thousand one hundred eleven'. Just like how in DEC you lose A-E from HEX.
Asraelite ยท 9 points ยท Posted at 16:23:39 on May 25, 2016 ยท (Permalink)*
1000000000 is 'billion' which contains 'bi' so I guess that's kinda two.
PM_ME_YOUR_MESMER ยท 6 points ยท Posted at 16:30:47 on May 25, 2016 ยท (Permalink)
Illuminati confirmed?
Dasbeerboots ยท 2 points ยท Posted at 17:24:58 on May 25, 2016 ยท (Permalink)
No, that's trinary.
bsievers ยท 2 points ยท Posted at 16:38:40 on May 25, 2016 ยท (Permalink)
Stop judging it was born that way.
CyclonusRIP ยท 4 points ยท Posted at 19:40:53 on May 25, 2016 ยท (Permalink)
In my experience when saying a number aloud that isn't base 10 you generally just recite the characters followed by whatever base it is in.
For instance 101 in binary would just be read aloud as 'one zero one base two'
phoenixrawr ยท 3 points ยท Posted at 17:30:54 on May 25, 2016 ยท (Permalink)
10 isn't ten in binary, it's just 10. Ten, hundred, thousand, etc are decimal labels. Here's one quick source off of Google.
dryfire ยท 1 points ยท Posted at 21:05:19 on May 25, 2016 ยท (Permalink)
"Lets, see. I get the answer as Dee Thousand Bee hundred Ceety-Eff... base 16 of course"
"Damn... I got Eteen"
Works for me :-)
derangerd ยท 1 points ยท Posted at 20:18:32 on May 25, 2016 ยท (Permalink)
But then it gets inconsistent when you get to 100. What do you call that?
The_Nipple_Tickler ยท 2 points ยท Posted at 15:39:36 on May 25, 2016 ยท (Permalink)
But I only have 00 hands.
mr_ewe ยท 7 points ยท Posted at 16:15:52 on May 25, 2016 ยท (Permalink)
You must be the worst nipple tickler ever with that few hands.
The_Nipple_Tickler ยท 6 points ยท Posted at 17:08:09 on May 25, 2016 ยท (Permalink)
I have other ways ( อกยฐ อส อกยฐ)
PJDubsen ยท 9 points ยท Posted at 16:12:50 on May 25, 2016 ยท (Permalink)
You mean 10 hands?
ShiftySharpe ยท 0 points ยท Posted at 15:24:37 on May 25, 2016 ยท (Permalink)
10 in binary is 1x2+0x1 = 2 in integers
TheBananaMonkey ยท 2 points ยท Posted at 16:40:58 on May 25, 2016 ยท (Permalink)
The base system doesn't effect whether numbers are integers or not. It's 2 in base 3+.
First_Utopian ยท 1 points ยท Posted at 15:51:56 on May 25, 2016 ยท (Permalink)
You mean 2 ha.... I see what you did there.
joeydee93 ยท 1 points ยท Posted at 18:55:13 on May 25, 2016 ยท (Permalink)
I don't not understand this 2 symbol? Is it a type of puntuation?
Mareaux ยท 1 points ยท Posted at 16:48:44 on May 25, 2016 ยท (Permalink)
... that took a while.
dkwangchuck ยท 1 points ยท Posted at 16:55:25 on May 25, 2016 ยท (Permalink)
Using binary, you can count to 101 on one hand and 1010 on two.
The_Ghast_Hunter ยท 1 points ยท Posted at 17:09:08 on May 25, 2016 ยท (Permalink)
I thought you were going in fingers, not hands. Fingers would be 101 fingers to 11111 and 0101 fingers to get to 1111111111
PsychoticLime ยท 1 points ยท Posted at 17:49:21 on May 25, 2016 ยท (Permalink)
Nerdifying an already nerdy habit
[deleted] ยท 1 points ยท Posted at 18:13:12 on May 25, 2016 ยท (Permalink)
I got something different..
One hand : 11111
Ten hands : 11111111111111111111111111111111111111111111111111
DredPRoberts ยท 1 points ยท Posted at 18:43:12 on May 25, 2016 ยท (Permalink)
There are only 10 types of people in the world: those who understand binary, and those who don't.
edit: aw someone beat me to it.
CripzyChiken ยท 1 points ยท Posted at 20:49:40 on May 25, 2016 ยท (Permalink)
how did this not get the gold? This is the correct answer.
d-a-v-e- ยท 1 points ยท Posted at 21:13:53 on May 25, 2016 ยท (Permalink)
I would need 1010 fingers to count to 1111111111
pretentiousRatt ยท 1 points ยท Posted at 01:06:06 on May 26, 2016 ยท (Permalink)
There are 10 types of ppl in the world. 1 that understand binary and 9 that don't. I am in the latter
cartmancakes ยท 1 points ยท Posted at 16:11:12 on May 25, 2016 ยท (Permalink)
There are 10 kinds of people in the world. Those who understand binary, and those who don't.
Primesauce ยท 3 points ยท Posted at 16:30:44 on May 25, 2016 ยท (Permalink)
And those who didn't expect that joke to be in base-3
Pm_me_any_dragon ยท 1 points ยท Posted at 16:58:25 on May 25, 2016 ยท (Permalink)
I personally like to vary that joke by using trinary.
Still gold
TaiserRY ยท 1 points ยท Posted at 17:17:28 on May 25, 2016 ยท (Permalink)
Although the joke sounds better this way, doesn't using 10 require 2 bits and therefore can have 4 different values assugned to types of people :p? (00, 01, 10, 11)
CubicMuffin ยท 2 points ยท Posted at 17:23:32 on May 25, 2016 ยท (Permalink)
But 0b10 is 2...
TaiserRY ยท 1 points ยท Posted at 17:29:55 on May 25, 2016 ยท (Permalink)
That's true haha
Tramsyrev ยท 0 points ยท Posted at 16:53:08 on May 25, 2016 ยท (Permalink)
There are 10 people in the world. Those who understand hexadecimal and f the rest.
kevtastic ยท -1 points ยท Posted at 16:46:24 on May 25, 2016 ยท (Permalink)
hahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha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
HardcoreUranium ยท 407 points ยท Posted at 14:05:38 on May 25, 2016 ยท (Permalink)*
It's all fun and games until you get to 4.
Edit: 4, not 8.
UristMasterRace ยท 37 points ยท Posted at 14:35:48 on May 25, 2016 ยท (Permalink)
losLurkos ยท 5 points ยท Posted at 16:16:56 on May 25, 2016 ยท (Permalink)
18
Snaperkids ยท 2 points ยท Posted at 02:38:59 on May 26, 2016 ยท (Permalink)
Or Five (I count ones on my thumb and move towards the pinkie)
ibn-alfatal ยท 7 points ยท Posted at 14:38:14 on May 25, 2016 ยท (Permalink)
Points middle finger...
AaroniusH ยท 4 points ยท Posted at 17:55:13 on May 25, 2016 ยท (Permalink)
Could be five, depending on how you prefer to flip people off.
gnorty ยท 1 points ยท Posted at 23:50:18 on May 25, 2016 ยท (Permalink)
or 12 if you are British (probably other countries too, but not really USA)
dexr23 ยท 1 points ยท Posted at 16:50:06 on May 25, 2016 ยท (Permalink)
and a binary 4 to you sir.
batnastard ยท 29 points ยท Posted at 15:13:01 on May 25, 2016 ยท (Permalink)
128 is bad too, and 132 is like insult to injury.
[deleted] ยท 1 points ยท Posted at 00:56:23 on May 26, 2016 ยท (Permalink)
Double pump.
HighRelevancy ยท 24 points ยท Posted at 15:18:37 on May 25, 2016 ยท (Permalink)
And then 19 is metal as fuck
AbsolutShite ยท 4 points ยท Posted at 16:27:40 on May 25, 2016 ยท (Permalink)
I like 23. It makes me feel like that Jim Carrey movie was on to something.
ItsComrade ยท 9 points ยท Posted at 18:15:23 on May 25, 2016 ยท (Permalink)
God dammit, I'm just sitting here moving my fingers around trying to figure out this joke.
What am I doing with my life
AbsolutShite ยท 2 points ยท Posted at 18:22:55 on May 25, 2016 ยท (Permalink)
base2(11101) == base10(23)
It's a fingering joke.
ItsComrade ยท 2 points ยท Posted at 18:25:55 on May 25, 2016 ยท (Permalink)
I got it but it took me too long.
Octopoid ยท 1 points ยท Posted at 23:06:39 on May 25, 2016 ยท (Permalink)
I'll go 22, it's much easier on the hand
dydtaylor ยท 1 points ยท Posted at 18:27:49 on May 25, 2016 ยท (Permalink)
18
19 just looks lame
[deleted] ยท 12 points ยท Posted at 14:47:01 on May 25, 2016 ยท (Permalink)
It's a code talk with my workmates. We say "four" spoken to reject a bad idea without the boss suspecting.
donovanBast ยท 10 points ยท Posted at 15:52:03 on May 25, 2016 ยท (Permalink)
So your boss just thinks you're weirdos who say four all the time? Got it.
FirelordPhoenix ยท 5 points ยท Posted at 15:19:03 on May 25, 2016 ยท (Permalink)
I'm more of a 20 guy.
Or maybe 13...
IlikeJG ยท 4 points ยท Posted at 15:17:35 on May 25, 2016 ยท (Permalink)
You mean 100?
CraigKostelecky ยท 2 points ยท Posted at 15:34:46 on May 25, 2016 ยท (Permalink)
๐๐ป
I_cut_my_own_jib ยท 1 points ยท Posted at 15:24:13 on May 25, 2016 ยท (Permalink)
Nah 4 is child's play compared to 132.
zerj ยท 1 points ยท Posted at 15:55:05 on May 25, 2016 ยท (Permalink)
Well 8's inoffensive but somewhat painful for me.
aldesuda ยท 1 points ยท Posted at 16:22:24 on May 25, 2016 ยท (Permalink)
What did you say? 4?! Well, 4 you too!
As a matter of fact, 132 to you!
anodyne_despot ยท 1 points ยท Posted at 16:23:00 on May 25, 2016 ยท (Permalink)
G3Otherm ยท 1 points ยท Posted at 16:31:40 on May 25, 2016 ยท (Permalink)
22... The Shocker
Nerdn1 ยท 1 points ยท Posted at 16:36:04 on May 25, 2016 ยท (Permalink)
That is one flaw of this method of counting I've realized.
JtHa77 ยท 1 points ยท Posted at 16:51:14 on May 25, 2016 ยท (Permalink)
4 you too, asshole!
PM_ME_2DISAGREEWITHU ยท 1 points ยท Posted at 16:52:12 on May 25, 2016 ยท (Permalink)
4 and 68 are my favorite numbers.
[deleted] ยท 1 points ยท Posted at 16:55:30 on May 25, 2016 ยท (Permalink)
[deleted]
gustywinds ยท 1 points ยท Posted at 17:14:14 on May 25, 2016 ยท (Permalink)
This exercise is NSFW.
PaulBGD ยท 1 points ยท Posted at 18:10:48 on May 25, 2016 ยท (Permalink)
Even better, 132!
Hendlton ยท 1 points ยท Posted at 18:22:09 on May 25, 2016 ยท (Permalink)
No, that's when the fun and games start. Well, the fun at least.
pound_sterling ยท 1 points ยท Posted at 19:44:20 on May 25, 2016 ยท (Permalink)
Ha. I didn't clock the joke until I physically went through it.
haavmonkey ยท 1 points ยท Posted at 20:04:17 on May 25, 2016 ยท (Permalink)
Then it gets real serious at 132.
cageyfanboy ยท 1 points ยท Posted at 20:20:11 on May 25, 2016 ยท (Permalink)
Hex 42 - double barrel!
plus it's the answer to the universe. ;)
NotACockroach ยท 1 points ยท Posted at 21:47:56 on May 25, 2016 ยท (Permalink)
Wait until you get to 132
Plsdontreadthis ยท 1 points ยท Posted at 23:54:40 on May 25, 2016 ยท (Permalink)
You can cross your fingers for four.
TheVeryMask ยท 1 points ยท Posted at 01:52:45 on May 26, 2016 ยท (Permalink)
Use the spaces. You do lose one bit by doing this, which turns your hands into hex digits.
0ba78683-dbdd-4a31-a ยท 365 points ยท Posted at 14:05:17 on May 25, 2016 ยท (Permalink)*
Or -512โ511 if you're feeling cocky.
Edit: -512 is the correct lower limit, not -511, as pointed out below.
IAmA_Catgirl_AMA ยท 86 points ยท Posted at 14:42:26 on May 25, 2016 ยท (Permalink)
You can actually count from -512 to 511 that way, unless you need to detect overflow while counting.
Log_Out_Of_Life ยท 6 points ยท Posted at 15:58:09 on May 25, 2016 ยท (Permalink)
Are you really a catgirl? If so pics of you doing math?
moon_potato ยท 2 points ยท Posted at 17:10:31 on May 25, 2016 ยท (Permalink)*
But what about negative zero?
Edit: Yeah, I know how two's complement works. My comment was more joking than serious anyway. The only standard I've seen that uses a signed zero is IEE 754, the most common standard for storing floating-point (real) numbers.
IAmA_Catgirl_AMA ยท 3 points ยท Posted at 17:42:03 on May 25, 2016 ยท (Permalink)
I thought about that when I wrote the comment, but I decided against mentioning it as I reckon it does not widely occur in the field of finger arithmetics. But yes, If you're in a situation where it is useful, its inclusion would also reduce the effective range by one.
[deleted] ยท 1 points ยท Posted at 23:04:47 on May 25, 2016 ยท (Permalink)
If you want to you can count in one's complement or sign and magnitude. But two's complement gives you one more number to work with.
hbgoddard ยท 1 points ยท Posted at 04:41:37 on May 26, 2016 ยท (Permalink)
In two's complement arithmetic, the standard method for binary numbers, 0 and -0 are represented by the same value.
[deleted] ยท 1 points ยท Posted at 17:36:24 on May 25, 2016 ยท (Permalink)
[deleted]
IAmA_Catgirl_AMA ยท 8 points ยท Posted at 17:47:30 on May 25, 2016 ยท (Permalink)
Yes
TaohRihze ยท 103 points ยท Posted at 14:27:48 on May 25, 2016 ยท (Permalink)
I would have thought it was 0 to 2047 if you included it.
Taokan ยท 6 points ยท Posted at 14:43:15 on May 25, 2016 ยท (Permalink)
And that's what happens when you don't use viagra only as directed.
TaohRihze ยท 7 points ยท Posted at 16:06:30 on May 25, 2016 ยท (Permalink)*
Are you saying you need more than 4 hours to count from 1024 to 2047? If so you might need to call a doctor.
super_aardvark ยท 1 points ยท Posted at 21:16:51 on May 25, 2016 ยท (Permalink)
No, I think he takes one every time he needs to flip that bit. Definitely not as directed.
mattenthehat ยท 2 points ยท Posted at 21:27:10 on May 25, 2016 ยท (Permalink)
Pretty sure with Viagra you'll only be counting from 1024 to 2047
SpareLiver ยท 61 points ยท Posted at 14:38:37 on May 25, 2016 ยท (Permalink)
If I'm feeling cocky, one of my hands is busy.
gjoel ยท 6 points ยท Posted at 16:13:59 on May 25, 2016 ยท (Permalink)
If you're feeling cocky you can only count to 31.
SpareLiver ยท 4 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
15 if I want to stick my thumb up my ass, which let's face it, I do.
branIflakes ยท 1 points ยท Posted at 14:57:26 on May 25, 2016 ยท (Permalink)
Cheeky
Project2r ยท 1 points ยท Posted at 15:15:40 on May 25, 2016 ยท (Permalink)
ha. I'd shake your hand, but you know...
VikingCoder ยท 4 points ยท Posted at 14:50:07 on May 25, 2016 ยท (Permalink)
-512 to 511 if you use standard two's compliment. (No repeated zero.)
beaverlyknight ยท 4 points ยท Posted at 15:40:08 on May 25, 2016 ยท (Permalink)
Are hands big endian or little endian? How can this be standardized? I think people will intuitively use big endian, but then there's always going to be "that guy" who wants to use little because that's what x86 uses.
VikingCoder ยท 3 points ยท Posted at 15:59:58 on May 25, 2016 ยท (Permalink)
I fear that righties and lefties will count differently.
Also, do you supinate or pronate your wrists?
And are we really going to be able to express the full bit code? Some of those ring-pinky combinations are a bitch.
Intrexa ยท 2 points ยท Posted at 15:45:55 on May 25, 2016 ยท (Permalink)
I think it's going to be a bit more nuanced than that. I think we can agree that it's a 5 bit byte, with a words size of 2 bytes. Well, start counting on your hands, palms facing towards to you. I personally start on my right hand, and go thumb to pinky, then move to my left hand, and start with my left thumb and work to the left pinky.
So the most significant bit is now in the middle, right next to the least significant digit.
RoadieRich ยท 1 points ยท Posted at 02:23:58 on May 26, 2016 ยท (Permalink)
The LSB would be on the outside, unless your hands are arranged differently to most people.
gsoto ยท 2 points ยท Posted at 16:28:06 on May 25, 2016 ยท (Permalink)
Nice punctuation.
0ba78683-dbdd-4a31-a ยท 2 points ยท Posted at 19:20:37 on May 25, 2016 ยท (Permalink)
Are you congratulating me on my correct usage of an en dash? If so, thanks :)
gsoto ยท 2 points ยท Posted at 21:30:19 on May 25, 2016 ยท (Permalink)
Yes, yes I am :)
redditlovesfish ยท 2 points ยท Posted at 16:40:04 on May 25, 2016 ยท (Permalink)
If you are feeling cocky - you can use your cock as an extra binary digit
0ba78683-dbdd-4a31-a ยท 2 points ยท Posted at 19:21:27 on May 25, 2016 ยท (Permalink)
Good idea, I'm a walking 20-bit signed integer hehe
sensation_ ยท 2 points ยท Posted at 17:40:42 on May 25, 2016 ยท (Permalink)
01000101 01111000 01110000 01101100 01100001 01101110 01100001 01110100 01101001 01101111 01101110 00100000 01101110 01101111 01110100 00100000 01100011 01101100 01100101 01100001 01110010 00100000 01100011 01101111 01100011 01101011 01111001 00100000 01100101 01101110 01101111 01110101 01100111 01101000 00101100 00100000 01100100 01101001 01100011 01101011 00100000 01110011 01110100 01110101 01100011 01101011 00100000 01101001 01101110 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00101110
0ba78683-dbdd-4a31-a ยท 1 points ยท Posted at 19:23:35 on May 25, 2016 ยท (Permalink)
Got your true stuck in a false, eh?
sensation_ ยท 1 points ยท Posted at 19:24:10 on May 25, 2016 ยท (Permalink)
1
trey_at_fehuit ยท 3 points ยท Posted at 14:39:37 on May 25, 2016 ยท (Permalink)
You'd have to since it's signed language.
colakoala200 ยท 1 points ยท Posted at 14:42:41 on May 25, 2016 ยท (Permalink)
If you're doing that, don't you only have one hand free?
arcosapphire ยท 1 points ยท Posted at 15:08:23 on May 25, 2016 ยท (Permalink)
Surely -512 to 511?
green_meklar ยท 1 points ยท Posted at 18:22:46 on May 25, 2016 ยท (Permalink)
Well, only if you're using sign language.
ydoowoody ยท 0 points ยท Posted at 17:41:01 on May 25, 2016 ยท (Permalink)
Or -511 to 511 if you feel like an asshole.
falco_iii ยท 6 points ยท Posted at 15:54:58 on May 25, 2016 ยท (Permalink)
4: Fuck off.
vipros42 ยท 4 points ยท Posted at 14:31:03 on May 25, 2016 ยท (Permalink)
Bah, I knew that someone else must have come up with this, but I hadn't been bothered to check.
Nerdn1 ยท 3 points ยท Posted at 16:38:10 on May 25, 2016 ยท (Permalink)
Yeah I figured it out too, but there is still the issue when you get to 4.
Anrza ยท 2 points ยท Posted at 20:25:52 on May 25, 2016 ยท (Permalink)
128-159 are worse.
[deleted] ยท 3 points ยท Posted at 14:46:59 on May 25, 2016 ยท (Permalink)
It is cool as a self-resort, but if you have to convey the count to a guy across the room he could understand 4 different numbers. FeelsBadMan.
JanitorMaster ยท 4 points ยท Posted at 15:43:34 on May 25, 2016 ยท (Permalink)
Also he gets strangely pissed off if the answer is 4, 128 or 132...
xsailerx ยท 3 points ยท Posted at 15:24:09 on May 25, 2016 ยท (Permalink)
Be careful about counting 4 though
usernamewillendabrup ยท 3 points ยท Posted at 15:37:13 on May 25, 2016 ยท (Permalink)
How the hell does binary work? It looks like a bunch of ones and zeros, how can it mean anything?
SkyKiwi ยท 7 points ยท Posted at 16:24:53 on May 25, 2016 ยท (Permalink)
I don't really know how we manage crazy shit like storing multiple numbers in binary or making computers out of black magic, but a single number out of binary is actually pretty simple. Easiest way to explain is with examples.
Okay, that's fairly simple. Now how do we get a 2? We add another digit. Any digit in the "tens" position counts the amount of "twos" we have.
Excellent! So what's the next number? 4! No, not 24. Just 4. Starting with the ones, each digit is double what the previous was. So the third added digit (the hundreds) is four. The fifth will be eight. So on so on. Using this combination, you can make any number, as 1000000 will always be +1 higher than 0111111 (with as many 0's are 1's, respectively, as each other).
[deleted] ยท 4 points ยท Posted at 16:30:16 on May 25, 2016 ยท (Permalink)*
Not sure if sarcastic or not, but it's just in base two, so I'll try to explain.
The first digit, furthest to the right, has a value of 1. If it is 1, then you add 1 to the total. If 0, you add nothing.
Each place value is a power of two, so: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. 2048, 4096, 8192, ect.
I like to think of it as a sort of 'gate' system, so to speak, and when counting, you have to have all precursor fingers up to be able to move onto the next one. When that one goes up, all the previously up go down. Sooo, for example:
00001 = 1
00010 = 2
00011 = 3
00100 = 4
00101 = 5
00110 = 6
00111 = 7
01000 = 8
01001 = 9
01010 = 10
01011 = 11
01100 = 12
01101 = 13
01110 = 14
01111 =15
10000 = 16
Tah-dah. \o\
Sorry for such a long comment.
Edit for values because yeah.
Nerdn1 ยท 2 points ยท Posted at 17:00:17 on May 25, 2016 ยท (Permalink)*
Think of it like "normal" decimal numbers, but you only have "0" and "1" digits. So you count 1, then when you add another, you can't use the digit "2", so you go to the next digit over which in binary is the 2's place (whereas it would be the 10's place in decimal). So two would be written 10 in binary. You go from there with each place to the left of being 2 times the value of the last (just like each place to the left in a decimal number is 10 times the last). So counting in binary works like this:
Binary: decimal ("normal")
0: 0
1: 1
10: 2
11: 3
100: 4
101: 5
110: 6
111: 7
1000: 8
1001: 9
1010: 10
We found that the easiest way to make compact memory is to store it in units that can be either ON or OFF, which we'll call 1 for ON and 0 for OFF. Since we're limited to 1s and 0s, binary is best way to store numbers.
While computers only store 0s and 1s, the hardware is designed to interpret those 0s and 1s as instructions and data. Normally you store instructions that tells the hardware what to do with the data and where it is. Depending on the instructions, a series of 1s and 0s could be interpretted as a number, a character, another instruction, a pixel in an image, or anything else on your computer.
Anthro_Fascist ยท 1 points ยท Posted at 20:49:11 on May 25, 2016 ยท (Permalink)
Look at it like this. Imagine in base 10, you have a line of zeros. I'll just demonstrate using 5 of them (or 1001 in binary!).
Imagine the numbers 10000,1000,100,10, 1 underneath each zero from left to right. To generalize, for radix (number base) b, each subsequent zero represents bn-1. So ten thousand is 104, one thousand 103, one hundred 102, ten 101, and one 100. Two facts that will stay the same no matter what radix you're in. The very first placement (the far right zero) will always be one, because b0 = 1. The one right next to it will always represent the base because b1 =b. And since this is base 10, there are 10 discrete values any placement can take: the numbers 0-9.
For example, let's have a number: 28495. Each discrete value represents value*placement. Then we add all the numbers together to get the final answer. Visualizing it looks like this:
Knowing this, let's apply it to binary. Imagine that line of zeroes again, except have the powers of two underneath them. So 16, 8, 4, 2, 1. Since binary is base-2, there are only two discrete values a placement can take: 0 and 1. Imagine the number 10100 in binary. Again, visualizing value*placement, we get:
Adding it together, we get the number 20!
occam7 ยท 5 points ยท Posted at 13:55:27 on May 25, 2016 ยท (Permalink)
132
rambi2222 ยท 2 points ยท Posted at 14:48:55 on May 25, 2016 ยท (Permalink)
I just counted to 31 with no knowledge of binary! Awesome. Probably a good way to demonstrate how useful binary is to someone for computers if they don't understand it.
Nerdn1 ยท 2 points ยท Posted at 16:47:49 on May 25, 2016 ยท (Permalink)
I can see this now. Telling a class that computer memory units can only be on and off. Think of them as your fingers being up or down (we'll take out the thumbs because we tend to arbitrarily group the bits into sets of 8). We tend to just count the number of fingers, but that will only get us 0-8.
That does something, but we can do better. Hey look, we can look at the POSITIONS of the fingers and each can be up or down, sort of like "normal" decimal numbers. Oh well, we only have up and not up. Let's give it a try anyway, and have down be 0 and up be 1. So we can only count to 1, before having to shift over, so the 2nd place over is the 2s place rather than the tens place. We can just keep doing this (please just do 4 in your heads, okay kids). You'll find that with just 4 fingers, we can get 0-15, almost double what we did with 8 fingers previously. With 8 fingers we can get 255. Now THAT is what I'm talking about!
CHE6yp ยท 2 points ยท Posted at 15:00:51 on May 25, 2016 ยท (Permalink)
There is a page about it? I used to do this sometimes to let people know how thoughful i am...
Turbojelly ยท 2 points ยท Posted at 16:13:44 on May 25, 2016 ยท (Permalink)
There are 10 types of people in the world. Those that understand binary and those that don't.
loptthetreacherous ยท 2 points ยท Posted at 16:19:43 on May 25, 2016 ยท (Permalink)
An Ancient Roman walks into a bar, holds up 2 fingers and says "5 please". The barman, who is a fan of binary, says "don't you mean 6?".
[deleted] ยท 1 points ยท Posted at 14:45:56 on May 25, 2016 ยท (Permalink)
33 is the both thumbs up age.
Mr_Fuchstrab ยท 2 points ยท Posted at 17:20:18 on May 25, 2016 ยท (Permalink)
Actually, you'd have your right thumb and left pinky up - or left thumb and right pinky - for 33.
513 is both thumbs.
cboski ยท 1 points ยท Posted at 15:22:50 on May 25, 2016 ยท (Permalink)
10
theflyingspaghetti ยท 1 points ยท Posted at 15:38:03 on May 25, 2016 ยท (Permalink)
The only problem with this is now the order matters and the number you see is different than the number the person you are showing it to sees.
shmameron ยท 1 points ยท Posted at 15:38:29 on May 25, 2016 ยท (Permalink)
That's really cool!
[deleted] ยท 1 points ยท Posted at 16:02:22 on May 25, 2016 ยท (Permalink)
There isn't anything special about binary that makes this possible, other than it being simple to represent 0 or 1 by raised or unraised fingers. The real magic is that instead of simply counting raised fingers, you've added the positions of the fingers into consideration. If you also allowed fingers to be half-raised (bent at the second knuckle), you could use ternary and increase your counting to 59,048.
[deleted] ยท 1 points ยท Posted at 16:13:09 on May 25, 2016 ยท (Permalink)
In sign language you can count to like... Whatever you want, man.
Nerdn1 ยท 1 points ยท Posted at 17:07:22 on May 25, 2016 ยท (Permalink)
Each number above a certain point would need multiple signs to express. Finger binary goes higher if you insist that all numbers are static. If we allow more than one hand state for a number we can add an arbitrary number of hands of digits (if we want the start and end to be unambiguous, we could restrict one of the fingers for a start or end flag).
[deleted] ยท 2 points ยท Posted at 17:20:39 on May 25, 2016 ยท (Permalink)
Sign language would still be infinitely more efficient in everyday use.
[deleted] ยท 1 points ยท Posted at 16:17:34 on May 25, 2016 ยท (Permalink)
I can't do this because I can't lift my ring fingers independently.
actual_factual_bear ยท 1 points ยท Posted at 16:30:26 on May 25, 2016 ยท (Permalink)
Oh yeah, well 132!
MindReaver5 ยท 1 points ยท Posted at 16:33:03 on May 25, 2016 ยท (Permalink)
You can count to 999 with one hand in sign language, and all the numbers with 2 hands :P.
Stewbodies ยท 1 points ยท Posted at 16:35:58 on May 25, 2016 ยท (Permalink)
My friend showed me how to do this, eventually I ended up learning the basics. It's super helpful, and it was great for my music theory class when I had to count above 5 often.
DigitalDVD ยท 1 points ยท Posted at 16:36:34 on May 25, 2016 ยท (Permalink)
You can count up to 1024, just assign it to jazz hands.
CanIGetAWotM8 ยท 1 points ยท Posted at 16:36:48 on May 25, 2016 ยท (Permalink)
"Hey, are you flipping me off??"
"No, just counted to 4"
pregnantandsober ยท 1 points ยท Posted at 16:39:54 on May 25, 2016 ยท (Permalink)
19: I love you
6: Peace
17: Hang loose
graaahh ยท 1 points ยท Posted at 16:42:10 on May 25, 2016 ยท (Permalink)*
You can count to 210 on one hand and 223,092,870 on two hands if you number your fingers 1,2,3,5,7,11,13,17,19,23 and count by prime products.
edit: Thought about this with a clearer head and realized I'm dumb. There's no way to count something like 2,048 where you'd have to have 11 2's.
jacob_ewing ยท 1 points ยท Posted at 16:42:48 on May 25, 2016 ยท (Permalink)
1048575 if you use your toes. 2097151 if you're male...
starwobble ยท 1 points ยท Posted at 16:55:54 on May 25, 2016 ยท (Permalink)
I'm a concert violinist. This is how I count measures when resting.
crow1170 ยท 1 points ยท Posted at 17:10:57 on May 25, 2016 ยท (Permalink)
64 and 4096 if you include zeroes and count your wrists.
jewdai ยท 1 points ยท Posted at 17:12:24 on May 25, 2016 ยท (Permalink)
While a smuller number, but easier for beginners to do, you can count to twelve on one hand.
using your thumb as a means of keeping track of where you are, start with the base of your index finger moving upwards count your inner knuckle using your thumb.
It's actually a lot less stressful on your fingers. Think about the number 3 you either hold it by using your thumb, index and middle finger up and the rest down or using your index, middle and ring finger with your thumb holding down your pinky.
wheras using 12 based system you're just holding the "OK" gesture to mean 3.
arbitrageME ยท 1 points ยท Posted at 17:17:29 on May 25, 2016 ยท (Permalink)
I 17 some of you.
[deleted] ยท 1 points ยท Posted at 17:25:11 on May 25, 2016 ยท (Permalink)
But you can't do it without accidentally flipping off your math teacher.
oditogre ยท 1 points ยท Posted at 17:35:44 on May 25, 2016 ยท (Permalink)
Thumb - - Ring Pinky...is it some kind of bird maybe?
*ETA: Just looked at the wiki. I was doing it palm facing away, heh. I get it now. :)
Wilhelm_Amenbreak ยท 1 points ยท Posted at 17:36:08 on May 25, 2016 ยท (Permalink)
I believed I have just flashed a gang sign at someone and made him very angry.
SuchCoolBrandon ยท 1 points ยท Posted at 17:38:52 on May 25, 2016 ยท (Permalink)
This works well for 20 Questions.
sign_on_the_window ยท 1 points ยท Posted at 17:44:47 on May 25, 2016 ยท (Permalink)
but how can I get my ring and index finger up without raising my pinky?
Keden16 ยท 1 points ยท Posted at 17:54:49 on May 25, 2016 ยท (Permalink)
Honestly expected a page called "Finger Binary" to be about something entirely different... TIL.
IGotSkills ยท 1 points ยท Posted at 17:56:28 on May 25, 2016 ยท (Permalink)
ha, this brings a new meaning to the number 4 if you start with your thumb.
4!!!!!!!!!!!!!!!!!!!!
AuspiciousValerian ยท 1 points ยท Posted at 17:57:00 on May 25, 2016 ยท (Permalink)
Its really awesome how simple yet effective binaries are. I wonder if children who were taught to count this way on their hands would have been better at mathematics. Like, they would still use the HinduโArabic numeral system as a main, but would count on their hands with the binary numeral system.
redsoxnets5 ยท 1 points ยท Posted at 18:09:54 on May 25, 2016 ยท (Permalink)
I got to 11 and felt rude. 27 too.
RarestarGarden ยท 1 points ยท Posted at 18:25:33 on May 25, 2016 ยท (Permalink)
I once counted all the way 1023 on my hands in binary. I was very bored.
ashuto0sh ยท 1 points ยท Posted at 18:37:20 on May 25, 2016 ยท (Permalink)
I stopped after I had counted till ..!..
imgonnacallyouretard ยท 1 points ยท Posted at 18:40:03 on May 25, 2016 ยท (Permalink)
If you can accurately hold your fingers half bent, you can then count in ternay and count to 242 on one hand or 59048 on two hands
Sheriff_K ยท 1 points ยท Posted at 18:53:17 on May 25, 2016 ยท (Permalink)
I actually do that sometimes when I need to count numbers greater than 10 and don't have a paper or phone or computer "handy."
I guess I'm a nerd.
rkain101 ยท 1 points ยท Posted at 18:55:41 on May 25, 2016 ยท (Permalink)
For years, I had a nervous habit of counting to 32 on my right hand (In a fidgety kind of way). But somehow, it never occurred to me to extend it onto my other hand.
KickassMcFuckyeah ยท 1 points ยท Posted at 19:02:06 on May 25, 2016 ยท (Permalink)
But what if you use your 10 toes and your pennis too?
Porridgeandpeas ยท 1 points ยท Posted at 23:49:59 on May 25, 2016 ยท (Permalink)
Pennies or penis?
x_Sinister_x ยท 1 points ยท Posted at 19:31:21 on May 25, 2016 ยท (Permalink)
I just learned to steer with my palm.
melikeybouncy ยท 1 points ยท Posted at 19:43:03 on May 25, 2016 ยท (Permalink)
That's worthy of a 513
EDIT: I'm sitting at my desk throwing up the nerdiest gang signs ever.
timmymac ยท 1 points ยท Posted at 19:48:58 on May 25, 2016 ยท (Permalink)
There are 10 types of people in the world. Those that understand binary and those that don't.
Anthro_Fascist ยท 1 points ยท Posted at 20:17:46 on May 25, 2016 ยท (Permalink)
If you count in ternary (base-3), you can count up to 242 on one hand and up to 59048 on both.
Better yet, you can count up to 1048575 on one hand and up to 1.0995116278ร1012 on both if you count in hexadecimal.
To generalize, for counting base b, you can count up to b5 -1 on one hand and b10 -1 on two.
ActualNameIsLana ยท 1 points ยท Posted at 21:03:43 on May 25, 2016 ยท (Permalink)
Well, 4 you too!
[deleted] ยท 1 points ยท Posted at 21:07:37 on May 25, 2016 ยท (Permalink)
I didn't know this was a real thing! I 'invented' it when I was a kid (probably 5-8 years old, not sure); I didn't know what binary was, but I used two positions (up and down) of the finger to count to large numbers when I couldn't sleep :) So glad it's been named!
BipedSnowman ยท 1 points ยท Posted at 21:10:42 on May 25, 2016 ยท (Permalink)
This is how I normally count on my hands!
UnfortunatelyEvil ยท 1 points ยท Posted at 21:11:30 on May 25, 2016 ยท (Permalink)
This is how I count things (that take time and distraction between items). Though, I push my fingers for 1 into my palm and let the 0 fingers relax, so that no rude gestures are formed.
Coffee-Anon ยท 1 points ยท Posted at 21:11:35 on May 25, 2016 ยท (Permalink)*
Fun fact: counting this way, 4 is a middle finger, 132 is double middle fingers
Edit: and 23 is the Shocker!
Edit 2: 17 is "hang ten", 18 is "rock n roll!", 19 is "I love you"
White_Lupin ยท 1 points ยท Posted at 21:23:03 on May 25, 2016 ยท (Permalink)
My dad taught me this when I was pretty young. I've actually ended up using this in math class.
[deleted] ยท 1 points ยท Posted at 21:43:20 on May 25, 2016 ยท (Permalink)
You could count even higher in ternary, where retracted is 0, extended is 2 and inbetween is 1. Gets a little difficult with your ring fingers though.
jay314271 ยท 1 points ยท Posted at 21:49:21 on May 25, 2016 ยท (Permalink)
Hey, there's 10 kinds of people in the world...
flammablepenguins ยท 1 points ยท Posted at 23:58:23 on May 25, 2016 ยท (Permalink)
Those who know binary and those who don't.
Arch_itect ยท 1 points ยท Posted at 22:16:02 on May 25, 2016 ยท (Permalink)
Binary digits :D
G_F_X ยท 1 points ยท Posted at 22:17:15 on May 25, 2016 ยท (Permalink)
How the fuk do i do 9 though...
I cant hands.
flammablepenguins ยท 1 points ยท Posted at 23:57:25 on May 25, 2016 ยท (Permalink)
Ring finger and thumb. If you can't hands it, imagine it.
G_F_X ยท 1 points ยท Posted at 02:25:07 on May 26, 2016 ยท (Permalink)
i just cant have my ring finger up without my pinky also being up. need to hold it down with my thumb
JamesEarlDavyJones ยท 1 points ยท Posted at 23:12:59 on May 25, 2016 ยท (Permalink)
I once sat on the steps out by the quad in college and made it all the way to 1023. It took me almost half an hour, and I'm pretty sure some people thought I was crazy.
Charlie24601 ยท 1 points ยท Posted at 23:24:02 on May 25, 2016 ยท (Permalink)
I'm partial to giving 22 myself.
nstablen ยท 1 points ยท Posted at 23:29:15 on May 25, 2016 ยท (Permalink)
You said you 19 most of us. That's ASL for love. Do you happen to know ASL or is that handshape actually just common knowledge? ASL is what I've always used to count on one hand.
Edit: I've completely forgotten that's also like a "rock on" symbol. Never mind, I'm dumb.
flammablepenguins ยท 2 points ยท Posted at 23:54:21 on May 25, 2016 ยท (Permalink)
Lol, no worries. I actually do know ASL and that is what I meant ; )
orcscorper ยท 1 points ยท Posted at 23:31:49 on May 25, 2016 ยท (Permalink)
I tried to count binary on my fingers, but it was so painful. Trying to hold up my left pinky and middle finger, and my right pointer and ring finger at the same time strained my tendons. It works better touching a table with a finger for 1 and raising the finger for 0.
It's easier to keep track of numbers up to 100. Left hand fingers are 1 each, the thumb is 5. Right hand is 10 for each finger, and 50 for the thumb. It works like Roman numerals; you can even draw I I I I V & L X X X X on your fingernails.
killgore25 ยท 1 points ยท Posted at 00:10:52 on May 26, 2016 ยท (Permalink)
The coolest one so far.
flammablepenguins ยท 2 points ยท Posted at 03:04:48 on May 26, 2016 ยท (Permalink)
Thanks!
barbecue_invader ยท 1 points ยท Posted at 00:25:21 on May 26, 2016 ยท (Permalink)
Even if you don't count using your thumbs you can still go up to Fleventy Ef.
Cgrimsl1 ยท 1 points ยท Posted at 01:42:38 on May 26, 2016 ยท (Permalink)
I spent far too long figuring out 19 and 132, bravo!
[deleted] ยท 1 points ยท Posted at 02:43:27 on May 26, 2016 ยท (Permalink)
17.... The number of the beast.
Tsunoba ยท 1 points ยท Posted at 03:21:15 on May 26, 2016 ยท (Permalink)
How are you doing 8-15? I don't know about you, but I can't hold up my ring finger without my pinky as well.
flammablepenguins ยท 1 points ยท Posted at 04:10:56 on May 26, 2016 ยท (Permalink)
Really it is just about representation. If you need to know binary 8 or 9, you can visualize it by going left to right and saying " 0 ouch 000 eight; 0 ouch 00 ouch nine. " Even if you can't physically make your fingers make the numbers you can easily visualize the values using your hands.
Tsunoba ยท 1 points ยท Posted at 04:15:30 on May 26, 2016 ยท (Permalink)
I was actually wondering about the purely physical aspect of it, since I'm perfectly find with representing it another way.
ktkps ยท 1 points ยท Posted at 05:00:57 on May 26, 2016 ยท (Permalink)
the wizard of 0s1s
boarhog ยท 1 points ยท Posted at 08:47:50 on May 26, 2016 ยท (Permalink)
You can count to 243 on one hand using finger ternary
kdsl2 ยท 1 points ยท Posted at 12:03:04 on May 26, 2016 ยท (Permalink)
If you use base 3 on your fingers you can get to 242 on one hand and 59048 on 2. It requires having a midway position between up and down, it is very difficult to do without the help of a prop such as a steering wheel or handle bar though.
Tm1337 ยท 1 points ยท Posted at 13:05:22 on May 26, 2016 ยท (Permalink)
Using decimal you can count to 10000000000 (10 ^ 10) with both hands.
At this point you should also see a doctor.
plinsdad ยท 0 points ยท Posted at 15:32:59 on May 25, 2016 ยท (Permalink)
If the lord hadn't intended us to count in units of k he wouldn't have given us ten fingers.
XxMONKABONKAxX ยท 1 points ยท Posted at 18:18:26 on May 25, 2016 ยท (Permalink)
4
[deleted] ยท 1461 points ยท Posted at 11:11:37 on May 25, 2016 ยท (Permalink)
There's no practical reason to memorize more than 39 digits of pi
jallenrt ยท 1110 points ยท Posted at 14:36:10 on May 25, 2016 ยท (Permalink)
No, no, no, you need to memorize more in order to impress girls! Hello...
Thud ยท 913 points ยท Posted at 16:39:28 on May 25, 2016 ยท (Permalink)
Technically you just need to memorize 1 more digit than the girl already knows. Then just recite random digits because who is going to check you?
[deleted] ยท 154 points ยท Posted at 16:55:39 on May 25, 2016 ยท (Permalink)*
[removed]
Thud ยท 146 points ยท Posted at 17:12:54 on May 25, 2016 ยท (Permalink)
Source: I'm married to a girl who knows the first two digits of pi.
MrPokemon ยท 128 points ยท Posted at 18:10:27 on May 25, 2016 ยท (Permalink)
Just 3.1? I thought standard was at least 3.14.
_JustAnAwfulPerson ยท 188 points ยท Posted at 18:20:13 on May 25, 2016 ยท (Permalink)
No one said she was a bright one
011010110 ยท 15 points ยท Posted at 20:54:29 on May 25, 2016 ยท (Permalink)*
You chose a dvd for tonight
Thud ยท 4 points ยท Posted at 21:04:16 on May 25, 2016 ยท (Permalink)
It's 3 or so.
AwesomeAutumns ยท 2 points ยท Posted at 23:47:30 on May 25, 2016 ยท (Permalink)
I can go up to 3.14159
CookieTheSlayer ยท 2 points ยท Posted at 06:31:21 on May 26, 2016 ยท (Permalink)
3.14159265357859274483837539275759937375929377429
I may have utilised the trick at some point
AwesomeAutumns ยท 2 points ยท Posted at 06:54:19 on May 26, 2016 ยท (Permalink)
Tell me about this trick...
CookieTheSlayer ยท 3 points ยท Posted at 07:36:38 on May 26, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j93vm
AwesomeAutumns ยท 2 points ยท Posted at 09:30:56 on May 26, 2016 ยท (Permalink)
Sure worked on me damnit
New__Math ยท 4 points ยท Posted at 22:26:18 on May 25, 2016 ยท (Permalink)
is she a physicist cause I've heard pi is ~5
meneldal2 ยท 3 points ยท Posted at 01:25:47 on May 26, 2016 ยท (Permalink)
In engineering pi is 3, and pi2 is 10.
[deleted] ยท 2 points ยท Posted at 06:36:32 on May 26, 2016 ยท (Permalink)
I did it, added on six digits to what I knew, completely at random. They turned out to be correct, I still remember it. 3.141592653589
PsychoticLime ยท 27 points ยท Posted at 17:52:34 on May 25, 2016 ยท (Permalink)
But how do you know how much digits the girl knows? What if she, too, starts saying random digits to impress you? Then you'd be locked in an endless spiral of meaningless digits. Too messy, dude, better impress her telling her that you know the last digit of pi
zanderkerbal ยท 28 points ยท Posted at 18:16:01 on May 25, 2016 ยท (Permalink)
1 in 10 chance of being correct.
blah_blah_blahblah ยท 15 points ยท Posted at 19:16:05 on May 25, 2016 ยท (Permalink)
1 in 9 because it cannot be zero. Unless he tells her it is zero.
zanderkerbal ยท 3 points ยท Posted at 19:49:40 on May 25, 2016 ยท (Permalink)
Right. Any unknown digit other than the last one could be 0.
joblessthehutt ยท 1 points ยท Posted at 20:23:29 on May 25, 2016 ยท (Permalink)
But wouldn't it have to be zero?
NotLawrence ยท 8 points ยท Posted at 18:40:59 on May 25, 2016 ยท (Permalink)
what if the last digit of pi is pi?
pielover88888 ยท 7 points ยท Posted at 18:46:04 on May 25, 2016 ยท (Permalink)
Pi is not a digit! Trust me, I have my ways of knowing relevant username
Thud ยท 1 points ยท Posted at 21:10:20 on May 25, 2016 ยท (Permalink)
Actually it just loops back around to the beginning.
[deleted] ยท 8 points ยท Posted at 17:42:23 on May 25, 2016 ยท (Permalink)
This guy fucks
Thud ยท 2 points ยท Posted at 22:19:35 on May 25, 2016 ยท (Permalink)
With kids to prove it....
MackerLad93 ยท 3 points ยท Posted at 19:15:32 on May 25, 2016 ยท (Permalink)
Or just start somewhere in the middle. Then you're basically always right.
BaddNeighbor ยท 3 points ยท Posted at 19:26:39 on May 25, 2016 ยท (Permalink)
In that case you need to memorize the same amount of digits that she knows.
killycal ยท 2 points ยท Posted at 18:34:38 on May 25, 2016 ยท (Permalink)
Every girl I've ever done this to whips out her calculator.
108241 ยท 7 points ยท Posted at 19:20:02 on May 25, 2016 ยท (Permalink)
You should know more than the calculator displays.
TheOldTubaroo ยท 2 points ยท Posted at 19:03:14 on May 25, 2016 ยท (Permalink)
Whenever I recite pi at girls to pull, they always bring out their phones and check online in case I'm lying
kylejamesjohnson9 ยท 2 points ยท Posted at 21:27:44 on May 25, 2016 ยท (Permalink)
Technically, you just need to know as much as her, then make up as much as you want.
lovesyouandhugsyou ยท 1 points ยท Posted at 18:20:09 on May 25, 2016 ยท (Permalink)
She could roll with a pi wingman/lady.
Alarid ยท 1 points ยท Posted at 19:15:50 on May 25, 2016 ยท (Permalink)
No one will check you out after that
108241 ยท 1 points ยท Posted at 19:20:36 on May 25, 2016 ยท (Permalink)
We must hang out in different circles, since I've been checked numerous times.
Birdyer ยท 1 points ยท Posted at 19:52:48 on May 25, 2016 ยท (Permalink)
I would...
ABagOfFritos ยท 1 points ยท Posted at 19:54:35 on May 25, 2016 ยท (Permalink)
This is why I have people bring it up on their phone so they can follow along. I do 50 decimal points currently and plan to eventually recite a few hundred at least.
deusset ยท 1 points ยท Posted at 20:17:52 on May 25, 2016 ยท (Permalink)
Sheldon would.
PotatoMusicBinge ยท 1 points ยท Posted at 20:41:45 on May 25, 2016 ยท (Permalink)
I'd give you gold but I'm going to start using this and I don't want other people knowing about it. Now, please present your arm for a routine dysentery inoculation...
[deleted] ยท 1 points ยท Posted at 21:02:12 on May 25, 2016 ยท (Permalink)
Except, we now live in the age of smartphones and she can check you as you recite
Thud ยท 1 points ยท Posted at 22:12:50 on May 25, 2016 ยท (Permalink)
And that sounds like a fun date!
UnfortunatelyEvil ยท 1 points ยท Posted at 21:14:28 on May 25, 2016 ยท (Permalink)
Do you know how hard it is to say a bunch of random digits without sounding totally fake?
And yes, technically an infinite sequence of 0's is a random sequence, but nobody is going to believe you when you always pick the girl 'randomly'.
Jutanium ยท 1 points ยท Posted at 21:37:10 on May 25, 2016 ยท (Permalink)
Actually, it's impossible for most people to recite convincingly random numbers quickly. Try it out! I always end up stumbling or repeating a cycle of numbers.
Thud ยท 1 points ยท Posted at 22:14:00 on May 25, 2016 ยท (Permalink)
True, and I end up accidentally reciting the digits of e.
ForceBlade ยท 1 points ยท Posted at 22:20:42 on May 25, 2016 ยท (Permalink)
Any computer even a phone is capable of find out out pretty fast. Not to mention we already have lots of them figured out online
Nerdybeast ยท 1 points ยท Posted at 22:36:35 on May 25, 2016 ยท (Permalink)
Have you tried doing that? Whenever I'm reciting pi and people say I could just be saying random numbers, so I challenge them to try that. It's really hard to come up with random numbers that quickly without repeating a number or a string of numbers. Of course, it's possible, but if the person is reciting what they know really quickly, then getting into random numbers will drastically throw off the rhythm/speed.
unimatrix_0 ยท 1 points ยท Posted at 22:45:05 on May 25, 2016 ยท (Permalink)
so, 4 digits of pi?
Mindless_Insanity ยท 1 points ยท Posted at 22:55:51 on May 25, 2016 ยท (Permalink)
Scandalous
FancyAssortedCashews ยท 1 points ยท Posted at 23:10:38 on May 25, 2016 ยท (Permalink)
Technically you just need to memorize
1 more digit thanas many digits as the girl already knows. Then just recite random digits because who is going to check you?shadowman1138 ยท 1 points ยท Posted at 23:26:30 on May 25, 2016 ยท (Permalink)
It's pretty much impossible to make up random digits on the fly. I alway trip up really quickly or start repeating the same sequence. It makes it pretty easy to tell if someone has it memorized as they can recite what are clearly non-repeating numbers quickly. I could probably get away with making up a couple extra, but it would become noticeable very quickly.
alien122 ยท 1 points ยท Posted at 23:43:43 on May 25, 2016 ยท (Permalink)
and if a certain conjecture is proved you can recite digits at random and still be correct!
xenonpulse ยท 1 points ยท Posted at 00:36:48 on May 26, 2016 ยท (Permalink)
Why one more? Once you say every digit she knows, you can start making them up.
Thud ยท 1 points ยท Posted at 01:16:37 on May 26, 2016 ยท (Permalink)
Because that would feel like cheating.
eltoro ยท 1 points ยท Posted at 01:05:10 on May 26, 2016 ยท (Permalink)
Just scan the room for Matt Damon first, then proceed as normal.
xereeto ยท 1 points ยท Posted at 01:24:25 on May 26, 2016 ยท (Permalink)
Why one more digit? Why not just exactly the number of digits she knows and then make up random shit?
Noremac812 ยท 1 points ยท Posted at 01:59:35 on May 26, 2016 ยท (Permalink)
It's very hard to do a sequence that even sounds random. Our minds just can't do that
jeaguilar ยท 1 points ยท Posted at 02:03:25 on May 26, 2016 ยท (Permalink)
I can recite an infinite sequence of the digits of pi. I'm just not sure where in pi they start.
Deliphin ยท 1 points ยท Posted at 02:41:54 on May 26, 2016 ยท (Permalink)
Thats why you memorize to 101, because everyone else stops at 100.
iloveapple314159 ยท 0 points ยท Posted at 19:14:11 on May 25, 2016 ยท (Permalink)
Female here and I know the first 8 digits, sucks to be the guy trying to impress me.
[deleted] ยท 2 points ยท Posted at 21:15:26 on May 25, 2016 ยท (Permalink)
3.14159265358
iloveapple314159 ยท 1 points ยท Posted at 21:35:51 on May 25, 2016 ยท (Permalink)
Nice ;-)
riyadhelalami ยท 1 points ยท Posted at 19:49:23 on May 25, 2016 ยท (Permalink)
3.1415926535
T_at ยท 3 points ยท Posted at 18:10:48 on May 25, 2016 ยท (Permalink)
Can confirm. Last time I recited pi to only 39 digits, girl told me to fuck off.
Edit : When I challenged her to beat that, she told me to fuck off again. Women, eh? Who can understand them?
green_meklar ยท 3 points ยท Posted at 18:23:55 on May 25, 2016 ยท (Permalink)
I memorized the entire list of Diablo 2 runes and I haven't been able to impress any girls with it...
[deleted] ยท 1 points ยท Posted at 21:25:55 on May 25, 2016 ยท (Permalink)
I'm not a girl, but I'm impressed.
El, Eld, Tir, Nef, Eth...
green_meklar ยท 1 points ยท Posted at 22:10:53 on May 25, 2016 ยท (Permalink)
...ith, tal, ral, ort, thul, amn, sol, shael, dol, hel, io, lum, ko, fal, lem, pul, um, mal, ist, gul, vex, ohm, lo, sur, ber, jah, cham, zod.
Now if only I actually had all those, I could make some decent runewords. :P
account_destroyed ยท 2 points ยท Posted at 17:19:40 on May 25, 2016 ยท (Permalink)
Like to 1000 places
Purplociraptor ยท 2 points ยท Posted at 17:26:11 on May 25, 2016 ยท (Permalink)
You fool! That's not the pie you are supposed to be interested in.
merelyadoptedthedark ยท 2 points ยท Posted at 17:56:31 on May 25, 2016 ยท (Permalink)
When I started dating my GF, I was talking to her over the phone and told her that I head memorized pi to 100 digits, and she obviously didn't believe me. So I rattled it off, and then she realized I was probably just saying random numbers, so she told me to do it again, so she could write it down, so I did, she wrote it down, and then I repeated it again verbatim. She was incredibly impressed with my intellectual feat. It was probably about a year or two later when I told her that I just googled it and was reading it off my computer monitor.
adamrsb48 ยท 1 points ยท Posted at 20:06:50 on May 25, 2016 ยท (Permalink)
Noice.
stickmanDave ยท 2 points ยท Posted at 20:44:07 on May 25, 2016 ยท (Permalink)
Not too many girls will be impressed by this, but when you find one that is... she's a keeper!
lacheur42 ยท 2 points ยท Posted at 21:45:18 on May 25, 2016 ยท (Permalink)
Pff. Casual. I memorize digits of e.
Lessee...2.71828182845904523536028747135266...um...49?
Fuck! 249. Now I'll never impress any girls :(
allora_fair ยท 2 points ยท Posted at 11:09:30 on May 26, 2016 ยท (Permalink)
Hey there, cutie takes deep breath 3.141592653589783238462643382795 GASPS FOR AIR
[deleted] ยท 2 points ยท Posted at 13:40:27 on May 26, 2016 ยท (Permalink)
I remember all the digits, I just forgot the order.
ChipsOtherShoe ยท 1 points ยท Posted at 15:48:17 on May 25, 2016 ยท (Permalink)
go to a tech school man, some math and physics major gals might be mildly impressed by it.
[deleted] ยท 1 points ยท Posted at 17:47:39 on May 25, 2016 ยท (Permalink)
I too have been told this.
[deleted] ยท 1 points ยท Posted at 18:40:03 on May 25, 2016 ยท (Permalink)
[deleted]
adamrsb48 ยท 2 points ยท Posted at 20:07:16 on May 25, 2016 ยท (Permalink)
A very good point others failed to bring up.
[deleted] ยท 1 points ยท Posted at 19:26:46 on May 25, 2016 ยท (Permalink)
Next time just remember to start with hello instead
adamrsb48 ยท 1 points ยท Posted at 20:07:27 on May 25, 2016 ยท (Permalink)
Very true.
RedditConsciousness ยท 1 points ยท Posted at 21:10:14 on May 25, 2016 ยท (Permalink)
I've memorized the sequence of integers that is 1-100 in pi.
master-cunt ยท 1 points ยท Posted at 22:17:05 on May 25, 2016 ยท (Permalink)
I've seen a woman knowing a great amount of the numbers that impressed a guy. Goes both ways
orangebeauty ยท 1 points ยท Posted at 03:22:02 on May 26, 2016 ยท (Permalink)
Actually, this is a real thing. When my husband and I first started dating he would whisper pi in my ear. So sexy!
lengau ยท 1 points ยท Posted at 20:22:15 on May 25, 2016 ยท (Permalink)
The key is to start memorising pi way after the last calculated digits. I did so. I don't quite remember where it begins, but my favourite section of pi is:
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...
It actually continues on for quite a bit longer.
Sheriff_K ยท 0 points ยท Posted at 18:58:05 on May 25, 2016 ยท (Permalink)
This.
rauschen ยท 203 points ยท Posted at 15:56:57 on May 25, 2016 ยท (Permalink)
Back in school aged 16 a bunch of us tried to memorize as many digits of pi as we could one evening (I know, freaking wild times). The next day we went up to our maths teacher expecting him to be impressed by our efforts. One of us had got up to near the 100 mark...
His response: Pi's an irrational number, so you have learned 100 digits out of infinity, 100/โ = 0, therefore you've learned absolutely nothing.
molrobocop ยท 48 points ยท Posted at 18:33:07 on May 25, 2016 ยท (Permalink)
Smart way of saying you guys were giant nerds.
[deleted] ยท 24 points ยท Posted at 16:16:21 on May 25, 2016 ยท (Permalink)
That's....kinda awesome and educating, in a bit of a brutal and ham-fisted way. And I can totally see my physics teacher pulling something like that back when I was in high school. In fact, he loved messing with us...but somehow that only made us learn.
davedawg2000 ยท 11 points ยท Posted at 20:06:00 on May 25, 2016 ยท (Permalink)
rekt
mythozoologist ยท 5 points ยท Posted at 23:19:54 on May 25, 2016 ยท (Permalink)
Bama Out
Superpat12 ยท 2 points ยท Posted at 00:20:36 on May 26, 2016 ยท (Permalink)
Your teacher was a ray of sunshine, wasnt he?
Vendetta1990 ยท 2 points ยท Posted at 11:49:46 on May 26, 2016 ยท (Permalink)
rekt
Askee123 ยท 1 points ยท Posted at 17:30:10 on May 26, 2016 ยท (Permalink)
Damn what a douche
CT2169 ยท 1 points ยท Posted at 11:08:11 on May 26, 2016 ยท (Permalink)
You're math teacher is wrong. 100/Infinity is not zero.
originalmetathought ยท 1 points ยท Posted at 00:33:59 on May 27, 2016 ยท (Permalink)
That's what I thought. Anything you do to infinity should be infinity. If I understood the 'HyperWebster' correctly.
LovepeaceandStarTrek ยท 265 points ยท Posted at 11:34:40 on May 25, 2016 ยท (Permalink)
I've heard a vareity of numbers as far as how many digits are needed, but they all agree that to get near perfect accuracy you need less than 100 digits (and often quite a bit less).
[deleted] ยท 495 points ยท Posted at 12:32:23 on May 25, 2016 ยท (Permalink)*
[deleted]
lordcheeto ยท 72 points ยท Posted at 15:10:44 on May 25, 2016 ยท (Permalink)
Yes, but this uses only the size of the observable universe, and only to within the size of a hydrogen atom, not the smallest known particle.
[deleted] ยท 67 points ยท Posted at 16:34:50 on May 25, 2016 ยท (Permalink)
Practically useless!
T_at ยท 80 points ยท Posted at 18:13:53 on May 25, 2016 ยท (Permalink)
Yeah! Planck length or nothing, motherfucker.
tesseract4 ยท 20 points ยท Posted at 18:30:46 on May 25, 2016 ยท (Permalink)
I burrowed all the way down this thread to find someone calling him out on not using the Planck length instead of the radius of a Hydrogen atom. You, sir, are a gentleman and a scholar.
T_at ยท 15 points ยท Posted at 18:52:57 on May 25, 2016 ยท (Permalink)
Yeah, yeah... The 'give gold' link is right up there--^
(Just kidding - reddit gold has about the same practical use as string theory, so don't bother)
[deleted] ยท 1 points ยท Posted at 05:39:45 on May 26, 2016 ยท (Permalink)
You might be onto something, I've always felt like our universe was actually made of tiny Reddit Golds
dlmcleo1 ยท 2 points ยท Posted at 19:01:18 on May 25, 2016 ยท (Permalink)
This reply perfectly encapsulates everything I love about Reddit.
semester5 ยท 13 points ยท Posted at 19:09:18 on May 25, 2016 ยท (Permalink)
exactly, if i am paying for a tailored suit. It better fit me down to Planck length
iwasacatonce ยท 14 points ยท Posted at 20:56:19 on May 25, 2016 ยท (Permalink)
Better not eat that donut for breakfast
lordcheeto ยท 2 points ยท Posted at 21:23:56 on May 25, 2016 ยท (Permalink)
I think the size of the observable universe is a fine measure for the large end, so that 8.8e26m. The plank length makes a lot of sense on the low end, so that's 1.616e-35m. You would need 63 digits for that.
Penisgrowl ยท 1 points ยท Posted at 18:33:33 on May 25, 2016 ยท (Permalink)
Because we will never be able to observe more of the universe, therefore we won't ever need anything bigger, and you can't know the position of a particle smaller than a proton maybe?
LovepeaceandStarTrek ยท 86 points ยท Posted at 13:20:33 on May 25, 2016 ยท (Permalink)
Yes. My point is while that video says the number is 39, I've heard a few others.
danhakimi ยท 6 points ยท Posted at 17:29:36 on May 25, 2016 ยท (Permalink)
There are smaller particles than hydrogen atoms, and also he only got the observable universe... but still that's pretty damn good.
lerjj ยท 8 points ยท Posted at 17:56:14 on May 25, 2016 ยท (Permalink)
The observable universe is, for all intents and purposes, all there is. The entire universe is most likely spatially infinite.
danhakimi ยท 0 points ยท Posted at 17:59:49 on May 25, 2016 ยท (Permalink)
But the observable universe is going to grow into that entire universe. And objects from the outer limits of the universe can move into the range of the observable universe -- we actually don't know what's in the range known as the observable universe right now.
Oh, also, Gravity has infinite range, right? That's pretty important.
lerjj ยท 5 points ยท Posted at 18:27:46 on May 25, 2016 ยท (Permalink)
It's not about range, it's about time. Something outside of the obervable universe can't have a gravitational impact because the time taken for the gravitational waves to reach us is longer than the age of the universe.
MrXian ยท -15 points ยท Posted at 15:02:41 on May 25, 2016 ยท (Permalink)
I think the point is that the other things you hear were just explained to be false.
ben_jl ยท 13 points ยท Posted at 15:14:36 on May 25, 2016 ยท (Permalink)
There are multiple ways to interpret things like the 'size' of an electron, and no obvious reason to prefer one interpretation over another.
SvalbardCaretaker ยท 8 points ยท Posted at 15:40:05 on May 25, 2016 ยท (Permalink)
Just go with Planck length, its the smallest conveivable thing our physics knows of at 10-35m. In the video he uses hydrogen atom with 10-11m and his 39 pi digits give him accuracy to 10-12m.
Minus-Celsius ยท 4 points ยท Posted at 16:36:29 on May 25, 2016 ยท (Permalink)
So you really need to know 62 digits of pi.
Damn, I only know 33.
Ordered_Chaos ยท 2 points ยท Posted at 16:46:02 on May 25, 2016 ยท (Permalink)
I know 6
[deleted] ยท 11 points ยท Posted at 16:59:05 on May 25, 2016 ยท (Permalink)*
I know 3. Not 3 digits, just the number 3. Seriously, you get like 3% error just using 3. You don't even have to remember how much error it gives, because it's also 3. It's so great.
198jazzy349 ยท 2 points ยท Posted at 18:11:19 on May 25, 2016 ยท (Permalink)
The Benbuzz Rationale of Three
One must only remember that pi is 3. The maximum error using 3 for calculations is about 3%.
[deleted] ยท 1 points ยท Posted at 23:15:50 on May 25, 2016 ยท (Permalink)
Actually the percent error for using 3 as pi is 4.5070340357462%, using the first 1000 digits of pi from Wolfram Alpha and the equation for percent error.
[deleted] ยท 1 points ยท Posted at 23:56:03 on May 25, 2016 ยท (Permalink)
dang. Well your percent error on your error is 33%. See, easy.
[deleted] ยท 1 points ยท Posted at 00:02:22 on May 26, 2016 ยท (Permalink)
It's roughly 50%, not 33%
4.5-3=1.5
1.5/3*100=50%
[deleted] ยท 1 points ยท Posted at 00:25:45 on May 26, 2016 ยท (Permalink)
1.5/4.5 = 33%
[deleted] ยท 1 points ยท Posted at 00:34:11 on May 26, 2016 ยท (Permalink)
Percent error is from the actual value not the measured value...
[deleted] ยท 1 points ยท Posted at 00:42:01 on May 26, 2016 ยท (Permalink)
Which is 4.5!
[deleted] ยท 2 points ยท Posted at 01:23:26 on May 26, 2016 ยท (Permalink)
oh shit.
[deleted] ยท 3 points ยท Posted at 16:52:18 on May 25, 2016 ยท (Permalink)
sine cosine cosine sine 3.14159
rzezzy1 ยท 11 points ยท Posted at 14:57:17 on May 25, 2016 ยท (Permalink)*
Thing about that, though, is that elementary particles, such as quarks and electrons, are thought to be point particles with zero radius.
Edit: considering /u/beeeel 's reply makes my comment much more accurate. Please do so.
beeeel ยท 18 points ยท Posted at 16:34:21 on May 25, 2016 ยท (Permalink)
They also don't have a strictly defined position, just a probability distribution for the position function, so you could say that the radius is just the standard deviation of the position distribution for a given state.
rzezzy1 ยท 7 points ยท Posted at 16:38:21 on May 25, 2016 ยท (Permalink)
Point taken, thank you
ApocDream ยท 8 points ยท Posted at 18:41:29 on May 25, 2016 ยท (Permalink)
Oh, you.
XavierSimmons ยท 7 points ยท Posted at 16:34:53 on May 25, 2016 ยท (Permalink)
That seems arbitrary.
What if I'm measuring Planck distances?
SybariticLegerity ยท 3 points ยท Posted at 17:13:04 on May 25, 2016 ยท (Permalink)
Then you only need a few more digits, doesn't really change the connotation of the fact
XavierSimmons ยท 5 points ยท Posted at 17:16:36 on May 25, 2016 ยท (Permalink)
If the connotation was "you only need as many digits as you need to get the precision you want" then that's a pretty obvious statement.
But that's not what the comment said:
So I was pointing out that this is a false statement, as there is the possibility of needing greater precision than the "radius of the smallest known particle."
ERRORMONSTER ยท 1 points ยท Posted at 18:03:47 on May 25, 2016 ยท (Permalink)
Plancks are absolutes. I was writing it generally such that no material discovery could make it inaccurate. We don't know for sure that nothing is smaller than a planck. We do know for sure than nothing is smaller than the smallest particle (by definition of it being the smallest particle)
4scoreand7feildgoals ยท 5 points ยท Posted at 17:01:08 on May 25, 2016 ยท (Permalink)
There was an /r/TheyDidTheMath post about this, thought it was quite interesting.
Turns out most digits of pi that are possibly useful in our universe is 62.
IAmTryingToOffendYou ยท 20 points ยท Posted at 14:23:12 on May 25, 2016 ยท (Permalink)
Which just so happens to be 42
DennethMayhem ยท 0 points ยท Posted at 16:22:16 on May 25, 2016 ยท (Permalink)
Does it actually? I can't be bothered doing the maths!
Also that would amazing as it may be the reason behind the hitchhikers guide to the galaxy.
IAmTryingToOffendYou ยท 1 points ยท Posted at 13:20:30 on May 26, 2016 ยท (Permalink)
Yep, explanation: http://i.imgur.com/6PlRXhI.gif
Tyrexas ยท 0 points ยท Posted at 20:07:04 on May 25, 2016 ยท (Permalink)
woooooosh
WhiskeyOnASunday93 ยท 2 points ยท Posted at 15:45:13 on May 25, 2016 ยท (Permalink)
Whoa
meh100 ยท 2 points ยท Posted at 16:24:14 on May 25, 2016 ยท (Permalink)
What if you're working on theoretical universes?
ERRORMONSTER ยท 1 points ยท Posted at 18:05:55 on May 25, 2016 ยท (Permalink)
There's no physical reason to use more digits. You could do thought experiments that analyze if pi were 4, but that's outside the bounds of our universe.
meh100 ยท 1 points ยท Posted at 18:25:53 on May 25, 2016 ยท (Permalink)
Is it outside the bounds of our universe if it has mathematical applications?
ERRORMONSTER ยท 1 points ยท Posted at 18:29:58 on May 25, 2016 ยท (Permalink)
I think it's outside the physical realm of our universe if the mathematics you're applying it to have no physical application.
thelegendarymudkip ยท 2 points ยท Posted at 17:32:06 on May 25, 2016 ยท (Permalink)
Why the radius of the smallest known particle? Why not a Planck length, the (theoretical) smallest possible length?
ERRORMONSTER ยท 1 points ยท Posted at 18:02:07 on May 25, 2016 ยท (Permalink)
Because a planck length is an absolute and I was writing it as generally as possible. We might discover a particle smaller than a planck length. We won't discover a particle smaller than the smallest particle.
PersonUsingAComputer ยท 1 points ยท Posted at 03:05:08 on May 26, 2016 ยท (Permalink)
The Planck length is not any sort of "smallest possible length". It's just a unit of length, like a meter or a mile or a light-year. Planck units are defined using basic physical constants like Planck's constant and the speed of light rather than having mostly arbitrary definitions like meters/miles/light-years, and it just so happens that 1 Planck unit of length is really small compared to 1 meter/mile/light-year. But it has no particular physical significance.
thelegendarymudkip ยท 1 points ยท Posted at 15:04:26 on May 26, 2016 ยท (Permalink)
On the contrary, the Planck length is (within an order of magnitude) the theoretical smallest possible detectable length. (according to the Generalized Uncertainty Principle)
PersonUsingAComputer ยท 1 points ยท Posted at 15:55:53 on May 26, 2016 ยท (Permalink)
While there are some speculative physical theories which suggest the universe is "pixelated" in this way, nothing has been verified by experiment that gives the Planck length physical significance.
thelegendarymudkip ยท 1 points ยท Posted at 16:55:39 on May 26, 2016 ยท (Permalink)
Of course, that's what I mean by theoretical.
marvin ยท 2 points ยท Posted at 17:54:34 on May 25, 2016 ยท (Permalink)
Except if you're in a competition that requires you to know a lot of digits of pi...
ERRORMONSTER ยท 1 points ยท Posted at 18:00:54 on May 25, 2016 ยท (Permalink)
Fair enough. But the most number you would mathematically need for the purposes of accuracy is as I described.
marvin ยท 2 points ยท Posted at 18:07:55 on May 25, 2016 ยท (Permalink)
Yeah, I was just pulling your leg :P
FreeBribes ยท 1 points ยท Posted at 20:24:01 on May 25, 2016 ยท (Permalink)
Pshh, I can recite pi to 1 million digits... the last digit is a 3.
mn_sunny ยท 2 points ยท Posted at 17:59:20 on May 25, 2016 ยท (Permalink)
this guy.
mating_toe_nail ยท 2 points ยท Posted at 20:54:11 on May 25, 2016 ยท (Permalink)
Unless you plan to do that in a simulation of the universe across time. I'm which case you'd have to multiply times the number of time steps to stay within the plank distance or something.
ERRORMONSTER ยท 1 points ยท Posted at 21:40:04 on May 25, 2016 ยท (Permalink)
Assuming the universe is purely deterministic (which we know it isn't) then knowing position and velocity is enough. But since QM makes that harder, it isn't (as far as we know) useful to know anything more accurate than a few angstroms.
mating_toe_nail ยท 2 points ยท Posted at 21:41:35 on May 25, 2016 ยท (Permalink)
Oh interesting! Is it that it doesn't matter because we can't know anyway?
ERRORMONSTER ยท 1 points ยท Posted at 00:18:22 on May 26, 2016 ยท (Permalink)
Pretty much. We know that quantum mechanics screws with the determinability of particles once they get down to the subatomic scale. This is the whole problem behind transistors right now. We can only work with particles over such small distances as defined on a probability space.
SeraphimNoted ยท 2 points ยท Posted at 07:48:26 on May 26, 2016 ยท (Permalink)
So how many places to the accuracy of a Planck length?
ERRORMONSTER ยท 1 points ยท Posted at 14:19:18 on May 26, 2016 ยท (Permalink)
Plank lengths are about 10-33 M, and 39 digits of pi gets you about 10-12 M of accuracy (within one hydrogen atom), so as a ballpark, you'd need about 60 digits of pi to calculate the circumference of the universe to within one planck length.
Verify if you'd like to correct me. Numberphile showed the error of a truncated pi (pit ) to be pi*duniverse - pit * duniverse.
TeutorixAleria ยท 1 points ยท Posted at 18:21:22 on May 25, 2016 ยท (Permalink)
More precisely to within the value of the planck length since at that point physics ceases to make sense.
ERRORMONSTER ยท 1 points ยท Posted at 18:30:10 on May 25, 2016 ยท (Permalink)
We think*
NotRoryWilliams ยท 1 points ยท Posted at 18:40:28 on May 25, 2016 ยท (Permalink)
And how many would that be?
ERRORMONSTER ยท 2 points ยท Posted at 20:30:40 on May 25, 2016 ยท (Permalink)
Depends on what the smallest particle is. If it turns out to be the size of a planck length then the number is around 40 digits. If the smallest particle is bigger, you probably don't need as much. If the smallest particle is smaller, you'll need more.
The_MoistMaker ยท 1 points ยท Posted at 18:45:11 on May 25, 2016 ยท (Permalink)
So infinite?
ERRORMONSTER ยท 1 points ยท Posted at 20:29:09 on May 25, 2016 ยท (Permalink)
Not necessarily. If the smallest particle were the size of a planck length and the universe was the size of the observable universe, you only need a certain number of digits to calculate an object's position in the universe to within one planck length. If the smallest particle were bigger, you need fewer digits.
StrangeRover ยท 1 points ยท Posted at 19:18:20 on May 25, 2016 ยท (Permalink)
Is this a joke I'm missing? Because that's not true at all.
ERRORMONSTER ยท 1 points ยท Posted at 20:23:50 on May 25, 2016 ยท (Permalink)
I'm assuming you didn't read surrounding comments and are referring to the theoretical uses of pi beyond calculating anything physical. Those things aren't "needs" per se because they don't give us any insight into the physical realm.
StrangeRover ยท 1 points ยท Posted at 01:34:08 on May 26, 2016 ยท (Permalink)
What if I ask you to tell me the location of the center of that particle? That requires more precision than just being able to name a point which falls inside its area.
ERRORMONSTER ยท 1 points ยท Posted at 01:47:11 on May 26, 2016 ยท (Permalink)
Not really. The center doesn't matter when you're on that small of a scale. the undeterministic nature of subatomic particles says that.
StrangeRover ยท 1 points ยท Posted at 01:57:51 on May 26, 2016 ยท (Permalink)
But locating said particle in the entirety of the universe does matter? Who's to say what matters and what doesn't?
You phrased your OP as if it was some kind of proven mathematical fact, but all it is is you saying to yourself, "this is all the precision I could ever fathom being necessary." You can't just discount greater precision as impractical when the example you used is already orders of magnitude beyond practical or useful.
ERRORMONSTER ยท 1 points ยท Posted at 04:08:35 on May 26, 2016 ยท (Permalink)
Let me explain what I mean by my last phrase, as it can be a bit confusing to those who don't get quantum mechanics. Let's say I have some number x digits of pi. This lets me calculate, if I know the radius of the universe and some universal coordinates that I could define myself arbitrarily, the location of a particle to within one radius, somewhere on the scale below the size of a proton. Knowing x + 1 digits will not make my positional calculation more accurate because that particle could spontaneously disappear and reappear in another location. By using a more accurate value for pi, I'm attempting to give more credence to the position that I'm calculating, when in reality, I can't know for sure that the particle is at that exact point. Ever. By using x - 1 digits (or maybe x - 2 or 3) I'm intentionally saying "this particle is somewhere in here. Dunno where, but it's in there." That's the nature of uncertainty in an answer and you're simply being explicit with it. Either your tool can't give you more accurate of an answer or your answer inherently can't be more accurate. It's like saying you're 5'11.56789234197891234578964231978" tall. You may be right, but it isn't useful to be that precise since the value is changing literally every second. Since the distance the particle could tunnel to decreases exponentially, I can give a pretty narrow area with high certainty. It very very likely won't be found an inch away, for example. So very unlikely that it's not even worth considering.
And my example is so not "orders of magnitude beyond practical or useful." Do you know why the computer you're using doesn't run faster than it does? There are limits to how small we can make transistors for this reason. To say that an electron is on one side of a transistor with a gate about an angstrom wide is to ignore the possibility that it could be on the other side of the gate, having tunneled to the other side. You can no longer determine the position by a vector. You have to describe it by a probability of vectors (probably here, maybe over here, probably not over there, but possibly, etc)
-widget ยท 1 points ยท Posted at 20:34:38 on May 25, 2016 ยท (Permalink)
Well yeah, unless you have a customer that insists that's not sufficient.
eebootwo ยท 1 points ยท Posted at 21:03:25 on May 25, 2016 ยท (Permalink)
you can get bigger numbers than that easily if you consider ordering things or multiparticle states
Tysonzero ยท 1 points ยท Posted at 21:39:55 on May 25, 2016 ยท (Permalink)
Not quite. With certain mathematically operations you can easily massively exacerbate errors in numbers you use. For example the error in 3.1416 vs the actually value is quite a bit smaller than the error in 103.1416 and the actual value. So you could definitely end up needing a ridiculous amount of accuracy in strange mathematical circumstances.
ERRORMONSTER ยท 1 points ยท Posted at 00:19:20 on May 26, 2016 ยท (Permalink)
If you read around the comments below, you'll see that we were talking about digits that are physically useful to us.
mc_nail ยท 1 points ยท Posted at 22:42:19 on May 25, 2016 ยท (Permalink)
Although you could definitely have many math problems that depend on more digits of pi.
ERRORMONSTER ยท 1 points ยท Posted at 00:15:52 on May 26, 2016 ยท (Permalink)
Right, but you can also have math problems that treat pi as equal to 4. It's possible, but that doesn't necessarily make it useful for us to do. I was pointing out digits that are useful to us.
mc_nail ยท 0 points ยท Posted at 01:13:29 on May 26, 2016 ยท (Permalink)
I think you misinterpret my meaning. I am saying that there are legitimate useful cases for using more digits of pi, or numbers so ridiculously large that they cannot represent physical quantities.
Saying "x digits of pi are sufficient to calculate any real world circle, therefore that is all that we will ever need for anything" is an extremely limited understanding of mathematics and its utility.
As a very simple example, consider the encryption used for sending this comment to reddit. 2048 bits represents a 617 decimal digit number. That is 10617 !! Why that is enormously more than there are atoms in the entire universe, you say. Nobody could ever possibly make use of a number that large....
ERRORMONSTER ยท 1 points ยท Posted at 01:49:03 on May 26, 2016 ยท (Permalink)
And I think you misunderstand my initial statement. The number 22048 is not physically useful for us. And we don't use it for anything. Similarly, 40 ish digits of pi is sufficient because we don't need that value for anything physical. To insist that more accuracy is required for anything shows a gross misunderstanding of quantum mechanics.
mc_nail ยท 1 points ยท Posted at 02:16:59 on May 26, 2016 ยท (Permalink)*
You need to reduce your claim then. If you only want to claim the cases where pi is physically useful, that is a much narrower claim and you should state it as such. But further, your statements are still not clarified:
There is a logical contradiction in this statement. You can't say "sufficient" as the claim, and imply that "physically useful" means sufficient. Since 22048 is not "physically useful" then 128 bit encryption is therefore sufficient for you?
More importantly, I would argue very strongly against the notion that using pi to calculate the circumference of a circle is the only physically meaningful utility that it has.
As a simple example, in 1995 pi was used to 200 digits in an Integer relation aglorithm to produce a new and very useful formula for calculating pi (along with numerous other mathematical constants of 200 significant digits each). This is the BBP formula. Without 200 significant digits of pi, humanity would never have been able to find this simple, elegant formula with its simple single digit constants.
The BBP formula is very useful in answering many questions. For example, before this many assumed that it was impossible to calculate the nth digit of pi without calculating all preceding digits. However, it is also arguable that it has physical utility. This algorithm allows us to use less physical hardware, for example.
Ultimately, we may find all sorts of other useful formula, using even more digits of pi. And these formula could answer very real and fundamental questions. Relativity, among other math, allows us to answer very real questions about what a distant stars chemical composition is. Many fundamentals of abstract mathematics were required to formulate relativity's elegant postulates. Integer relation algorithms might derive the next useful formulas that answer questions about dark energy or other difficult unsolved real world physical problems.
Think like a physicist, not an engineer.
ERRORMONSTER ยท 1 points ยท Posted at 03:57:17 on May 26, 2016 ยท (Permalink)
You seem to be a bit sensitive on this subject. I'll gently clarify.
the number itself is not useful to us. The range it can be found in is useful to us simply because there are lots of numbers in that area. The fact that 22048 has any specific property (other than obviously being a power of 2. I assume we're talking about large numbers in the ballpark and not that specific value) is of no consequence to us other than being very big. Similarly, knowing that the next digit of pi is a 7 and not a 2 is of no consequence because any additional accuracy we gain from such a digit is immediately canceled out by the fact that anything existing at a spot with such higher accuracy could very likely spontaneously tunnel to another location within the realm of uncertainty provided by the next higher decimal place of pi.
I do find it funny that you're claiming the usefulness of pi is that it allows us to calculate more digits of pi. It's a little circular, but I'm not picky.
mc_nail ยท 1 points ยท Posted at 14:11:14 on May 26, 2016 ยท (Permalink)
I'm not sure if you didn't even read anything I wrote. You're back to thinking that pi is only a means to calculate a circumference? Remember, pi and e are intimately involved in many, many formulas, from trig, to simple harmonic motion, to the Schrodinger equation.
ERRORMONSTER ยท 1 points ยท Posted at 17:04:50 on May 26, 2016 ยท (Permalink)
Sorry, I was just trying to figure out a situation where you can scale pi enough such that you'd need more digits.
And my initial point was not "we will never need more digits of pi for anything." I agree with you that we can gain theoretical insight into other fields and situayions by using more digits. But as for physical applications of the value there is no need for more digits.
pretentiousRatt ยท 1 points ยท Posted at 01:11:33 on May 26, 2016 ยท (Permalink)
Which is?
ERRORMONSTER ยท 1 points ยท Posted at 01:49:31 on May 26, 2016 ยท (Permalink)
Depends on who you ask. The general consensus is about 40.
imgonnacallyouretard ยท 0 points ยท Posted at 18:40:53 on May 25, 2016 ยท (Permalink)
This value is constantly changing...
Why not planck length?
ERRORMONSTER ยท 1 points ยท Posted at 20:29:37 on May 25, 2016 ยท (Permalink)
Read surrounding comments. I've already explained multiple times.
imgonnacallyouretard ยท 2 points ยท Posted at 21:02:56 on May 25, 2016 ยท (Permalink)
But why male models?
[deleted] ยท 3 points ยท Posted at 14:09:39 on May 25, 2016 ยท (Permalink)
it really depends with what you're doing
capnofasinknship ยท 2 points ยท Posted at 16:37:41 on May 25, 2016 ยท (Permalink)
http://kottke.org/16/03/how-many-digits-of-pi-does-nasa-use
[deleted] ยท 1 points ยท Posted at 20:48:44 on May 25, 2016 ยท (Permalink)
Fewer.
jagrbomb ยท 1 points ยท Posted at 21:15:24 on May 25, 2016 ยท (Permalink)
The word "often" is derived from "1 out of ten"
I made that up.
IWentToTheWoods ยท 21 points ยท Posted at 15:08:44 on May 25, 2016 ยท (Permalink)
Memorizing 762 digits so that you could say "...999999, and so on" would be kind of practical.
-100-Broken-Windows- ยท 9 points ยท Posted at 16:59:05 on May 25, 2016 ยท (Permalink)
We seem to have very differing opinions on what constitutes as "practical".
actual_factual_bear ยท 5 points ยท Posted at 16:33:17 on May 25, 2016 ยท (Permalink)
Guys, I found Richard Feynman's ghost's account!
IWentToTheWoods ยท 1 points ยท Posted at 16:44:06 on May 25, 2016 ยท (Permalink)
Interestingly, it was actually Douglas Hofstadter (the Gรถdel, Escher, Bach: An Eternal Golden Braid author) who said this. There's no record of Feynman making a similar remark.
[deleted] ยท 8 points ยท Posted at 15:11:07 on May 25, 2016 ยท (Permalink)
There really isn't a practical reason to memorize any of it. We have calculators
dupelize ยท 3 points ยท Posted at 22:19:29 on May 25, 2016 ยท (Permalink)
Right? Maybe use, but "a little more than three" is probably good enough for anything that isn't worth grabbing a calculator for.
zcbtjwj ยท 4 points ยท Posted at 15:58:57 on May 25, 2016 ยท (Permalink)
99% of the time, 3 or 3 and a bit is good enough
3 and a bit is also square root of 10 (useful for log scales and areas) and 10/3
[deleted] ยท 3 points ยท Posted at 15:33:45 on May 25, 2016 ยท (Permalink)
355/113 is a really useful fraction.
frugalNOTcheap ยท 3 points ยท Posted at 15:40:12 on May 25, 2016 ยท (Permalink)
Good, cause I typically just use 3 when estimating areas
ParanoidDrone ยท 3 points ยท Posted at 15:52:21 on May 25, 2016 ยท (Permalink)
How precise can I get with 3.14159? That's as far as I've bothered to memorize.
Hawkdagon ยท 7 points ยท Posted at 14:53:28 on May 25, 2016 ยท (Permalink)
I've never trusted Numberphile after they went ahead and didn't explain this video at all, other than calling it "mathematical hocus pocus" (which was said by a fucking professor who I would never take a class from). So now I have to deal with idiots trying to sound smart by passing this off as the sum of a divergent infinite series. For anyone out there that believed this to be true, the "sum" that they are talking about is not the "sum" you have encountered in school, it's a completely different thing.
bobbfwed ยท 3 points ยท Posted at 17:49:36 on May 25, 2016 ยท (Permalink)
There's more explanation in this video by Numberphile.
Hawkdagon ยท 4 points ยท Posted at 17:58:14 on May 25, 2016 ยท (Permalink)
That's a much better video. I hate the first one so much because I feel like it helps reinforce the idea that math is all "magic" and so regular people assume they will never understand it. Whenever I've tutored math I've always found that that people get so easily flustered and forget all logic. That first numberphile is the exact type of "explanation" that I think adds to that problem.
TotalyNotMyPornAcc ยท 2 points ยท Posted at 15:35:55 on May 25, 2016 ยท (Permalink)
To be fair, its not their fault. Anyone who really cared should have read the article and they would have understood it.
Ranzear ยท 2 points ยท Posted at 15:57:39 on May 25, 2016 ยท (Permalink)
Ctrl+F'd for '39', was not disappointed.
malefiz123 ยท 2 points ยท Posted at 16:19:32 on May 25, 2016 ยท (Permalink)
Implying there is a practical reason for measuring the circumference of the observable universe within the width of one hydrogen atom.
[deleted] ยท 1 points ยท Posted at 16:26:52 on May 25, 2016 ยท (Permalink)
Point taken :)
DV_shitty_music ยท 1 points ยท Posted at 15:21:41 on May 25, 2016 ยท (Permalink)
I wonder why didn't he add a few more digits to measure down to Planck length.
[deleted] ยท 1 points ยท Posted at 15:22:32 on May 25, 2016 ยท (Permalink)
That'd just be overkill I suppose. Or maybe it'd take more digits than we think, who knows.
DV_shitty_music ยท 2 points ยท Posted at 15:28:07 on May 25, 2016 ยท (Permalink)
Size of the observable universe in Planck units goes to around ~1061, so another 20 or so should suffice.
[deleted] ยท 2 points ยท Posted at 15:31:22 on May 25, 2016 ยท (Permalink)
Yeah, I was guessing 20-25. But, at that point (or indeed, at the "proton diameter" point) we're already in the "you're just showing off" area, on the other hand....
The_Legend_of_Groose ยท 1 points ยท Posted at 16:10:47 on May 25, 2016 ยท (Permalink)
I like how he seems so exited talking about math, that man loves his work.
tree_dweller ยท 1 points ยท Posted at 16:26:22 on May 25, 2016 ยท (Permalink)
Yes there is. We had a contest in my class during like 7th or 8th grade so I memorized 100 digits thinking I could win. This fucker memorized 101. I just quizzed myself and got 45 before I messed up. That double 9 got me.
rawrthundercats_ ยท 1 points ยท Posted at 16:26:26 on May 25, 2016 ยท (Permalink)
"Shall we write out the 39 digits?" "Yup"
"Did we just become best friends?" "Yup"
[deleted] ยท 1 points ยท Posted at 16:30:20 on May 25, 2016 ยท (Permalink)
LBH there's no practical reason to memorize more than 1 digit of pi
[deleted] ยท 2 points ยท Posted at 16:32:20 on May 25, 2016 ยท (Permalink)
Damn, I simply can't un-remember the second one myself :(
Gsus_the_savior ยท 1 points ยท Posted at 16:33:03 on May 25, 2016 ยท (Permalink)
How many digits would you need to get it within a Planck length?
[deleted] ยท 2 points ยท Posted at 16:33:47 on May 25, 2016 ยท (Permalink)
No clue, it's several orders of magnitude, so my guess would be 20-25 more? Not sure though.
SexyIsMyMiddleName ยท 1 points ยท Posted at 16:35:21 on May 25, 2016 ยท (Permalink)
All you need for practicalities is 355/113 which is incredibly accurate approximation.
drchaos2000 ยท 1 points ยท Posted at 16:40:27 on May 25, 2016 ยท (Permalink)
wouldnt plank length make more sense then a hydrogen atom though ?
zarraha ยท 1 points ยท Posted at 16:46:42 on May 25, 2016 ยท (Permalink)
There's no practical reason to memorize more than 3 digits of pi. Anything that you need more precision on should be done with a calculator, which knows the digits.
GoldenWizard ยท 1 points ยท Posted at 16:46:47 on May 25, 2016 ยท (Permalink)
3.14159365358979323846264338327950 is all I have memorized.. Only like 7 more to go!
PianoMastR64 ยท 1 points ยท Posted at 16:53:25 on May 25, 2016 ยท (Permalink)
How many digits of pi do you need for an accuracy of within a Planck length?
TheReaver88 ยท 1 points ยท Posted at 16:55:48 on May 25, 2016 ยท (Permalink)
Shudders
greenlaser3 ยท 1 points ยท Posted at 16:56:58 on May 25, 2016 ยท (Permalink)
That's interesting, but pi is used for a lot more than just geometry. I'm curious if there are any other applications that could potentially require greater precision. Maybe something in the computation/simulation world?
_dismal_scientist ยท 1 points ยท Posted at 16:57:26 on May 25, 2016 ยท (Permalink)
Getting laid isn't a practical reason?
[deleted] ยท 2 points ยท Posted at 16:58:14 on May 25, 2016 ยท (Permalink)
Believe me, if she was impressed by your pi, she was going to sleep with you anyway. Because she already found you appealing.
RickHalkyon ยท 1 points ยท Posted at 17:19:57 on May 25, 2016 ยท (Permalink)
You and I think of the word "practical" quite differently.
I'm gonna stick with "3.1415926" for my 8-digit TI-34 from middle school.
Zingy_Zombie ยท 1 points ยท Posted at 17:30:13 on May 25, 2016 ยท (Permalink)
Too bad I know pi to like over a hundred digits thanks to this song
CrazyPieGuy ยท 1 points ยท Posted at 17:31:25 on May 25, 2016 ยท (Permalink)
How long will it be before the error is off by one helium atom instead of a hydrogen atom?
JordHardwell ยท 1 points ยท Posted at 17:41:37 on May 25, 2016 ยท (Permalink)
It took me so much scrolling to find a Numberphile video. I'm ashamed of reddit.
mirakdva ยท 1 points ยท Posted at 17:44:28 on May 25, 2016 ยท (Permalink)
and yet, I know a guy that last week prooved that he knows more than 2300 digits of pi. He wrote 3000 of them, but he made a mistake at 2351. digit http://kosice.korzar.sme.sk/c/8191080/kosicky-stredoskolak-vie-spamati-vyse-2-300-cislic-z-ludolfovho-cisla.html
workbean ยท 1 points ยท Posted at 17:48:17 on May 25, 2016 ยท (Permalink)
What practical thing couldn't you do if you only knew 15 digits of pi?
mrthesis ยท 1 points ยท Posted at 18:28:49 on May 25, 2016 ยท (Permalink)
That is the most enthusiastic and charismatic mathematician I ever saw. Meaning the first dude with both values >0.
Kingy_who ยท 1 points ยท Posted at 18:44:55 on May 25, 2016 ยท (Permalink)
The vast majority of my physics department got away with 1 digit.
Goodkall ยท 1 points ยท Posted at 18:47:53 on May 25, 2016 ยท (Permalink)
To change your name.
chequilla ยท 1 points ยท Posted at 18:55:46 on May 25, 2016 ยท (Permalink)
With a miniature computer always handy in 2016, there's no practical reason to memorize any digits of pi.
8979323 ยท 1 points ยท Posted at 18:58:48 on May 25, 2016 ยท (Permalink)
Haha, I memorised 40 places one night 20-odd years ago when I couldn't sleep. This might explain why I haven't found the need for it since
ilovemusic_s ยท 1 points ยท Posted at 19:01:58 on May 25, 2016 ยท (Permalink)
Lets see what i have memorized... 3,14159265358979323846264338327950
NegroConFuego ยท 1 points ยท Posted at 19:02:56 on May 25, 2016 ยท (Permalink)
At my high school on pi day (march 14th) whichever student could recite the most numbers of pi won a free pie of their choice. There were also slices for whoever came close to the winner. As you can tell my school was pretty big on science and math (nerds) so to win you had to know at least 120 digits of the sequence.
I think a free pie is pretty damn practical, sir.
KickassMcFuckyeah ยท 1 points ยท Posted at 19:03:22 on May 25, 2016 ยท (Permalink)
The sequence 42 happens 42 times in the first 4200 digits of pi and the sequence 4200 happens 42 times.
WhyIsTheNamesGone ยท 1 points ยท Posted at 19:07:37 on May 25, 2016 ยท (Permalink)
There's no practical reason to memorize any. Just use Math.PI; magic numbers make your code smell.
[deleted] ยท 1 points ยท Posted at 19:18:56 on May 25, 2016 ยท (Permalink)
now, if you put a rope around the entire observable universe...
Collinnn7 ยท 1 points ยท Posted at 19:54:45 on May 25, 2016 ยท (Permalink)
I know 50 because I'm a good little nerd
aaronsherman ยท 1 points ยท Posted at 20:06:18 on May 25, 2016 ยท (Permalink)
The meta-fact (metas fact if you're in the UK, I guess ;-) is that every math(s)-fact that you will ever want to know is on Numberphile.
Rude-E ยท 1 points ยท Posted at 21:14:58 on May 25, 2016 ยท (Permalink)
Clicked on the video and thought: "I'm not going to watch 5 and a half minutes about Pi" but I did. Great video!
TheInvisibleDuck ยท 1 points ยท Posted at 22:00:00 on May 25, 2016 ยท (Permalink)
Not a good day to know the first hundred
D-Shap ยท 1 points ยท Posted at 22:05:02 on May 25, 2016 ยท (Permalink)
To win a contest i had in 5th grade
[deleted] ยท 1 points ยท Posted at 22:21:05 on May 25, 2016 ยท (Permalink)
There is no practical reasons to memorize pi at all, someones written it down...
Hagathor1 ยท 1 points ยท Posted at 22:36:09 on May 25, 2016 ยท (Permalink)
Nonsense, you zetta dolt. Memorize 151 digits and you can use a lvl i flare.
spartanburt ยท 1 points ยท Posted at 22:41:54 on May 25, 2016 ยท (Permalink)
I always figured that point where there are 6 9's in a row is enough.
rtomek ยท 1 points ยท Posted at 23:01:25 on May 25, 2016 ยท (Permalink)
So he gets his point across in the first 15 seconds of the video. Then he repeats his statement. Then he writes down 39 digits of pi. Then he repeats why. Then he says it again.
At that point I took my mouse over the video to see that it was over 5 minutes long, so I closed the tab.
fittygitty ยท 1 points ยท Posted at 23:19:07 on May 25, 2016 ยท (Permalink)
Can anyone explain to me how people use computers to calculate Pi, or even how historic mathematicians did it? Are they using super accurate measurements of some kind of known perfect circle or something? How does this work?
RiotMontag ยท 1 points ยท Posted at 23:20:18 on May 25, 2016 ยท (Permalink)
Nasa only uses 15:
2_Sheds_Jackson ยท 1 points ยท Posted at 00:09:54 on May 26, 2016 ยท (Permalink)
I can recite the last 39 digits of pi. Is that at all practical?
es9spec ยท 1 points ยท Posted at 00:47:09 on May 26, 2016 ยท (Permalink)
3.14159265358979323846264338327950288420
ayyy
CyberTractor ยท 1 points ยท Posted at 01:05:32 on May 26, 2016 ยท (Permalink)
I just memorize the first part. 3 is good enough for me.
PacoTaco321 ยท 1 points ยท Posted at 02:20:22 on May 26, 2016 ยท (Permalink)
I've found there is no practical reason to memorize beyond 3 digits
[deleted] ยท 1 points ยท Posted at 07:24:16 on May 26, 2016 ยท (Permalink)
Yeah, but it's not like that's the only place in maths or science that pi crops up. There are a million uses for it and I'm willing to believe some of them need more precise measurements of pi.
[deleted] ยท 1 points ยท Posted at 07:26:00 on May 26, 2016 ยท (Permalink)
Greater precision is needed when orders of magnitude are further apart. And it's hard to get further apart on orders of magnitude than "size of the universe vis-a-vis quantum level".
yCloser ยท 1 points ยท Posted at 13:35:00 on May 26, 2016 ยท (Permalink)
Nasa says:
source. So, 15 digits. If it's good enough for NASA, it's good enough for me
GardensOfBoydstylon ยท 1 points ยท Posted at 21:16:46 on May 27, 2016 ยท (Permalink)*
How many digits do I need to to calculate the circumference of the observable universe to within 1 planck length?
EDIT: Answer = 64 digits of pi. Another person posted it in this link.
EDIT 2: 3.14159265358979323846264338327950288419716939937510582097494459
[deleted] ยท 1 points ยท Posted at 15:23:55 on May 25, 2016 ยท (Permalink)
Do irrational numbers even exist or are they a human abstraction to approximate the real world? If, when you zoom in far enough, everything in the universe is discretized into particles, then there really is no such thing as a perfect circle.
[deleted] ยท 4 points ยท Posted at 15:25:11 on May 25, 2016 ยท (Permalink)
Math is a language, really. It's a way to express what we see when we observe the universe, it's not an observation in and of itself.
deepsoulfunk ยท 725 points ยท Posted at 16:42:00 on May 25, 2016 ยท (Permalink)
There is a prime number named after one of the seven princes of hell.
1000000000000066600000000000001
Belphegor's Prime
scratchisthebest ยท 97 points ยท Posted at 18:29:46 on May 25, 2016 ยท (Permalink)
another fun prime number: 1025742 - 1012871 -1 (which consists of 25741 9's and one 8)
(via @bballing1 on twitter)
Sambob0418 ยท 5 points ยท Posted at 22:00:28 on May 25, 2016 ยท (Permalink)
Would 25742 9's and one 8 also be a prime?
mjmaher81 ยท 6 points ยท Posted at 22:49:47 on May 25, 2016 ยท (Permalink)
Depends on where the 8 is, and also has the chance of no position being prime.
[deleted] ยท 1 points ยท Posted at 22:26:17 on May 25, 2016 ยท (Permalink)
[deleted]
ryrysweetiepie ยท 5 points ยท Posted at 22:28:07 on May 25, 2016 ยท (Permalink)
not if the 8 wasn't at the end
IHaveGotQuestions ยท 4 points ยท Posted at 08:48:50 on May 26, 2016 ยท (Permalink)
Hey, /u/99999999999999999989, is that a relative of yours?
99999999999999999989 ยท 5 points ยท Posted at 12:30:55 on May 26, 2016 ยท (Permalink)
We call him Fat Uncle Vinny.
onemanlan ยท 3 points ยท Posted at 22:33:53 on May 25, 2016 ยท (Permalink)
I believe there is a numberphile ep that covers this number as well. Could dig it up if you're interested.
loptthetreacherous ยท 2 points ยท Posted at 10:45:26 on May 26, 2016 ยท (Permalink)
That would be /u/99999999999999999989 's older brother.
coffedrank ยท 1 points ยท Posted at 08:11:32 on May 26, 2016 ยท (Permalink)
you're right, that was fun
VaultBoy3 ยท 13 points ยท Posted at 22:37:02 on May 25, 2016 ยท (Permalink)
It's also a palindrome! I didn't know there were any prime palindromes besides the one digit primes. Then again, I never really considered the possibility before.
uberguby ยท 13 points ยท Posted at 22:47:23 on May 25, 2016 ยท (Permalink)
Well... Uh... There's 11.
And someone will probably give us the next one
Edit:You know what i think it's 111 but someone better should be along shortly to confirm or disprove it
VaultBoy3 ยท 7 points ยท Posted at 22:54:44 on May 25, 2016 ยท (Permalink)
I checked and it would be 101, not 111. 111 is not prime as it is a multiple of 3 and 37.
uberguby ยท 6 points ยท Posted at 22:59:08 on May 25, 2016 ยท (Permalink)
That's like math porn to me.
Also I'm really disapointed I didn't try and factor that myself, now that I know I would have hit it at 3.
VaultBoy3 ยท 3 points ยท Posted at 23:08:46 on May 25, 2016 ยท (Permalink)
Not to worry. Also, if you're interested, I started a palindromic prime counting thread over at /r/counting. Here is the link: redd.it/4l2ebv
VaultBoy3 ยท 1 points ยท Posted at 23:11:41 on May 25, 2016 ยท (Permalink)
Oops. I should have checked first. There already is a thread for that. Disregard mine and join here: redd.it/4ji415
uberguby ยท 1 points ยท Posted at 23:38:00 on May 25, 2016 ยท (Permalink)
...yeah, sure, why not.
[deleted] ยท 1 points ยท Posted at 23:09:23 on May 25, 2016 ยท (Permalink)
An easy way to check if something is divisible by three is to see if the digits add up to be a multiple of 3. (It's not as easy when you have huge numbers though.)
Stevey854 ยท 3 points ยท Posted at 23:44:21 on May 25, 2016 ยท (Permalink)
Just keep adding the digits untill it's manageable.
Edmonty ยท 22 points ยท Posted at 19:58:33 on May 25, 2016 ยท (Permalink)*
How many zeros are those, im drunk
edit : 13 zeros each side the voice in my head helped me
Slingshot_Louie ยท 23 points ยท Posted at 20:25:51 on May 25, 2016 ยท (Permalink)
At least 8.
Source: sober.
uberguby ยท 8 points ยท Posted at 22:29:13 on May 25, 2016 ยท (Permalink)
Classic Belphagor
Pixel_Veteran ยท 5 points ยท Posted at 22:33:19 on May 25, 2016 ยท (Permalink)
BELIAL. BEHEMOTH. BEELZEBUB.
ADAMANTIUM1802 ยท 6 points ยท Posted at 22:39:15 on May 25, 2016 ยท (Permalink)
ASMODEUS. SATANAS. LUCIFER.
uberguby ยท 9 points ยท Posted at 22:46:30 on May 25, 2016 ยท (Permalink)
HEART! GO PLANET!
KickItInTheNutz ยท 2 points ยท Posted at 05:52:03 on May 26, 2016 ยท (Permalink)
That is so great. 666 with 13 zeroes on each side and two 1 devil horns. and 14 digits on either side divided by 2 devil horns is 1/7th or 1 of the 7 princes of hell. Yay symbolic conspiracy math.
BecauseWeCan ยท 2 points ยท Posted at 22:09:08 on May 25, 2016 ยท (Permalink)
First I read "printers of hell". I should go sleep now.
denikar ยท 11450 points ยท Posted at 11:09:01 on May 25, 2016 ยท (Permalink)
x% of y is the same as y% of x
971365 ยท 4990 points ยท Posted at 13:34:37 on May 25, 2016 ยท (Permalink)
For example, if you need to figure out 2% of 50, it would be easier to get 50% of 2.
ImApoopieFartFaceAMA ยท 2412 points ยท Posted at 15:26:11 on May 25, 2016 ยท (Permalink)
This blew my mind.
Bspammer ยท 1097 points ยท Posted at 16:48:39 on May 25, 2016 ยท (Permalink)
I mean it looks more amazing because of the % symbol, but really if you do it with actual numbers it's pretty obvious that 0.02*50 = 2*0.5. You multiply one number by 100 and divide the other by 100 so of course the total stays the same.
tommit ยท 45 points ยท Posted at 17:07:53 on May 25, 2016 ยท (Permalink)
Exactly. And when you look at it in fractions, it becomes even more clear imo.
(1/50)*2
(2/50)*1
(1*2)/50 = (2*1)/50.
Looking at it like this, it may actually not make it more clear for everyone, but hey it's just another intuition.
telegetoutmyway ยท 35 points ยท Posted at 17:35:14 on May 25, 2016 ยท (Permalink)
I'm just gonna piggy back onto you to make it even more clear for some.
The percents in fraction form:
(2/100) * 50 = 2 * (50/100)
Same thing everyone's been saying but visually leaving in that the % symbol is the same as (1/100).
SqueakzMcGee ยท 14 points ยท Posted at 18:10:22 on May 25, 2016 ยท (Permalink)
And making it even more clear than that...
(2 * 50)/100 = (2 * 50)/100
mcal24 ยท 18 points ยท Posted at 18:38:47 on May 25, 2016 ยท (Permalink)
And to make it a little more clear, cancel the 2, the 50, and the 100, leaving you with 1=1
Flamingtomato ยท 21 points ยท Posted at 19:07:11 on May 25, 2016 ยท (Permalink)*
Then to really illustrate the point you can write it as 2+epi*i = 1
Then since 2 equals 2(2 + epi*i) , which we get from the above equation, we can write it as 4+3epi*i = 1
Extending this we can see a pattern and get n+(n-1)epi*i = 1
q.e.d.
[deleted] ยท 14 points ยท Posted at 20:03:47 on May 25, 2016 ยท (Permalink)
[deleted]
Triantaffelow ยท 2 points ยท Posted at 20:10:42 on May 25, 2016 ยท (Permalink)
It has, if anything, become TOO clear.
jvjanisse ยท 1 points ยท Posted at 07:30:36 on May 26, 2016 ยท (Permalink)
I'm sure you confused a lot of people with those fractions because they're not the same as 2% of 50, you did 2% of 2.
freeflowfive ยท 1 points ยท Posted at 14:58:04 on July 3, 2016 ยท (Permalink)
Actually I think it's just easier to look at it like this: x% of y = x*y/100 = y% of x ?
patrickmurphyphoto ยท 4 points ยท Posted at 18:53:45 on May 25, 2016 ยท (Permalink)
Thanks, this is the info I need to actually remember this trick for longer than an afternoon
Matrillik ยท 6 points ยท Posted at 22:03:37 on May 25, 2016 ยท (Permalink)
What's amazing is that this was the second highest comment when I came across it.
Favorite math fact: Multiplication is commutative.
Y'all need junior high school.
wiithepiiple ยท 3 points ยท Posted at 20:57:28 on May 25, 2016 ยท (Permalink)
Think of the percent as a number. 2*%*50 = 2*50*%
improperlycited ยท 3 points ยท Posted at 14:54:34 on May 26, 2016 ยท (Permalink)
Especially since percent literally is a number: 1/100
Lobo2ffs ยท 3 points ยท Posted at 19:33:46 on May 25, 2016 ยท (Permalink)
One that made me pause for a bit in trigonometry was that 1/sqrt(2) was the same as sqrt(2)/2. But of course, multiplying either of them by 1 = sqrt(2)/sqrt(2) and then simplifying leaves the other.
jyonsin ยท 3 points ยท Posted at 19:35:40 on May 25, 2016 ยท (Permalink)
Yeah I'm kind of upset this got gold.
evilone17 ยท 3 points ยท Posted at 17:49:37 on May 25, 2016 ยท (Permalink)
Shh just let him enjoy this.
mahmudzero ยท 1 points ยท Posted at 19:01:29 on May 25, 2016 ยท (Permalink)
This way is more mind blowing for me
plantfollower ยท 1 points ยท Posted at 21:33:34 on May 25, 2016 ยท (Permalink)
Booooo. Go away. Magic is more fun. :)
extraordinary15 ยท 1 points ยท Posted at 21:33:57 on May 25, 2016 ยท (Permalink)
You made it hard again :(
bestbiff ยท 1 points ยท Posted at 22:57:17 on May 25, 2016 ยท (Permalink)
I prefer the magic explanation.
Bonolio ยท 1 points ยท Posted at 03:57:37 on May 26, 2016 ยท (Permalink)
Or 2/100x50=2x50/100
JackBond1234 ยท -15 points ยท Posted at 17:53:42 on May 25, 2016 ยท (Permalink)
This is incorrect.
0.02/50=1/2500
2/0.5=4
You have to multiply or divide the numerator and the denominator by the same amount. Not multiply one and divide the other.
Bspammer ยท 8 points ยท Posted at 17:55:27 on May 25, 2016 ยท (Permalink)
Show me where the fractions are in my comment...
JackBond1234 ยท 1 points ยท Posted at 21:39:39 on May 25, 2016 ยท (Permalink)
Either I'm spacing, or just illiterate, but what are you denoting with the backslashes if not fractions?
Bspammer ยท 1 points ยท Posted at 00:42:25 on May 26, 2016 ยท (Permalink)
I dunno what you're using to read reddit but those backslashes are to cancel the asterisks to stop them from italicizing the text. without backslashes, *with backslashes*. You shouldn't be able to see them.
JackBond1234 ยท 2 points ยท Posted at 11:52:14 on May 26, 2016 ยท (Permalink)
Ohhhh shoot, I'm on the official reddit app, and it's really weird about formatting notation
bietekwiet ยท 3 points ยท Posted at 19:32:57 on May 25, 2016 ยท (Permalink)
it works because
% ofjust means* 0.01 *.So
2% of 50becomes2 * 0.01 * 50which is equal to50 * 0.01 * 2aka50% of 2.Random832 ยท 1 points ยท Posted at 21:07:10 on May 25, 2016 ยท (Permalink)
You can break it down further;
%means* 0.01andofmeans*(as in "half of", "two of", etc.)plipyplop ยท 5 points ยท Posted at 16:41:36 on May 25, 2016 ยท (Permalink)
Same! My jaw actually dropped with this one.
Nicekicksbro ยท 2 points ยท Posted at 19:26:27 on May 25, 2016 ยท (Permalink)
I feel like my life would have been so much easier if I knew this.
KristinnK ยท 1 points ยท Posted at 16:49:40 on May 25, 2016 ยท (Permalink)
Mine too! I mean I've known for a long time that multiplication is independent of the order, ab=ba. But for some reason I've never thought to use the fact to more intuitively calculate percentages.
[deleted] ยท 1 points ยท Posted at 20:49:43 on May 25, 2016 ยท (Permalink)
This is ACTUALLY me as I read this ...
I can actually use this for work. I do a shit ton of math for work, I am 40, and I have used math most of my life for work, and I did not know this. Holy shit I am blown away
YouBlewMyMind ยท 1 points ยท Posted at 21:03:30 on May 25, 2016 ยท (Permalink)
Brah
Lucidmike78 ยท 1 points ยท Posted at 23:21:37 on May 25, 2016 ยท (Permalink)
more simpler way to do this is x * y, then divide by 100 (just move two decimal places).
bucket888 ยท 1 points ยท Posted at 02:42:40 on May 26, 2016 ยท (Permalink)
Want to know how much you save when something is 20% off? How about how much 20% of your meal was for a tip? Example: 20% of 47 = 2 X 4.7 = $9.40.
ThePr1d3 ยท 1 points ยท Posted at 17:56:39 on May 25, 2016 ยท (Permalink)
I like how people are amazed when it is kinda obvious. (x*y)/100 = (y *x)/100
Yet it seems no one thought about it
muuus ยท 3 points ยท Posted at 18:54:34 on May 25, 2016 ยท (Permalink)
People get confused when they see percents.
Baeshun ยท 115 points ยท Posted at 15:27:45 on May 25, 2016 ยท (Permalink)
Game changer!
LifeCrisisKate ยท 461 points ยท Posted at 16:34:50 on May 25, 2016 ยท (Permalink)*
WTF, why didn't anyone teach me this?! This literally changes everything.
Edit: I get it, you guys are very impressed with your mathematical knowledge, and this concept should be "obvious". The point is that the association between cumulative multiplication DOESN'T necessarily easily translate into real-world applications like calculating percents. This concept wouldn't have over 5000 upvotes if people didn't agree, so get off your damn high horse.
Mac2492 ยท 11 points ยท Posted at 21:36:58 on May 25, 2016 ยท (Permalink)*
100% is the same as 100/100 or 1.0
50% is the same as 50/100 or 0.50
If you want to get 50% of 40 then it's just 50/100 * 40. You can simply reorder this to 50*40 (or 40*50) / 100, which is equivalent to moving the decimal point to the left twice. This gives you 2000./100 = 20.00 = 20. In some cases it's easier to simplify the fraction first. Here 50/100 = 5/10 = 1/2, so you can get 50% of something just by dividing that number by 2.
This operation works in reverse as well. If you want to multiply something by 25 you can instead multiply it by 100 and divide it by 4 (because 100/4 is 25). In other words, just divide the number by 4 and move the decimal to the right two times.
64 * 25 = 64/4 * 100 = 1600
You can calculate discounts pretty easily in this same manner. If a product is 30% off that's the same as saying it's 30% off 100%. This is just 100%-30% = 70%. You can now calculate the final price if you multiply by 70 and move the decimal point to the left twice.
30% off $95 = 70*95 / 100 = $66.50
Personally, I tend to ignore trailing 0s for quick mental math and put the decimal point back "logically". Why keep track of more digits when you don't have to? Let's say you want 40% off $95. 40% off means you want 60% of the original value. 95 times 6 is 570. You know it can't be $5.7 or $570 so the correct result is obviously $57 even if you forgot how many zeros were in the problem to begin with!
As a final tip, it's still manageable to calculate something like 45% of 75 mentally (though depending on the purpose you may just want to round). I'll usually tackle this by using the distributive property to turn the problem into 40% of 75 plus 5% of 75. For this I'll use the "ignoring zero trick", though feel free not to, to get 4*75 = 300 => 30 by logic. For the second part it's just 5*75 = 375 => 3.75 by logic (5% should be less than 40%). Add them together to get 33.75. It takes some practice, but my best advice is to use whatever shortcut helps you get the answer easily and accurately. Break the problem into pieces that you understand and don't listen if someone says there's only one way to solve a simple math problem. For example, if you are good at visualizing things then you can straight up picture
45
x 75
and use your mind like a chalkboard. If you're terrible at visualizing but good at recognizing patterns then you can transform that 75 into "3/4" and turn the problem into 45*3/4-- a fairly simple multiplication followed by a simple division.
How does this work?
45% * 75 = 45 * 75% = 45 * 75/100 = 45 * 3/4
As usual, you can ignore trailing zeros or percent signs and figure out where to put the decimal point logically. The final answer has to be remotely close to 50% of 75 (37.5). It can't be larger than 75 (337.5) or super puny (3.375) so you can deduce that the correct place to put the decimal point is 33.75.
It's disappointing that so many schools teach rigid, inflexible approaches to problem-solving that carry on to adulthood. For example, I do my arithmetic from left to right because reading the numbers left->right and solving the problem right->left makes me constantly forget and scramble digits. It's pointless to teach people the commutative and distributive properties without also teaching students how to adapt them into their own solutions and benefit from them. Tricks for doing higher math are fascinating, but it really hits home for me when some of the most basic properties of math are considered an eye-opener. It's really sad how cool so many things are and how uncool we end up thinking they are simply because of the way they're taught in school.
Terrafire123 ยท 12 points ยท Posted at 22:19:05 on May 25, 2016 ยท (Permalink)
An utterly amazing example of "Figuring out the zeros later" came from a redditor a few comments down.
"What's 3% of 7?"
3x7 = 21
212.10.21 looks about right.You can solve something so stupidly complicated in under 10 seconds, easily.
Chicken_McFlurry ยท 3 points ยท Posted at 21:55:29 on May 25, 2016 ยท (Permalink)
I really enjoyed this. Thanks :)
[deleted] ยท 3 points ยท Posted at 20:47:22 on May 25, 2016 ยท (Permalink)
Because mathematics education is almost universally awful, but that's not helped by the cultural attitude most seem to have towards the subject for some reason.
TheVeryMask ยท 1 points ยท Posted at 02:31:01 on May 26, 2016 ยท (Permalink)
Arithmetic is to maths what spelling is to literature. If your art classes was nothing but how to apply primer paint from first year through graduation, you'd hate art.
[deleted] ยท 9 points ยท Posted at 19:44:01 on May 25, 2016 ยท (Permalink)
Maybe the next thing someone will teach you is the definition of literally
dupelize ยท 7 points ยท Posted at 22:24:36 on May 25, 2016 ยท (Permalink)*
Interesting fact: Literally has been used to mean figuratively literally since the word started being used.
Of course I am using literally to mean figuratively here, but it has actually been used for a couple hundred years IIRC. I'll check for a...(edit) source. Not the best, but I have literally millions of other things to do.
[deleted] ยท 9 points ยท Posted at 22:32:39 on May 25, 2016 ยท (Permalink)
Why are there so many redditors who simply don't know this or they refuse to accept it's true.
MrFace1 ยท 5 points ยท Posted at 00:17:54 on May 26, 2016 ยท (Permalink)
It removes their ability to be annoying pedants. Can't have that.
TheVeryMask ยท 1 points ยท Posted at 02:25:34 on May 26, 2016 ยท (Permalink)
There are many ways to say "figuratively", but only one word for "literally". If you lose its meaning, you no longer have a way to refer to or use that concept.
chromeless ยท 1 points ยท Posted at 03:36:50 on May 26, 2016 ยท (Permalink)
Pretty much this. Literally is the one word I'm happy to have policed, since all of its power comes from its unambiguity in principal. Even if it was used in a particular way before, it's better to make sure as few people use it figuratively in excessive ways as possible.
kangareagle ยท 2 points ยท Posted at 23:27:39 on May 25, 2016 ยท (Permalink)
I think that someone needs to teach you the definition of definition.
Solkre ยท 6 points ยท Posted at 18:29:25 on May 25, 2016 ยท (Permalink)
It's like my teacher trying to explain the exact situations when you can, or can't use a comma. Then someone just tells you it's when you want to pause. It's correct often enough for me!
worsedoughnut ยท 8 points ยท Posted at 19:47:45 on May 25, 2016 ยท (Permalink)
Yeah that's not always correct though. Especially in current vernacular where people abuse commas where they might pause if they were speaking, yet it does not apply at all in the same sentence when in writing.
Solkre ยท 15 points ยท Posted at 20:04:30 on May 25, 2016 ยท (Permalink)
It's close enough, for me.
Sometimes, I like, to use the, Shatner Comma!
TheVeryMask ยท 1 points ยท Posted at 02:29:32 on May 26, 2016 ยท (Permalink)
The reverse of this is why Christopher Walken talks like that. He used commas his own set of rules, and when his teachers told him not to, he exaggerated his verbal pauses to match his comma rules. After trolling for a consistent while, it stuck.
Caleb_Krawdad ยท 2 points ยท Posted at 20:39:21 on May 25, 2016 ยท (Permalink)
It's just tyke associative property of where to apply multiplying by .01
I-Downloaded-a-Car ยท 3 points ยท Posted at 19:54:46 on May 25, 2016 ยท (Permalink)
Am I the only one this was obvious to?
ImTheGuyWithTheGun ยท 3 points ยท Posted at 01:50:57 on May 26, 2016 ยท (Permalink)
Yes, snowflake. Yes.
kanated ยท 1 points ยท Posted at 22:17:51 on May 25, 2016 ยท (Permalink)
If you use percentages it's hard to figure out. If you just write 0.02*50 it's pretty obvious that that's the same as 2*0.5. Either way is equal to 2*50*0.01, you just choose which number to multiply by 0.01.
Adolf_rockwell ยท 1 points ยท Posted at 08:36:15 on May 26, 2016 ยท (Permalink)
In algebra 2 I was taught what of in math means multiply and I thought "no way, Isnt it when you divide". But I have never found that rule to be wrong. So then when you find some percentage of something you just multiply the percentage times the thing. And due to the combative property either one can go first.
Imsdal2 ยท 0 points ยท Posted at 19:52:33 on May 25, 2016 ยท (Permalink)
No, it doesn't change anything. If it did, it wouldn't stay the same...
super_aardvark ยท 0 points ยท Posted at 21:14:34 on May 25, 2016 ยท (Permalink)
I'm sure there's a really good your-mom joke to be made here, but I can't quite put it together. sigh... I was so much more clever before you discovered this math fact.
[deleted] ยท 0 points ยท Posted at 21:58:22 on May 25, 2016 ยท (Permalink)
Know it by intuition?
rtomek ยท 0 points ยท Posted at 23:09:08 on May 25, 2016 ยท (Permalink)
Because the percent sign literally means that the number is a fraction with a denominator of 100. If you were taught multiplications of fractions in school, they taught you how to do this.
StressOverStrain ยท 0 points ยท Posted at 23:13:25 on May 25, 2016 ยท (Permalink)
You were taught this when you learned the definition of what a percent is: a fraction of 100. 2/100 reduces to 1/50 and 1/50 of 50 is obviously 1.
Anyone who bothered to learn math in grade school finds both operations trivial.
ManPumpkin ยท 0 points ยท Posted at 04:25:16 on May 26, 2016 ยท (Permalink)
High education standard, not high horse.
Dr-K-G ยท -2 points ยท Posted at 19:20:40 on May 25, 2016 ยท (Permalink)
Nobody taught you that multiplication is commutative?
Mathnetic ยท 66 points ยท Posted at 16:27:47 on May 25, 2016 ยท (Permalink)
And if you need to figure out 3% of 7, it would be easier to get 7% of 3.
PeteEckhart ยท 33 points ยท Posted at 16:46:02 on May 25, 2016 ยท (Permalink)
Yea!! Oh fuck...
Tromboneofsteel ยท 7 points ยท Posted at 17:23:51 on May 25, 2016 ยท (Permalink)
It's not too hard.
3%= .03
3x7 = 21
So .03x7 = .21
It's how I do tips at restaurants
PeteEckhart ยท 2 points ยท Posted at 17:53:56 on May 25, 2016 ยท (Permalink)
It was a joke...
Ordies ยท -3 points ยท Posted at 18:35:09 on May 25, 2016 ยท (Permalink)
People can normally find the percent of something.
If you can't, you're still in school I hope.
film_composer ยท -2 points ยท Posted at 16:59:35 on May 25, 2016 ยท (Permalink)*
Both of those are still trivialโฆ
EDIT: Downvoted because multiplying 3 and 7 and then dividing by 100 apparently is /r/iamverysmart-level pretentiousness.
MrLmao3 ยท 1 points ยท Posted at 03:48:29 on May 26, 2016 ยท (Permalink)
No, you are being down voted because instead of being helpful, you just insulted anyone that didn't understand it.
deusnefum ยท 4 points ยท Posted at 17:27:27 on May 25, 2016 ยท (Permalink)
I'd say the other way around.
7% of 3? Hard.
3% of 7? Much easier.
1% of 7 is 0.07 and 3 times that is 0.21.
nut_hoarder ยท 6 points ยท Posted at 17:53:52 on May 25, 2016 ยท (Permalink)
But everything you just did can be used for 7% of 3 just as easily...
LiquidSilver ยท 2 points ยท Posted at 18:56:14 on May 25, 2016 ยท (Permalink)
Percentages are just easy, nothing we can do about it.
JFosters ยท 7 points ยท Posted at 16:52:02 on May 25, 2016 ยท (Permalink)
Broan13 ยท 1 points ยท Posted at 18:43:22 on May 25, 2016 ยท (Permalink)
This is when doing the multiplication is perhaps best...
stillusesAOL ยท 0 points ยท Posted at 17:16:16 on May 25, 2016 ยท (Permalink)
:(
christhesexyone ยท 9 points ยท Posted at 16:28:15 on May 25, 2016 ยท (Permalink)
My girlfriend was taking an online exam while I was over, and was freaking out over percentages when I told her this. She looked at me like I changed her life.
BloodFartTheQueefer ยท 3 points ยท Posted at 16:53:00 on May 25, 2016 ยท (Permalink)
To do these I usually just multiply one of them to 10 by some factor n (in this case, 2) and divide the other by the same factor. 2/2 = 1, out of the 100%
weezyheff ยท 5 points ยท Posted at 15:39:35 on May 25, 2016 ยท (Permalink)
Thank you sir
Youreprobablygay ยท 2 points ยท Posted at 16:01:30 on May 25, 2016 ยท (Permalink)
Fuckin eh
komali_2 ยท 2 points ยท Posted at 16:14:26 on May 25, 2016 ยท (Permalink)
FUCK
chefatwork ยท 2 points ยท Posted at 17:04:50 on May 25, 2016 ยท (Permalink)
Oh my fucking word.
[deleted] ยท 2 points ยท Posted at 18:11:50 on May 25, 2016 ยท (Permalink)
WOWAWA. I work with stats all day every day and never realised this WHAT THE FUCK. This genuinely sits in my top 3 revelations.
morcerfel ยท 1 points ยท Posted at 16:59:03 on May 25, 2016 ยท (Permalink)
This is the exact comment that was posted the last time this askreddit was posted.
Tillos ยท 1 points ยท Posted at 16:59:52 on May 25, 2016 ยท (Permalink)
I'm speechless. I love you. Why wasn't I taught this?
BelongingsintheYard ยท 1 points ยท Posted at 17:21:38 on May 25, 2016 ยท (Permalink)
Wut?
Ujio2107 ยท 1 points ยท Posted at 17:33:21 on May 25, 2016 ยท (Permalink)
someone has been studying for the GMAT...at least that's where I read that. Or maybe it was Reddit..
kidbeer ยท 1 points ยท Posted at 18:05:00 on May 25, 2016 ยท (Permalink)
So if needed to know what 3% of 100 is, I could just figure out 100% of 3! Thanks!
IWugYouWugHeSheMeWug ยท 1 points ยท Posted at 18:28:59 on May 25, 2016 ยท (Permalink)
It's only easier if you have simple numbers like that. I would say 90% of 8 and 8% of 90 take an equal amount of work to figure out. But it's not really hard. Just take 1% or 10% and multiply. 10% of 8 is .8, 100 - 10 = 90, so 8 - 0.8 = 7.2.
wasirapd ยท 1 points ยท Posted at 18:39:47 on May 25, 2016 ยท (Permalink)
This is my favorite thread. All this stuff is so freaking useful
daemon01001 ยท 1 points ยท Posted at 20:23:30 on May 25, 2016 ยท (Permalink)
Flips Table Im done. My brain needs to nap now.
[deleted] ยท 1 points ยท Posted at 20:47:12 on May 25, 2016 ยท (Permalink)
In that case it's just as easy to find 1% of 50 then multiply by 2.
kawarazu ยท 1 points ยท Posted at 21:21:28 on May 25, 2016 ยท (Permalink)
I'm really dumb thank you for doing that.
supafly208 ยท 1 points ยท Posted at 21:26:04 on May 25, 2016 ยท (Permalink)
Whoooaaaaa.... this would have made school easier.
llamaman17 ยท 1 points ยท Posted at 21:53:49 on May 25, 2016 ยท (Permalink)
1?
drichk ยท 1 points ยท Posted at 22:17:31 on May 25, 2016 ยท (Permalink)
Tried to do that in a restaurant. Instead of doing 18% of $23.74, I tried to do 23.74% of 18. My brain melted.
notjames1 ยท 1 points ยท Posted at 00:06:03 on May 26, 2016 ยท (Permalink)
haven't I seen this comment years ago?
971365 ยท 1 points ยท Posted at 05:58:49 on May 26, 2016 ยท (Permalink)
It was in the last thread though I don't remember the numbers exactly.
DocJawbone ยท -2 points ยท Posted at 16:01:11 on May 25, 2016 ยท (Permalink)*
But wait... 25% of 100 is 4, but 100% of 25 is 25. What am I doing wrong?
EDIT: omg I had a total brain lapse guys. This is embarrassing. If only you knew what I did for a living
iHateTetris ยท 36 points ยท Posted at 16:05:54 on May 25, 2016 ยท (Permalink)
what?
Canvaverbalist ยท 5 points ยท Posted at 16:17:30 on May 25, 2016 ยท (Permalink)
Ahah, he just made a silly mistake:
DocJawbone ยท 1 points ยท Posted at 19:10:16 on May 25, 2016 ยท (Permalink)
Yes you are right. And boy, is my inbox paying for that silly, silly mistake.
Canvaverbalist ยท 1 points ยท Posted at 19:41:13 on May 25, 2016 ยท (Permalink)
Ahah it's okay, you're far from the bad guys here! Out of sheer curiosity, what do you do for a living?
DocJawbone ยท 1 points ยท Posted at 19:57:48 on May 25, 2016 ยท (Permalink)
I can't even say, I'm too embarrassed!
JimmyBoombox ยท 10 points ยท Posted at 16:10:18 on May 25, 2016 ยท (Permalink)
You need more math classes.
dustontheground ยท 4 points ยท Posted at 16:06:18 on May 25, 2016 ยท (Permalink)
25% of 100 is 25.
fnord_happy ยท 3 points ยท Posted at 16:17:08 on May 25, 2016 ยท (Permalink)
Dude per cent literally means per hundred. So any per cent of hundred is just that number.
isrly_eder ยท 3 points ยท Posted at 16:46:33 on May 25, 2016 ยท (Permalink)
this is hilarious
Streetwalker- ยท 2 points ยท Posted at 16:06:48 on May 25, 2016 ยท (Permalink)
No 25% of 100 is 25 not 4.
PM_ME_YOUR_MESMER ยท 2 points ยท Posted at 16:29:23 on May 25, 2016 ยท (Permalink)
25% of 100 is not the same as 100/25:
100/25 = 4
25% of 100 == 1/4 of 100 == (1 x 100)/4 = 25
And then 100% of 25 = 25
971365 ยท 1 points ยท Posted at 16:16:57 on May 25, 2016 ยท (Permalink)
Must have divided 100 by 25 by mistake
Dexaan ยท 1 points ยท Posted at 17:47:36 on May 25, 2016 ยท (Permalink)
25% of 100 is 25, not 4.
MustBeNice ยท 1 points ยท Posted at 16:16:35 on May 25, 2016 ยท (Permalink)
Can't tell if making a lame attempt at a joke...or actually retarded.
greenfly ยท 1 points ยท Posted at 17:02:13 on May 25, 2016 ยท (Permalink)
Don't forget - you have to be nice!
amalgam_reynolds ยท 0 points ยท Posted at 17:00:39 on May 25, 2016 ยท (Permalink)
Less helpful when you need to figure out what 37% of 219 is.
liarandathief ยท 4874 points ยท Posted at 11:55:33 on May 25, 2016 ยท (Permalink)
10% of 100 is 10
100% of 10 is 10
checks out.
christoffles ยท 5778 points ยท Posted at 12:55:53 on May 25, 2016 ยท (Permalink)
classic engineer's proof by example
Nebathemonk ยท 2543 points ยท Posted at 13:46:08 on May 25, 2016 ยท (Permalink)
First, we have to assume that this percentage is in a perfect vacuum. Also, each 0 is a perfect sphere.
Ky1arStern ยท 1572 points ยท Posted at 14:15:14 on May 25, 2016 ยท (Permalink)
And frictionless!
rzezzy1 ยท 1123 points ยท Posted at 14:58:42 on May 25, 2016 ยท (Permalink)
With uniform mass!
[deleted] ยท 956 points ยท Posted at 15:11:55 on May 25, 2016 ยท (Permalink)
And no radiation heat transfer!
[deleted] ยท 748 points ยท Posted at 15:16:43 on May 25, 2016 ยท (Permalink)
In a smooth pipe!
PublicAngelZero ยท 560 points ยท Posted at 15:30:26 on May 25, 2016 ยท (Permalink)
With a uniformly distributed energy input.
[deleted] ยท 479 points ยท Posted at 15:37:59 on May 25, 2016 ยท (Permalink)
And a uniform flow velocity.
FINALAVENUE ยท 37 points ยท Posted at 16:22:07 on May 25, 2016 ยท (Permalink)
Don't forget to assume steady state.
[deleted] ยท 44 points ยท Posted at 16:36:03 on May 25, 2016 ยท (Permalink)
I don't know how not to.
Octofur ยท 11 points ยท Posted at 17:48:41 on May 25, 2016 ยท (Permalink)
gotta assume constant properties at control surfaces too
gr4_wolf ยท 15 points ยท Posted at 17:54:47 on May 25, 2016 ยท (Permalink)
and inviscid and laminar flow
BrundenG ยท 13 points ยท Posted at 18:49:46 on May 25, 2016 ยท (Permalink)
and adiabatic
ldr5 ยท 9 points ยท Posted at 19:34:31 on May 25, 2016 ยท (Permalink)
Don't forget that it's also a homogenous mixture, atmospheric pressure, has a reflux ratio of about 1.4...
TunaLobster ยท 9 points ยท Posted at 19:55:13 on May 25, 2016 ยท (Permalink)
And zero electrical resistance.
adamrsb48 ยท 7 points ยท Posted at 20:04:05 on May 25, 2016 ยท (Permalink)
With a perfectly convex reflective surface.
[deleted] ยท 7 points ยท Posted at 20:42:43 on May 25, 2016 ยท (Permalink)
[Intelligent input.]
lgastako ยท 6 points ยท Posted at 20:59:31 on May 25, 2016 ยท (Permalink)
And a sufficiently smart compiler.
shybamboo ยท 2 points ยท Posted at 23:38:20 on May 25, 2016 ยท (Permalink)
[Sounds like an intelligent input, but in actuality a huge simplification of something that is super complicated that we don't know how to solve accurately yet]
[deleted] ยท 1 points ยท Posted at 00:44:27 on May 26, 2016 ยท (Permalink)
In a uniform magnetic field.
btribble ยท 1 points ยท Posted at 02:35:12 on May 26, 2016 ยท (Permalink)
And the equals sign does not convey any gravitational effects.
Masstch ยท 1 points ยท Posted at 22:34:52 on May 25, 2016 ยท (Permalink)
KLaxxon alarm!! He said "about"! Security! We have a breach!This fellow used a vague number! You, sir, are no Enjuneer
ldr5 ยท 1 points ยท Posted at 12:55:36 on May 26, 2016 ยท (Permalink)
Reflux ratio of 1.4 is just the ideal starting point and it gets tweaked as you go through your calculations! Oh no what have I done, the world is going to collapse into a black hole and the sun is going to explode!!!!! ๐ฑ๐ฑ๐ฑ๐ฑ๐ฑ
BEN_therocketman ยท 14 points ยท Posted at 18:19:46 on May 25, 2016 ยท (Permalink)
And my axe.
LewsTherinTelamon ยท 2 points ยท Posted at 21:50:25 on May 25, 2016 ยท (Permalink)
And
my bow!a Boltzmann distribution of velocities!SurprisedPotato ยท 2 points ยท Posted at 01:13:11 on May 26, 2016 ยท (Permalink)
Neglecting rotational effects!
zachm26 ยท 1 points ยท Posted at 07:30:30 on May 26, 2016 ยท (Permalink)
Wind resistance is negligible.
VikingTeddy ยท 1 points ยท Posted at 18:37:33 on May 25, 2016 ยท (Permalink)
And no particle decay.
Robo94 ยท 5 points ยท Posted at 18:09:43 on May 25, 2016 ยท (Permalink)
This honestly deserves gold for how true it is.
[deleted] ยท 3 points ยท Posted at 18:57:05 on May 25, 2016 ยท (Permalink)
<3
giantEngineer ยท 5 points ยท Posted at 18:57:48 on May 25, 2016 ยท (Permalink)
And isentropic
tylertennisman ยท 12 points ยท Posted at 16:03:50 on May 25, 2016 ยท (Permalink)
In a closed system
[deleted] ยท 5 points ยท Posted at 17:24:11 on May 25, 2016 ยท (Permalink)
Assuming Newtonian fluid.
Ozijj ยท 2 points ยท Posted at 16:31:51 on May 25, 2016 ยท (Permalink)
On a monday
panascope ยท 7 points ยท Posted at 15:41:10 on May 25, 2016 ยท (Permalink)
It's okay, I put a safety factor of 4 on it!
JWson ยท 9 points ยท Posted at 15:48:42 on May 25, 2016 ยท (Permalink)
Let's round the safety factor to 10, just to be safe!
BLAZINGSORCERER199 ยท 4 points ยท Posted at 16:04:44 on May 25, 2016 ยท (Permalink)
and a uniform magnetic field
piperiain ยท 3 points ยท Posted at 17:53:18 on May 25, 2016 ยท (Permalink)
AND MY AXE!
nellis_island ยท 3 points ยท Posted at 16:15:30 on May 25, 2016 ยท (Permalink)
With all objects described by an infinitely small point
helloreddits456464 ยท 4 points ยท Posted at 17:55:31 on May 25, 2016 ยท (Permalink)
and my Axe.
Educated_Spam ยท 1 points ยท Posted at 17:10:16 on May 25, 2016 ยท (Permalink)
With a constant directional vector!
maybe_awake ยท 1 points ยท Posted at 17:28:29 on May 25, 2016 ยท (Permalink)
This sounds like a sweet pipe!
kevtherev11 ยท 1 points ยท Posted at 17:47:09 on May 25, 2016 ยท (Permalink)
With a 10% safety factor!
[deleted] ยท 1 points ยท Posted at 18:10:24 on May 25, 2016 ยท (Permalink)
I love you guys
kuilin ยท 1 points ยท Posted at 18:22:47 on May 25, 2016 ยท (Permalink)
In an ideal gas
d3m0li5h3r ยท 1 points ยท Posted at 18:31:13 on May 25, 2016 ยท (Permalink)
With clean flash of the OS on the machine
Use_The_Sauce ยท 1 points ยท Posted at 18:46:38 on May 25, 2016 ยท (Permalink)
At sea level
ETChunter95 ยท 1 points ยท Posted at 19:27:55 on May 25, 2016 ยท (Permalink)
And ignore air resistance.
Hahnsolo11 ยท 1 points ยท Posted at 19:31:50 on May 25, 2016 ยท (Permalink)
Laminar flow!
FBIDIRECTOR ยท 1 points ยท Posted at 20:01:46 on May 25, 2016 ยท (Permalink)
I'm just a humble blacksmith but I like this string of comments.
kylerjt ยท 1 points ยท Posted at 20:13:16 on May 25, 2016 ยท (Permalink)
And no air resistance
handlebartender ยท 1 points ยท Posted at 20:33:29 on May 25, 2016 ยท (Permalink)
And a 4.0 GPA.
Wait, what were we talking about again?
gofishx ยท 1 points ยท Posted at 20:36:39 on May 25, 2016 ยท (Permalink)
At non relativistic speeds
[deleted] ยท 1 points ยท Posted at 21:30:10 on May 25, 2016 ยท (Permalink)
Using physical intuition....
thatwentwell ยท 1 points ยท Posted at 21:33:18 on May 25, 2016 ยท (Permalink)
Assuming supersymmetry
HypoG1 ยท 1 points ยท Posted at 22:44:38 on May 25, 2016 ยท (Permalink)
And in a uniform
jedicharliej ยท 1 points ยท Posted at 22:47:10 on May 25, 2016 ยท (Permalink)
And is an ideal black body
Rockonfoo ยท 1 points ยท Posted at 23:15:31 on May 25, 2016 ยท (Permalink)
Damn this dudes got a ton of uniforms on
ShinyPants42 ยท 1 points ยท Posted at 00:19:14 on May 26, 2016 ยท (Permalink)
And a uniform
countnightlock ยท 1 points ยท Posted at 18:35:35 on May 25, 2016 ยท (Permalink)
And my axe!
Birdyer ยท 1 points ยท Posted at 18:58:02 on May 25, 2016 ยท (Permalink)
And my axe!
Daswandiggler ยท 1 points ยท Posted at 20:03:11 on May 25, 2016 ยท (Permalink)
And my axe
[deleted] ยท 1 points ยท Posted at 21:01:43 on May 25, 2016 ยท (Permalink)
and 25% excess of reactant B.
[deleted] ยท 1 points ยท Posted at 04:58:58 on May 26, 2016 ยท (Permalink)
And uniform density
nliausacmmv ยท 23 points ยท Posted at 16:05:16 on May 25, 2016 ยท (Permalink)
And the resistance of the wire is negligible.
jobblejosh ยท 3 points ยท Posted at 18:51:39 on May 25, 2016 ยท (Permalink)
And all collisions are perfectly elastic.
nliausacmmv ยท 1 points ยท Posted at 19:07:13 on May 25, 2016 ยท (Permalink)
At sea level.
deyesed ยท 2 points ยท Posted at 18:25:38 on May 25, 2016 ยท (Permalink)
With laminar flow
Python4fun ยท 1 points ยท Posted at 17:32:00 on May 25, 2016 ยท (Permalink)
infinitely long
linkletonsan ยท 1 points ยท Posted at 03:08:52 on May 26, 2016 ยท (Permalink)
Bow chicka bow wow!
Grayslake_Gisox ยท 6 points ยท Posted at 15:50:59 on May 25, 2016 ยท (Permalink)
And an ohmic resistor
[deleted] ยท 5 points ยท Posted at 16:31:26 on May 25, 2016 ยท (Permalink)
And phenomena I'm not familiar with don't contribute to anything unexpected.
Dremora_Lord ยท 5 points ยท Posted at 16:44:05 on May 25, 2016 ยท (Permalink)
AND MY AXE!
Weirwood_Face ยท 2 points ยท Posted at 20:12:16 on May 25, 2016 ยท (Permalink)
Everything has to be a black body!
betterhappier ยท 1 points ยท Posted at 18:56:02 on May 25, 2016 ยท (Permalink)
How do you explain that to marketing?
iprefertau ยท 1 points ยท Posted at 20:48:27 on May 25, 2016 ยท (Permalink)
you dont
Cpt_seal_clubber ยท 1 points ยท Posted at 23:18:25 on May 25, 2016 ยท (Permalink)
Also applying Rigid Body Mechanics
I_hate_your_nose ยท 4 points ยท Posted at 15:50:55 on May 25, 2016 ยท (Permalink)
Cue relevant xkcd: https://xkcd.com/669/
sensicle ยท 3 points ยท Posted at 15:26:16 on May 25, 2016 ยท (Permalink)
And fractionless.
max96a ยท 1 points ยท Posted at 16:23:39 on May 25, 2016 ยท (Permalink)
The pulleys are always frictionless right?
Hogie23 ยท 1 points ยท Posted at 18:35:06 on May 25, 2016 ยท (Permalink)
Perfectly insulated
ViperZer0 ยท 1 points ยท Posted at 18:38:40 on May 25, 2016 ยท (Permalink)
Obligatory XKCD: https://xkcd.com/669/
sargeantbob ยท 52 points ยท Posted at 14:18:34 on May 25, 2016 ยท (Permalink)
You went too far. You stopped at physics.
[deleted] ยท 99 points ยท Posted at 14:47:32 on May 25, 2016 ยท (Permalink)
[deleted]
goodguygaymer ยท 14 points ยท Posted at 17:15:55 on May 25, 2016 ยท (Permalink)
So 100% of 10 is 13.
wubalubadubscrub ยท 14 points ยท Posted at 17:30:53 on May 25, 2016 ยท (Permalink)
Well, no, but that's the contractor's fault
meno123 ยท 1 points ยท Posted at 20:40:00 on May 25, 2016 ยท (Permalink)
100% of 10 is 13, but I'll say it's 7 just to make sure nothing falls over.
[deleted] ยท 7 points ยท Posted at 17:32:14 on May 25, 2016 ยท (Permalink)*
[deleted]
EllisDee_4Doyin ยท 2 points ยท Posted at 17:43:16 on May 25, 2016 ยท (Permalink)*
Yep. "Good enough for practical use/most cases"
I feel like that's why in the Civil/Structural field, when something loses serviceability: the ability to perform it's use, it's basically unfit. The bridge may not collapse, but if it sways too much, it's no longer useful
rngtrtl ยท 2 points ยท Posted at 18:07:24 on May 25, 2016 ยท (Permalink)
yup. I am an EE in power transmission/distribution. We have so much slop built into our models for estimates it would amaze most engineers not in the power industry.
Marvelgirl234 ยท 7 points ยท Posted at 15:16:45 on May 25, 2016 ยท (Permalink)
That's the physicist
PandaCasserole ยท 4 points ยท Posted at 15:23:10 on May 25, 2016 ยท (Permalink)
"Imagine a spherical chicken"
deal-with-it- ยท 3 points ยท Posted at 14:46:07 on May 25, 2016 ยท (Permalink)
Now just up the necessary material and tolerances by, what, some 30% to compensate those assumptions and send to manufacturing!
[deleted] ยท 2 points ยท Posted at 14:10:25 on May 25, 2016 ยท (Permalink)
Yours aren't .....;-P
fb5a1199 ยท 2 points ยท Posted at 14:50:56 on May 25, 2016 ยท (Permalink)
And don't forget to add your 4x safety factor at the end.
jayd16 ยท 2 points ยท Posted at 18:49:24 on May 25, 2016 ยท (Permalink)
Thats a physicist. Engineers just double what they need.
Raccoonial ยท 2 points ยท Posted at 20:06:05 on May 25, 2016 ยท (Permalink)
Percentage
Pascalwb ยท 2 points ยท Posted at 21:21:24 on May 25, 2016 ยท (Permalink)
And has infinite length.
square--one ยท 2 points ยท Posted at 22:14:24 on May 25, 2016 ยท (Permalink)
Just round everything to the nearest hundred, that'll do it.
A-Little-Stitious ยท 1 points ยท Posted at 15:35:18 on May 25, 2016 ยท (Permalink)
Engineers wouldn't make these assumptions, mathematicians would.
shapu ยท 1 points ยท Posted at 15:38:59 on May 25, 2016 ยท (Permalink)
If we were economists, we'd need an imaginary perfect can opener in a marketplace of one consumer.
Antarcaticaschwea ยท 1 points ยท Posted at 15:40:56 on May 25, 2016 ยท (Permalink)
Also inviscid flow around 0
ninjazombiemaster ยท 1 points ยท Posted at 15:49:24 on May 25, 2016 ยท (Permalink)
Who invited the physicist?
Nebathemonk ยท 1 points ยท Posted at 00:08:31 on May 26, 2016 ยท (Permalink)
No one invites physicists. We just assume.
jamese1313 ยท 1 points ยท Posted at 16:11:20 on May 25, 2016 ยท (Permalink)
O?
-Don_Corleone- ยท 1 points ยท Posted at 16:28:21 on May 25, 2016 ยท (Permalink)
I thought it was an ellipse!
z500 ยท 1 points ยท Posted at 17:34:58 on May 25, 2016 ยท (Permalink)
Mine are ovals. Sometimes they have a dot or a slash in them.
[deleted] ยท 1 points ยท Posted at 17:47:48 on May 25, 2016 ยท (Permalink)
Engineering =/= freshman physics. Regretfully all those silly assumptions start to disappear over the years
animosityiskey ยท 1 points ยท Posted at 17:50:13 on May 25, 2016 ยท (Permalink)
Engineer, not physicist. Classically engineers have charts for all that stuff.
[deleted] ยท 1 points ยท Posted at 18:01:44 on May 25, 2016 ยท (Permalink)
As an engineer who works with vacuum systems... no such perfect vacuum exists. Even the depths of space are not perfect zero.
gavilin ยท 1 points ยท Posted at 18:18:21 on May 25, 2016 ยท (Permalink)
You're talking about a physisisist, engineers have never seen a perfect sphere in their lives.
randomguy186 ยท 1 points ยท Posted at 18:20:26 on May 25, 2016 ยท (Permalink)
That's elementary physics, not engineering!
nusigf ยท 1 points ยท Posted at 15:42:39 on May 25, 2016 ยท (Permalink)
I always started my heat mass transfer equations with, "assuming a spherical cow". Professor never questioned it.
wubalubadubscrub ยท 2 points ยท Posted at 17:33:16 on May 25, 2016 ยท (Permalink)
My first heat transfer exam had a question calculating heat transfer from a cat standing on a roof. Most of the class assumed the cat was a rectangular prism
atomheartother ยท 254 points ยท Posted at 15:28:56 on May 25, 2016 ยท (Permalink)
"Does it work with 1 and 2? Ok, does it work with these 2 random numbers? Ok, cool, it's a law now"
[deleted] ยท 200 points ยท Posted at 16:30:22 on May 25, 2016 ยท (Permalink)
If it works with 0,1,2 and two random big numbers, it's enough proof for an engineer.
ric2b ยท 24 points ยท Posted at 18:57:49 on May 25, 2016 ยท (Permalink)
And if you really want to make sure you also try one negative number and a decimal.
UNIScienceGuy ยท 23 points ยท Posted at 17:16:26 on May 25, 2016 ยท (Permalink)
No truer words have been said. Who needs your formal proofs.
random_name_0x27 ยท 5 points ยท Posted at 23:27:07 on May 25, 2016 ยท (Permalink)
If you're an EE you have to check it with a complex number too.
[deleted] ยท 8 points ยท Posted at 17:38:06 on May 25, 2016 ยท (Permalink)
[deleted]
Sibraxlis ยท 26 points ยท Posted at 18:14:24 on May 25, 2016 ยท (Permalink)
No, they designed it to use helium which the us controlled, then some idiot said fuck it, put hydrogen in, it's lighter and will work better, then kaboom.
[deleted] ยท 5 points ยท Posted at 19:23:27 on May 25, 2016 ยท (Permalink)
Probably jeff from accounting said that helium is too expensive.
Fuck you, jeff
gjoeyjoe ยท 3 points ยท Posted at 19:44:59 on May 25, 2016 ยท (Permalink)
"But the hydrogen guys let us use their beach house for our company barbecue!"
TheShadowKick ยท 1 points ยท Posted at 20:50:54 on May 25, 2016 ยท (Permalink)
Using an open flame around the hydrogen guys sounds like a recipe for disaster... oh wait.
Eipa ยท 1 points ยท Posted at 18:29:09 on May 25, 2016 ยท (Permalink)
It successfully completed three test cycles.
scraggledog ยท 1 points ยท Posted at 19:30:24 on May 25, 2016 ยท (Permalink)
and the Hubble lens error, the Titanic, leaning tower of Pisa....
Tasgall ยท 2 points ยท Posted at 00:45:07 on May 26, 2016 ยท (Permalink)
Don't know about the Hubble or the tower, but the Titanic at least was a result of the company cutting costs, not flaws in the engineer's original design.
nikkitgirl ยท 2 points ยท Posted at 19:58:04 on May 25, 2016 ยท (Permalink)
Engineering student here, that's painfully accurate.
Let_It_Sano ยท 4 points ยท Posted at 18:28:23 on May 25, 2016 ยท (Permalink)
Just throw in a k and k+1 and you have yourself a proof by induction!
Zequez ยท 2 points ยท Posted at 22:01:02 on May 25, 2016 ยท (Permalink)
I mean that basically how you do unit testing.
TestSubject45 ยท 1 points ยท Posted at 19:55:18 on May 31, 2016 ยท (Permalink)
Holy fuck did you watch me when I tested my computer science code?
atomheartother ยท 1 points ยท Posted at 22:24:11 on May 31, 2016 ยท (Permalink)
CompSci as well here~
beaverlyknight ยท 77 points ยท Posted at 15:30:36 on May 25, 2016 ยท (Permalink)
3 is prime, 5 is prime, 7 is prime, 9 is not, 11 is prime. This is within the acceptable margin for error, so all odd numbers are prime QED.
[deleted] ยท 1 points ยท Posted at 20:50:35 on May 25, 2016 ยท (Permalink)
What is the Optimal Prime?
Tasgall ยท 3 points ยท Posted at 00:46:07 on May 26, 2016 ยท (Permalink)
The guy who made the thread.
We'll shorten it to OP.
TheVeryMask ยท 2 points ยท Posted at 02:45:39 on May 26, 2016 ยท (Permalink)
The pair 3 and 11 are Octimus Primes, that's similar. The pair 5 and 11 are sexy primes.
Tom2Die ยท 1 points ยท Posted at 02:26:19 on May 26, 2016 ยท (Permalink)
I know you're being facetious, but you might enjoy looking at Mersenne Primes, as they're found using a similar idea, just without the absurd conclusion. :)
mattsprofile ยท 20 points ยท Posted at 16:03:19 on May 25, 2016 ยท (Permalink)
I would think that a smart person would at least use numbers that are unlikely to result in coincidental confirmation, e.g. almost any two numbers that aren't 100 and 10.
57.72% of 364 is 210.1008
364% of 57.72 is 210.1008
Now I believe it.
scandii ยท 1 points ยท Posted at 21:29:29 on May 25, 2016 ยท (Permalink)
but, head math and stuff.
finlan101 ยท 3 points ยท Posted at 15:14:32 on May 25, 2016 ยท (Permalink)
Nah, needs more assumptions that roughly equals and equals are the same thing.
heyjew1 ยท 3 points ยท Posted at 16:19:29 on May 25, 2016 ยท (Permalink)
Proof:
x% = x/100
y% = y/100
x/100 * y = y/100 * x
(xy)/100 = (xy)/100
Same calculation in different orders.
Iamamanlymanlyman ยท 2 points ยท Posted at 17:04:11 on May 25, 2016 ยท (Permalink)
But in the second to last line you're assuming they're equal... CLEAN IT UP!
Bafipusa ยท 6 points ยท Posted at 16:28:33 on May 25, 2016 ยท (Permalink)
Physicist's proof every odd number is prime: 2 check 3 check 5 check 7 check 9 measuring error 11 check 13 check 15 measuring error 17 check .... q.e.d.
BipedSnowman ยท 1 points ยท Posted at 18:45:43 on May 25, 2016 ยท (Permalink)
2 isn't an odd number...
tha-snazzle ยท 0 points ยท Posted at 19:31:24 on May 25, 2016 ยท (Permalink)
Yes it is. Re-enroll in your math class, you didn't get enough out of it.
BipedSnowman ยท 1 points ยท Posted at 20:27:26 on May 25, 2016 ยท (Permalink)
Source me up brosef.
mbleslie ยท 2 points ยท Posted at 15:27:48 on May 25, 2016 ยท (Permalink)
is there another way? ;)
PacoTaco321 ยท 2 points ยท Posted at 02:01:41 on May 26, 2016 ยท (Permalink)
No, it needs to be simpler to remove any chance of possibly having to do math.
0% of 100 is 0
100% of 0 is 0
Wee2mo ยท 1 points ยท Posted at 15:04:45 on May 25, 2016 ยท (Permalink)
I think you mean prototype.
frugalNOTcheap ยท 1 points ยท Posted at 15:33:31 on May 25, 2016 ยท (Permalink)
Works for me
I_cut_my_own_jib ยท 1 points ยท Posted at 15:41:51 on May 25, 2016 ยท (Permalink)
Nah a real engineers proof would be using x=50, y=50
scotscott ยท 1 points ยท Posted at 16:31:10 on May 25, 2016 ยท (Permalink)
I tried to find a model number for the proof and couldn't find one so we'll just say it's wrong.
Saganasm ยท 1 points ยท Posted at 16:38:53 on May 25, 2016 ยท (Permalink)
Yeah it totally works if we assume each chicken is spherical and in a vacuum...but yeah, it works.
jaredjeya ยท 1 points ยท Posted at 19:14:06 on May 25, 2016 ยท (Permalink)
The mathmos and physicists may poke fun at one another but we are all united in our disdain for engineers.
TheShadowKick ยท 1 points ยท Posted at 20:49:16 on May 25, 2016 ยท (Permalink)
TIL I'm an engineer.
jay314271 ยท 1 points ยท Posted at 21:45:49 on May 25, 2016 ยท (Permalink)
100 % is 200 proof
SubatomicCake ยท 1 points ยท Posted at 21:52:26 on May 25, 2016 ยท (Permalink)
Is that a real thing? I just do this on math tests if I need to make sure I remember a formula correctly
shenglow ยท 1 points ยท Posted at 22:44:15 on May 25, 2016 ยท (Permalink)
Throw away the unnecessary complexities and approximate. That's how shit gets done and bridges get built.
ConcernedBrother420 ยท 1 points ยท Posted at 03:05:03 on May 26, 2016 ยท (Permalink)
As an engineer. Kindly fuck off.
SupersonicSpitfire ยท 1 points ยท Posted at 06:04:11 on May 26, 2016 ยท (Permalink)
Wonder how the likelyhood of it being correct increases with the number of examples. Maybe an S function of some sort?
BEN_therocketman ยท 0 points ยท Posted at 18:19:18 on May 25, 2016 ยท (Permalink)
I did it in my head. You're not wrong.
BipedSnowman ยท 0 points ยท Posted at 18:43:57 on May 25, 2016 ยท (Permalink)
Nah, you're supposed to use variables.
(X/100)*Y = (X*Y)/100 = (Y/100)*X
TheBQE ยท 69 points ยท Posted at 14:12:07 on May 25, 2016 ยท (Permalink)
100% of 100 is 100
100% of 100 is 100
confirmed
TheIndustryStandard ยท 7 points ยท Posted at 16:39:05 on May 25, 2016 ยท (Permalink)
This helps with estimating percentages and fractions easily with "pairs"
4 and 25 are pairs. 1/4 is 25%, 4% is 1/25
5 and 20 are pairs. 1/4 is 20%, 5% is 1/20
10 and 10 are pairs as you pointed out.
The rest are close, and are good for quick estimations.
6 and 17 are pairs. 1/6 is 17%, 6% is 1/17
7 and 14 are pairs. 1/7 is 14%, 7% is 1/14
8 and 12.5 are pairs. 1/8 is 12.5%, 8% is 1/12.5
9 and 11 are pairs. 1/9 is 11%, 9% is 1/11
I use these all the time to make rough estimates and impress people. "We need 17% of these for this to work" "Ok then we need about 1 out of 6 of these to work" "how did you do that so fast?" Happens all the time.
edit: formatting
MadFlavour ยท 3 points ยท Posted at 21:23:01 on May 25, 2016 ยท (Permalink)
How the fuck have I never noticed this. Plus 1 internets.
Tuzi_ ยท 2 points ยท Posted at 23:30:34 on May 25, 2016 ยท (Permalink)
I was expecting you to insert a Bush did 911 joke. Props to you for holding off.
annoyingstranger ยท 1 points ยท Posted at 20:03:47 on May 25, 2016 ยท (Permalink)
You missed a 5
Plastonick ยท 8 points ยท Posted at 15:03:17 on May 25, 2016 ยท (Permalink)
At least use co-prime integers for the horrible generalisation!
leonardof91 ยท 14 points ยท Posted at 15:36:27 on May 25, 2016 ยท (Permalink)
yeah, for some reason things feel more correct with a bunch of primes.
Pick a random number from 1 to 10. 10? no, really, pick a random one. 7? ok, now it's random.
[deleted] ยท 3 points ยท Posted at 18:00:52 on May 25, 2016 ยท (Permalink)
a%b = a/100 * b = a * b/100 = b%a
DoesCheckOut ยท 2 points ยท Posted at 16:23:02 on May 25, 2016 ยท (Permalink)
It checks out!
838h920 ยท 2 points ยท Posted at 16:36:04 on May 25, 2016 ยท (Permalink)
For those who doubt that it works for all numbers:
Since 1% = 0.01, we can replace the % with 0.01. Now we got:
0.01 * x * y = a
0.01 * y * x = a
dexr23 ยท 2 points ยท Posted at 16:47:40 on May 25, 2016 ยท (Permalink)
(x/100) * y = (y*x)/100
(y/100) * x = (x*y)/100
(yx)/100 = (xy)/100
ok, I believe you now.
progenyofeniac ยท 2 points ยท Posted at 17:01:03 on May 25, 2016 ยท (Permalink)
You did the math...but I'm not sure you quite qualify for /r/theydidthemath.
supersimha ยท 2 points ยท Posted at 18:07:32 on May 25, 2016 ยท (Permalink)
Check from a lazy guy:
10% of 10 is 1.
Works perfect
beeprog ยท 2 points ยท Posted at 18:15:46 on May 25, 2016 ยท (Permalink)
Maths confirmed.
cswooll ยท 2 points ยท Posted at 19:35:18 on May 25, 2016 ยท (Permalink)
10% of 1 is .1 100% of 1 is 1
Not sure bout this
Ameisen ยท 2 points ยท Posted at 20:35:27 on May 25, 2016 ยท (Permalink)
100% of 100 is 100
100% of 100 is 100
still checks out.
[deleted] ยท 2 points ยท Posted at 21:38:19 on May 25, 2016 ยท (Permalink)
50% of 10 is 5, 10% of 50 is 5. Yep!
adamrcarmack ยท 2 points ยท Posted at 21:46:17 on May 25, 2016 ยท (Permalink)
Exactly what popped into my head as s soon as I read it
coleosis1414 ยท 2 points ยท Posted at 22:03:45 on May 25, 2016 ยท (Permalink)
9% of 54 is 4.86
54% of 9 is 4.86
Works for more complex numbers as well. Neat!
ilambiquated ยท 2 points ยท Posted at 22:14:35 on May 25, 2016 ยท (Permalink)
Yeah % means divide by 100
Is means =
Of means *
So
10% of 100 is 10
means
(10/100) * 100 = 10
and
100% of 10 is 10
means
(100/100) * 10 = 10
afbrh ยท 2 points ยท Posted at 23:25:15 on May 25, 2016 ยท (Permalink)
7.6% of 84.5 is 6.4 84.5% of 7.6 is 6.4
Shiiiiiiiiiiiit
tehosiris ยท 2 points ยท Posted at 07:58:59 on May 26, 2016 ยท (Permalink)
say no more
Turdsworth ยท 1 points ยท Posted at 17:50:19 on May 25, 2016 ยท (Permalink)
That's because they both equal XY/100
Pro_Googler ยท -3 points ยท Posted at 12:55:07 on May 25, 2016 ยท (Permalink)*
Found the programmer. He meant it as in percentage not as in mod. I was confused as well.
Sataris ยท 22 points ยท Posted at 13:14:53 on May 25, 2016 ยท (Permalink)
I think you're the only one confused here
Pro_Googler ยท -7 points ยท Posted at 13:30:24 on May 25, 2016 ยท (Permalink)
He changed the comment after mine...
hydrogen_wv ยท 12 points ยท Posted at 13:58:38 on May 25, 2016 ยท (Permalink)
If his comment was edited, it happened within the first few seconds because there is no mention the comment is edited. You posted exactly an hour after him. His comment was not edited after you posted.
pblokhout ยท 2 points ยท Posted at 15:24:37 on May 25, 2016 ยท (Permalink)
Bam! Logic motherfucker!
illwon ยท 1 points ยท Posted at 16:18:42 on May 25, 2016 ยท (Permalink)
Found the programmer.
Dernom ยท 1 points ยท Posted at 14:21:07 on May 25, 2016 ยท (Permalink)
He hasn't edited the comment...
massivecomplexity ยท -1 points ยท Posted at 14:55:06 on May 25, 2016 ยท (Permalink)
Well 100%10 is 0...
ktkps ยท 583 points ยท Posted at 11:37:42 on May 25, 2016 ยท (Permalink)
this fact got gold once
53bvo ยท 304 points ยท Posted at 11:41:43 on May 25, 2016 ยท (Permalink)
But will it get gold again?
ktkps ยท 421 points ยท Posted at 11:47:54 on May 25, 2016 ยท (Permalink)
Tune in next week to know...
[deleted] ยท 93 points ยท Posted at 11:58:06 on May 25, 2016 ยท (Permalink)*
[deleted]
ktkps ยท 23 points ยท Posted at 12:20:53 on May 25, 2016 ยท (Permalink)
hope we need not wait 10 episodes just to see gold
MKSLAYER97 ยท 5 points ยท Posted at 15:29:49 on May 25, 2016 ยท (Permalink)
Nah, just 9 so it's cool.
barbarr ยท -9 points ยท Posted at 15:42:25 on May 25, 2016 ยท (Permalink)
lmao I'm just throwing a comment here to see if I can get gold
soccerfreak67890 ยท 0 points ยท Posted at 20:57:09 on May 25, 2016 ยท (Permalink)
Nice try
Pure_Reason ยท 2 points ยท Posted at 18:58:38 on May 25, 2016 ยท (Permalink)
No, the next episode is just clicking on "give gold", it will take at least three episodes to type the credit card number
Obscu ยท 1 points ยท Posted at 23:33:22 on May 25, 2016 ยท (Permalink)
I came here to say this <4
amiuhle ยท 3 points ยท Posted at 16:28:37 on May 25, 2016 ยท (Permalink)
You mean in 10!/6 seconds.
someone2639 ยท 4 points ยท Posted at 14:33:51 on May 25, 2016 ยท (Permalink)
AT THE WWE SUUUUUUUUUUUUUUUUUUUUUUUUU PERSLAM!
[deleted] ยท 2 points ยท Posted at 16:47:25 on May 25, 2016 ยท (Permalink)
๐ฃ๐ฏ๐ฃ๐ฏ๐ฃ๐ฏ๐ฃ๐ฏ
Jerlko ยท 2 points ยท Posted at 15:23:22 on May 25, 2016 ยท (Permalink)
RemindMe! 1 week
Bandin03 ยท 2 points ยท Posted at 16:55:16 on May 25, 2016 ยท (Permalink)
We didn't even have to wait a week!
ooleshh ยท 2 points ยท Posted at 17:07:40 on May 25, 2016 ยท (Permalink)
remindme! one week
[deleted] ยท 2 points ยท Posted at 17:20:51 on May 25, 2016 ยท (Permalink)
Remindme! One week
ROTMGMagum ยท 1 points ยท Posted at 17:44:43 on May 25, 2016 ยท (Permalink)
Or in a few hours. He got gold Reddit!
Evan9512 ยท 1 points ยท Posted at 19:14:58 on May 25, 2016 ยท (Permalink)
Next time on DragonballZ!
[deleted] ยท 1 points ยท Posted at 19:59:49 on May 25, 2016 ยท (Permalink)
Next week? Im pretty sure ill see this question again by the end of the week
[deleted] ยท 1 points ยท Posted at 20:56:22 on May 25, 2016 ยท (Permalink)
It's making me irrationally angry that you put "to know" instead of "to find out".
AeAeR ยท 1 points ยท Posted at 00:02:17 on May 26, 2016 ยท (Permalink)
His power level is over 50% of 18000!
shutupjoey ยท 1 points ยท Posted at 00:51:03 on May 26, 2016 ยท (Permalink)
On dragon ball ZZZZZZZZZZ
redweasel ยท 1 points ยท Posted at 06:47:45 on May 26, 2016 ยท (Permalink)
It could get x% of gold.
Jerlko ยท 1 points ยท Posted at 15:30:23 on June 1, 2016 ยท (Permalink)
I need to know.
OneTrueKingOfOOO ยท 7 points ยท Posted at 15:53:32 on May 25, 2016 ยท (Permalink)
Yes. Yes it did
lordtuts ยท 1 points ยท Posted at 15:59:16 on May 25, 2016 ยท (Permalink)
Yes
[deleted] ยท 1 points ยท Posted at 17:40:11 on May 25, 2016 ยท (Permalink)
it did
btc3399 ยท 1 points ยท Posted at 19:32:07 on May 25, 2016 ยท (Permalink)
It did.
uprightbaseball ยท 1 points ยท Posted at 20:43:57 on May 25, 2016 ยท (Permalink)
12 Amazing Math Tricks you've never heard off...
terminbee ยท 1 points ยท Posted at 20:51:03 on May 25, 2016 ยท (Permalink)
63% it will get gilded again.
mythical_legend ยท 1 points ยท Posted at 02:38:07 on May 26, 2016 ยท (Permalink)
x% of y is the same as y% of x
jonminkin ยท -1 points ยท Posted at 16:41:50 on May 25, 2016 ยท (Permalink)
x% of y is the same as y% of x
Say-It-Aloud ยท 1 points ยท Posted at 22:21:12 on May 25, 2016 ยท (Permalink)
You really dont need gold, shouldnt really want it either
Tuner420 ยท 2 points ยท Posted at 15:38:41 on May 25, 2016 ยท (Permalink)
Once I got gold for this fact
elee0228 ยท 1 points ยท Posted at 16:29:45 on May 25, 2016 ยท (Permalink)
100% of 2 times now. Or 2% of 100 times.
ktkps ยท 2 points ยท Posted at 04:50:20 on May 26, 2016 ยท (Permalink)
as I said elsweyr... 10% 10 = 1 and 10% of 10 is also = 1
newredditact15 ยท 1 points ยท Posted at 17:34:53 on May 25, 2016 ยท (Permalink)
Twice*
[deleted] ยท 1 points ยท Posted at 18:39:07 on May 25, 2016 ยท (Permalink)
Will I get gold?
ktkps ยท 1 points ยท Posted at 05:13:02 on May 26, 2016 ยท (Permalink)
apparently not
mimicgogo ยท 1 points ยท Posted at 23:25:33 on May 25, 2016 ยท (Permalink)
The same as once this fact got gold
lginthetrees ยท 24 points ยท Posted at 14:53:36 on May 25, 2016 ยท (Permalink)
I use this for tip calculation all the time. 15% of 33 makes me think. 33% of 15? Piece of cake.
mysticrudnin ยท 14 points ยท Posted at 15:41:17 on May 25, 2016 ยท (Permalink)
i like 20% for tips because you divide by ten then double it
riraito ยท 3 points ยท Posted at 18:48:20 on May 25, 2016 ยท (Permalink)
to keep it 15% just go a bit further: divide by 10 then take half and triple it
tojoso ยท 3 points ยท Posted at 21:34:59 on May 25, 2016 ยท (Permalink)
Or divide by 10, take half, and add it to the first number. That's usually one step quicker than multiplying by 3, depending on your method.
riraito ยท 1 points ยท Posted at 21:44:14 on May 25, 2016 ยท (Permalink)
good point
ChocolateSandwich ยท 1 points ยท Posted at 17:09:40 on May 25, 2016 ยท (Permalink)
But what kind of cake was it?
TripleUltraMini ยท 1 points ยท Posted at 18:46:33 on May 25, 2016 ยท (Permalink)
33% tip? It better be chocolate
Turdsworth ยท 1 points ยท Posted at 17:55:33 on May 25, 2016 ยท (Permalink)
If you want to give a 20% tip just give one dollar for every five you spent pretax. 30 meal tip 30/5=6.
Solkre ยท 1 points ยท Posted at 18:31:12 on May 25, 2016 ยท (Permalink)
When sales tax was 5% I just tripled it. Now it's 7%, thanks INDIANA!
tojoso ยท 1 points ยท Posted at 21:33:48 on May 25, 2016 ยท (Permalink)
But what if you ordered pie instead of cake. Does the math still work out?
prophile ยท 68 points ยท Posted at 15:58:08 on May 25, 2016 ยท (Permalink)
So if 50% of people are female, people% of 50 is female?
film_composer ยท 5 points ยท Posted at 18:51:15 on May 25, 2016 ยท (Permalink)
Yes. .5(7,200,000,000) = 72,000,000(50)
Jaaqo ยท 2 points ยท Posted at 23:06:36 on May 25, 2016 ยท (Permalink)
50% of 2 people are female, so 2% of 50 people are female.
Bens_Dream ยท 1 points ยท Posted at 14:02:25 on May 26, 2016 ยท (Permalink)
No, 50% of females are people.
Thomas9002 ยท 284 points ยท Posted at 12:57:06 on May 25, 2016 ยท (Permalink)*
This sounds really alien at first, but when you think about it it's easy.
You're just multiplying 2 things and those by 100 (because of %).
And of course: A*B*100% = B*A*100%
[deleted] ยท 213 points ยท Posted at 14:05:34 on May 25, 2016 ยท (Permalink)
You mean divide by 100. X% = X/100
X% * Y = X/100 * Y = X * Y / 100 = X * Y%
Poromenos ยท 11 points ยท Posted at 15:22:42 on May 25, 2016 ยท (Permalink)
You're both kinda right. 100% = 100/100 = 1.
He meant you multiply 0.5 * 100/100 = 50%
You meant you divide 50/100 = 50%.
QuantumPolagnus ยท 3 points ยท Posted at 18:03:59 on May 25, 2016 ยท (Permalink)
Or even easier, you just multiply by 0.01. The commutative property holds for every permutation of multiplying X, Y, and .01.
redweasel ยท 1 points ยท Posted at 06:52:15 on May 26, 2016 ยท (Permalink)
That's what % means. "Per cent." Cent- is the prefix, or Roman word, or something, for "100," and "per" means "divide by." So, "per cent" is literally, "Divide by 100."
The one that blew my mind recently was that I was perusing a font and discovered that there's such a thing as "per mille" -- division by 1000 rather than 100 -- and that its symbol looks like the % sign except there are two zeros "under the slash." Hm, I wonder if I can type it here... Ah yes: โฐ
notsew93 ยท 4 points ยท Posted at 13:06:11 on May 25, 2016 ยท (Permalink)
Thank you
HipHomelessHomie ยท 1 points ยท Posted at 15:26:12 on May 25, 2016 ยท (Permalink)
You're not multiplying by 100% but by 1% which is the same as dividing by 100
h-jay ยท 1 points ยท Posted at 15:56:01 on May 25, 2016 ยท (Permalink)*
In fact, you're multiplying A*B*1%, not 100%. 1%=0.01. E.g. 2% of 50 is 2*50*0.01=100*0.01=1
Thomas9002 ยท 1 points ยท Posted at 16:11:37 on May 25, 2016 ยท (Permalink)
You are correct
perverse_sheaf ยท 1 points ยท Posted at 17:57:54 on May 25, 2016 ยท (Permalink)
Mathematically it's easy, sure. But it's hard to grasp at an intuitive level, because x% of y always assume the existence of some y which does no longer hold if you switch.
Actually, if you think a little harder, you'll find that AB = BA is not that obvious, and we all accept it because we know it to be true from experience.
QuantumPolagnus ยท 1 points ยท Posted at 18:05:00 on May 25, 2016 ยท (Permalink)
Yeah, that's the commutative property at work - the same as adding A+B=B+A.
raydialseeker ยท 1 points ยท Posted at 18:09:18 on May 25, 2016 ยท (Permalink)
To me, it's always come naturally. I dunno why, but this is what I used be default, even before we were taught this in school.
matt-s-perrin ยท 1 points ยท Posted at 20:21:14 on May 25, 2016 ยท (Permalink)
It really annoys me when people add percentages in equations. Did you stop learning maths when you were 6 or something?
Lucidmike78 ยท 1 points ยท Posted at 23:23:22 on May 25, 2016 ยท (Permalink)*
Thank you for proving that we should use calculators.
FTFY: "You're just multiplying 2 things and those by 1/100"
A more simpler way to look at it is: A/100 * B = (A*B)/100
LamarMillerMVP ยท 1 points ยท Posted at 01:12:55 on May 26, 2016 ยท (Permalink)
That's math for you. A proof is just thinking about things.
wiiya ยท 19 points ยท Posted at 14:01:06 on May 25, 2016 ยท (Permalink)
It's just switching variables. The percentage is just multiplying one of the variables by .01.
x*.01*y = y*.01*x
nc61 ยท 7 points ยท Posted at 16:37:37 on May 25, 2016 ยท (Permalink)
Jesus, I graduated with two STEM degrees and I have never thought of this...
BigRedRobotNinja ยท 5 points ยท Posted at 18:26:48 on May 25, 2016 ยท (Permalink)
Seriously, EE here with a blown mind gasket.
crossroads1112 ยท 1 points ยท Posted at 20:51:31 on May 25, 2016 ยท (Permalink)
Right? Now that it was said it makes sense. It's just the good ol' associative property of multiplication e.g.
The rules are really simple, I just never would have thought to apply them like this.
boboguitar ยท 1 points ยท Posted at 22:25:24 on May 25, 2016 ยท (Permalink)
I thought he was talking mods this whole time, not percentages.
CockGobblin ยท 1 points ยท Posted at 23:10:25 on May 25, 2016 ยท (Permalink)
So what you are saying is you have two STE degrees?
6chan ยท 4 points ยท Posted at 15:31:46 on May 25, 2016 ยท (Permalink)
I remember reading this the last time and being blown away by it.
But then i wrote it down and was dumbfounded by why i didn't realize this sooner
x% of y is xy/100, which is x* y/100, which is y% of x
Nicekicksbro ยท 2 points ยท Posted at 19:33:16 on May 25, 2016 ยท (Permalink)
Beautiful. If math ever did turn me on...
-___-_-_-- ยท 8 points ยท Posted at 15:09:16 on May 25, 2016 ยท (Permalink)
I though the
%was the modulo operator at firstjorellh ยท 3 points ยท Posted at 15:03:32 on May 25, 2016 ยท (Permalink)
1/2 of 2/3 is 2/3 of 1/2
CockGobblin ยท 1 points ยท Posted at 23:11:59 on May 25, 2016 ยท (Permalink)
4/5/21 of 3.14 is 3.14 of 16.8?
[deleted] ยท 5 points ยท Posted at 15:20:29 on May 25, 2016 ยท (Permalink)*
[removed]
edrudathec ยท 1 points ยท Posted at 21:14:33 on May 25, 2016 ยท (Permalink)
punriffer5 ยท 2 points ยท Posted at 14:57:57 on May 25, 2016 ยท (Permalink)
Sure -
x% of y = x/100 * y = xy/100
y% of x = y/100 * x = xy/100
HelloImRIGHT ยท 2 points ยท Posted at 16:01:24 on May 25, 2016 ยท (Permalink)
this is just about the only one i understand in this entire thread.
FlexGunship ยท 2 points ยท Posted at 17:40:31 on May 25, 2016 ยท (Permalink)
I'm going to use this next time there's a sale by purchasing exactly $100 worth of something on sale.
20% off of $100 is the same as 100% off of $20. So... free!
That's how this works, right?
RelevantSignFeld ยท 1 points ยท Posted at 21:43:55 on May 25, 2016 ยท (Permalink)
Take out "off" and yes!
Whitsoxrule ยท 2 points ยท Posted at 20:55:53 on May 25, 2016 ยท (Permalink)
I thought that was a modulus and spent a really long time trying to figure figure out how that could be possible
139mod70 ยท 1 points ยท Posted at 15:35:36 on May 25, 2016 ยท (Permalink)
(x/100)y = (y/100)x = xy/100
lunaroyster ยท 1 points ยท Posted at 15:36:12 on May 25, 2016 ยท (Permalink)
x/100 * y = y/100 * x = (xy)/100
watabadidea ยท 1 points ยท Posted at 16:04:33 on May 25, 2016 ยท (Permalink)
This is a classic GRE question.
Not sure if that is where you got it from or not, just giving a heads up to the other GRE folks out there.
tennisdrums ยท 1 points ยท Posted at 16:05:26 on May 25, 2016 ยท (Permalink)
Holy shit, I had never realized this once in my life, and I just graduated from a math heavy major. It's so simple too, since all you're ever doing is using basic properties of multiplication: (0.01x)y=x(0.01y). I guess the percent part just threw me off thinking about it that way.
ivanhoe90 ยท 1 points ยท Posted at 16:08:02 on May 25, 2016 ยท (Permalink)
Are you aware, that you are just saying, that "A times B = B times A" ? :)
loptthetreacherous ยท 1 points ยท Posted at 16:09:59 on May 25, 2016 ยท (Permalink)
This seems quite trivial when you turn it into fractions.
x% of y is (x/100)*y=(x*y)/100
y% of x is (y/100)*x)=(y*x)/100
pnoozi ยท 1 points ยท Posted at 16:23:43 on May 25, 2016 ยท (Permalink)
That's because "%" literally just means "times .01"
x * .01 * y is the same as y * .01 * x which is pretty obvious
ivanvzm ยท 1 points ยท Posted at 16:25:28 on May 25, 2016 ยท (Permalink)
Holy Shit
[deleted] ยท 1 points ยท Posted at 16:32:08 on May 25, 2016 ยท (Permalink)*
x% of y = y% of x
(x * (1/100)) * y = (y * (1/100)) * x
Following order of operation, it reduces:
(x * y)/100 = (y * x)/100
Factor out 100
x * y = y * x
True, by the commutative property.
Stacia_Asuna ยท 1 points ยท Posted at 16:34:57 on May 25, 2016 ยท (Permalink)
This is simple associative property, though it's useful in application:
(x * .01) * y = x * (.01 * y)
Aski09 ยท 1 points ยท Posted at 16:42:48 on May 25, 2016 ยท (Permalink)
If you want to know what Y% is of X is, PM me your Email and I will send you a file to download an app that does it for you. (It is made by me so please do ;))
DDRundo ยท 1 points ยท Posted at 16:56:02 on May 25, 2016 ยท (Permalink)
Ahh this is so handy!
vesomortex ยท 1 points ยท Posted at 16:59:23 on May 25, 2016 ยท (Permalink)
So wait, 10% of 100 is the same as 100% of 10...
And you're right.
-HeisenBird- ยท 1 points ยท Posted at 17:01:14 on May 25, 2016 ยท (Permalink)
Here's a proof:
Suppose p is the percentage and x and y are numbers such that 0<x,y<100.
Then x% of y is p=y(x/100) and y% of x is p=x(y/100). Both of these are equal to p=(xy)/100
colucci ยท 1 points ยท Posted at 17:03:50 on May 25, 2016 ยท (Permalink)
I've had that question given to me at interviews, lol.
TIL_this_shit ยท 1 points ยท Posted at 17:12:45 on May 25, 2016 ยท (Permalink)
When I saw this I was think of Modulo, since in most languages it is used via the % operand. I guess you know you are a programmer when you see a % and think modulo instead of percent.
rawling ยท 1 points ยท Posted at 17:13:03 on May 25, 2016 ยท (Permalink)
Random C fact: x[y] is the same as y[x]
A__NEW__USER ยท 1 points ยท Posted at 17:14:33 on May 25, 2016 ยท (Permalink)
Neat. And it works because you can rearrange products around.
x% of y is really x(1/100)y
rearrange as you pls.
jpsi314 ยท 1 points ยท Posted at 17:15:24 on May 25, 2016 ยท (Permalink)
That looks so profound despite being totally trivial to show. I love it when that happens.
danhakimi ยท 1 points ยท Posted at 17:17:52 on May 25, 2016 ยท (Permalink)
"Of" is just multiplication.
[deleted] ยท 1 points ยท Posted at 17:33:06 on May 25, 2016 ยท (Permalink)
x% of y = (x/100)y
or, 1/100 (xy)
Factoring out the 1/100 here makes it clear that you're just re-stating the commutative property of multiplication. It's still interesting though.
DerbyTho ยท 1 points ยท Posted at 17:38:38 on May 25, 2016 ยท (Permalink)
Wow, I actually felt my little hamster fall off the wheel.
robb0688 ยท 1 points ยท Posted at 17:43:25 on May 25, 2016 ยท (Permalink)
This is just straight up practical. Much more useful than the hairy tennis ball thing a few comments up. Talking about hairy balls gets me on lists. This I can use.
AbominableShrine ยท 1 points ยท Posted at 17:43:57 on May 25, 2016 ยท (Permalink)
Is there a proof for that?
Morophin3 ยท 1 points ยท Posted at 23:01:49 on May 25, 2016 ยท (Permalink)
(.01x)y = (.01y)x
hrg_ ยท 1 points ยท Posted at 17:48:35 on May 25, 2016 ยท (Permalink)
Proof:
drinks_antifreeze ยท 1 points ยท Posted at 17:58:40 on May 25, 2016 ยท (Permalink)
A poor man's proof:
Even though it's a really simple trick it's still a surprising revelation when put into that context. It's seriously cool that 2% of 50 is the same as 50% of 2, calculating tips will never be the same.
redsoxnets5 ยท 1 points ยท Posted at 18:00:03 on May 25, 2016 ยท (Permalink)
ah the old associative property
panslangjoes91 ยท 1 points ยท Posted at 18:12:05 on May 25, 2016 ยท (Permalink)
This is kind of how I figure out how much to tip at a restaurant. Instead of taking 20% of the total bill, you can just multiply the bill by 2 and move the decimal 2 digits over.
MrPoletski ยท 1 points ยท Posted at 18:20:24 on May 25, 2016 ยท (Permalink)
That's just
X x 0.01 x Y = Y x 0.01 x Xsahuxley2 ยท 1 points ยท Posted at 18:27:57 on May 25, 2016 ยท (Permalink)
That's just multiplication. X * Y = Y * X
Still cool though.
zeekar ยท 1 points ยท Posted at 18:29:17 on May 25, 2016 ยท (Permalink)
Sure. They both work out to xy / 100.
[deleted] ยท 1 points ยท Posted at 19:00:27 on May 25, 2016 ยท (Permalink)
50% of 100 is 100% of 50. Damn you OP, 30 years I've been doing it the hard way.
TheHYPO ยท 1 points ยท Posted at 19:12:59 on May 25, 2016 ยท (Permalink)
Which is another way of saying .01*x*y is the same as .01*y*x
Richard-Butts ยท 1 points ยท Posted at 19:13:43 on May 25, 2016 ยท (Permalink)
I'm learning so much today
qweqweteqwt ยท 1 points ยท Posted at 19:16:13 on May 25, 2016 ยท (Permalink)
eh, that's more of a verbal thing.
the word "of" implies multiplication.
when you write it as a mathematical equation it's no longer so impressive.
x% * y = y% * x
then realize that the % sign literally means for every one hundred (or divide by hundred) and you have
x/100 * y = y/100 *x
[deleted] ยท 1 points ยท Posted at 19:16:35 on May 25, 2016 ยท (Permalink)
Instantly makes a lot of sense if you rewrite the equation as (X * Y) / 100
7% of 100, it's the same thing as (7 x 100) / 100
31% of 57 = (31 * 57) / 100
vikinick ยท 1 points ยท Posted at 19:22:47 on May 25, 2016 ยท (Permalink)
This is just the associative property of multiplication (as well as the commutative property) for those that don't understand.
So
krelin ยท 1 points ยท Posted at 19:27:28 on May 25, 2016 ยท (Permalink)
Really just the commutative property of multiplication, but still mind blown.
bottomfeeder_ ยท 1 points ยท Posted at 19:27:49 on May 25, 2016 ยท (Permalink)
22 years of education and nobody ever taught me this shit
Norwegian_whale ยท 1 points ยท Posted at 19:37:57 on May 25, 2016 ยท (Permalink)
I'm 27 fucking years old and I haven't realized this.
rockidol ยท 1 points ยท Posted at 19:38:15 on May 25, 2016 ยท (Permalink)
Proof for anyone interested:
X% of Y =.01X * Y
.01X * Y = .01X * Y *100 *.01 (since 100 *.01 = 1)
.01X *Y = .01X *100 *Y *.01
.01X * Y = X * .01Y
.01X * Y = .01Y * X
X% of Y = Y% of X
NothingCrazy ยท 1 points ยท Posted at 19:40:15 on May 25, 2016 ยท (Permalink)
Holy shit, this would have saved me so much time on word problems if I'd realized it before now!
bluegender03 ยท 1 points ยท Posted at 19:41:59 on May 25, 2016 ยท (Permalink)
Super neat
voidsoul22 ยท 1 points ยท Posted at 19:46:10 on May 25, 2016 ยท (Permalink)
x% of y = .01 * x * y = x * .01 * y = y% of x
MegaGoomy ยท 1 points ยท Posted at 19:46:51 on May 25, 2016 ยท (Permalink)
so the commutative property?
MicroLovesMacro ยท 1 points ยท Posted at 19:48:49 on May 25, 2016 ยท (Permalink)
....omg... how did I NEVER NOTICE THIS!!! I feel really dumb now, because it is so obvious.
introvertedintooit ยท 1 points ยท Posted at 19:55:07 on May 25, 2016 ยท (Permalink)
not surprising given that multiplication is commutative.
x*y*(1/100) can do it in any order you want
EatATaco ยท 1 points ยท Posted at 19:57:15 on May 25, 2016 ยท (Permalink)
The commutative property of multiplication, how does that work?
bezdomni ยท 1 points ยท Posted at 19:57:30 on May 25, 2016 ยท (Permalink)
Well, % is equal to 1/100. So your statement can be written as:
(x/100) * y = (y/100) * x
Weirwood_Face ยท 1 points ยท Posted at 19:57:46 on May 25, 2016 ยท (Permalink)
That looks beautiful. Even if it's obvious.
tgames56 ยท 1 points ยท Posted at 20:12:41 on May 25, 2016 ยท (Permalink)
got confused cuz i thought % was modulo for a second, and i was like that is not true.
phforNZ ยท 1 points ยท Posted at 20:21:58 on May 25, 2016 ยท (Permalink)
I'm no slouch at maths... But hot damn son! That just made my life easier.
[deleted] ยท 1 points ยท Posted at 20:48:02 on May 25, 2016 ยท (Permalink)
Omg... I'm going to the nearest mall to try this out.
jpmcglone ยท 1 points ยท Posted at 21:05:58 on May 25, 2016 ยท (Permalink)
(x/100) * y - (y/100) * x = 0
GoFidoGo ยท 1 points ยท Posted at 21:12:33 on May 25, 2016 ยท (Permalink)
To demonstrate this further,: x% of y = (x/100)y = (xy)/100 y% of x = (y/100)x = (yx)/100
Since (xy)/100 == (yx)/100, this i always true for any x or y.
stormypumpkin ยท 1 points ยท Posted at 21:12:49 on May 25, 2016 ยท (Permalink)
Is this percentages or modularity?
muchmadeup ยท 1 points ยท Posted at 21:29:16 on May 25, 2016 ยท (Permalink)
Oh. My. God.
Plasma_000 ยท 1 points ยท Posted at 21:32:39 on May 25, 2016 ยท (Permalink)
You can also multiply them together then divide by 100
superev12 ยท 1 points ยท Posted at 21:33:45 on May 25, 2016 ยท (Permalink)
Because getting % of is percentage * number, and y * x = x * y
TheSling ยท 1 points ยท Posted at 21:36:21 on May 25, 2016 ยท (Permalink)
I study maths and this blew my mind for the two seconds that it took me to realize why this is true. Damn my maths brain always trying to proof things.
Im_A_Viking ยท 1 points ยท Posted at 21:50:18 on May 25, 2016 ยท (Permalink)
Am I the only one who thought you were initially describing modulo division?
taddl ยท 1 points ยท Posted at 21:55:54 on May 25, 2016 ยท (Permalink)
That's because % = รท100
[deleted] ยท 1 points ยท Posted at 22:19:07 on May 25, 2016 ยท (Permalink)
10% of 21 = 2.1
21% of 10 = 2.1
my god...
dupelize ยท 1 points ยท Posted at 22:30:23 on May 25, 2016 ยท (Permalink)
This is such an easy idea, but at a quick glance seems impossible.
cardioZOMBIE ยท 1 points ยท Posted at 22:52:23 on May 25, 2016 ยท (Permalink)
WAT.
achoo678 ยท 1 points ยท Posted at 22:55:29 on May 25, 2016 ยท (Permalink)
x% of y is (x/100)y -> y% of x is (y/100)x -> (x/100)y=(y/100)x -> xy/100=yx/100 -> Q.E.D.
amyberr ยท 1 points ยท Posted at 22:58:32 on May 25, 2016 ยท (Permalink)
I was really confused and excited until I realized you actually meant percent and not modulo. 7%4=3, and 4%7=4, so it doesn't work for both meanings of %, which is a bummer.
Charli3R ยท 1 points ยท Posted at 23:27:47 on May 25, 2016 ยท (Permalink)
Is there a theory for this? I'm creating one if not.
mrh99 ยท 1 points ยท Posted at 23:27:52 on May 25, 2016 ยท (Permalink)
This doesn't work when % means modulus
alien122 ยท 1 points ยท Posted at 23:47:22 on May 25, 2016 ยท (Permalink)
this fact just follows from multiplication being associative.
specifically
(x*1/100)*y=x*(1/100*y)
which is
x%*y=x*y%
[deleted] ยท 1 points ยท Posted at 00:17:27 on May 26, 2016 ยท (Permalink)
x*y/100 = y*x/100
[deleted] ยท 1 points ยท Posted at 00:28:35 on May 26, 2016 ยท (Permalink)
This is the commutative property of multiplication.
xereeto ยท 1 points ยท Posted at 01:20:08 on May 26, 2016 ยท (Permalink)
That blew my mind at first but then I realized it's actually fairly simple. x% of y is just x * 0.01 * y, multiplication is commutative.
[deleted] ยท 576 points ยท Posted at 13:24:12 on May 25, 2016 ยท (Permalink)
10 11 12 and 13 squared are 100 121 144 and 169. 01 11 21 and 31 squared are 001 121 441 and 961.
971365 ยท 22 points ยท Posted at 15:40:29 on May 25, 2016 ยท (Permalink)
Is it explained by math or a coincidence?
shmameron ยท 48 points ยท Posted at 16:29:02 on May 25, 2016 ยท (Permalink)
Let the two digit number be represented by 10a+b, where a is the first digit and b is the second. (For 10, a=1 and b=0).
Then (10a+b)2 = 100a2 + 20ab + b2.
Notice that in all of these, a=1, so we have 100 + 20b + b2.
When we flip the digits, we get (10b+a)2 = 100b2 + 20b + 1.
Notice that for bโค3, we have b2 < 10 and 2b<10.
So if we rewrite the above as:
(100) * 1 + (10) * 2b + (1) * b2
(100) * b2 + (10) * 2b + (1) * 1
We can clearly see that the digits are flipped.
mr_ewe ยท 20 points ยท Posted at 16:39:57 on May 25, 2016 ยท (Permalink)
Is this something you have seen or studied before, or do proofs like this just come so naturally to some people?
beeeel ยท 31 points ยท Posted at 16:51:47 on May 25, 2016 ยท (Permalink)
Once you've studied maths and learned to see the patterns, it starts to come more naturally, but there is the argument that the only people who study maths are the ones who can see the patterns in the first place.
DWe1 ยท 6 points ยท Posted at 23:21:26 on May 25, 2016 ยท (Permalink)
Yes, besides learning a lot of useful things while studying maths, you also create what some call "mathematical maturity"; you will be able to grasp more and more complicated structures faster. I am at the end of the second year of my mathematics bachelor's, and if I would have to learn a completely new mathematical concept that is thaught at the speed of a first course for freshmen, I would probably be able to deal with it a lot faster than when I was a freshman myself.
rabbitlion ยท 11 points ยท Posted at 17:03:55 on May 25, 2016 ยท (Permalink)
It comes naturally, but it's a process and the whole proof doesn't spontaneously appear in our heads. When working with "digit problems" like this it's frequently very useful to break the numbers up into their digits, like instead of using the number 'ab' you work with a*10+b. You figure out that:
(10a+b)2 = 100a2 + 20ab + b2
(10b+a)2 = 100b2 + 20ab + a2
At this point it becomes obvious that it doesn't work with any number. For a2 and b2 to fit in one digit neither can be above 3, and for 20ab to be smaller than 100 you need ab<5. This basically only leaves a small number of numbers that it works with; 00, 01, 02, 03, 10, 11, 12, 13, 22, 30, 31.
In the specific example given we knew that a was always equal to 1, so the proof reduces to the one given above.
mr_ewe ยท 4 points ยท Posted at 19:37:52 on May 25, 2016 ยท (Permalink)
Just the star is what tripped. I haven't been in a math class or done any may beyond plugging numbers into pre build equations in almost 4 years. Coming up with 10a+B=ab wasn't where I went first.
After that, yes it was easy to follow.
Thanks!
shmameron ยท 3 points ยท Posted at 16:54:09 on May 25, 2016 ยท (Permalink)
I'm an undergraduate in physics with a minor in math, so I have a fair bit of experience in working proofs out. I don't think I've seen this particular problem before, I just tried working it out and it worked.
I've always had a knack for math, but I really think it's my experience with solving a lot of hard math problems that has made proofs like this easy to do. Nothing in this problem requires more than high-school algebra, but it might be difficult for a high-school student to prove this because they haven't been using algebra for very long. The more you study, the easier it is to understand how to connect the dots.
starfall-invoker ยท 3 points ยท Posted at 19:09:46 on May 25, 2016 ยท (Permalink)
Generalising to base k (where k is a positive integer greater than 1) and any integer a,b (where 0 <= a,b < k):
The original number is (ak+b), and its square is (a2k2+2abk+b2).
In base k it is written left to right as "a2 2ab b2" if no carrying occurs.
The flipped number is (bk+a), and its square is (b2k2+2abk+a2).
In base k it is written left to right as "b2 2ab a2" if no carrying occurs.
Notice that they are flipped versions of each other. The no-carrying condition is true only when k is greater than a2, 2ab and b2 (e.g. in base 10 a=1,b=3 works, a=2,b=3 does not because 2ab=12>10)
BrewCrewKevin ยท 2 points ยท Posted at 18:22:33 on May 27, 2016 ยท (Permalink)
And I'd I'm not mistaken, a pretty basic eli5 would be because you can square without carrying for 3 or less, right?
shmameron ยท 1 points ยท Posted at 18:27:12 on May 27, 2016 ยท (Permalink)
Yep pretty much. That's why I emphasized that b2 < 10 and 2b < 10 (so they're digits), and then sorted the final answers by the place each digit is in (hundreds, tens, and ones).
hjqusai ยท 1 points ยท Posted at 18:09:26 on May 31, 2016 ยท (Permalink)
It's explained by math. If you do the multiplication the long way, you never carry a one over, so all the numbers kinda stay in their own place
AsterJ ยท -1 points ยท Posted at 18:40:51 on May 25, 2016 ยท (Permalink)
It's not that interesting
(x + y)2 = x2 + 2xy + y2
(y + x)2 = y2 + 2yx + x2
x10x ยท 2 points ยท Posted at 18:58:48 on May 25, 2016 ยท (Permalink)
To add to this, each unit (ones, tens, hundreds) does not overflow into the next as x and y are less than 4.
e.g:
x2 < 10
y2 < 10
2x < 10
2y < 10
skizfrenik_syco ยท 7 points ยท Posted at 15:13:24 on May 25, 2016 ยท (Permalink)
Is there a pattern I'm missing?
Floom101 ยท 17 points ยท Posted at 15:28:08 on May 25, 2016 ยท (Permalink)
If you flip the first group of numbers and square it, the result is the second group of numbers flipped.
skizfrenik_syco ยท 4 points ยท Posted at 15:51:12 on May 25, 2016 ยท (Permalink)
Thanks, now I see it!
Ardub23 ยท 3 points ยท Posted at 00:25:56 on May 26, 2016 ยท (Permalink)
102 = 100โ|โ001 = 012
112 = 121โ|โ121 = 112
122 = 144โ|โ441 = 212
132 = 169โ|โ961 = 312
DiamondSentinel ยท 2 points ยท Posted at 20:39:30 on May 25, 2016 ยท (Permalink)
13 and 14 squared are 169 and 196, respectively, as well.
ilambiquated ยท 2 points ยท Posted at 23:01:09 on May 25, 2016 ยท (Permalink)
Also
(1+0)2 = 1+0+0
(1+2)2 = 1+4+4
(1+3)2 = 1+6+9
Generally speaking, the palindrome of the square of a number equals the square of the palindrome of the number if and only if the cross sum of the square of the number equals the square of the cross sum of the number.
It also works in other bases, not just base 10
For example, in base 8 (octal)
122 = 144
(This is 102 = 100 decimal)
But 132 fails because 32 > 8
In base 5
122 = 144
(this is 72 = 49 decimal)
In base 16 (hexadecimal)
122 = 144
(This is 182= 324 decimal)
In base 20 you also get
142 = 18G, where G (the seventh letter of the alphabet) is the symbol for 16. 1+8+16 =25 = (1+4)2
In base 30 you get
152 =1AZ where Z (the 26th letter of the alphabet) is the symbol for 25, and A is 10.
This is 352 = 1225 decimal. 1AZ= 900 + 750 + 5
1+A+Z = 1+10+25 = 36 = (1+5)2
And so on.
[deleted] ยท 2 points ยท Posted at 15:28:56 on May 25, 2016 ยท (Permalink)
Sorry but I don't see what's special about this. What is it?
derrman ยท 10 points ยท Posted at 15:38:18 on May 25, 2016 ยท (Permalink)
Flip the numbers.
12:144 :: 21:441
13:169 :: 31:961
Franky2shoes ยท 1 points ยท Posted at 18:22:07 on May 25, 2016 ยท (Permalink)
I just called 100-121-144
Sw4rmlord ยท 3 points ยท Posted at 00:45:10 on May 26, 2016 ยท (Permalink)
Don't leave us hanging, m8
salma86q ยท 1 points ยท Posted at 00:52:43 on May 26, 2016 ยท (Permalink)
now, how are you today?
[deleted] ยท 1 points ยท Posted at 06:40:24 on May 26, 2016 ยท (Permalink)
Think about it for a second guys. Maybe do it longhand, and it'll be really obvious why this is.
Thomas9002 ยท 1327 points ยท Posted at 13:04:28 on May 25, 2016 ยท (Permalink)
There are 3D objects which have an infinite surface area, but a limited volume.
E.g.: The Gabriels Horn
nachofiend ยท 145 points ยท Posted at 17:13:35 on May 25, 2016 ยท (Permalink)
that's like having a cake and then cutting it into an infinite number of pieces - you have infinite surface area but finite volume
epicblob ยท 43 points ยท Posted at 22:31:08 on May 25, 2016 ยท (Permalink)*
this is much more intuitive than the horn, thanks.
liquidpig ยท 5 points ยท Posted at 22:11:38 on May 25, 2016 ยท (Permalink)
I just came up with the best diet plan ever.
Shadax ยท 2 points ยท Posted at 00:43:41 on May 26, 2016 ยท (Permalink)
Cake so good you will literally inhale the slices.
jesset77 ยท 4 points ยท Posted at 23:18:20 on May 25, 2016 ยท (Permalink)
An even better way of phrasing it (than cutting the cake into an infinite number of even sized pieces, because each would be zero volume and questionable surface area.. lol!) would be:
Because then, like even slices of Gabriel's horn, each piece itself is relatively ordinary. :3
AwesomeAutumns ยท 3 points ยท Posted at 23:54:08 on May 25, 2016 ยท (Permalink)
Is it similar to the idea where I want to move a distance and go half that distance every time, so I never reach it?
GOpencyprep ยท 2 points ยท Posted at 22:35:43 on May 25, 2016 ยท (Permalink)
vsauce has an excellent video explaining this (at work, can't provide link, sorrrry)
CaveJohnsonOfficial ยท 3 points ยท Posted at 02:12:23 on May 26, 2016 ยท (Permalink)
https://youtu.be/ffUnNaQTfZE I gotchu buddy
GOpencyprep ยท 2 points ยท Posted at 02:45:47 on May 26, 2016 ยท (Permalink)
there he go
WouldYouTurnMeOn ยท 2 points ยท Posted at 23:24:37 on May 25, 2016 ยท (Permalink)
Infinite frosting.
CMariko ยท 1 points ยท Posted at 00:17:45 on May 26, 2016 ยท (Permalink)
Brilliant
RulerOf ยท 1 points ยท Posted at 01:42:17 on May 26, 2016 ยท (Permalink)
So if I use a knife instead of a fork, I can eat an infinite number of pieces of cake?
Woohoo!
[deleted] ยท -1 points ยท Posted at 23:47:02 on May 25, 2016 ยท (Permalink)*
[deleted]
yohohoy ยท 2 points ยท Posted at 03:45:49 on May 26, 2016 ยท (Permalink)
C/p
its volume is an infinite sum that converges to a finite value. For example, cut the cake into a set of infinite slices. The first slice has volume 1, the second 1/2, the fourth 1/4, the fifth 1/8 and so on. Such a cake would have volume 1+1/2+1/4+1/8+1/16+... = 2, as the sum of 1/( 2n ) from n = 0 to infinity is 2.,
MustardBucket ยท 866 points ยท Posted at 14:25:38 on May 25, 2016 ยท (Permalink)
You can fill it with paint, but will never have enough to cover the outside.
Gielpy ยท 158 points ยท Posted at 14:43:20 on May 25, 2016 ยท (Permalink)
One of the few things I remember from my calculus class, and my favorite.
TastyBurgers14 ยท 4 points ยท Posted at 19:09:30 on May 25, 2016 ยท (Permalink)
can it be made in real life?
I-Downloaded-a-Car ยท 12 points ยท Posted at 20:04:00 on May 25, 2016 ยท (Permalink)
It's 3d so conceivably yes, practically probably not
LoLjoux ยท 21 points ยท Posted at 20:21:25 on May 25, 2016 ยท (Permalink)*
The premise is that as the horn tapers it goes to infinity in the x direction. To build it you'd need an infinite amount of space, and the ability to build infinitely small objects
Pure_Reason ยท 8 points ยท Posted at 21:02:56 on May 25, 2016 ยท (Permalink)
So you're saying I need a better 3D printer? What if my new 3D printer isn't infinitely better than my current one but only infinitely approaches the quality of an infinitely better 3D printer? If only I had an infinite amount of money to buy it
botlemon ยท -2 points ยท Posted at 01:29:27 on May 26, 2016 ยท (Permalink)
favorite. Check out of my spreadsheets, but I'm [Name]." Did they cant trust somewhere!
[deleted] ยท 147 points ยท Posted at 15:08:43 on May 25, 2016 ยท (Permalink)
What if you dipped the whole thing in paint?
MustardBucket ยท 78 points ยท Posted at 15:21:03 on May 25, 2016 ยท (Permalink)
You could conceivably create a larger gabriel's horn which converges along the same point and axis as the original, in which case the new, larger horn would hold a finite amount of paint, but would never fully cover the surface of the smaller horn. Which is insane. The function for the surface area of both diverge no matter how you arrange them.
eliasv ยท 42 points ยท Posted at 16:25:58 on May 25, 2016 ยท (Permalink)
Nah, if you cover the outside in any constant thickness of paint (i.e. what happens when you dip something in paint, roughly speaking) the new volume is infinite.
This makes sense, as the horn is infinitely long and converges to essentially a cylinder with a radius of 0. If you cover it in paint, that line becomes a shape converging into an infinitely long cylinder with a radius t, where t is the thickness of paint.
SashaTheBOLD ยท 9 points ยท Posted at 17:19:09 on May 25, 2016 ยท (Permalink)
OK, maybe this would make it more clear:
You can fill it with a surprisingly small amount of paint (depending on the dimensions, but you could build one that would hold exactly one gallon of paint, or one liter of paint if you're metric).
However, while you can completely fill the horn with a small amount of paint, you would need an infinite amount of paint to paint the inside of the horn.
candygram4mongo ยท 30 points ยท Posted at 17:46:09 on May 25, 2016 ยท (Permalink)
If "painting" implies a constant thickness of paint, then you can't "paint" the interior at all, because at some point the layers of paint on the interior would need to intersect each other, and then further along, the walls of the horn itself. Alternatively, if "painting" only implies some positive thickness of paint at every point, you can paint either the outside or the inside by reducing the thickness of paint as you proceed down the length.
almightySapling ยท 10 points ยท Posted at 20:01:26 on May 25, 2016 ยท (Permalink)
Painting here implies zero thickness, because we are talking about hypothetical mathematical constructions.
It doesn't really hold up to more realistic interpretations... it's not actually about the paint, it's about the surface area.
candygram4mongo ยท 6 points ยท Posted at 20:39:22 on May 25, 2016 ยท (Permalink)
The OP definitely was phrasing it in physical terms, I think. From a purely mathematical standpoint it doesn't even make sense to think that it's weird that you can "fill" the horn but not "paint" it, because you're talking about completely different spaces. It is weird to discover that finite volumes can have infinite boundaries, but not in quite the same way.
almightySapling ยท 1 points ยท Posted at 21:31:55 on May 25, 2016 ยท (Permalink)
The OP was phrasing it the way it is always phrased: in a way that "makes sense" to the layman and captures the oddity of an object with finite volume and infinite surface area. It's meant to be intuitive and surprising, not realistic.
I fail to see any difference between the former and the latter that would justify one being "weird" and the other not. The boundary of a domain tends to be in a "completely different space". Keep in mind that this statement is only meant to be weird for someone at the level of calculus. Past that it's just a fact of life.
candygram4mongo ยท 3 points ยท Posted at 22:38:56 on May 25, 2016 ยท (Permalink)
The problem is that the intuition that people get from this seems to be a flat contradiction in terms -- if every point on the interior consists of paint, how can it be that the interior surface isn't painted? What people are trying to do here is explain that this isn't really a contradiction.
almightySapling ยท 0 points ยท Posted at 22:52:00 on May 25, 2016 ยท (Permalink)
Well that's why it is never stated this way. It's always stated that you can fill it with paint but you can't paint the outside. It just so happens to be the case that the interior surface is the exterior surface.
It's supposed to be a very simple volume versus surface area comparison. It's not meant to be very nuanced and it certainly isn't meant to be deeply analyzed in terms of physical reality.
It's nothing more than a quip in a calculus text book.
candygram4mongo ยท 2 points ยท Posted at 23:14:23 on May 25, 2016 ยท (Permalink)
Except people quite readily make the intuitive leap that if the exterior is unpaintable then so should the interior be.
It's a poor comparison that confuses people, and I'm trying to alleviate the confusion. Why is that a problem?
almightySapling ยท 1 points ยท Posted at 23:31:40 on May 25, 2016 ยท (Permalink)
As someone that teaches calculus, I can tell you with certainty that "people" do not readily make that leap.
It's not all that confusing, and I fail to see how anything you've said attempts to clarify anything. Finite volume, infinite surface area. That's all there is to it. What this "means" is that you can fill it (with something 3 dimensional), but you can't cover it (with something 2 dimensional). Paint is something that both fills (comes as a liquid) and covers. Nothing in our everyday reality is truly 2 dimensional, but paint comes damn close. Hence the comparison.
Very rarely you come across a clever student that does see the inherent flaw that filling it "should" paint it, and asks how it is possible to be filled yet not painted. To which I generally respond with "you bring me a real Gabriel's Horn and I'll buy the paint to show you".
eliasv ยท 1 points ยท Posted at 14:05:30 on May 26, 2016 ยท (Permalink)
I disagree that it actually captures it, though. There is no self-consistent interpretation which even makes sense, so far as I can see. To anyone who actually somewhat understands what you're saying it's going to add to the confusions and misunderstandings (just look at this thread), and for everyone else it's at best a false sense of understanding.
almightySapling ยท 0 points ยท Posted at 15:54:51 on May 26, 2016 ยท (Permalink)
As I've said before, it's a matephor. It lends to understanding what is being said, and it isn't meant to be perfectly analogous.
And this isn't usually met with confusion from students (except for any confusion they still have from evaluating an improper integral itself, but that has nothing to do with the metaphor). Most understand what is being said by "can be filled, can't be painted". The only people "confused" by this are those trying to apply physical real-world properties to the 2D notion of a "painted" surface.
eliasv ยท 1 points ยท Posted at 17:00:48 on May 26, 2016 ยท (Permalink)
Sure, that or self-consistent mathematical properties... It's confusing because it contradicts itself. It's objectively nonsense.
almightySapling ยท 1 points ยท Posted at 20:14:02 on May 26, 2016 ยท (Permalink)
They are self-consistent mathematical properties. You are attempting to twist them into something that doesn't make sense for sake of argument.
The mathematician makes no claims to your interpretation of events. Thus he does not contradict himself. He simply says the volume of the solid bounded by Gabriel's horn (Vol in R3) is finite while simultaneously the surface area of the boundary (Vol in R2) is infinite. This is perfectly consistent.
If one tries to interpret "paint the surface" as covering the surface with a real-life 3-D substance, you're going to have a bad time, because mathematicians make zero claims to that effect. "Paint the surface" refers to a completely 2-dimensional phenomena.
At best one may attempt to 3D-ify the statement by "unrolling" the horn into a flat surface and attempting to paint it with "real paint" of a constant thickness (such that we may speak of volume in 3D) which, for some, is enough to remedy the "inconsistencies" in the metaphor. However, I don't like this interpretation because, while the paint is now "realistic" in that it has a minimum thickness on the surface (say, it has a constant width in the z-dimension) we still need to allow the paint to get arbitrarily small in the y-dimension. Which, again, can't happen with real 3D paint, so all we have done is push the goalpost.
TheShadowKick ยท 4 points ยท Posted at 20:55:19 on May 25, 2016 ยท (Permalink)
So if you fill it with paint how is the inside not painted? I'm having trouble picturing this in my head. A 'full' container ought to have paint touching every part of its interior surface, otherwise how is it full? Unless some of the interior surface isn't adjacent to interior space? But then how is it an interior surface?
almightySapling ยท 3 points ยท Posted at 21:17:58 on May 25, 2016 ยท (Permalink)
That's why it doesn't hold up to realistic interpretation. Mathematically speaking, paint (the substance) taking up volume is drastically different than the same paint over a surface. Incomparably different.
[deleted] ยท 2 points ยท Posted at 22:26:41 on May 25, 2016 ยท (Permalink)*
[removed]
almightySapling ยท 1 points ยท Posted at 22:48:45 on May 25, 2016 ยท (Permalink)
It's just a metaphor. Don't over think it.
duck_of_d34th ยท 0 points ยท Posted at 00:13:19 on May 26, 2016 ยท (Permalink)
The only thing I could think of that makes sense to explain this, is that at some point, the diameter of the inside of the horn would be smaller than the size of one 'paint' molecule, thus leaving every part of the horn, past that single-molecule-wide point without paint.
eliasv ยท 2 points ยท Posted at 13:53:23 on May 26, 2016 ยท (Permalink)
If painting really implies zero thickness then the only even vaguely consistent and logical way to resolve that is by saying you can paint the horn. You start with a non-zero volume of paint. Painting a given area reduces your total volume of paint by zero.
If painting implies zero thickness, then either you can paint nothing (because it doesn't really make sense to subtract an area from a volume), or you can paint the entire infinite surface. Just the same as with any other shape, in other words.
That's not an interesting result.
almightySapling ยท 1 points ยท Posted at 16:03:22 on May 26, 2016 ยท (Permalink)*
Well painting does imply zero thickness, because the property being described is volume in R2.
If you don't like the metaphor because that doesn't seem "interesting" to you, or you think it's a bad metaphor, that's absolutely fine, I'm just explaining what is meant by mathematicians when they say it can be filled but can't be painted. The metaphor's been around longer than I've been alive, so I take no offense to your opinion of it one way or the other.
You aren't subtracting an area from a volume when you paint a surface.
zak13362 ยท 2 points ยท Posted at 02:12:44 on May 26, 2016 ยท (Permalink)
From Wikipedia: [Since the Horn has finite volume but infinite surface area, it seems that it could be filled with a finite quantity of paint, and yet that paint would not be sufficient to coat its inner surface โ an apparent paradox. In fact, in a theoretical mathematical sense, a finite amount of paint can coat an infinite area, provided the thickness of the coat becomes vanishingly small "quickly enough" to compensate for the ever-expanding area, which in this case is forced to happen to an inner-surface coat as the horn narrows. However, to coat the outer surface of the horn with a constant thickness of paint, no matter how thin, would require an infinite amount of paint.
Of course, in reality, paint is not infinitely divisible, and at some point the horn would become too narrow for even one molecule to pass. But the horn too is made up of molecules and so its surface is not a continuous smooth curve, and so the whole argument falls away when we bring the horn into the realm of physical space, which is made up of discrete particles and distances. We talk therefore of an ideal paint in a world where limits do smoothly tend to zero well below atomic and quantum sizes: the world of the continuous space of mathematics.](https://en.wikipedia.org/wiki/Gabriel%27s_Horn)
Strangely_quarky ยท 1 points ยท Posted at 01:10:06 on May 26, 2016 ยท (Permalink)
am i having a stroke
CyberTractor ยท 0 points ยท Posted at 01:07:49 on May 26, 2016 ยท (Permalink)
Once the horn's radius is smaller than a molecule of paint, a paint molecule would be to big to fit deeper into the horn. This checks out.
syzygy919 ยท 2 points ยท Posted at 21:26:56 on May 25, 2016 ยท (Permalink)
Does it have a finite length?
avatam123 ยท 2 points ยท Posted at 22:37:40 on May 25, 2016 ยท (Permalink)
No, it's essentially the graph of f(x)=1/x rotated about the x axis
PsychoticLime ยท -1 points ยท Posted at 18:40:23 on May 25, 2016 ยท (Permalink)*
That's why I love Maths, it can
literallybreak your brain.EDIT: many users were kind enough to let me know that my use of the world "literally" was inappropriate. I personally find it unhelpful to use the downvote button for punishing grammar mistakes, but I did get the point.
SilverStar9192 ยท 3 points ยท Posted at 21:58:56 on May 25, 2016 ยท (Permalink)
Well we can tell English isn't your strong subject. Literally???
[deleted] ยท 1 points ยท Posted at 22:43:06 on May 25, 2016 ยท (Permalink)
[deleted]
ImTheGuyWithTheGun ยท 1 points ยท Posted at 01:53:46 on May 26, 2016 ยท (Permalink)
Oh shut up. Just because many people make a mistake doesn't mean it's not a mistake.
PsychoticLime ยท 1 points ยท Posted at 04:28:00 on May 26, 2016 ยท (Permalink)
I'm sorry, English is not my first language... Where did I mess up exactly? I double-checked on Google translate to be sure and I thought it was correct
[deleted] ยท 2 points ยท Posted at 05:55:53 on May 26, 2016 ยท (Permalink)
[deleted]
PsychoticLime ยท 2 points ยท Posted at 12:15:51 on May 26, 2016 ยท (Permalink)
Thank you, I'll try to be more precise next time.
EDIT: I am literally grateful to you ;)
ImTheGuyWithTheGun ยท 1 points ยท Posted at 08:21:48 on May 26, 2016 ยท (Permalink)
I disagree the goal is to "sound smart" when you correct someone for saying their head "literally exploded". I simply think someone that says their head "literally exploded" doesn't know what "literally" means.
Is calling them out on it a dick move? Sure, that can be argued... but I don't accept that just because so many people make this mistake, it somehow becomes "correct" because language is "fluid" or "evolving"...
[deleted] ยท 1 points ยท Posted at 05:49:29 on May 26, 2016 ยท (Permalink)*
[deleted]
ImTheGuyWithTheGun ยท 1 points ยท Posted at 08:43:21 on May 26, 2016 ยท (Permalink)*
Saying a noise is the "loudest thing they ever heard" is an exaggeration and a subjective opinion, which is fine - no one can refute an opinion. But saying your ears "literally exploded" is not the same thing - it's objectively wrong and a misuse of the language. Yes, I understand that when enough people misuse a word that the word can take on that second, incorrect definition. But if you want to be more accurate, don't say your ears "literally exploded" unless, well,.. they literally exploded (in which case, get to a hospital immediately).
CKtheFourth ยท 5 points ยท Posted at 19:15:18 on May 25, 2016 ยท (Permalink)
It'd be a different color.
imgonnacallyouretard ยท 7 points ยท Posted at 18:44:03 on May 25, 2016 ยท (Permalink)
It's infinitely long, so you could never have a trough of paint deep enough
alexthelyon ยท 8 points ยท Posted at 19:41:15 on May 25, 2016 ยท (Permalink)
What about another horn!
imgonnacallyouretard ยท 1 points ยท Posted at 20:02:59 on May 25, 2016 ยท (Permalink)
The horn only has a finite amount of volume, so no
SuchCoolBrandon ยท 1 points ยท Posted at 22:26:14 on May 25, 2016 ยท (Permalink)
How many horns do we need then?
imgonnacallyouretard ยท 1 points ยท Posted at 23:07:07 on May 25, 2016 ยท (Permalink)
infinitely many
kickasserole ยท 2 points ยท Posted at 18:37:57 on May 25, 2016 ยท (Permalink)
Wait, was this Gabriel's Horn dipped in gold?
acidYeah ยท 2 points ยท Posted at 19:37:46 on May 25, 2016 ยท (Permalink)
It's infinitely long, you wouldn't find a bucket infinitely deep, and even if you did dipping would take you an infinite amount of time.
Though, you can fill it as a normal bottle.
jaredjeya ยท 1 points ยท Posted at 19:18:16 on May 25, 2016 ยท (Permalink)
It's infinitely long
RasmusSW ยท 1 points ยท Posted at 20:03:05 on May 25, 2016 ยท (Permalink)
Well for that you'll need an infinitely tall bucket of paint
ataxiastumbleton ยท 1 points ยท Posted at 17:32:36 on May 26, 2016 ยท (Permalink)
I just asked my student intern this and it's the first time he's been quiet for more than three minutes at once. Thank you
SPACKlick ยท 42 points ยท Posted at 16:15:32 on May 25, 2016 ยท (Permalink)
I don't know why people talk about painting the outside because the more mindbending fact is that you can fill it with paint but never cover the inside even though it's full and so there's paint everywhere inside but not all of the inside is covered.
My brain breaks every time I try to think about what that means.
visor841 ยท 32 points ยท Posted at 16:31:48 on May 25, 2016 ยท (Permalink)
You can paint the inside if you don't need a constant thickness. Think of it this way. Choose a thickness of paint. Go down the smaller part of the horn. Eventually you'll get to a point where the diameter of the horn is smaller than that thickness. Even if you make the paint thinner, you still can find a part with a smaller diameter. So it's never possible to paint the inside with a constant thickness. The tricky part is that the paint thickness has to get continuously thinner as you go down the tube, forever.
SPACKlick ยท 6 points ยท Posted at 17:10:32 on May 25, 2016 ยท (Permalink)
That logic still applies to the outside of the horn, if you're allowed to thin the paint rather than have negligible thickness then you can paint the outside.
candygram4mongo ยท 1 points ยท Posted at 17:50:38 on May 25, 2016 ยท (Permalink)
Well, yes.
ilovemusic_s ยท 0 points ยท Posted at 19:16:18 on May 25, 2016 ยท (Permalink)
What if...the paint is so thin it goes through the horn?
super_aardvark ยท 1 points ยท Posted at 21:19:17 on May 25, 2016 ยท (Permalink)
How can paint be real if our horns aren't real?
ilovemusic_s ยท 1 points ยท Posted at 21:34:47 on May 25, 2016 ยท (Permalink)
Nothing is ever real
KypDurron ยท 1 points ยท Posted at 23:16:10 on May 25, 2016 ยท (Permalink)
HOW? If you fill it with paint, there's no space left inside, right? So the paint is touching all the inside surface. That's how filling something works, isn't it?
SPACKlick ยท 1 points ยท Posted at 23:23:53 on May 25, 2016 ยท (Permalink)
Because the volume is finite, so you only have a finite amount of paint in it but the surface is infinite so you cannot cover it with a finite amount of paint.
zuccs ยท 4 points ยท Posted at 15:19:34 on May 25, 2016 ยท (Permalink)
I don't get it. Looks like you could paint it?
joshthewaster ยท 17 points ยท Posted at 15:27:02 on May 25, 2016 ยท (Permalink)
It's a mathematical object being related to a physical one (the paint). This means you can't try it in the real world. So the thought experiment is trying to make the idea of infinite surface area relatable by attempting to paint it. The mathematical idea that's interesting is the shape has finite volume (can be filled with a finite amount of something) but infinite surface area (can't be covered by any amount of anything).
[deleted] ยท 4 points ยท Posted at 18:03:33 on May 25, 2016 ยท (Permalink)
But why does it have infinite surface area ? it doesn't look infinite at all.
PointyOintment ยท 14 points ยท Posted at 18:08:52 on May 25, 2016 ยท (Permalink)
Because it's infinitely long.
SomeBadJoke ยท 2 points ยท Posted at 05:36:20 on May 26, 2016 ยท (Permalink)
Then how can you fill it?
cocorebop ยท 0 points ยท Posted at 23:50:31 on May 25, 2016 ยท (Permalink)
Yeah, when you get to this part of the fact it just becomes uninteresting when you're trying to apply it to real life topology. Like yeah, if I had a cup in the real world that held a liter of water, but the handle of the cup was infinitely large, then you could fill it with paint but you couldn't paint the exterior.
joshthewaster ยท 6 points ยท Posted at 18:27:50 on May 25, 2016 ยท (Permalink)
See where it gets really skinny, that keeps getting skinnier and skinnier the farther out you go and it goes out forever. Unfortunately there is no way to have a picture of the whole thing because, well, it's infinitely long.
[deleted] ยท -1 points ยท Posted at 19:43:08 on May 25, 2016 ยท (Permalink)
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joshthewaster ยท 3 points ยท Posted at 19:51:23 on May 25, 2016 ยท (Permalink)
You are correct that the paint is a physical object and the horn is mathematical which makes the idea fall apart under scrutiny. However, the mathematical object DOES have finite volume and infinite surface area. The paint is just to try and help people understand what that means.
[deleted] ยท 0 points ยท Posted at 20:27:22 on May 25, 2016 ยท (Permalink)*
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Godd2 ยท 3 points ยท Posted at 21:58:54 on May 25, 2016 ยท (Permalink)
The volume is not calculated by numerical approximation. We can find the volume exactly. The integral of pi*x-2 dx from 1 to infinity is precisely pi*(-(infinity)-1 ) - pi*(-(1)-1 ). The limit as x approaches infinity of 1/x is zero, so the first part is zero, and we're left with -pi * -1, which is precisely pi.
This can be shown to be false by counterexample. The area under the curve x-2 from 1 to infinity is 1.
In short, there exist functions which increase forever, but don't diverge. Any function with a horizontal asymptote which the function approaches from below is an example of this concept.
Also, the irrationality of pi is a red herring. While the decimal representation of pi requires an infinite amount of digits to precisely represent, pi is indeed finite. It is as finite as any other number between 3 and 4. In fact, if we took the integral of 4*x-2 from 1 to infinity, we'd get the exact answer of 4, and your argument would become "the digits of 4 go on forever, thus adding volume infinitely". But the digits of 4 do not go on. They stop after one digit.
[deleted] ยท 1 points ยท Posted at 23:05:44 on May 25, 2016 ยท (Permalink)*
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Godd2 ยท 2 points ยท Posted at 23:14:59 on May 25, 2016 ยท (Permalink)
There are no segments to add if the exact volume has been found. The volume wasn't calculated by sitting there and counting segments and adding them to a running total. The integral was found by doing a constant-time calculation at the boundaries.
If you were correct, then integrals could never be taken, since there are an infinite number of infinitely thin rectangles to add up. But you only need to evaluate the antiderivative at two places and then take their difference to know what the total is. That's why we do F(b) - F(a). That's why the integral of x-2 from 1 to infinity is precisely 1, and I don't have any more work to do.
I'm happy you're asking these questions though, so that passers-by have the correct math to learn.
[deleted] ยท 1 points ยท Posted at 23:26:23 on May 25, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 23:52:46 on May 25, 2016 ยท (Permalink)
Alright, I'll give you an example that will hopefully help you understand this better.
Suppose you have a cake that has a volume of 1. You then take the cake and cut it in half. Then you take one of the halves and cut it again. Then you take the quarter and so on.. until you have infinitely small pieces.
Yes, in real world this would be impossible but not in the realm of math. Now suppose you want to add all the pieces together again. So you start doing just that. With each piece you add the volume gets bigger obviously, but originally the cake had a volume of 1 and that didn't change.
As you can see you can have infinitely many parts of something that add up to a finite value. It is determined by how quickly the parts shrink. For example this series: 1 + 1/2 + 1/3 + ... adds up to infinity. But this one: 1 + 1/2 + 1/4 + 1/8 + ... adds up to exactly 2.
[deleted] ยท 0 points ยท Posted at 00:06:39 on May 26, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:23:26 on May 26, 2016 ยท (Permalink)
Alright, check this out. You have infinitely many cake crumbs, but each crumb is one tenth in volume of the previous one. Arguably they all have a measurable volume.
What happens though when you try to add them up. You claim that the volume should be infinite. Let's see:
1 + 1/10 + 1/100 + 1/1000 .... = = 1.111111.............. This doesn't look infinite to me. It is 10/9.
Godd2 ยท 1 points ยท Posted at 00:42:28 on May 26, 2016 ยท (Permalink)
They're two different integrals. The volume calculation is the integral of pi*x-2 dx from 1 to infinity, and the area calculation is the integral of 2*pi*x-1 * (1+-x-2 )1/2 dx from 1 to infinity. Area and volume are two different things. The surface area of a cube with edge length 1 is 6, but its volume is 1. 1 does not equal 6. Do you have a problem with the difference between a cube's surface area and its volume? I would hope not.
This betrays a fundamental mistake. The mathematical conclusion has nothing to do with physical things in the real world.
There are an infinite number of numbers between 0 and 1. The length of a line segment from 0 to 1 is 1. Are you going to claim that it is more than 1 just because there are an infinite number of points there?
[deleted] ยท 1 points ยท Posted at 01:07:53 on May 26, 2016 ยท (Permalink)
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Godd2 ยท 1 points ยท Posted at 03:46:23 on May 26, 2016 ยท (Permalink)
I agree that if you have an infinite collection of "points", each with the same non-zero length, that the resulting length will be infinity. But the cake and the horn deal with collections where the size of each one is different. Namely, that the size of each one gets smaller and smaller as you go along.
Let's talk about the distance between me and the grocery store. It's one mile away. Let's imagine the point halfway there. We'll call it P_0. The distance from me to P_0 is one half of a mile, and the distance from P_0 to the grocery store is one half of a mile. Let's mark another point P_1. P_1 is halfway between P_0 and the grocery store. It's 3/4 of a mile away from me, 1/4 a mile away from P_0, and 1/4 of a mile away from the grocery store. We can keep naming points. Let's say that each new point is halfway between the old point and the grocery store. So P_2 is halfway between P_1 and the store, P_3 is halfway between P_2 and the store, and so on.
Since there are an infinite number of points between me and the grocery store, I can keep cutting the distance in half, and the resulting distance in half, and so on.
As a result, we have an infinite number of line segments. Here they are in a list
As you can see, each line segment is half the length of the previous. We also know that the total length is 1 mile.
So we have a case where we have an infinite number of line segments, and each line segment is non-zero in length. But their sum is a finite value.
So just because you add together an infinite amount of non-zero segments doesn't mean you get a total that is infinite.
We can think of it a slightly different way. Consider points A and B where A is less than B. There's a distance between A and B. If I move A toward B, but I move it such that A move less than the previous distance, A will still be less than B. If I do this again, but with the new distances, A will still be less than B. I would have to move A at least the distance it is away from B in order for A to stop being less than B. However, as long as A is less, there will always be a distance I can move A such that A remains less than B.
So, if we were to inspect the distances I move A over time, we would see a number that is getting smaller and smaller. This is why we can add up an infinite list of values that are smaller and smaller, and end up with a total that is finite. (Of course, we can end up with a number that is infinite too, if the "smaller and smaller" values are still too big. The next number just has to be smaller than the previous)
Here are some math questions to illustrate the concept:
The answer is C.
The answer is A.
The answer here is C again.
For the case of 1 + 1/2 + 1/4 + 1/8 + 1/16 + ..., the answer is 2, but for 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ..., the answer is infinity, so it depends on how quickly the successive lengths are decreasing.
joshthewaster ยท 2 points ยท Posted at 22:12:57 on May 25, 2016 ยท (Permalink)
Sorry but this isn't accurate at all. The fact that pi has an infinite number of digits does not negate the fact that it is a finite number. Involving pi in calculations doesn't make the result infinite or cause any paradoxes. What is making this possible is the fact that it is a purely mathematical object we are talking about. It cannot exist as a physical thing. So of course it is confusing to try and make it fit into our physical way of thinking about it. I'm happy to try and explain more if you have questions.
[deleted] ยท 1 points ยท Posted at 23:02:51 on May 25, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:01:14 on May 26, 2016 ยท (Permalink)
I'm sorry but you're wrong. The increase in volume is very much different from the increase in area. The area of the horn is defined by an integral of 1/x, while the volume is an integral of pi*(1/x)2. This difference is enough to make the volume finite. And no, there is no paradox because of pi. Pi is no different from any other number.
[deleted] ยท 0 points ยท Posted at 00:16:09 on May 26, 2016 ยท (Permalink)*
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zedpowa ยท 2 points ยท Posted at 00:25:51 on May 26, 2016 ยท (Permalink)
Integral is just an infinite sum. When the parts it sums are small enough the result will be finite, simple as that.
[deleted] ยท 1 points ยท Posted at 00:26:35 on May 26, 2016 ยท (Permalink)
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zedpowa ยท 2 points ยท Posted at 00:33:34 on May 26, 2016 ยท (Permalink)
Not always. As I explained before, the volume is given by a different function than the area is. As you keep adding smaller and smaller parts to the horn, both its area and volume grow slower too. But because they are defined by different functions they grow at different speeds. It just so happens that the area keeps growing infinitely while the volume never goes over a finite threshold.
joshthewaster ยท 1 points ยท Posted at 01:01:03 on May 26, 2016 ยท (Permalink)
You can't decide a proof isn't valid. Anyway, the beauty of math really hits when you understand these things which it's obvious you don't want to do. I tried.
jywn4679 ยท 2 points ยท Posted at 00:23:54 on May 26, 2016 ยท (Permalink)
This is totally wrong. 1.999... does not get infinitely large. It is bounded by 2. If you claim it gets infinitely large then prove it, it goes against accepted mathematics.
[deleted] ยท 1 points ยท Posted at 00:30:10 on May 26, 2016 ยท (Permalink)
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jywn4679 ยท 2 points ยท Posted at 00:31:13 on May 26, 2016 ยท (Permalink)
I have no idea what you are trying to say.
Godd2 ยท 2 points ยท Posted at 00:52:19 on May 26, 2016 ยท (Permalink)
If there are not an infinite number of numbers between 1 and 2, then there is some number that is closest to 2, but not equal to 2, correct? Let's call this number B, for Biggest Number Less Than 2.
If I take B, and find the average of B and 2, or (B+2)/2, I'll get a number that is larger than B, but less than 2. But B is the largest number smaller than 2. This is a contradiction, therefore, it is not the case that there are a finite number of numbers between 1 and 2. Thus, there are an infinite number of numbers between 1 and 2.
Is this convincing to you?
[deleted] ยท 1 points ยท Posted at 00:56:53 on May 26, 2016 ยท (Permalink)
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Godd2 ยท 2 points ยท Posted at 01:09:13 on May 26, 2016 ยท (Permalink)
You seemed not completely convinced it was the case.
Also, it's worth noting that I'm not being as rigorous as I ought to be. There are sets where there aren't an infinite number of numbers between 1 and 2. In the set of integers, there aren't any numbers between them. But in the set of rationals and reals, there is an infinite number between them. In the set of complex numbers, being between two numbers doesn't have an obvious or natural definition, since the set isn't ordered.
My proof above only technically applies to the rational numbers, but could be used on the real numbers as well.
[deleted] ยท 4 points ยท Posted at 18:41:28 on May 25, 2016 ยท (Permalink)
Basically, it's like taking the integral (aka finding the area under the curve) of x-2 from 1 to โ. The answer is finite, and actually will be equal to exactly 1 if you work it out. Now, if you find length of the curve, you'll get infinity, because, well, the domain of the curve is pretty much infinite.
So let's say you revolve that entire segment from 1 to โ around the x axis. Now we are adding a whole new dimension to our universe, so basically the properties of the previous two calculations kinda jump up a dimension too. Long story. But basically, because the area was finite in 2 dimensions, the volume is also finite in three dimensions. Also, because the arc length was infinite in 2 dimensions, the SURFACE area is also infinite.
kyledawg92 ยท 8 points ยท Posted at 17:26:39 on May 25, 2016 ยท (Permalink)*
It extends forever, so there is no end to its surface. The only reason you can fill it with paint is because, since the object becomes narrower as it extends to the right, the volume is approaching a finite number.
A similar problem with a number series may make more sense. Such as:
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...
Try it in a calculator. The number gets infinitely close to 2 as you continue. In mathematics, this mean it actually is 2.
Now think of each of those numbers in the series as periodic measurements of the horn's circumference as you move to the right.
971365 ยท 3 points ยท Posted at 15:50:05 on May 25, 2016 ยท (Permalink)
Imagine a flat stretch of desert with a small hole in the sand. You could fill it up but not paint the whole place.
[deleted] ยท 8 points ยท Posted at 17:24:37 on May 25, 2016 ยท (Permalink)
Why not
SashaTheBOLD ยท 3 points ยท Posted at 17:21:54 on May 25, 2016 ยท (Permalink)
It's an object with a finite volume (so it could be "filled") but an infinite surface area (so it can't be "painted").
Moofies ยท 1 points ยท Posted at 17:12:39 on May 25, 2016 ยท (Permalink)
But if you filled it with paint, would you not be covering the whole inside (and infinite) surface area?
memcginn ยท 1 points ยท Posted at 17:55:14 on May 25, 2016 ยท (Permalink)
You can fill it with paint, but you'll never have enough paint to paint the entire inside.
WhyIsTheNamesGone ยท 1 points ยท Posted at 19:10:21 on May 25, 2016 ยท (Permalink)
Nor the inside.
johnklos ยท 1 points ยท Posted at 20:08:49 on May 25, 2016 ยท (Permalink)
Use thick paint.
Virtlink ยท 1 points ยท Posted at 20:43:32 on May 25, 2016 ยท (Permalink)
You can fill the inside with a finite amount of paint, but need an infinite amount of paint to paint the inside!? :P
hobo_champ ยท 1 points ยท Posted at 21:41:35 on May 25, 2016 ยท (Permalink)
Forget the outside, you can fill it with paint, but you will never have enough to cover the inside.
[deleted] ยท 1 points ยท Posted at 21:44:16 on May 25, 2016 ยท (Permalink)*
.
sikyon ยท 1 points ยท Posted at 21:49:46 on May 25, 2016 ยท (Permalink)
That's easy, you just have an infinitely long cylinder with a finite divot in 1 end. Fixed interior volume, infinite exterior surface area.
The more interesting thing is that you can fill it with paint but you will never have enough to cover the inside (except of course that paint has a finite volume).
Pretagonist ยท 1 points ยท Posted at 22:16:02 on May 25, 2016 ยท (Permalink)
I thought I had fractals clear in my head but that comment just blew my mind.
YashFace ยท 1 points ยท Posted at 22:33:53 on May 25, 2016 ยท (Permalink)
Da fuk?
TILtonarwhal ยท 1 points ยท Posted at 22:41:17 on May 25, 2016 ยท (Permalink)
So you're tellin me you can paint the inside of my trumpet, but not the outside?
If I didn't know better, I'd think this was a scam.
...okay you have yourself a deal.
[deleted] ยท 1 points ยท Posted at 23:34:10 on May 25, 2016 ยท (Permalink)
You cannot fill it with paint. Any physical analogy fails.
If you were to "fill it with paint", you'd be implying that an ideal liquid could travel an infinite distance in finite time. Which is impossible. If you state that physical matter has definite size, then you don't have infinite surface area.
I'm being pedantic as all fuck, I know, it just irks me that people seem to be unable to recognize that all physical analogies of Gabriel's horn fail.
MagnusCallicles ยท 1 points ยท Posted at 00:53:41 on May 26, 2016 ยท (Permalink)
Eh, I like the concept but I don't think that's very accurate. You're assuming you can't paint infinitely fast but I can if I just dip paint in and accept that the paint is covering the sides.
It's not a mathematical problem, just a language one but it irked me a little bit.
onacloverifalive ยท 1 points ยท Posted at 01:20:18 on May 26, 2016 ยท (Permalink)
Or the inside.
superiority ยท 1 points ยท Posted at 06:26:05 on May 26, 2016 ยท (Permalink)
You'll never have enough to cover the inside, either!
jvjanisse ยท 1 points ยท Posted at 02:58:52 on May 27, 2016 ยท (Permalink)
Question: so, you can fill gabriels horn, and therefore cover 1/2 of the surface of the 3D object with paint.
The surface area is infinite, and you just covered the inner half of the surface with paint.
Now, 1/2 of infinity is still infinity.
Therefore you just covered an infinite surface area with a finite amount of paint.
Can you prove me wrong?
supera8y ยท 100 points ยท Posted at 15:14:13 on May 25, 2016 ยท (Permalink)
The doot doot trumpet
WraithCadmus ยท 50 points ยท Posted at 18:21:22 on May 25, 2016 ยท (Permalink)
thank mr gabrel
Bobby_Hilfiger ยท 4 points ยท Posted at 21:54:28 on May 25, 2016 ยท (Permalink)
I'm cryin' lol
donteatmenooo ยท 27 points ยท Posted at 16:24:00 on May 25, 2016 ยท (Permalink)
I'm not sure I understand why it has finite volume...? Can someone please explain?
D1g1talAli3n ยท 20 points ยท Posted at 17:25:28 on May 25, 2016 ยท (Permalink)*
Mathematically, it's because its volume is an infinite sum that converges to a finite value. For example, cut the horn into a set of infinite rings. The first ring has volume 1, the second 1/2, the fourth 1/4, the fifth 1/8 and so on. Such a horn would have volume 1+1/2+1/4+1/8+1/16+... = 2, as the sum of 1/( 2n ) from n = 0 to infinity is 2.
donteatmenooo ยท 19 points ยท Posted at 18:47:33 on May 25, 2016 ยท (Permalink)
But... why can't the same apply to the surface area, then? God how did I manage to graduate from college...
800alpha ยท 9 points ยท Posted at 19:56:27 on May 25, 2016 ยท (Permalink)*
Many infinite sums do not converge to a finite value (for example 1/1 + 1/2 + 1/3 + 1/4... does not converge). It just so happens that the volume sum converges, while the surface area does not. Gabriel's horn can be modeled by 1/x. This is a rough explanation, but because volume uses cubes, volume can be modeled by the sum of (1/x)2, which converges (sum of (1/x)2 is sort of like cubing). On the other hand, surface area doesn't. It can roughly be modeled by (1/x), which does not converge. Using the volume and surface area formulas in single variable calculus can easily show this. https://en.wikipedia.org/wiki/Gabriel%27s_Horn#Mathematical_definition shows the calculus application clearly.
Edit: converge to an infinite value --> converge to a finite value
croserobin ยท 1 points ยท Posted at 23:48:03 on May 25, 2016 ยท (Permalink)*
Youre using the term converge wrong. You mean diverge in this instance. A sum that converges is equivalent to a sum that doesn't diverge.
edit: wait I think you just made a typo. Converge to finite value is what you meant sorry
800alpha ยท 1 points ยท Posted at 00:25:40 on May 26, 2016 ยท (Permalink)
Yeah it was a typo my bad. Thanks for pointing that out.
MrWoohoo ยท 3 points ยท Posted at 20:00:33 on May 25, 2016 ยท (Permalink)
This is like a 3D version of the Koch Snowflake that has an infinite perimeter contained within a bounded area.
donteatmenooo ยท 1 points ยท Posted at 22:10:26 on May 25, 2016 ยท (Permalink)
Ah, that helps, thank you. It's still a bit mind-bending, though, understanding the infinite surface but knowing there's a finite interior... Thank you!
Sharohachi ยท 1 points ยท Posted at 21:57:51 on May 25, 2016 ยท (Permalink)
The horn has a radius of 1/x, the volume of a slice is proportional to r2 while the surface area of a slice is proportional to r so the volume of sections approaches 0 faster than the surface area. When you integrate the volume equation from 1 to infinity you'll see that it converges to a finite number but when you integrate the surface area from 1 to infinity it will give an infinite result.
MrSenorSan ยท 1 points ยท Posted at 23:28:41 on May 25, 2016 ยท (Permalink)
because the way I see it is that to measure the volume for one segment one puts a virtual lid on either side. So we will always get a limit on volume.
jroddie4 ยท 3 points ยท Posted at 20:33:36 on May 25, 2016 ยท (Permalink)
Then it wouldn't have a tip, right? It would be a shape of infinite length.
D1g1talAli3n ยท 2 points ยท Posted at 20:50:48 on May 25, 2016 ยท (Permalink)
Yep, it would have infinite length, infinite surface area but finite volume and width/depth
jroddie4 ยท 2 points ยท Posted at 20:51:55 on May 25, 2016 ยท (Permalink)
but if it has no tip, how could there be an end to the interior volume? Wouldn't it go on and follow the rest of the shape?
relvant_usernam ยท 3 points ยท Posted at 21:05:36 on May 25, 2016 ยท (Permalink)
I'm with you man, really struggling to comprehend this one
D1g1talAli3n ยท 2 points ยท Posted at 21:28:48 on May 25, 2016 ยท (Permalink)
It does go on, but it gets smaller and smaller. These values are "small enough" to add up to a finite value. Some others are not - like the 1/2+1/3+1/4+1/5 mentioned above. Why some sums add up (or "converge") and why others don't takes an understanding of calculus, notably limits.
jroddie4 ยท 1 points ยท Posted at 21:55:44 on May 25, 2016 ยท (Permalink)
ok, that makes sense. I know next to nothing about calculus, other than kerbal space program, so I'll assume you're right.
D1g1talAli3n ยท 3 points ยท Posted at 22:17:21 on May 25, 2016 ยท (Permalink)*
The first sum can actually quite simple, as it is a geometric sum, it can be proven with algebra and a simple limit. If you're curious:
Let Sn = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2n-1 + 1/2n
2Sn = 2/2 + 2/4 + 2/8 + 2/16 + ... + 2/2n-1 + 2/2n
2Sn = 1 + (1/2 + 1/4 + 1/8 + ... + 1/2n-2 + 1/2n-1)
Note the part in the brackets is exactly the same as the original sum Sn, but without the last term 1/2n, so
2Sn = 1 + Sn - 1/2n.
Rearrage,
Sn = 1 - 1/2n
That is the formula for the sum with n terms. But what if there are infinite terms? then n = โ and
Sn = 1 - 1/2โ
Put simply, we say that 1/2โ is so small it's 0, thus Sn = 1. More formally, the limit of 1/2n as n->โ is 0.
My original example was 1+1/2+1/4+1/8+... = 1+Sn, which is 2.
jroddie4 ยท 1 points ยท Posted at 22:20:55 on May 25, 2016 ยท (Permalink)
So pretty much any measurable amount of paint would fill up the smallest sections at the end? Even if it was infinite, the amount of paint required would be effectively zero?
D1g1talAli3n ยท 3 points ยท Posted at 22:30:28 on May 25, 2016 ยท (Permalink)
Thinking of it in physical terms is a bit tricky, as it is impossible to actually construct and more of an abstract shape. If you put 1 volume of paint into the cone, it would fill up exactly half of it. Doing it again will fill up the whole thing. However, no matter how much paint you tried to put on the outside, you will never end up finishing the painting, never reaching the "end" of the tip. This is all because the sum of the volume converges, while the sum of the surface area diverges.
donteatmenooo ยท 1 points ยท Posted at 22:12:56 on May 25, 2016 ยท (Permalink)
So the interior approaches a finite number while the exterior approaches infinity, right? I think I understand now.
donteatmenooo ยท 1 points ยท Posted at 22:11:30 on May 25, 2016 ยท (Permalink)
This is exactly what I was trying to say.
donteatmenooo ยท 1 points ยท Posted at 22:13:12 on May 25, 2016 ยท (Permalink)
So the interior approaches a finite number while the exterior approaches infinity, right? I think I understand now.
D1g1talAli3n ยท 1 points ยท Posted at 22:19:56 on May 25, 2016 ยท (Permalink)
Yes! that's exactly what happens.
DCdictator ยท 10 points ยท Posted at 19:15:17 on May 25, 2016 ยท (Permalink)*
If you didn't understand the other explanations here's what I think is an easier one.
Surface area is in units squared, volume is in units cubed, this means that if something is decreasing in size it's volume is decreasing faster than it's surface area. If something is getting smaller at a fast enough rate, even if it goes on forever, it eventually converges to a finite number.
For instance, 1 + 1/2 +1/4 + 1/8+ 1/16... can be said to equal 2 if the series goes on forever.
The case of the horn is that the radius of the cone as the figure moves from left to right is decreasing, but not fast enough for the surface area to ever equal a finite number. However, the volume, which decreases even faster than the surface area, is getting smaller to offset the fact that it's going on forever and eventually reaches a finite number.
[deleted] ยท -1 points ยท Posted at 23:52:45 on May 25, 2016 ยท (Permalink)
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udbluehens ยท 1 points ยท Posted at 02:17:18 on May 26, 2016 ยท (Permalink)
What? I don't understand your point. Also some infinite can be bigger than other infinites. Like the real numbers are bigger than the integers, which are the same size as the natural numbers
oiturtlez ยท 4 points ยท Posted at 17:14:16 on May 25, 2016 ยท (Permalink)
Take the graph of f(x) = 1/x where 1< x < infinity
rotate that graph around the x axis, you have gabriels horn
integrate that object you produce to obtain its volume and it is a finite number. However the object clearly extends on to infinity as per the initial conditions of the statement, giving it infinite surface area
donteatmenooo ยท 2 points ยท Posted at 18:47:04 on May 25, 2016 ยท (Permalink)
And not infinite volume? f(x) = 1/x will never reach the axis, so there will always be some space/volume, right? I understand the infinite surface area.
oiturtlez ยท 1 points ยท Posted at 18:52:41 on May 25, 2016 ยท (Permalink)
using the integral of the planar area (pi * r2 where r = 1/x) over the length of the trumpet ( lets say from 1 to a to give it any length right now) gives us the volume
V = pi * integral ((1/x)2 dx) from 1 to a
= pi ( 1-1/a)
and so for any a, this volume is finite
[deleted] ยท 2 points ยท Posted at 19:18:58 on May 25, 2016 ยท (Permalink)
Yeah, I don't get this either. Isn't pi, as an irrational number, technically infinite?
(Pardon my ignorance. I enjoy math and find it all fascinating, but public school let me down...)
oiturtlez ยท 2 points ยท Posted at 19:24:06 on May 25, 2016 ยท (Permalink)*
What? Pi is not infinite. Pi has a value. It is a constant. It is irrational meaning it has infinite non-terminating non-repeating decimal places, but it does not have infinite value
If this still confuses you, remeber that pi can be approximated quite well as 3.14 or as 22/7. Replace pi with either of those values in my previous post and the result is the same
[deleted] ยท 1 points ยท Posted at 23:35:19 on May 25, 2016 ยท (Permalink)
Huh. I guess the irrationality is what confuses me. The fact that the digits go on and on is hard to wrap one's head around. Then again, I know I'm not alone in that thought. Thank you for helping!
oiturtlez ยท 2 points ยท Posted at 00:20:47 on May 26, 2016 ยท (Permalink)
well think about it like this
if pi is 3.14xxxxxx where the x's go on to infinity, and lets say for our purposes we have no idea what these x are. In the largest case, every single x would be a 9, giving us 3.149999999999999999 repeating to infinity. This number is easily seen to be less than 3.15. The same can be done for the lower limit of 3.14xxxxxxxx being always equal to or greater than 3.14 no matter what x we chose. ( if all x are 0, we get 3.14)
So we know forsure the value of pi is between 3.14 and 3.15, despite the fact that it has infinite digits. The infite digits just let us understand precisely where between 3.14 and 3.15 pi actually lies on the "number line"
Plasmodicum ยท 1 points ยท Posted at 16:43:03 on May 26, 2016 ยท (Permalink)
This is a great explanation, but one nitpick, IIRC...
I'm pretty sure in that case it actually would equal 3.15. The logic holds however for any other example besides infinite 9s.
oiturtlez ยท 1 points ยท Posted at 17:49:25 on May 26, 2016 ยท (Permalink)
you are correct, technically if those 9's continued on to infinity, it would be impossible to pick a number between 3.14999999999 and 3.15 making them effectivley the same number
Katastic_Voyage ยท 12 points ยท Posted at 17:20:48 on May 25, 2016 ยท (Permalink)
Fuck Calc 2.
3 was easy by comparison. Diff Eq probably still not as bad as Calc 2 integration methods of "here's 5 techniques that take a page of writing each time, they can be used in any order, some multiple times, and you may or may not get a workable answer."
[deleted] ยท 2 points ยท Posted at 18:29:46 on May 25, 2016 ยท (Permalink)*
[removed]
KnobGoblin96442 ยท 8 points ยท Posted at 18:40:42 on May 25, 2016 ยท (Permalink)
When studying for the exams, just do the review problems over and over and over until you know how to do them all...sounds stupidly simple but it's what I ended up doing to pass. The exam will be just like the review problems with different numbers.
ShitDuchess ยท 3 points ยท Posted at 18:54:25 on May 25, 2016 ยท (Permalink)
The key is knowing how to do them, as in why you are doing each part. I have seen people do ok for a few small tests/problem sets by using the same systematic procedure to solve things. It doesn't help in exams though, they often will throw two concepts from review problems together into on question.
JonnyNashEquilibria ยท 3 points ยท Posted at 14:58:59 on May 25, 2016 ยท (Permalink)
This takes ages to get your head around, but what a sit back in your chair in awe moment after you do.
dont_worry_im_here ยท 1 points ยท Posted at 21:46:16 on May 25, 2016 ยท (Permalink)
Well, consider me on the edge of my seat... can't wrap my head around this one to save my life.
[deleted] ยท 1 points ยท Posted at 22:56:50 on May 25, 2016 ยท (Permalink)*
[deleted]
udbluehens ยท 1 points ยท Posted at 02:18:50 on May 26, 2016 ยท (Permalink)
Is there really?
PotatoFruitcake ยท 3 points ยท Posted at 15:47:57 on May 25, 2016 ยท (Permalink)
Menger Sponge
oopsa-daisy ยท 2 points ยท Posted at 17:39:05 on May 25, 2016 ยท (Permalink)
I love these objects!!! Gabriels Horn and fractals are so cool!
Arandur ยท 2 points ยท Posted at 18:11:19 on May 25, 2016 ยท (Permalink)
But are there objects with an infinite volume and finite surface area?
Hydropos ยท 3 points ยท Posted at 20:04:36 on May 25, 2016 ยท (Permalink)
Well, black holes could qualify for this given the distortion of spacetime approaching a singularity. Ironically, these are more physically real than the infinite surface area objects (which can't exist in this universe, since atoms have finite size).
Exomnium ยท 2 points ยท Posted at 07:33:05 on May 26, 2016 ยท (Permalink)
I'm pretty sure the 3D analog of the isoperimetric inequality implies that there isn't.
Swagfag9000 ยท 1 points ยท Posted at 01:29:48 on May 26, 2016 ยท (Permalink)
the tardis
Arandur ยท 1 points ยท Posted at 01:49:40 on May 26, 2016 ยท (Permalink)
Exterior surface area is finite. I dunno about interior.
LBJSmellsNice ยท 1 points ยท Posted at 17:07:46 on May 25, 2016 ยท (Permalink)
How does it have an infinite surface area?
JangXa ยท 1 points ยท Posted at 19:45:51 on May 25, 2016 ยท (Permalink)
Its the sum of 1/x2 which doesnt converge with x-> infinity while the volume is 1/x3 which converges to 0.
CorrectBatteryStable ยท 1 points ยท Posted at 17:20:21 on May 25, 2016 ยท (Permalink)
Something something the dirac delta function or any convergent function in L2 space.
kyleqead ยท 1 points ยท Posted at 18:07:35 on May 25, 2016 ยท (Permalink)
any volume described by pi*integral(1/xn ) from 1 to infinity will have this property so long as n>1.
rouseco ยท 1 points ยท Posted at 18:14:05 on May 25, 2016 ยท (Permalink)
So they are smaller on the inside, that's pretty cool.
KarlKastor ยท 1 points ยท Posted at 18:39:01 on May 25, 2016 ยท (Permalink)
We build a Sierpinski pyramid out of toothpicks and beans at our last math lesson. The teacher wanted us to calculate the surface and volume, but nobody did, because we wanted to build a really large pyramid.
MartinLoofah ยท 1 points ยท Posted at 19:46:03 on May 25, 2016 ยท (Permalink)
Well that limited volume is still pretty goddamn loud. Fuckin South Africa.
latenitekid ยท 1 points ยท Posted at 19:52:43 on May 25, 2016 ยท (Permalink)
Learned this in Calc 2 and still can't fathom it.
sourc3original ยท 1 points ยท Posted at 20:43:43 on May 25, 2016 ยท (Permalink)
*In math, tho not actually possible.
SnipeCity73 ยท 1 points ยท Posted at 20:51:18 on May 25, 2016 ยท (Permalink)
Is it because the smaller ends combine so there is no volume, but surface area continues?
Thomas9002 ยท 2 points ยท Posted at 21:20:51 on May 25, 2016 ยท (Permalink)
There is still volume, but the volume gets lower and lower.
It sounds unintuitive but you can add more and more and still get to a finite value.
Just as: 1+1/2+1/4+1/8+1/16+.... Equals 2
FIERY_BUTTHOLE ยท 1 points ยท Posted at 21:02:32 on May 25, 2016 ยท (Permalink)
It looks like Gabriel's horn has infinite length as well. Couldn't you get infinite surface area and limited volume and length by taking a fractal/"infinite coastline" and giving it some depth?
Thomas9002 ยท 1 points ยท Posted at 21:18:41 on May 25, 2016 ยท (Permalink)
It depends on the fractal, but yes it's true for many of them
[deleted] ยท 1 points ยท Posted at 21:11:56 on May 25, 2016 ยท (Permalink)
Does the name Gabriel's horn come from the play 'Fences' by any chance ?
ActualNameIsLana ยท 1 points ยท Posted at 21:14:09 on May 25, 2016 ยท (Permalink)
And on the other side of the equation, there are 3D objects that have infinite surface area, but zero volume.
E.g.: The Menger Sponge
[deleted] ยท 1 points ยท Posted at 21:19:46 on May 25, 2016 ยท (Permalink)
Integrals are fun
Sharp_Espeon ยท 1 points ยท Posted at 21:27:12 on May 25, 2016 ยท (Permalink)
Like a menger sponge?
muchmadeup ยท 1 points ยท Posted at 21:31:33 on May 25, 2016 ยท (Permalink)
can someone ELI5 this? is it that at the narrow end it has no "inside" to fill?
bbtvvz ยท 1 points ยท Posted at 21:31:51 on May 25, 2016 ยท (Permalink)
So basically like a bell curve in 3D
ThaShadowHunter ยท 1 points ยท Posted at 21:55:30 on May 25, 2016 ยท (Permalink)
Sorry if I sound like an idiot, I'm just some high schooler that likes math. But to my knowledge, if the smallest unit of space is a Planck length, then how can the cone keep getting smaller forever? Shouldn't the space inside the cone eventually be the size of a Planck length?
llamaman17 ยท 1 points ยท Posted at 21:55:36 on May 25, 2016 ยท (Permalink)
How?
TILtonarwhal ยท 1 points ยท Posted at 22:41:37 on May 25, 2016 ยท (Permalink)
y tho?
nissepik ยท 1 points ยท Posted at 23:01:00 on May 25, 2016 ยท (Permalink)
like your mom.
andrak7 ยท 1 points ยท Posted at 23:35:40 on May 25, 2016 ยท (Permalink)
Explain this to me
FlexibleToast ยท 1 points ยท Posted at 01:24:56 on May 26, 2016 ยท (Permalink)
I was looking for this. This is still crazy to me.
MX72 ยท 1 points ยท Posted at 01:45:04 on May 26, 2016 ยท (Permalink)
So basically this is just some "math trickery" with no possible way for it to actually exist in real life.. Which in my opinion makes it false. I get it, the math says its possible, but in reality it is not.
xkcdFan1011011101111 ยท 1 points ยท Posted at 02:16:05 on May 26, 2016 ยท (Permalink)
A Menger sponge has infinite surface area and ZERO volume.
HillaryBot9000 ยท 1 points ยท Posted at 03:34:27 on May 26, 2016 ยท (Permalink)
I have looked into this... The volume being limited makes sense... But as the volume approaches its limit it approaches but never reaches the limit. What happens when the volume of the horn is increasing by less than the size of a single atom? While that increase is happening is the surface area still able to increase.
In short, could Gabriels Horn only hold in theory?
Thomas9002 ยท 2 points ยท Posted at 04:02:45 on May 26, 2016 ยท (Permalink)
It only works in theory
HillaryBot9000 ยท 1 points ยท Posted at 06:52:07 on May 26, 2016 ยท (Permalink)
Yea that's that I was thinking. Thanks. Your answer was concise.
Emphursis ยท 1 points ยท Posted at 07:38:25 on May 26, 2016 ยท (Permalink)
As far as I can tell, that's just an 'imaginary' object, which stretches on forever. So it's sort of cheating to say you couldn't paint it, because it doesn't exist to paint in the first place.
Vendetta1990 ยท 1 points ยท Posted at 11:53:38 on May 26, 2016 ยท (Permalink)
Omg I had this yesterday! The teacher explained it using integration on surf
WillyMacBatman ยท 1 points ยท Posted at 15:27:44 on May 26, 2016 ยท (Permalink)
Explain please
_Eerie ยท 1 points ยท Posted at 15:59:14 on May 25, 2016 ยท (Permalink)
Can I build such an object in the real life?
Thomas9002 ยท 7 points ยท Posted at 16:03:47 on May 25, 2016 ยท (Permalink)
No. You would need an infinite amoint of space
svennnn ยท 3 points ยท Posted at 16:56:38 on May 25, 2016 ยท (Permalink)
And live for an infinite amount of time. Even then you'd never finish.
sottt31 ยท 3 points ยท Posted at 17:15:14 on May 25, 2016 ยท (Permalink)
Eventually the diameter would be less than the size of an atom. So even theoretically with infinite space/time/matter, it's impossible to build it.
_Eerie ยท 2 points ยท Posted at 17:04:29 on May 25, 2016 ยท (Permalink)
And infinite amount of materials. But I really can't imagine how such a thing looks like.
oopsa-daisy ยท 3 points ยท Posted at 17:47:47 on May 25, 2016 ยท (Permalink)
Like others have said you can't really "build" one, but there are real life examples where you can see this in practice. For example, what is the length of the coastline of the UK? You could measure in the perimeter and area with a milestick. Then you could measure them both with yardstick, the perimeter would be much larger but the total measured area wouldn't change that much. Then you could measure the coastline with a foot-long ruler. Again, the measured coastline would be much larger but the total area added would not increase in the same way. It's called the coastline paradox and sites like this might help explain it better than I did. I love fractals!
Rocky87109 ยท 2 points ยท Posted at 18:21:31 on May 25, 2016 ยท (Permalink)
Thanks for writing that out. I was curious of how this represented something real.
Weirfish ยท 1 points ยท Posted at 17:51:12 on May 25, 2016 ยท (Permalink)
You could build an approximation of a Menger Sponge in real life, but it wouldn't be a true fractal.
AmericanFromAsia ยท 1 points ยท Posted at 16:21:20 on May 25, 2016 ยท (Permalink)
What do you mean infinite surface area? Does that point just extend out infinitely in a single line so there is no inside?
Like this
karlexceed ยท 1 points ยท Posted at 17:24:30 on May 25, 2016 ยท (Permalink)
Yes, but technically it never becomes a "single" line, it becomes an infinitely thin and narrow tube that keeps shrinking as it moves toward infinity
[deleted] ยท -1 points ยท Posted at 17:27:58 on May 25, 2016 ยท (Permalink)*
First of all, lines don't have surface area, so no. Surface area is defined for 3D objects, and area is defined for 2D objects. A line is one dimensional.
Also, Gabriel's horn converges to a line (the x axis), but is never actually equal to it.
Gabriel's horn is defined to be the 3D shape you get from rotating the function f(x) = 1/x around the x axis with a domain of x >= 1.
If you know some calculus, it's actually not that hard to prove that this has a finite volume and an infinite surface area.
EDIT: I forgot to mention, Gabriel's horn is only one surface with these properties. However, the converse cannot be true. There is no object with infinite volume and finite surface area.
[deleted] ยท -1 points ยท Posted at 17:24:01 on May 25, 2016 ยท (Permalink)
Yea but things like this are so pointless. Doesn't exist in real life. It's just a limit that goes to infinity.
YOLO_HASHTAG_SWAG ยท 1714 points ยท Posted at 14:28:28 on May 25, 2016 ยท (Permalink)
The Monty Hall problem.
You're on a gameshow. There is one grand prize that you can win but it's hidden behind one of three closed doors. The other two doors have nothing. You are asked to select one of the three closed doors. Once you choose a door the host opens one of the remaining two doors that does not contain the fabulous prize.
The host then asks if you'd like to switch your choice to the one other unopened door. Do you switch?
Statistically you should because there is a 66.6% chance the other door is correct and only a 33.3% chance your door is correct.
Most people will argue, vehemently, that there is a 50/50 chance of having the correct choice so switching is irrelevant. But you actually had a 66.6% chance to choose the wrong door to begin with. Math-Magic!
Wassayingboourns ยท 273 points ยท Posted at 14:55:41 on May 25, 2016 ยท (Permalink)
You might have to explain that some more to us non-mathematicians
halberdierbowman ยท 585 points ยท Posted at 15:09:24 on May 25, 2016 ยท (Permalink)
The important thing is that the host knows which door has the prize and which door is empty. You pick first and have a 1/3 chance of picking the prize, and a 2/3 chance of not. Then the host picks a door and opens it, but he will never pick to show you the prize. So there's still a 2/3 chance that the prize is one of the two doors you didn't pick, since there's still three doors. The 1/3 probability of the door that opened goes to the third door that neither of you picked, because the host knows where the prize is and would never pick it. Since the door he picked is now worth 0/3, the door he didn't pick is worth 2/3 to add up to the 2/3 that those doors have, combined.
If the host picked first then you picked, there would be a 1/2 chance for both doors.
Wassayingboourns ยท 342 points ยท Posted at 15:51:01 on May 25, 2016 ยท (Permalink)
That's the crucial sentence right there. Thanks for the in-depth explanation.
halberdierbowman ยท 11 points ยท Posted at 16:05:32 on May 25, 2016 ยท (Permalink)
You're welcome!
Yep, the host is providing vital information by picking the door, not just crossing off a random 1/3 chance.
[deleted] ยท 9 points ยท Posted at 17:13:56 on May 25, 2016 ยท (Permalink)
Why doesn't the probability of the door that the host opened split evenly between the two remaining doors? I just can't wrap my head around the fact that if you take the situation as it is, it's a 2/3 chance if you switch, but if your choice were to get "forgotten" after the host opens a door and you have to make an independent selection from the two remaining doors, then it's a 1/2 chance for each.
halberdierbowman ยท 14 points ยท Posted at 17:22:09 on May 25, 2016 ยท (Permalink)
It's a good question: someone else asked it as well, so check my response there. I walked through all the possible picks. Sorry on mobile so I don't know how to link it.
The crux of it is that you're right, if you forgot what happened before then you'd have a 1/2 chance with the he two remaining doors. The fact that you know something about the doors that were picked helps out.
It also may think of it by thinking of their loss rates. You have a 2/3 chance of losing with your first pick. The host then picks a door which is always a losing door. That gives the third door only a 1/3 chance of being a losing door. Yours has a 2/3 chance of being a losing door still. That makes your door twice as likely to lose as the third door, so you should switch.
[deleted] ยท 4 points ยท Posted at 17:57:03 on May 25, 2016 ยท (Permalink)
Couldn't you explain it by saying that the host is not only showing which door is a losing one but also showing which one is a possibly winning one ?
Or said otherwise he didn't choose to reveal your door as a losing one because it is your door while the third door wasn't chosen because it is possibly the winning one compared to the second door which is a losing one ? or is that faulty logic that has nothing to do with the real logic in action ?
halberdierbowman ยท 3 points ยท Posted at 18:12:59 on May 25, 2016 ยท (Permalink)
Sure that probably works too. The crux of it is as you said that he's telling you useful information by picking his door. You know his door loses, so that makes the one he didn't pick more likely to be a winner. The hard part is understanding why the information doesn't apply to your door like it does to the third door. Like you said, the fact is that he only picks between the other two options, not yours.
Actually if he picked your door when you had an empty door he'd be better off, because you'd have two options to pick from with 1/2 chance each.
Eaglesun ยท 1 points ยท Posted at 04:41:07 on May 26, 2016 ยท (Permalink)
The way I prefer to explain it is that, if you initially choose an empty door, then the host HAS to show you the other empty door, since he can't show you the prize door. This means that, if you initially picked a dud (and there is a 2/3 chance you did), then there is a 100% chance that the remaining door holds the prize. This is why your chances of winning are 66% if you always switch, because if you picked wrong and then switch you are guaranteed a victory.
TheDarkMusician ยท 3 points ยท Posted at 19:22:53 on May 25, 2016 ยท (Permalink)
Thanks for the description, I'm finally starting to get it more.
So...
One thing I'm still working through is how the odds can change depending on the person picking the doors. By what I understand here, if we had the same situation occur, then they brought in someone from outside the studio who has no idea which door the 1st contestant chose, and only knows that one of the two doors in front of them has the prize, then they would have a 50% chance.
So does this mean that 50% of the time, they'll choose the 66.6% door, and 50% of the time they'll choose the 33.3% door, and then the average between the two percentages is 50%, so there's a 50% chance in total that they pick the correct door? Holy shit this is starting to click.
halberdierbowman ยท 3 points ยท Posted at 19:33:58 on May 25, 2016 ยท (Permalink)
Yup, exactly!
mrjollypirate ยท 4 points ยท Posted at 18:34:13 on May 25, 2016 ยท (Permalink)
As fun as this math is, and all the media its featured in, isn't the real answer is that you SHOULD forget what happened before? Once the door is opened this is an entirely new instance, and the probability of the choices beforehand do not affect the probability of the second choice.
deong ยท 13 points ยท Posted at 20:56:26 on May 25, 2016 ยท (Permalink)
You're confusing independence of trials with prior knowledge.
Very often in statistics, you deal with independent trials. If you're playing roulette and the wheel has turned up red 10 times in a row, the odds of the next spin yielding red are still 1/2. One spin of the wheel doesn't have anything to do with the previous one.
In the Monty Hall problem, you only have one trial -- playing the entire game. The reason is because the outcome does depend on earlier actions. If the prize was under door number 2 when the host opened door number 3, there's a 0% chance that it will be under door number 1 when you open it. It's all one connected trial.
When the host opened door number 3, you didn't start a new game. You gained information about the current one. In the face of new information, you update your beliefs. In this game, you update them in what most people find a counterintuitive way, for sure, but you can't just assume that opening one door tells you nothing, or else you'd conclude that you should still have a 1/3 probability that the prize is behind door number 3 -- a door that's wide open with obviously no prize there.
halberdierbowman ยท 7 points ยท Posted at 19:03:27 on May 25, 2016 ยท (Permalink)
It's the same instance, but you've learned more about your options. The probability of each door's having been the winner in the beginning was 1/3. That's still true. But now that you know something new, namely one door that the host picked and one door that they might have picked but didn't, you can use this information.
If it were the same instance and you forgot what the host did, then yes you'd have a 1/2 chance. But since the winning and losing doors haven't changed, you have more information than that.
Odds-Bodkins ยท 3 points ยท Posted at 20:07:40 on May 25, 2016 ยท (Permalink)
The host will always open a losing door. That means if you choose to switch and lose, you must have had the winning door in the first place. What are the chances of that? 1/3. Therefore there is 2/3 chance you will win if you switch.
The crux is that he always shows you a losing door.
BipedSnowman ยท 3 points ยท Posted at 21:50:16 on May 25, 2016 ยท (Permalink)
The chance doesn't change, it's that you get different chances if you follow different paths. If you look at the second half of the scenario independently, there IS a 50/50 chance of getting the door with the prize if you switch doors. However, if you include the first part, then the number of scenarios where switching doors is better is doubled.
Here's a diagram!
BRedd10815 ยท 1 points ยท Posted at 19:02:39 on May 25, 2016 ยท (Permalink)*
Yes this is a bad example in my opinion. Since you don't open the door that you initially pick, you can't draw any conclusions from simply picking it and standing in front of it. The fact is the host is always going to open an empty door regardless of your pick. 50% chance for either your pick or the other one left.Edit: I'm probably wrong.. its starting to make more sense to me the more I think about it.
Snakeeyes839 ยท 7 points ยท Posted at 17:24:46 on May 25, 2016 ยท (Permalink)
You can think of it like this. If you have to choose 1 door out of 100 doors you have a 1/100 chance of choosing the correct door. After you choose a door all but 1 remaining door are opened. Given your original choice you had a 1% of choosing the correct door. So by switching you are more likely to choose the correct door
I_LOVE_POTATO ยท 1 points ยท Posted at 21:47:59 on May 25, 2016 ยท (Permalink)
That does make it easier, thanks.
[deleted] ยท 1 points ยท Posted at 17:58:24 on May 25, 2016 ยท (Permalink)
No matter the number of doors, it still seems to boil down to one door vs. another. In your example, it intuitively seems like each of those two final doors have a chance of 1/100, or 1/2 when compared with each other.
Publix_Deli ยท 12 points ยท Posted at 18:18:39 on May 25, 2016 ยท (Permalink)
The important part is that the host knows which door contains the prize. You know with 100% certainty that the host will not eliminate the door containing the prize.
It's much easier to understand if you don't think of it as "do you want to switch doors?" Instead, think of it as "do you think you were correct on your first guess?"
Now, imagine that there were a million doors, and you get to choose one of them. Then, the host eliminates 999,998 doors from the equation. You're given the option to open your original choice, or open the other door with the knowledge that the host would never eliminate the door containing a prize. Do you think it's more likely that you correctly guessed the door out of a million? Or is it more likely that the prize-winning door was one of the 999,999 that you didn't choose?
insomniacmercury ยท 3 points ยท Posted at 23:57:25 on May 25, 2016 ยท (Permalink)
this is the response that made it click. thank you!
littlebeanie ยท 1 points ยท Posted at 02:58:21 on May 26, 2016 ยท (Permalink)
For me too!
Ulrezaj ยท 4 points ยท Posted at 18:13:30 on May 25, 2016 ยท (Permalink)
It's only 1/2 compared to each other if you didn't already know which door you originally picked.
We can make it more extreme if it makes it easier to understand. If there are a million doors, your chances of picking the right one are more or less zero. Now, the host opens 999,998 other doors and leaves 1 other door closed. Do you see now that it HAS to be that remaining door?
BaseVilliN ยท 1 points ยท Posted at 18:26:57 on May 25, 2016 ยท (Permalink)
But it's not one door vs. another.
If you pick 1 out of 100 doors, you have a 1% chance of picking the correct door and there is a 99% chance the remaining group has the correct door in it. It necessarily has 98 incorrect doors and a 1% chance of having 99 incorrect doors. Seeing 98 incorrect doors doesn't change the odds of the correct door being in that group.
CaptainSasquatch ยท 1 points ยท Posted at 19:37:38 on May 25, 2016 ยท (Permalink)
Here's another way to think of the 100 door variant. You choose Door A. Instead of opening 98 empty doors and leaving one mystery door. They take all the contents of those 99 doors and put them in one room and label that Door X. There's a 99% chance that Door X has the prize in it, because there's a 99% chance that it wasn't in Door A. This is exactly the same as the normal 100 door Monty Hall Problem.
BipedSnowman ยท 1 points ยท Posted at 21:50:44 on May 25, 2016 ยท (Permalink)
Diagram!
[deleted] ยท 1 points ยท Posted at 18:07:36 on May 25, 2016 ยท (Permalink)*
[deleted]
CaptainSasquatch ยท 6 points ยท Posted at 19:17:40 on May 25, 2016 ยท (Permalink)
That's not the correct probability space. I'll copy what I said in a different part of this thread
There's three equally likely situations the prize is behind Door A, B or C.
You can start by choosing door A (without loss of generality).
There's a 1/3 chance that Door A contains the prize. In that case the host will randomly reveal Door B or C to be empty. You will be better of staying with your first choice.
There's a 1/3 chance that Door B contains the prize. In that case the host will reveal Door C to be empty (they'll never open door B because the host knows where the prize is). You will be better off changing your choice.
There's a 1/3 chance that Door C contains the prize. In that case the host will reveal Door B to be empty (they'll never open door C because the host knows where the prize is). You will be better off changing your choice.
So 1/3 chance that your original guess was right. 2/3 chance that you would be better off switching.
Publix_Deli ยท 2 points ยท Posted at 18:23:20 on May 25, 2016 ยท (Permalink)
They will never happen, but you need to include them in your calculation of probability because you don't know which door definitely does not contain the prize until after you've made your original choice. The host opening the door provides you with additional information. The choice is not "should I switch doors?" The choice is "was it more likely that I was right or wrong when I made my original choice."
See my explanation here where I expand the example to a million doors.
BipedSnowman ยท 1 points ยท Posted at 21:51:17 on May 25, 2016 ยท (Permalink)
Here's a diagram of why you are wrong.
Odds-Bodkins ยท 3 points ยท Posted at 20:06:27 on May 25, 2016 ยท (Permalink)
Sorry because I know you've got replies, but I want to throw my 2 cents in.
The host will always open a losing door. That means if you choose to switch and lose, you must have had the winning door in the first place. What are the chances of that? 1/3. Therefore there is 2/3 chance you will win if you switch.
JPK314 ยท 2 points ยท Posted at 02:48:32 on May 26, 2016 ยท (Permalink)
This one is nice and concise - great work.
UniverseChamp ยท 1 points ยท Posted at 18:15:58 on May 25, 2016 ยท (Permalink)
This nice little video is a good visual.
It's not 1/2, because you're door is never improved. It's a bit of a mind-fuck.
Lobo2ffs ยท 1 points ยท Posted at 20:04:47 on May 25, 2016 ยท (Permalink)
Let's expand it to 100 doors. You pick one door at random, and that door has a 1% chance of having the prize. The other 99 doors have a combined 99% chance of having the prize. At this point, would you want to stay with the door you picked, or all of the other doors where you get the prize if it's behind any of them?
Of course you'd choose the 99 doors. The host now opens 98 empty doors out of the 99. Would you want to stay with your 1% door, or the combined 99% chance of the other doors which is now down to only 1 door?
jxuberance ยท 1 points ยท Posted at 21:21:01 on May 25, 2016 ยท (Permalink)
Imagine the question was now you pick one door out of a million doors.
Afterwards the host offers you the same choice, between your door and one other door, one of which is guaranteed to have the prize in it.
Your original pick had a one in a million shot at being right, but the host is now saying your door + this other door contain the winning door.
Would you still think its 50/50 in that scenario? You need to separate your original choice (which you knew was 1/million), and the new information presented, that your 1/million shot and some other door is guaranteed to be the winner.
BipedSnowman ยท 1 points ยท Posted at 21:42:51 on May 25, 2016 ยท (Permalink)
I made you a diagram!
Pandamana ยท 2 points ยท Posted at 19:01:07 on May 25, 2016 ยท (Permalink)
Very easy to envision that same problem, but with 100 doors. If you pick a door at the beginning, and the host opens 98 other doors, then there's a 99% chance the last door has the prize. Your 1% chance at the beginning did not improve.
[deleted] ยท 1 points ยท Posted at 18:03:01 on May 25, 2016 ยท (Permalink)
If you want to see it in action, mythbusters actually did this one. Confirmed.
[deleted] ยท 1 points ยท Posted at 19:07:23 on May 25, 2016 ยท (Permalink)
I've read so many explanations and this one finally makes sense.
d-a-v-e- ยท 1 points ยท Posted at 21:21:56 on May 25, 2016 ยท (Permalink)
After all these years, I finally get it. What keeps breaking it in my head though: confronted with the choice to pick another door, doesn't that reset the chances to 50/50, or am I throwing information away?
Alonewarrior ยท 1 points ยท Posted at 21:28:07 on May 25, 2016 ยท (Permalink)
That sentence was the tipping point for me finally understanding this whole thing!
roomandcoke ยท 18 points ยท Posted at 16:23:08 on May 25, 2016 ยท (Permalink)
We did this in math class in 8th grade. Playing the show host really helps make you understand it. As the host, you'll find that the majority of the time (66% of the time), there's only one door you can open because the contestant has already selected one empty door, so you have to reveal the only other empty door.
JamEngulfer221 ยท 4 points ยท Posted at 19:06:54 on May 25, 2016 ยท (Permalink)
You know what, your post has made the problem make more sense than any other explanation I've heard
fireball_73 ยท 1 points ยท Posted at 20:35:05 on May 25, 2016 ยท (Permalink)
You must've had an outstanding maths teacher!
Wilhelm_Amenbreak ยท 5 points ยท Posted at 17:39:28 on May 25, 2016 ยท (Permalink)
I found the best way to think about it is if you had 100 doors. You choose 1, Monty Hall uncovers 98 doors and then asks if you want to switch. Seems obvious that you would want to switch in that case. But when there are 3 doors, it becomes much less intuitive.
halberdierbowman ยท 1 points ยท Posted at 17:42:38 on May 25, 2016 ยท (Permalink)
Yup, that would really highlight how important the host's information is!
makemisteaks ยท 11 points ยท Posted at 16:17:31 on May 25, 2016 ยท (Permalink)
But why does the 1/3 probability of the door that opened go to the third door and not the one that I picked? That doesn't make any sense.
If the gameshow host is giving me the option of switching doors, then it's technically a new roll of the dice, no? I can pick, out of the two remaining doors, which one I want, and would that not make it a 50% chance of picking the right one? I can't wrap my head around this concept...
PersonUsingAComputer ยท 62 points ยท Posted at 16:32:36 on May 25, 2016 ยท (Permalink)
Let's say the prize is behind door A. There are three possibilities:
The reason it works is that if you choose either losing door to start with, the host is obligated to open the other losing door, and then switching guarantees you the win. It's only in the case where you actually chose the correct door to start with (a 1/3 chance) that switching makes you lose.
makemisteaks ยท 10 points ยท Posted at 16:34:41 on May 25, 2016 ยท (Permalink)
This explained it perfectly, thank you.
frater_horos ยท 4 points ยท Posted at 16:37:05 on May 25, 2016 ยท (Permalink)
Thanks, it makes sense now.
ovie707 ยท 1 points ยท Posted at 18:07:46 on May 25, 2016 ยท (Permalink)
This is the only explanation that actually made it less complicated. It also demonstrates why the extra 1/3 chance doesn't get distributed evenly between the 2 remaining unopened doors.
TheShadowKick ยท 1 points ยท Posted at 20:58:27 on May 25, 2016 ยท (Permalink)
I've heard about the Monty Hall problem a dozen times and now I finally got it.
halberdierbowman ยท 3 points ยท Posted at 16:48:29 on May 25, 2016 ยท (Permalink)*
You picked a door at random and have 1/3 chance at the prize. If the host picked a door at random as well, then you could take his 1/3 chance and put it in half, 1/6 to each other door. That would give you 1/2 for each door, like you expect.
But the host does NOT pick a door at random. When he picks, you have 1/3 for your choice, 1/3 for the choice he didn't pick, and 1/3 for the door he picks. That last third becomes 0/3 (you saw nothing behind the door, so you know those odds). So you need to put it on a different door. His information doesn't tell you anything about your door, but it tells you about the door he didn't pick.
This means that while it is a new roll of the dice, you have extra information about one of the choices, namely that it wasn't one of the losing doors. It could be the other losing door, or it could be the winning door. But its chance of being the losing door just went from 2/3 to 1/3, while your door is still at 2/3 chance to be a losing door. Comparing your door to the third door, you'd half your chances of a losing door by switching.
There's three doors, so let's see how it plays, switching first then not switching.
1/3 time A will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks B. B has 0/3 chance to win.
You switch to C. C has 2:1 odds to win, because 1/3 chance to lose compared with 2/3 chance to lose.
You lose.
1/3 of the time B will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks C. C has 0/3 chance to win.
You switch to B. B has 2:1 odds to win, because 1/3 chance to lose compared with 2/3 chance to lose.
You win.
1/3 of the time C will win.
You pick A. A has 1/3 chance to win, 2/3 chance to lose.
He picks B. B has 0/3 chance to win.
You switch to C. C has 2:1 odds to win, because 1/3 chance to lose. compared with 2/3 chance to lose.
You win.
Now the other option is to not switch.
1/3 of the time A will win.
You pick A. A has 1/3 chance to win.
He picks B. B has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You win.
1/3 of the time B will win.
You pick A. A has 1/3 chance to win.
He picks C. C has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You lose.
1/3 of the time C will win.
You pick A. A has 1/3 chance to win.
He picks B. B has 0/3 chance to win.
You keep A, thinking incorrectly that you have a 1/2 chance to win.
You lose.
So if you switch, you will win 2/3 games, winning each time you pick a losing door to start.
If you don't switch, you will win 1/3 games, winning each time you pick the winning door to start.
The door letters can be rearranged however you like. After all, it doesn't matter if door A is on the left, right, or center stage. Same for B and C, before or after you pick.
Goddamnit_Clown ยท 2 points ยท Posted at 16:30:46 on May 25, 2016 ยท (Permalink)
When you picked a door, you created two categories. You put your door in Category A which probably doesn't have the prize and you put all the other doors in Category B which probably does.
When the host gives you the option to swap, you're choosing between sticking with A (bad) or changing to B (good). The fact that a gameshow host theatrically walks along most of the B doors and opens them for you doesn't change anything.
Imagine you were given the option to stick with A or to go and open all the doors in Category B yourself instead of just the final one.
butterandguns ยท 1 points ยท Posted at 16:33:05 on May 25, 2016 ยท (Permalink)
I think it makes more sense if you think about the problem if it had 100 doors.
You pick a door. And then the host opens up 98 other doors. Now would you switch or stay?
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:06:09 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
aaronsherman ยท 1 points ยท Posted at 20:18:58 on May 25, 2016 ยท (Permalink)
The key thing, here is that the probabilities don't change, ever. You simply start asking new questions or considering different doors.
It really gets obvious when you think in terms of "odds I was right to start," and, "remaining odds that it's any of the remaining doors".
Of course, with 3 doors, that logic doesn't occur to you because you're left with 1 door you chose and 1 door that's left unchosen. But with 4 doors:
With 1000 doors:
dv_ ยท 3 points ยท Posted at 17:07:21 on May 25, 2016 ยท (Permalink)
Another way to view it this:
There is only one case where you picked the right door from the beginning. In this case, the other two doors are equal - they both have no prize behind. In this case, it doesn't matter which one is picked by the host.
There are however two cases where you picked the wrong door. In these cases, the other two doors are not equal - one will have nothing behind, one will be holding the prize. And in these two cases, the host's pick does matter. (I agree that this is the heart of the whole thing - his pick is never random in these two cases.) And what's more, the host's pick gives you unmabiguous information, because in these two cases, you picked an empty door, he picked an empty door, so there is only one door left.
So, given that in 66% of all cases you get valid and unambiguous information from the host, it makes sense to rely on that information and pick the other door.
crappymathematician ยท 1 points ยท Posted at 23:01:03 on May 25, 2016 ยท (Permalink)
I still can't quite figure out how this trips people up. It's quite apparent that the two doors you're left to choose from are tremendously dependent on which of the three you picked originally.
dv_ ยท 1 points ยท Posted at 06:17:29 on May 26, 2016 ยท (Permalink)
Because we rely so much on the "common sense". And the human "common sense" is abysmal at statistics. We intuitively look at the two remaining doors and at nothing else, and conclude that it's a 50:50 chance.
BRedd10815 ยท 3 points ยท Posted at 18:57:44 on May 25, 2016 ยท (Permalink)*
No, it would be split between both doors left because either of them could still have the prize. The host is going to pick an empty door regardless of your initial pick.Yes, but you aren't really picking first when you aren't told if your pick is correct or not. I'm no math teacher, but I feel it's wrong to draw conclusions statistically in this case.Edit: fuck me, I think I understand now that I've read through more comment chains. Expanding the problem to a million doors instead of 3 helped me wrap my mind around it somewhat.
halberdierbowman ยท 1 points ยท Posted at 19:20:54 on May 25, 2016 ยท (Permalink)
Sorry for the confusion! Maybe it would have helped if I added that the host will not pick the winning door, but he ALSO won't pick the door you picked. So you are picking first, only in that he won't pick your pick also.
BRedd10815 ยท 2 points ยท Posted at 19:32:18 on May 25, 2016 ยท (Permalink)
Yeah, thats key. The host has conditions for his pick that involve your initial choice. You can definitely draw statistical conclusions from that.
w00ki33 ยท 3 points ยท Posted at 19:06:32 on May 25, 2016 ยท (Permalink)
How do I use this on Deal or No Deal?
halberdierbowman ยท 2 points ยท Posted at 19:29:15 on May 25, 2016 ยท (Permalink)
Sorry but I actually don't remember that show well enough to answer. I think one important idea is to overcome your psychological fallacy of thinking the thing you "picked" from the beginning is the best. You may need to think logically to overcome the fear of uncertainty.
You also may want to consider whether you're happy winning 40% of your payout for sure rather than 50% chance of winning double. If I went on the show, I'd probably take one of the deals because I don't think having $1,000,000 is twice as good (or will make me twice as happy) as having $500,000. It may be twice as much money, but I won't get to play on the show again, so I'd rather take the guaranteed win.
SharksFan4Lifee ยท 3 points ยท Posted at 20:44:17 on May 25, 2016 ยท (Permalink)
The answer is, you really cant on Deal or No Deal until you get down to a few choices left. And even then, if the million is on the board, your case + 2 cases left, and you get any offer, you should take that offer and run, no matter what.
But Deal or No Deal is much more complex for most of the game because of the differing amounts of in each briefcase and the offers.
Danno558 ยท 2 points ยท Posted at 17:44:39 on May 26, 2016 ยท (Permalink)
It doesn't work at all in Deal or No Deal. The host has to know the cases he is revealing isn't the "winner". If he's just opening cases at random (you selecting being random) then it doesn't actually work, and the last 2 cases are a 50/50 split.
If instead you selected your case and then Howie proceeded to open all the cases for you knowing that he wouldn't be opening the "winner" then you should switch cases when given the option because the "winner" has a very high probability of being the one Howie left remaining.
It's key that the host is knowingly avoiding opening the "winner" for the Monty Hall problem to be true.
ninjalink84 ยท 2 points ยท Posted at 16:41:32 on May 25, 2016 ยท (Permalink)
An elegant explanation for a difficult to grasp fact. Congratulations.
halberdierbowman ยท 1 points ยท Posted at 16:54:25 on May 25, 2016 ยท (Permalink)
Thank you!
Bladelink ยท 2 points ยท Posted at 17:32:46 on May 25, 2016 ยท (Permalink)
Yeah, the trick to that is realizing that the host is adding information by picking a door.
CaptainSasquatch ยท 1 points ยท Posted at 19:22:45 on May 25, 2016 ยท (Permalink)
and that they are only adding information to the doors you didn't pick. If the host randomly reveals that a door you didn't pick is empty (they have no knowledge about the prize) that gives you information about both the remaining door and the door you chose.
BigSpud ยท 2 points ยท Posted at 17:33:51 on May 25, 2016 ยท (Permalink)
Every time I read about the Monty Hall problem I promise myself I will memorise an explanation.
Today is no different.
halberdierbowman ยท 1 points ยท Posted at 17:40:51 on May 25, 2016 ยท (Permalink)
Haha I know what you mean! It took me a bunch of times to figure it out. If that explanation didn't do it, I replied in more detail to one of my other replies (sorry mobile, don't know how to link) that may help. It explains it in terms of your chance of losing and then walks you through how each scenario would play out.
CaptainSasquatch ยท 1 points ยท Posted at 19:23:59 on May 25, 2016 ยท (Permalink)
It's easier to gain an understanding than to memorize it. The trick is to explain why the situation would be different if the host had no knowledge about the prize and randomly revealed door that happened to be empty.
Uhu_ThatsMyShit ยท 2 points ยท Posted at 18:05:33 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
vincentrm ยท 2 points ยท Posted at 18:54:17 on May 25, 2016 ยท (Permalink)
I had to come up with like 10 ways to explain this because my co-workers couldn't wrap their head around it. I extrapolated and said "Let's say there's 1,000,000 doors. And you pick one. And the host opens 999,998 of the doors that didn't have the car behind it and asks you if you want to switch. Well, thinking of the 1,000,000 doors sitting there and every door open except the one you randomly chose at a 1/1M chance and one other one that we know only has a 1/1M chance of being random (since he would never open the door with the car behind it since he knows where it is)... I think everyone would make that switch.
Unfortunately, my manager refused to believe that The Monty Hall problem was accurate. So, we tried the game by him writing 1, 2 or 3 and then me guessing. Well, I won every single time by cheating (in an effort to prove the point, which I understand is cheap). I just watched how he wrote the number. If he made a single stroke, I knew he wrote a 1 and then I would say 2 or 3, he would open 2 or 3 and I would switch and get 1. If his hand moved at all when scribbling the number, I knew it was a 2 or a 3, and I would pick 1, he would open 2 or 3 and I would switch. I was like 12 for 12... he still refused to believe it worked. I left the company within two months...
halberdierbowman ยท 2 points ยท Posted at 19:23:31 on May 25, 2016 ยท (Permalink)
Haha well it should work even without cheating if you play enough and approach 2/3 but sorry he never got it! Yeah that makes a lot of sense once you think of more doors and the host is opening lots of them. It really emphasizes how important the host's information is.
deityblade ยท 2 points ยท Posted at 20:29:48 on May 25, 2016 ยท (Permalink)
I have never been able to wrap my head around this and I trust to believe it's true
MinkOWar ยท 1 points ยท Posted at 21:53:04 on May 25, 2016 ยท (Permalink)
You have a 1/3 chance of picking the right door the first time, which means you have a 2/3 chance the prize is behind another door.
The host eliminates one wrong door of the 2 doors you didn't pick, but you still have that 2/3 chance the prize is behind a different door than you first picked except now you know which door of those other 2 was wrong.
last657 ยท 2 points ยท Posted at 21:08:17 on May 25, 2016 ยท (Permalink)
Another crucial point that is inherent to the problem but is often skipped over is that the host has to open another door independent of whether or not you picked the right door. If the host had the option of just opening your door and saying you lose if you pick the wrong door initially then him giving you the option to switch is a different kind of game entirely
halberdierbowman ยท 2 points ยท Posted at 21:27:26 on May 25, 2016 ยท (Permalink)
Yup, the host has to open a second door, and he is not allowed to open your door. Of course that means he picks an empty door, rather than a winning door, giving you information.
last657 ยท 1 points ยท Posted at 05:30:50 on May 26, 2016 ยท (Permalink)
Yep. When I was younger it bothered me and I didn't get it. It was actually the 100 door example that finally made it clear to me. After that I became a little unnecessarily pedantic about the wording of it though. Its portrayal in 21 especially bothered me because they even directly addressed the possibility of it being a trick and dismissed it as unimportant. You can only garner that information when you know the rules of the hosts actions. If not the whole thing becomes a lot more complicated.
joombaga ยท 2 points ยท Posted at 23:55:34 on May 25, 2016 ยท (Permalink)
"The important thing is that the host knows which door has the prize and which door is empty."
This isn't quite correct, and I've seen it trip up people in the past. What matters is that the host picks a door that does not have have the prize. His knowledge makes no difference. It doesn't seem like an important distinction, but 3 separate occasions I've seen the requirement of knowledge cause confusion.
halberdierbowman ยท 1 points ยท Posted at 00:11:12 on May 26, 2016 ยท (Permalink)
Interesting, thanks. I suppose you're right. They could always tell him off camera which door to pick, so then the host wouldn't need to know which door is the winner.
In any case though, someone needs to know which door is the winner, or else the host might accidentally reveal it, right?
joombaga ยท 2 points ยท Posted at 00:46:42 on May 26, 2016 ยท (Permalink)
Perhaps it depends on your audience, and maybe mine is pedantic :)
The minimum requirement is that the host always picks a non-prize door. The logistics behind this (knowledge, luck) do not matter.
No one needs to know the winner from the outset. What matters is that we as the contestant have the knowledge that the host picked a non-prize door. It is this knowledge that allow us to concentrate the probability of failure (1/3 + 1/3) behind the originally picked door.
The picking of the first door is just a mechanism; requiring the host to have knowledge casts him as an intelligent actor. I thinks this is the source of the confusion.
halberdierbowman ยท 1 points ยท Posted at 00:57:55 on May 26, 2016 ยท (Permalink)
Fair enough! Haha I just feel like unless I'm misunderstanding you, someone's having knowledge of the prize door would be almost necessary. This is a television game show after all, so relying on luck or some other mechanism to pick a non-winning door would be unnecessarily complicated.
You're right of course that it doesn't matter how or why you were provided the information about the second door. An audience member could accidentally trip and knock over one of the doors, revealing nothing behind it. You'd still learn that nothing was behind it.
Thehunterforce ยท 2 points ยท Posted at 00:58:49 on May 26, 2016 ยท (Permalink)
So if I make a game show and run it like this 1 million times, are you going to say, that because I swifted my opinion, that I would win roughly 666.666 times while losing only 333.334 times?
halberdierbowman ยท 1 points ยท Posted at 01:06:48 on May 26, 2016 ยท (Permalink)*
I'm not sure if you're the contestant or the host in this scenario, but yes. The contestant should win 2/3 games if they play with the better strategy of switching every time.
Of course the reality is that many people won't play with this best strategy. Plus, it isn't like the gameshow is betting that you'll lose, so they might be fine with 2/3 contestants winning.
You could run the same game as a betting game, just adjust the payouts to $0.45 and $0.55. You'd think you're winning by $0.05 (expecting $0.50 as break even) but in reality I'd be winning by $0.11 (knowing $0.66 is break even).
Omegasedated ยท 2 points ยท Posted at 01:08:20 on May 26, 2016 ยท (Permalink)
I know that mathematically this is how it works, but you could argue that you have always only had a 50% chance of picking the correct door.
If the host always removes one WRONG door, you are effectively only picking from 2 options anyway, regardless of what you choose. They will remove one incorrect option, so there is only ever two valid options. One correct, one incorrect.
halberdierbowman ยท 1 points ยท Posted at 01:17:00 on May 26, 2016 ยท (Permalink)
You're right, if the host picked first, but in this game the host picks second and has to pick a door that is empty and not yours.
Try this way: I'll pick a random card and not show you, then put it back in the deck. Now you take a card. Now I'll discard all but one card from the deck, keeping my card if it was still there, or keeping a random card if you picked mine. Do you think your card is the one I picked first, or do you think the card in my hand is the one I picked first?
You're right that there are two options, but one of them is much more likely, because I added information by discarding cards AFTER you picked yours.
Omegasedated ยท 2 points ยท Posted at 01:26:33 on May 26, 2016 ยท (Permalink)
Yea, i know that's how the math works, and that card example is a really good one! way better than the three door one.
Entropic_Entity ยท 1 points ยท Posted at 17:39:15 on May 25, 2016 ยท (Permalink)
The assumption here is limited information from the perspective of the player and complete info on the side of the host. Practically, however, anyone who has watched the show more than a couple of times knows that the host will "burn" one of the two void choices no matter the choice of the player. Due to updating, one might argue that with this info on the hands of the player the probability transforms to a 50% one. In other words, a partially informed player knows that one of the two doors s/he didn't choose has an a priori 0% chance of containing the prize.
[deleted] ยท 1 points ยท Posted at 17:53:58 on May 25, 2016 ยท (Permalink)
I've seen it and heard it explained a thousand times, I can just never conceptually agree that the
1/3 1/3 1/3 Becomes 1/3 2/3
Like... The 1/3 chance is absorbed by the other....
Somehow I am still only to see a completely new math problem, that is mutually exclusive from the previous one.
halberdierbowman ยท 1 points ยท Posted at 18:03:50 on May 25, 2016 ยท (Permalink)
Hi! Try my other post, unfortunately on mobile so I can't link. It's much longer and walks through the chances of all possible outcome, as well as comparing what happens if you switch or don't.
It also may help to think of your chances of losing, rather than your chances of winning (also in that post).
Grandmashoes ยท 1 points ยท Posted at 19:27:25 on May 25, 2016 ยท (Permalink)
If you choose the wrong door he can only open the other wrong door, the only door left is the one with the prize, switch and win. All you need to do is to pick a wrong door at the start.The chances of that happening are 2/3.
[deleted] ยท 1 points ยท Posted at 19:48:42 on May 25, 2016 ยท (Permalink)
But we are operating on the assumption that I chose a loser, which I am doing based on statistics...
So it's not "switch and win", it's "switch and probably win.", correct?
Grandmashoes ยท 1 points ยท Posted at 20:07:52 on May 25, 2016 ยท (Permalink)
Well yeah, it's not an assured win, but 66% is pretty good.
dogfish83 ยท 1 points ยท Posted at 17:55:53 on May 25, 2016 ยท (Permalink)
The host knowing which door has the prize is not important; in fact the host opening a door actually shows you no new information, since he is going to show you an empty door no matter what.
CaptainSasquatch ยท 2 points ยท Posted at 19:25:58 on May 25, 2016 ยท (Permalink)
The host knowing which door has the prize is fundamental to the problem. If they randomly choose a door and it just so happens that the door is empty, then it's a 50/50 shot.
dogfish83 ยท 1 points ยท Posted at 19:32:09 on May 25, 2016 ยท (Permalink)
This proves my point. If they randomly choose a door then you have information to work with. But since the host isn't going to show you a door with the prize in it, you know he's going to show you a door without the prize, so which particular door he shows you does not help you or change your situation in the slightest.
CaptainSasquatch ยท 1 points ยท Posted at 19:55:34 on May 25, 2016 ยท (Permalink)
It gives you information about the remaining doors that are left open. Let's say you choose Door A and the host knowingly reveals that Door B is empty. That gives you information about Door C, but not Door A.
dogfish83 ยท 1 points ยท Posted at 20:17:49 on May 25, 2016 ยท (Permalink)
But your selection is going to be between staying with door A, or switching to doors B and C. After you select door A, you already know that one of the remaining doors is empty, and it doesn't matter which one. He could show you door B or he could show you door C, (whichever is empty) and it doesn't change your dilemma. You already know your dilemma before he shows you a door. There's three possibilities after you choose a door and before he reveals: prize is in your door, prize is in unchosen door, or prize is in other unchosen door. At this point there's a 2/3's chance that the prize is not in your door and a 100% chance that the host will show you an empty door (that's part of the setup/rules). So he opens an empty door. Now we're to the dilemma that you knew you'd be in before he opened a door, before you even went on the game show. Doesn't give you any useful information. You are choosing between staying or switching, that's it. Sorry does that make sense?
guffetryne ยท 1 points ยท Posted at 00:13:50 on May 28, 2016 ยท (Permalink)
I'm late to this thread, but you seem so close to understanding it, but not quite. You're either misunderstanding something or arguing a technicality.
That's not what happens in the game. It would be "staying with door A, or switching to whichever of doors B or C is still unopened."
That is true, it doesn't change your dilemma. You should still switch, no matter what door he opens. The math says you have a 2/3 chance of winning if you do. But if he opens door B, you will choose door C. If he opens door C, you will choose door B. The host has to open one of the doors in order to give you the information you need to choose the correct door. You can't choose both doors. At that point you've changed the game, and are talking about a different problem.
dogfish83 ยท 1 points ยท Posted at 05:05:03 on May 28, 2016 ยท (Permalink)
I mean yes which door he opens indicates which door you can switch to but statistically it doesn't matter. Even before he opens a door you are really choosing between having one door or having two doors. You already know one of the two doors is empty before he even opens one. Expand it to 10k doors, and you get to select between your door and the 9,999 other doors. Play the game a couple times and what's the chances that every time you play you've selected the right door? Very slim. Always go with the switch. Again, him opening a particular door doesn't give any useful meaningful helpful information. Edit: yes a technicality, but you can look at it like you are choosing between one door and two doors (or 1 door and 9,999 doors).
guffetryne ยท 1 points ยท Posted at 09:41:13 on May 28, 2016 ยท (Permalink)
The opening of doors is the critical component here. Statistically, you know that you have a 1/N chance of having picked the prize at first, thus a 1-1/N chance of not having picked the prize. You already know this. The host opening all non-picked doors that do not contain a prize thus gives you a 1-1/N chance of getting the prize if you switch. That doesn't change with the opening of doors, correct. But he still has to do it before he lets you choose between switching or staying! This is the entire point of the game!
If you could start the game with picking a door, and the host says "alright, do you want to keep that door or do you want all the other doors?" -- that would be the situation you're describing. Statistically, they give you the same chance of winning if you switch/stay. But now you've reformulated the Monty Hall problem to take out the confusing part. Intuitively, in the situation I've just described you would obviously switch every time. N doors (for N>1) is better than 1 door. In the Monty Hall formulation, made evident by this thread, it's not immediately obvious that you should switch.
It is determined in advance that you should always switch, if you want the highest probability of winning the prize. We agree on this. Statistically, you should always switch. So specifically which door he opens doesn't matter, no. But he has to open a door to let you know which of the remaining doors now contains the entire probability of "all other doors" having the prize. This is the entire point of the problem. If he doesn't, how would you pick which of the two doors to switch to? Because he still won't let you choose both of them.
But not which one. He won't let you choose two doors. He has to open one of them first.
Again, no, you've changed the problem. The host has to open the doors before you can switch.
dogfish83 ยท 1 points ยท Posted at 13:11:43 on May 28, 2016 ยท (Permalink)*
He is effectively giving you a door and thus it's equivalent to if he were to say "one of the remaining doors is empty, would you like to switch to doors B and C or stay with A?" Of course he's not going to let you have two doors directly but it's effectively what he's doing.
Edit: of course the way it actually is done makes it look like you have a 50-50 shot, which is why they make it a feature in a game show I'm 2/3 sure.
All of what I've been saying is to reduce the problem to what's really going on statistically as in why is it not 50/50, what's the trick etc.
guffetryne ยท 1 points ยท Posted at 14:05:58 on May 28, 2016 ยท (Permalink)
Yes, that's effectively what he's doing by actually opening the empty doors. That is the point. Until he has actually opened the empty doors, he has not given you any advantage by switching.
Your last two posts here have not been wrong, per se, but you're talking about a different problem. You clearly understand the math that makes this work. I don't understand why you won't realize that the host knowing which door contains the prize and opening the ones that don't is the crucial part of this problem.
This was your first comment in this thread. That is absolutely, entirely, 100% wrong. The entire problem works precisely because the host knows which door has the prize.
dogfish83 ยท 1 points ยท Posted at 15:44:26 on May 28, 2016 ยท (Permalink)
I'm not talking about him knowing whether it's not B or not C, I'm talking about the illusion that he is giving you information that helps your statistics. He is setting up your perceived choice sure but whether you end up getting to choose between A and B or A and C is the same. As given in an explanation of the problem somewhere, it's as if he is giving you the choice between A and BC
guffetryne ยท 1 points ยท Posted at 00:02:23 on May 29, 2016 ยท (Permalink)*
That's not what happens when he opens the door. It doesn't change the statistics you should take into account when making your decision, but it definitely affects your choice! It has to! He opens the door not containing a prize. You've already determined in advance that you should always switch, but you don't know which door to switch to until the host has opened an empty door.
Yep, it most certainly is. But you still can't make that choice until he's opened a door. A door which he must know does not contain the prize.
Yes, him opening the doors is what effectively gives you the choice between A or BC. That happens at the moment he opens the door not containing a prize. Not before. It is the action of opening a non-prize door that does that. You should still always switch. But you can't switch to the one remaining door before he has opened the one without a prize. This problem does not work at all if the host does not know which door contains the prize. You started this discussion by claiming that he host's information is not important, which is absolutely false. The problem doesn't work if the host doesn't know which door contains the prize.
I honestly don't know how else to explain this.
That is from an earlier post of yours. How can you say that is not useful information? In your scenario, where you pick a door, and the host does not open more doors. What do you do? You claim it's irrelevant that he host opens more doors, because you already know that you have to switch. But which door do you switch to? There's still two unopened doors in addition to the one you initially picked. How can you know which one to choose? And how does that help your chances of winning? Yes, you should always switch. But you cannot switch until the host has opened the doors without a prize. It is the act of opening the doors that turns the problem into effectively choosing A or BC.
I swear I'm only continuing this discussion because I'm genuinely curious as to why you would claim the host's knowledge is irrelevant.
dogfish83 ยท 1 points ยท Posted at 03:28:23 on May 29, 2016 ยท (Permalink)
Lol I'm explaining why the host's action is designed as smoke and mirrors, why it looks like you have a 50/50 shot. I'm not talking about you and me who get the math. I'm talking about people who see the host do something and think it changes the stats.
guffetryne ยท 1 points ยท Posted at 09:14:30 on May 29, 2016 ยท (Permalink)
But it does.... Opening an empty door changes the stats from 1/3 for each door into 1/3 for the door you initially picked and 2/3 for the remaining unopened door, as the set of unopened doors with a combined probability 2/3 is turned into a single door thanks to the host's knowledge. The statistics work out because you know the host will open a door without a prize. Which door it ends up being is irrelevant, but a door still has to be opened. The host doing something is the element that makes the math what it is. It does not work without that element.
You started this discussion with that claim, and you still maintain that the host's knowledge does not give you important information. Again, this is blatantly false. Super wrong. Entirely not correct. It is the complete opposite of that. It doesn't change your decision, but knowing that an empty door will be opened is what lets you determine that switching is the best decision in the first place.
You cannot possibly still claim that the host knowing which door has the prize is not important. You can't. Please.
dogfish83 ยท 2 points ยท Posted at 13:16:41 on May 29, 2016 ยท (Permalink)
ok maybe I should say which door it happens to be behind, which the host knows, is not important.
halberdierbowman ยท 1 points ยท Posted at 17:58:49 on May 25, 2016 ยท (Permalink)*
That's not correct, because knowing which options are losses helps you to find the one that's a win. Seeing an empty door is just as important in probability as seeing a winning door.
You can calculate the probability of winning by subtracting the probability of losing from 1, the probability of all the possible outcomes or 100% of the choices. So for the first pick you have a 1-2/3 chance to win, because you have all of the possible options (1.00) minus the chances of losing (.33) and (.33). That's 1/3 just the same by counting losses as by counting wins.
dogfish83 ยท 1 points ยท Posted at 18:06:53 on May 25, 2016 ยท (Permalink)
The math is right, but the empty door doesn't tell you anything. He is going to show you an empty door no matter what. He doesn't even have to show you a door period.
AT-ST ยท 1 points ยท Posted at 20:46:49 on May 25, 2016 ยท (Permalink)
The host would also never pick the door that you picked. So really the 1/3 of a chance that belonged to the Host's door would get split to both the remaining doors.
shelvac2 ยท 1 points ยท Posted at 21:09:53 on May 25, 2016 ยท (Permalink)
OH MY GOD
I'VE ACCEPTED THE ANSWER TO THE MONTY HALL PROBLEM FOR SO LONG BUT NOW I FUNALLY UNDERSTAND AND I FEEL SO DUMB
THANK YOU
halberdierbowman ยท 1 points ยท Posted at 21:26:02 on May 25, 2016 ยท (Permalink)
Haha you're welcome! Those rules are often not explained clearly when people bring up the question, so it's easy to overlook.
be_my_plaything ยท 1 points ยท Posted at 08:36:39 on May 26, 2016 ยท (Permalink)
Can you explain to an idiot why the 1/3 that now isn't the open door all goes to the third do and isn't split between your pick and the third door?
Obviously I get you start with:
Then he opens the empty door:
What I don't get is why that becomes:
As opposed to:
Obviously if nothing was said and he just continued opening doors you are still on your initial 1/3 chance but at the point he asks if you want to change your decision as long as you make a choice, be it to stick or change, that choice is now surely 50:50 whichever way you decide.... right?
I mean obviously not right or the problem wouldn't exist, but I can't get my head round why not, if you just put your fingers in your ears "la-la-lala-lala I can't hear you" you are still 1/3, but I can't see how the choice to stay or change have different odds once a door has been eliminated.
Sibraxlis ยท 1 points ยท Posted at 18:21:24 on May 25, 2016 ยท (Permalink)
But your removing data from the set! The creates a separate set of data in itself where each door is weighted equally.
https://ablestmage.wordpress.com/2013/04/09/5050-is-king-classic-monty-hall-problem-re-addressed-and-re-debunked/
halberdierbowman ยท 1 points ยท Posted at 19:15:56 on May 25, 2016 ยท (Permalink)
I don't follow his logic, maybe you want to explain it differently? It sounds like he's claiming that the eliminated door doesn't matter, but I say it definitely does, because you know the host will pick an empty door and never on with the prize. He gave a lot of examples of various things, but I don't see how any of them proves that you should disregard the information the host provides with his selection. Sure we could pick doors by throwing darts or rolling a die, but the host has to pick an empty door, so he won't do that.
Maybe I'm confused because it sounds like he admits to the truth/probability tables that explain the possible options and how switching doors is better, but then says they don't matter because it's now a new game. I explained the possible options in another post and how you can follow them to see that switching gives you double the chance of winning. There's an easily countable number of doors and options, so it's not hard to list them all.
Each door would be weighted equally in the new set, but only if you forgot that the host has to pick one that's empty. If the host picked randomly, your odds would change depending on which door he picked.
Sibraxlis ยท 0 points ยท Posted at 19:50:42 on May 25, 2016 ยท (Permalink)
I didn't bother with the examples.
Just because he chose an empty door doesn't invalidate your choice.
If you have a sample of 3 doors, then remove a specimen because it was invalid, it doesn't change the results of the other two, it would remove it from the original sample leaving you with 2 doors or a 50/50 shot
halberdierbowman ยท 2 points ยท Posted at 19:59:32 on May 25, 2016 ยท (Permalink)
You're right, that's how it would work if you were picking doors randomly and so was he, or if you walked into the studio after the host opened a door.
In this game though, the host knows which door has a prize, and the host is obligated to pick an empty door that you didn't pick. Knowing those rules gives you valuable information. From the host's action, you have learned that the third door is not one of the empty doors. It may still be the other empty door, or it may be the prize door. That's better odds than your first door has, since your first door had two chances to be an empty door rather than one.
Sibraxlis ยท 1 points ยท Posted at 20:06:46 on May 25, 2016 ยท (Permalink)
Hm. I still feel like it's applying a reduction in value to your current door via increasing the value on the door left over, which is like changing the outcome, despite it already being fixed.
SmokeyBear81 ยท 479 points ยท Posted at 15:06:17 on May 25, 2016 ยท (Permalink)
Think about it like this. Imagine he asked you to pick 1 door out of 100. He then opens up 98 doors except for yours and one other and one of them is right. Would you switch doors then, considering that you only had a 1% chance of getting it right in the first place?
dluminous ยท 22 points ยท Posted at 15:25:11 on May 25, 2016 ยท (Permalink)*
The way I see it (and I've studied this problem multiple times before) is that it's irrelevant now that my chance was once 1%. My probability changes with each new door that opens up. When 98 are open, each door is now 50/50..
Please help me understand!
EDIT: I got it, and out of all the explanations, 3 really stood out. Those 3 people earned my precious reddit silver.
Korlus ยท 78 points ยท Posted at 16:19:50 on May 25, 2016 ยท (Permalink)
When he reveals the empty door, you are right that there are two options available, however you are mistakenly giving both of them an equal chance of being right.
Because the quiz host knows which door the prize is behind, by knowingly not opening it he makes it less likely you have picked the correct door.
I think it's easiest to understand if instead of trying to apply abstract logic, we instead walk through each scenario.
There are three doors - A, B and C. You pick Door A (leaving B and C). Now then:
Because you are now presented with three outcomes and two of them result in you winning, you win 66% of the time if you swap, and only 33% of the time if you keep.
I get that this doesn't explain the logic behind it, but people so often struggle to grasp the concept that it might even be right (Don't worry - it bothered many high level mathematicians at the time, so you are not in any way slow), I don't know why I have never seen it explained this way before.
Thatcubanescapee ยท 18 points ยท Posted at 17:00:15 on May 25, 2016 ยท (Permalink)
Out of all the explanations in this thread, this is the one where it finally clicked!
dogfish83 ยท 2 points ยท Posted at 17:59:28 on May 25, 2016 ยท (Permalink)
I think the best explanation is for you to do a probability tree starting from the beginning and including all of the possibilities including which doors the host opens. It all collapses to the 66% and 33% given above.
yhsanave ยท 6 points ยท Posted at 21:01:28 on May 25, 2016 ยท (Permalink)
This is an excellent explanation, however there is one issue:
When you first pick the door, you have a 33% chance of getting it right. This never changes. What he does do, however, is condense all the wrong choices and the one right choice (assuming you didn't pick it) into a single option. This means that he has actually made it more likely that the other choice is correct.
But this is more of an error in your wording than your explanation.
dluminous ยท 1 points ยท Posted at 17:05:19 on May 25, 2016 ยท (Permalink)
I think this may be the best way to explain it... there are 3 final outcomes, 2 of which grant a favorable condition.
EDIT: you get my prize
jaaval ยท 64 points ยท Posted at 15:32:47 on May 25, 2016 ยท (Permalink)
You only win by not changing if you chose the right door to begin with. You win by changing if the prize was behind any of the other doors since the host opens all but one of them.
YouWillRememberMe ยท 11 points ยท Posted at 16:55:00 on May 25, 2016 ยท (Permalink)
You are correct when the choices are independent. The explanation others are not clarifying is that in this case they choice is dependent on the previous choice so they are not independent of each other.
ds580 ยท 53 points ยท Posted at 16:11:51 on May 25, 2016 ยท (Permalink)
I finally get it. The trick to this is that the host will never open the door with the prize. The number of doors is irrelevant.
There's a 1/n chance you picked the door with the prize. There's a (n-1)/n chance that door lies in the group you didn't pick.
ASSUMING the host will never pick the door with the prize, when his group is down to one door, you can switch. The key here is that you aren't picking the odds of a single door. You're collectively picking the odds of EVERY door that you didn't choose, but all but one of those you know is empty. This leaves the final door with (n-1)/n probability of holding the prize IF THE HOST HAS PURPOSEFULLY AVOIDED THAT DOOR.
irishsultan ยท 19 points ยท Posted at 16:26:13 on May 25, 2016 ยท (Permalink)
Yes, that's the important bit: the host has to purposefully avoid the winning door.
If it's just by accident that he doesn't open it the chance after switching is 50/50.
bebemaster ยท 5 points ยท Posted at 16:36:55 on May 25, 2016 ยท (Permalink)
But it's only be 50/50 because (n-2)/n% of the time he'd open up the prize door and you'd lose. By knowing which door has the prize and avoiding it you're avoiding those (n-2)/n% of scenarios.
[deleted] ยท 1 points ยท Posted at 17:15:31 on May 25, 2016 ยท (Permalink)
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irishsultan ยท 6 points ยท Posted at 17:19:49 on May 25, 2016 ยท (Permalink)
It is 50/50 when it happens by accident. Look for Monty Fall in this list of Monty Hall variants
[deleted] ยท 2 points ยท Posted at 17:38:38 on May 25, 2016 ยท (Permalink)*
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irishsultan ยท 2 points ยท Posted at 17:48:44 on May 25, 2016 ยท (Permalink)
How is it not clear that I meant to change the rules? I pointed out the part that made switching beneficial (which the person I responded to already highlighted, so that was really for emphasis) and then mentioned that if you changed that to an accidental reveal of the losing door the odds would become 50/50
[deleted] ยท 1 points ยท Posted at 18:01:15 on May 25, 2016 ยท (Permalink)*
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CaptainSasquatch ยท 2 points ยท Posted at 20:05:05 on May 25, 2016 ยท (Permalink)
The variants of that give you the 50/50 odds illustrate that the hosts knowledge of the prize is the crucial part of the Monty Hall problem.
[deleted] ยท 1 points ยท Posted at 21:05:55 on May 25, 2016 ยท (Permalink)*
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irishsultan ยท 2 points ยท Posted at 21:55:05 on May 25, 2016 ยท (Permalink)
Once again you seem to be missing that a crucial part of the problem is in how you arrive at that second state. (Also the original problem is already counterfactual, the real Monty never allowed you to switch)
[deleted] ยท 1 points ยท Posted at 22:18:33 on May 25, 2016 ยท (Permalink)
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irishsultan ยท 3 points ยท Posted at 22:26:58 on May 25, 2016 ยท (Permalink)
Are you aware that it's possible to have variations on mathematical problems? Are you disagreeing with what happens in the Monty Fall variation? I have no idea what problem you think I actually have.
[deleted] ยท 1 points ยท Posted at 22:38:04 on May 25, 2016 ยท (Permalink)
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irishsultan ยท 2 points ยท Posted at 22:44:05 on May 25, 2016 ยท (Permalink)
Again, what problem do you think we have?
guffetryne ยท 1 points ยท Posted at 00:25:32 on May 28, 2016 ยท (Permalink)
The reply you're looking for is "Shut up, nerd."
Holy fedora, batman.
Danno558 ยท 2 points ยท Posted at 17:41:59 on May 25, 2016 ยท (Permalink)
That's messed up... the accidental reveal actually increase the likelihood that you picked correctly since there was a 50/50 shot that the stumble would reveal a car... since no car was revealed, it's likely both of the remaining doors actually contained goats, thus making it a 50/50 shot between the two remaining doors.
That one is extremely difficult to wrap the mind around... I think I still switch in that situation though.
irishsultan ยท 2 points ยท Posted at 17:45:18 on May 25, 2016 ยท (Permalink)*
See my explanation
(edit: on rereading you already seem to understand that? switching doesn't decrease your chances, so it doesn't hurt to switch, still why change?)
Danno558 ยท 2 points ยท Posted at 18:02:30 on May 25, 2016 ยท (Permalink)*
So in this scenario these are the following possibilities:
Scenario 1: Pick L1 host falls and opens L2 . W remains.
Scenario 2: Pick L1 host falls and opens W.
Scenario 3: Pick L2 host falls and opens L1 . W remains.
Scenario 4: Pick L2 host falls and opens W.
Scenario 5: Pick W host falls and opens L1 . L2 remains.
Scenario 6: Pick W host falls and opens L2 . L1 remains.
So ignoring Scenario 2 and 4 due to them revealing the winner accidentally (and we know a goat was revealed) we are left with Scenario 1, 3, 5, and 6 where 2 out of 4 of them resulting in winning scenarios... 50/50.
When the host knows the outcome scenario 2 and 4 actually become 1 and 3 respectively causing the 66% win position.
Edit: This was just for me working it out, I know you get it... just needed to try and get a better view of what's going on.
[deleted] ยท 1 points ยท Posted at 18:29:44 on May 25, 2016 ยท (Permalink)
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Danno558 ยท 1 points ยท Posted at 18:46:49 on May 25, 2016 ยท (Permalink)
All of those scenarios have equal chance of occurring? Am I missing something?
[deleted] ยท 1 points ยท Posted at 19:10:53 on May 25, 2016 ยท (Permalink)
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Danno558 ยท 0 points ยท Posted at 19:38:18 on May 25, 2016 ยท (Permalink)
I did say I would still switch in the scenario... I am with you on this one, but the math definitely shows that if there is a possibility that he could have opened the car by accident (scenarios 2 and 4 on my list) that the chances are 50/50.
Given the knowledge that he will "accidentally" open the goat every time due to the scenario saying that that's what is the outcome gives it an unfair advantage since scenario 2 and 4 physically cannot happen (artificially giving additional weight to scenario 1 and 3) and turns this into the "Monty Hall" problem instead of the "Monty Fall" because the scenario you describe isn't actually random.
In theory, if it was truly random and I was knocked unconscious... 1/3 of the time I would be waking up to an open car door.
[deleted] ยท 1 points ยท Posted at 20:49:29 on May 25, 2016 ยท (Permalink)
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Danno558 ยท 1 points ยท Posted at 20:54:42 on May 25, 2016 ยท (Permalink)
You're the one who is wrong... so whatever?
It only works if it's not a random selection.
[deleted] ยท 1 points ยท Posted at 21:08:47 on May 25, 2016 ยท (Permalink)
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Danno558 ยท 2 points ยท Posted at 22:21:59 on May 25, 2016 ยท (Permalink)*
You're wrong though... look at my scenarios. We agree that there are 6 total scenarios correct?
There is only 4 possibilities that could possibly result with a goat door being revealed right? Two possibilities being removed due to a winning door being opened.
So given that we know there are 4 possibilities, and we know that 2 of those possibilities result in losses... its a 50/50 shot! I've shown you the probabilities, where do you think I've messed up the math?
Edit: I am still going to switch in this situation since maybe the host knew and meant to do it, and since it's a 50/50 shot there's no downside to switching.
[deleted] ยท 0 points ยท Posted at 22:27:49 on May 25, 2016 ยท (Permalink)
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Danno558 ยท 2 points ยท Posted at 22:29:03 on May 25, 2016 ยท (Permalink)
They do have the same probabilities. Why would any of them have a higher likelihood?
irishsultan ยท 1 points ยท Posted at 22:45:32 on May 25, 2016 ยท (Permalink)
And you were the one speaking about not wanting to consider counterfactuals?
Danno558 ยท 3 points ยท Posted at 22:55:55 on May 25, 2016 ยท (Permalink)
Just checked this guy's history... he talks like he's coming straight from /r/iamverysmart.
Once you lay out the scenario it becomes fairly obvious that it's a 50/50 probability, I don't know why he's fighting this so hard.
[deleted] ยท 1 points ยท Posted at 18:25:19 on May 25, 2016 ยท (Permalink)
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rawling ยท 1 points ยท Posted at 21:03:08 on May 25, 2016 ยท (Permalink)
If the host opened one of the two doors at random, and he happened to open one with a goat, your chances of winning if you switch (or don't) become 50/50.
[deleted] ยท 1 points ยท Posted at 21:11:54 on May 25, 2016 ยท (Permalink)
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rawling ยท 1 points ยท Posted at 21:23:34 on May 25, 2016 ยท (Permalink)
OK, there are two possible states:
The two possible states that leads to you observing "the host randomly opened a door, and there was a goat" have equal probaiblity, so there is a 1/2 chance that you have the car and a 1/2 chance you will win if you switch.
The remaining 1/3 of the starting probability is lost to the impossible-given-what-you-observed state:
[deleted] ยท 1 points ยท Posted at 21:37:02 on May 25, 2016 ยท (Permalink)*
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rawling ยท 1 points ยท Posted at 21:41:16 on May 25, 2016 ยท (Permalink)
If the host opens a door at random, it is more likely to be a goat in a you-picked-a-car universe than a you-picked-a-goat universe.
That means if the host opens a door at random and it is a goat, it becomes more likely that you are in a you-picked-a-car universe.
By Bayes' theorem,
P( Y_C | H_G ) = P( H_G | Y_C ) * P( Y_C ) / P( H_G ) = 1 * 1/3 / (2/3) = 1/2[deleted] ยท 0 points ยท Posted at 22:06:36 on May 25, 2016 ยท (Permalink)
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rawling ยท 1 points ยท Posted at 22:42:51 on May 25, 2016 ยท (Permalink)
I'm afraid you've lost me. By how, do you mean what are the numbers, or do you mean how is it possible that the host randomly opening a door and revealing a goat have any effect on the situation?
irishsultan ยท 1 points ยท Posted at 21:59:24 on May 25, 2016 ยท (Permalink)
/u/Danno558 worked it out in more detail
The difference is that in the original problem the second and third option lead to the same result (host reveals goat), instead of being split into two different results (host reveals goat vs. host reveals car).
[deleted] ยท 1 points ยท Posted at 22:21:04 on May 25, 2016 ยท (Permalink)
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irishsultan ยท 2 points ยท Posted at 22:25:03 on May 25, 2016 ยท (Permalink)
I'm not oversimplifying anything and I'm not losing any information, but if you still disagree feel free to give a none oversimplified explanation so that I can point out where you go wrong.
overconvergent ยท 1 points ยท Posted at 16:19:51 on May 26, 2016 ยท (Permalink)
/r/irishsultan is correct. Just look at a simulation and stop arguing.
lazyl ยท 1 points ยท Posted at 17:37:21 on May 25, 2016 ยท (Permalink)*
That table is incorrect. The wiki editor must have misunderstood the paper he sourced for that information. If there are three doors, and you pick one, and then the host opens one of the two that you didn't pick revealing a goat, then the chance that the third door has the car is 2/3. It is irrelevant whether or not he knew where the car was.Oops, looks like I'm wrong. You can ignore me.
irishsultan ยท 1 points ยท Posted at 17:46:06 on May 25, 2016 ยท (Permalink)
No, that table is correct, see my explanation for the case where it's at random
irishsultan ยท 1 points ยท Posted at 17:37:43 on May 25, 2016 ยท (Permalink)
I'll actually also explain why the intention matters. Suppose he revealed a door at random instead, and look at the odds before he reveals a random goat:
Now suppose the host opens a losing door at random, there are two possible scenarios that lead to this and they were equally likely before he opened that lost door, so logically they are equally likely after he revealed that losing door and they remain equally likely until one of the two remaining doors is opened.
tripletstate ยท 1 points ยท Posted at 16:57:44 on May 25, 2016 ยท (Permalink)
Finally someone gets it.
dluminous ยท 1 points ยท Posted at 17:08:28 on May 25, 2016 ยท (Permalink)
This also makes sense of out the explanations. You are also awarded my prize.
Andy_B_Goode ยท 1 points ยท Posted at 18:44:44 on May 25, 2016 ยท (Permalink)
Exactly, the game would be equivalent to first being told to pick a door and then being told to bet on your choice being either right or wrong.
visor841 ยท 6 points ยท Posted at 16:17:46 on May 25, 2016 ยท (Permalink)
So, we'll take the 100 doors scenario.
Each door has 1/100th probability of having the prize behind it. You choose one door. Now we separate the doors into two groups: "your door" and "the other doors". Each door has 1/100th probability having a prize behind it. Take what's behind your door, and put it in a one door building. Take what's behind the other doors, and put it in a 99-door building with 98 doors having cement behind them.
If asked to guess which building has the prize inside, which would you choose? The 1-door building has a 1/100 chance of the prize being inside, and the 99-door building has one a 99/100 chance of the prize being inside, even with 98 doors with cement behind them. Now Monty tells you he has opened the 98 doors in the other building that have cement behind them. This is no different that the normal situation, because monty is always choosing doors without the prize behind them. You know the other building has 98 doors with cement behind them. Opening and seeing them didn't affect the probability of something being inside the building. If given the option to open the door without cement behind it in the 99 door building, instead of the one door building, you should take it. Even though you have an option of two doors, one has a 99% chance of having the prize behind it.
SmokeyBear81 ยท 2 points ยท Posted at 15:39:28 on May 25, 2016 ยท (Permalink)
The thing to remember here is the host knows which door has the prize behind it, the other 98 doors that he opened (imagine it all at once not one at a time) wasn't done randomly
dluminous ยท 3 points ยท Posted at 15:47:08 on May 25, 2016 ยท (Permalink)
So the fact that its not random is what changes it? But as the contestant, its random for you is it not?
Carefully_random ยท 6 points ยท Posted at 16:38:57 on May 25, 2016 ยท (Permalink)
I like to look at it this way, as it helped me get my head around it.
You split yourself into three alternate realities, in each one you pick a different door. Now, in all three realities, the prize is in door number three.
It's really important that you pick a door first and then are shown a door that is dud.
So let's play it out:
In reality A you pick door number 1. The host then shows you door number 2, knowing that it's the only empty door that isn't the one you picked. You're then asked if you want to switch?
No, you're good. Stick with your choice. You open door 1 and boo, you lose.
Reality B, you pick door two. The host shows you door 1, because it doesn't have the prize and you haven't picked it. Want to change?
No, you stick with door 2, and lose.
In reality C, you pick door three. The host can open either of the other doors as there are no prizes there, so he shows you door 1 as empty. Want to change?
No, you're fine sticking with your choice. Bam! You win, kudos.
In your three realities you just won 33% of the time.
The prize was in fact a time machine and you (or reality C you) use it to go back to the reality splitting moment, let's do it all again:
Ok, so same situation, three realities, the prize is in door number 3 in each one. This time we're going to switch in each reality.
So reality A plays out that you pick door 1, are shown the empty door 2, and then switch to door 3. Boom! Winner.
Reality B has you pick door 2, you're shown door 1 as empty, and then you switch to door 3. Awesomesocks, the prize is yours.
In reality C, you pick door 3, are shown an empty door 1, and then switch to door 2, which is empty so you lose. Darnit.
The point is that by switching, you won 66% of the time in the exact same scenario.
So though the initial door location and your first pick are two random factors, the rules of the game means that if you switch after being shown an empty door, you're 66% likely to be switching to the winning door.
a third of all contestants won't like the fact that they switched and lost, but the rest will be quiet happy.
sweetpatata ยท 2 points ยท Posted at 10:11:58 on May 26, 2016 ยท (Permalink)
From all the explanations I've read, I like yours the most. Now I finally get it. Thanks.
Carefully_random ยท 1 points ยท Posted at 13:41:54 on May 26, 2016 ยท (Permalink)
You're welcome. Anytime you have obscure mathematical queries, drop me a line :)
sweetpatata ยท 2 points ยท Posted at 15:02:12 on May 27, 2016 ยท (Permalink)*
Okay I've got something I can't seem to solve.
The third derivative of: e2x2 -7x+3
I came this far: (32x-56)e2x2 -7x+3+(16x2 -56x+53)(4x-7)*e2x2 -7x+3
But the sheet says as a solution it has to be: (16x2 -56x+61)((4x-7)e2x2 -7x+3)
I don't understand what happens to 32x-56 and why the 53 in 16x2 -56x+53 turns into 61. Can you help me there?
Carefully_random ยท 1 points ยท Posted at 16:48:56 on May 27, 2016 ยท (Permalink)
Absolutely.
Let [(32x-56)]=A
and
[(16x2 -56x+53)(4x-7)]=B
and just to make it simple to represent let
[e2x2 -7x+3 ]=Y
(We're going to keep this as Y until the end as this term because this is a common term for both parts of the equation since exponents stay the same after being differentiated.
What we're doing first is rearranging AY + BY into (A+B)Y
Which looks like all of that out gives:
((32x-56) + (16x2 -56x+53)(4x-7))Y
Now we need to multiply out of all these brackets before we can simplify, like so:
(32x - 56 + 64x3 - 224x2 + 212x - 112x2 + 392x -371)Y
We have some same order terms here that can be added or subtracted from each other, giving:
(64x3 - 336x2 + 636x -427)Y
Now, we want to simplify this further, but trying to figure out what divides into that could be a headache. However, we can cheat a bit and look at a few lines above, where we had (4x-7) as the 1st order differentiation coefficient. What's the bet that will divide into this monstrosity still?
Well dividing through with the 4x will make that 64x3 become 16x2 like we expect, and dividing the -427 by -7 will give you the +63 that you weren't sure where the hell it came from. The middle two terms also divide in and give you your result:
((4x-7)(16x3 - 56x + 61))Y
So we'll bring Y back into it's full form now:
((4x-7)(16x3 - 56x + 61))e2x2 -7x+3
And there we have it. Let's leave it to 3 derivatives though, nobody needs a fourth derivative unless it's a full moon in November.
tl;dr Take out the common term (the exponential), expand, then simplify.
mysticrudnin ยท 3 points ยท Posted at 15:52:31 on May 25, 2016 ยท (Permalink)
Random is objective, not subjective.
anowlcalledjosh ยท 3 points ยท Posted at 15:31:53 on May 25, 2016 ยท (Permalink)*
There are 100 doors. You pick 1. You're then offered the chance to switch to
9899 of the others.971365 ยท 3 points ยท Posted at 15:38:09 on May 25, 2016 ยท (Permalink)
I get the problem but why 98 others? Wouldn't it be like switching to the other 99?
[deleted] ยท 3 points ยท Posted at 15:46:59 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 16:05:51 on May 25, 2016 ยท (Permalink)
Here is the way I see it (in the original problem). When you first pick a door you have 66% chance of it not being the prize. So let's say that it's not the prize since that is most likely. That means the prize should be in one of the other doors. Well when the host opens up the other door he has to open a door without a prize meaning that if your original selection was 66% chance no prize then the other door shoild now have 66% chance being the prize
SushiAndWoW ยท 1 points ยท Posted at 17:45:51 on May 25, 2016 ยท (Permalink)
Putting it this way may actually confuse people more, because if N=3, you are switching to just 1 other door. One is open, and you had already picked another one. There is one choice left.
But that is incorrect, that one door has 2/3 winning probability.
Similarly, if N=100, and the host opens 98 doors, the remaining one has 99% winning probability, not 98%, or 0.9898...%.
washufize ยท -2 points ยท Posted at 15:51:44 on May 25, 2016 ยท (Permalink)
There is the door you pick (1/100), the door that contains the prize (1/100), and all the other doors (98/100).
ClareDeLoon ยท 1 points ยท Posted at 15:33:04 on May 25, 2016 ยท (Permalink)
This is a great way of explaining it!
I might try it next time...
dluminous ยท -2 points ยท Posted at 15:41:38 on May 25, 2016 ยท (Permalink)
Right but your odds change with each eliminated door.
aonome ยท 8 points ยท Posted at 15:48:30 on May 25, 2016 ยท (Permalink)
No they don't.
ICantSurvivee ยท 3 points ยท Posted at 15:48:13 on May 25, 2016 ยท (Permalink)
You were much much more likely to have picked one that was wrong than the right one
You had a 99/100 chance to be wrong on the first pick, and now that 98 wrong options were removed and you know that you had a 99/100 chance of being wrong initially you can assume that you picked one of the wrong doors since the odds of you picking the right door initially was much lower than picking the wrong door
washufize ยท 1 points ยท Posted at 15:50:49 on May 25, 2016 ยท (Permalink)
The odds actually don't change. There is the door you pick (1/100), the door that contains the prize (1/100), and all the other doors (98/100).
Since the host has knowledge of which door contains the prize, he will never open that door. IF he was truly opening the doors randomly, then your odds WOULD increase (with a potential that they drop to zero if he were to open the door with the prize).
So, are you willing to bet that you happened to pick the correct door when you were offered 100 doors?
mysticrudnin ยท 0 points ยท Posted at 15:51:55 on May 25, 2016 ยท (Permalink)
You think you were 50% likely to have picked the correct door out of 100?
golden_boy ยท 1 points ยท Posted at 16:10:06 on May 25, 2016 ยท (Permalink)
If you were wrong the first time, you want to switch because the only remaining door has the car/money/whatever. You had a 2/3 chance of being wrong the first time.
You're thinking that his opening the one door and leaving the other means you're down to 2 options, but that logic stops making sense when you realze he's not opening a random door.
Imagine you took the same scene, played it out 3 times and opened all 3 doors. Two of those times, your picking a goat forced the host to show you the other goat, so those two times you only win if you switch.
Zanzaben ยท 1 points ยท Posted at 16:24:17 on May 25, 2016 ยท (Permalink)
Another way to think of it is chosing between your door and montys door. you will pick 1 door out of the hundred so you have 1% chance to get the prize. Monty will always pick the door that has the prize unless you have already picked the prize so he has a 99% chance to pick the prize since the only way he couldn't would be if you picked it. So then Monty gives you the choice of keeping your door or picking his door. Your door has a 1% chance and his door has a 99% chance. Does that help.
BabyNinjaJesus ยท 1 points ยท Posted at 16:24:30 on May 25, 2016 ยท (Permalink)
at the start you had 1% chance to pick the right one
at the end the other door has a 98% chance of been right because all the other doors were opened
the doors at the end would only be 50 / 50 if you didnt force one to not open in the first place by picking it if the host picked two doors at random (one been correct and one not) it would then be 50 / 50
but you picked one at the start and thus eliminated every single other door except (in 98/100 cases) the right one
its the same reason behind deal or no deal and why you always swap if you had a low number and a high number left, at the start you picked 1/28, at the end you eliminated 26 of them, and a high one was still left, either you got insanely lucky and picked the correct one out of 28
or the other one is right.
1/28 or 27/28 which seems more likely?
veggiesama ยท 1 points ยท Posted at 16:34:43 on May 25, 2016 ยท (Permalink)
You gotta look at the total game and not the the new choice in isolation. It's 50/50 only if you have no other information. But you do have info: you know that your first door had a 1/100 chance of being right. If all other doors are closed except 1 unknown and the 1 you picked, and 1 of those 2 is absolutely the right door, then it's far more likely that the unpicked door is the right door.
Play the game 100 times. 99 of those times, staying with your 1st choice would be wrong. Only in that 100th game, you would be wrong to switch. So you have a 99% better shot at taking the option the host reveals, and only a 1% shot at taking the completely random door you started with.
dluminous ยท 1 points ยท Posted at 17:00:29 on May 25, 2016 ยท (Permalink)
Right, but that information is no longer true given the new information: there are only 2 doors left.
veggiesama ยท 1 points ยท Posted at 19:54:01 on May 25, 2016 ยท (Permalink)
Think from the host's perspective. The host sees you choose 1 door out of 100. 99 times, you'll choose wrong. 1 time, you choose right. After you choose, the host picks 1 other door for you.
99 times the host MUST pick the correct door. Only 1 time would the host get the option of trying to trick you by choosing an incorrect door.
Knowing that, you can alter your strategy because you have complete knowledge of the rules here. You don't have complete knowledge of the doors, but you should know that you have a 99/100 chance when you go with the host's "choice" (because he was obeying a certain rule that said you must have 2 choices and 1 of those must be the correct door).
Shrink it down from 100 doors to 3 doors and the logic still checks out.
Saytahri ยท 1 points ยท Posted at 16:56:01 on May 25, 2016 ยท (Permalink)
It hasn't though.
No new information is gained. Your probability starts as 1/100, the doors that are opened are always picked by the host to be goats (not selected randomly).
The intuition is that 2 doors means 50/50 odds. But this is easy to show as incorrect.
If in the game, instead, whenever you pick the correct door the host flips a d100 (without you seeing) and if it doesn't come up as 100 then he swaps what's behind the 2 doors (without you seeing).
It's easy to see now that it is not 50/50, almost every time you pick the car at first it is swapped. Even though there are 2 doors.
Maybe this will help your thinking for the Monty Hall problem:
When a goat is revealed this does NOT change the probability that your chosen door is a goat. You had a 2/3 chance of selecting a goat, there is always an available goat in the 2 that you didn't choose, so showing you a goat tells you nothing about the probability of what you picked.
Saytahri ยท 1 points ยท Posted at 17:05:10 on May 25, 2016 ยท (Permalink)
Here's another way of seeing why the idea that the probability changes doesn't work:
Say it's a billion doors. All across the world. A car is only behind one of them. The doors can detect what is behind them and be remotely activated to open.
One of the doors happens to be just down the road from you.
You want the car to be where you are, even though it could be behind any of the doors in the world.
So what you do is, you "pick" the door near you. You then press a button which makes all the other doors that aren't your door receive a command to open if they have a goat behind them, but one door other than yours has to remain closed. If the car is elsewhere it will be the door with the car, otherwise it is selected randomly which one will be kept closed.
Now, a billion minus 2 doors open. They all send information back verifying they have goats behind them.
One door, somewhere on the other side of the world from you let's say, is still closed.
So now it's 2 doors. Is there a 50% chance the car is behind your door?
If there is, that means that with a billion doors you can, every time, shift the probabilities so that there is a 50% chance it's behind whatever door you want. Isn't this getting close to teleportation?
You could have picked any of the billion doors to start with and there would be a 50% chance it would be behind that one once the other doors are opened. You basically have a teleporter that works 50% of the time.
Garrett_Dark ยท 1 points ยท Posted at 17:42:31 on May 25, 2016 ยท (Permalink)*
When you picked 1 door out of 100, you had 1% chance of getting it right. When 98 doors were eliminated, the prize isn't randomly reshuffled behind one of the last two doors to reset the probability to 50/50....the prize stayed where it always was, so the door you picked is still 1% and the other door is still 99%.
I think where you're getting hung up is thinking of it like a coin flip. It's not that each 100 doors has a 50% chance of a prize behind it, you would need 50 randomly placed prizes for each door to be like a coin flip. It's more like rolling a 100 sided dice to roll a 1.
hrg_ ยท 1 points ยท Posted at 18:07:38 on May 25, 2016 ยท (Permalink)
You can think of it like this:
You have a 1/3 chance of picking any door at the beginning. Say you choose door A. This is the equivalent of saying there is a 1/3 chance you were right, and 2/3 chance you were wrong (there is a 2/3 chance the car is behind doors B or C).
So we have:
Suppose the gameshow host opens door C, showing the door to be empty. The key thing to realize is that the above rule still holds true:
However, this time, we just know that Door C is a 0/3 chance (by itself). So Door A has a 1/3 chance (this can't simply change just because a door was opened) and Door C has a 0/3 chance. So what does that leave in Door B? 2/3. Thus, we are left with:
Should we switch our choice to Door B? Every time.
Goddamnit_Clown ยท -3 points ยท Posted at 15:55:42 on May 25, 2016 ยท (Permalink)*
EDIT: I chose a poor example to try to get to the solution in two steps as there are at least two sticking points for most people.
Better example follows:
When choosing out of a hundred doors, you probably picked wrong. So, when you picked, you created one category of 'your-door' which is hiding 'probably-no-prize' and another category of 'every-other-door' which is hiding 'probably-the-prize'.
Of those two categories, one is better. You're given the choice of switching from the poor 'your-door' category to the better 'every-other-door' category, which you should do. The fact that a gameshow host walks along most of the doors in the better category, theatrically opening them one at a time is meaningless. It just serves to leave the show with a dramatic decision between two single doors.
What if you got to open all 99 of the doors in the better category? You'd do that instead of sticking with your one door, right?
thosethatwere ยท 3 points ยท Posted at 16:05:10 on May 25, 2016 ยท (Permalink)
This is wrong. You do not get two games, you get one. You get two probabilities: one where you don't know anything about any door, and one where you're given information about the doors you did not choose. It's the fact that the second one is a conditional probability that changes the answer. The condition is: You've chosen a door, and every other door than the "swap to" door is wrong.
Your example is also very confusing, because it would suggest that the second choice is 50/50, which is wrong.
Goddamnit_Clown ยท 2 points ยท Posted at 16:20:31 on May 25, 2016 ยท (Permalink)
You're right, it wasn't a helpful way of looking at it. I'd already amended my original comment.
bunnysnack ยท 2 points ยท Posted at 16:06:21 on May 25, 2016 ยท (Permalink)
That's not at all a good analogy. In the Monty Hall problem, switching is intuitively 50/50, but intuition is wrong. Comparing it to a switch to a coin flip game does not help overcome that intuition.
Goddamnit_Clown ยท 1 points ยท Posted at 16:19:19 on May 25, 2016 ยท (Permalink)
You're right, I'd already amended my original comment.
bunnysnack ยท 2 points ยท Posted at 16:35:48 on May 25, 2016 ยท (Permalink)
Yes, I missed your edit. That is much better.
dluminous ยท 2 points ยท Posted at 17:09:38 on May 25, 2016 ยท (Permalink)
I would, that makes sense too, here you go
nicksalf ยท 1 points ยท Posted at 18:09:57 on May 25, 2016 ยท (Permalink)
Please can somebody explain this to me:
If there were 100 doors, and I got to pick one. Then the host opened a door and I got to choose whether to choose a new door or stay with my remaining door, and this continued until there were only 2 cups remaining.
Am I right to think that I should swap cups every time to have the highest chance of winning?
dluminous ยท 1 points ยท Posted at 18:37:04 on May 25, 2016 ยท (Permalink)
I believe so, since your pick remains static with the odds but constantly switching increases your odds.
Goddamnit_Clown ยท 1 points ยท Posted at 18:33:39 on May 25, 2016 ยท (Permalink)
I'm mildly honoured.
Zenabel ยท 1 points ยท Posted at 17:11:55 on May 25, 2016 ยท (Permalink)
Holy shit i think this just clicked. My friend literally spent hours trying to get me to understand this
Kevsim ยท 1 points ยท Posted at 17:12:30 on May 25, 2016 ยท (Permalink)
I've had a really hard time explaining this one before. Totally stealing this version of the explanation!
BiffManly ยท 1 points ยท Posted at 17:29:08 on May 25, 2016 ยท (Permalink)
Finally, I get it. Having only three doors in other explanations really did not help me understand this, but your explanation makes much more sense.
DickSituation ยท 1 points ยท Posted at 18:13:34 on May 25, 2016 ยท (Permalink)
Instead of one door out of 100, maybe using the lottery will help some people. Suppose you buy a lottery ticket with the numbers 1, 2, 3, 4, 5, and 6. You don't watch the drawing that night, but instead, you have your friend come over and read the results in the paper. Your friend, who knows the winning numbers, then tells you "Okay, either you won, or the winning numbers are 12, 14, 22, 25, 28 and 39".
Do you now have a 50% chance of winning the lottery? If you had the opportunity to change your ticket to the other numbers your friend read out, would you?
gunfire09 ยท 1 points ยท Posted at 19:45:43 on May 25, 2016 ยท (Permalink)
This is what really made it click for me when first hearing about it.
Birdyer ยท 1 points ยท Posted at 19:56:55 on May 25, 2016 ยท (Permalink)
Great way to explain it. Never understood it before this.
SamuraiShark13 ยท 1 points ยท Posted at 20:21:50 on May 25, 2016 ยท (Permalink)
This is the best explanation I've seen of this yet. Thank you.
Masklin ยท 1 points ยท Posted at 21:40:07 on May 25, 2016 ยท (Permalink)
What an excellent perspective. Thank you!
liquidpig ยท 1 points ยท Posted at 22:14:47 on May 25, 2016 ยท (Permalink)
Depends on how much he's sweating.
Uh, are you SURE you don't want to switch doors?
C'mon man... I'll even give you two.
Vozor ยท 1 points ยท Posted at 22:48:44 on May 25, 2016 ยท (Permalink)*
For me this isn't very clear, but I understand the idea. Here is my interpretation:
The opening of the doors is irrelevant info, which confuses the participant. The real trick is that you get to choose one door or all but one door!
kingaardvark ยท 1 points ยท Posted at 23:11:56 on May 25, 2016 ยท (Permalink)
oh man I've struggled with this for years since first hearing it and this has made it clearer than any other explanation.
_reeses_feces ยท 1 points ยท Posted at 08:40:08 on May 26, 2016 ยท (Permalink)
This explanation made it click for me. 2 and 3 were too close together but the way you put it makes perfect sense
Skyzorz ยท 1 points ยท Posted at 05:57:19 on May 31, 2016 ยท (Permalink)
Damn you just blew my mind. I finally get it.
Glossyy ยท 4 points ยท Posted at 15:33:46 on May 25, 2016 ยท (Permalink)
For the visual learners of the group check out this video. Love this channel! https://www.youtube.com/watch?v=9vRUxbzJZ9Y
JeddHampton ยท 3 points ยท Posted at 15:45:46 on May 25, 2016 ยท (Permalink)
There are three scenarios.
You pick Goat A. You pick Goat B.
You pick the prize.
In two of the three scenarios, you win by switching. Only in one scenario do you win by staying.
CaptainSasquatch ยท 8 points ยท Posted at 15:36:31 on May 25, 2016 ยท (Permalink)
There's three equally likely situations the prize is behind Door A, B or C. You start by choosing door A.
There's a 1/3 chance that Door A contains the prize. In that case the host will randomly reveal Door B or C to be empty. You will be better of staying with your first choice.
There's a 1/3 chance that Door B contains the prize. In that case the host will reveal Door C to be empty (they'll never open door B because the host knows where the prize is). You will be better off changing your choice.
There's a 1/3 chance that Door C contains the prize. In that case the host will reveal Door B to be empty (they'll never open door C because the host knows where the prize is). You will be better off changing your choice.
So 1/3 chance that your original guess was right. 2/3 chance that you would be better off switching.
For extra credit consider if the host doesn't know where the prize is and randomly opens a door to reveal that it's empty.
[deleted] ยท 2 points ยท Posted at 16:16:46 on May 25, 2016 ยท (Permalink)
This is a much better explanation, thanks.
I'm not terrible at maths but just couldn't picture why the 1/3 chance of the host's door went to the door her didn't open.
CaptainSasquatch ยท 1 points ยท Posted at 16:22:01 on May 25, 2016 ยท (Permalink)
As someone else said. It's either in the door you originally chose or not. There's a 1/N chance it's in your door. If it's not in the door you chose it's the door the host left unopened which has a N-1/N chance.
Herbert_Von_Karajan ยท 3 points ยท Posted at 15:48:43 on May 25, 2016 ยท (Permalink)
Instead of using 3 doors, use 1000. You pick 1, monty opens up 998 of them so there are 2 doors left over: one that you picked and one that may have the prize unless you already picked the one with the prize.
Wassayingboourns ยท 4 points ยท Posted at 15:55:53 on May 25, 2016 ยท (Permalink)
That's pretty brilliant expansion of the logic to make it make more sense.
By the time he's picked 998 doors (knowing which one is the winner beforehand, and therefore not picking it yet on purpose), the chances of the one door neither of you picked having the prize is very, very high, because the odds of you picking the right door yourself, randomly, out of 1000 doors, right at the start, is insanely low.
So you switch, and are almost guaranteed to win, because he's basically shown you which door is the winner, unless you were just obscenely lucky with your first pick.
PBRontheway ยท 2 points ยท Posted at 15:17:03 on May 25, 2016 ยท (Permalink)
ASAPScience did a great video about it on YouTube if you still can't figure it out. It didn't really make sense to me for the longest time but as soon as I saw that video it clicked
StressOverStrain ยท 1 points ยท Posted at 23:16:55 on May 25, 2016 ยท (Permalink)
The Wikpedia article explains it a few ways that should be understandable for anyone with a basic understanding of probability to begin with.
myheartisstillracing ยท 2 points ยท Posted at 16:27:48 on May 25, 2016 ยท (Permalink)*
In the simplest possible way I can explain it:
[deleted] ยท 1 points ยท Posted at 21:23:42 on May 25, 2016 ยท (Permalink)
There's a lot of good examples and descriptions here. My favorite way of thinking about it is:
You own Door 1 which has a 33.3% chance of being a winner. The host has the other 2 doors have a combined 66.6% chance. He opens one of them, which is a dud, so that doesn't change the odds that the host has a winning door. So the one door now has a 66.6% chance of being a winner, and you still have a 33.3% chance. He then offers you his door and his odds.
So, when you switch, you actually get pick the two doors you didn't choose, you get the dud the host opened for free, and you get the new one which has a 66% chance of being the right one.
When you switch, you actually get pick the two doors you didn't choose.
aJrenalin ยท 2 points ยท Posted at 16:29:01 on May 25, 2016 ยท (Permalink)
If I pick one of the wrong doors first round then the host will open the other wrong door leaving me only with the right door, thus if I pick the a wrong door the first round I will necessarily be presented with the choice to pick the right door the next round.
Similarly if I pick the right door in the first round the host will open one of the wrong doors leaving the other wrong door, thus if I pick the right door first round I will necessarily be presented with a wrong door in the second round.
To sum up if I pick wrong in the first round I will be presented with the right door and if I pick right in the first round then I will be presented with a wrong door. Since there is a 66.7% I chose the wrong door in the first round there is a 66.7% I will be presented with the right door. Since there is a 33.3% that I picked right the first time there is a 33.3% I will be presented with the wrong door. So the door I'm presented with will always have 66.7% of being right and a 33.3% of being wrong.
zcramz23 ยท 2 points ยท Posted at 16:48:20 on May 25, 2016 ยท (Permalink)
If you never switch, the chance of you winning is simply 1/3.
If you always switch, the only way you can lose is if you chose the correct one to begin with(before you switched), which is 1/3.
1 - 1/3 = 2/3
GodzillaLikesBoobs ยท 1 points ยท Posted at 15:51:38 on May 25, 2016 ยท (Permalink)
Just try it. Get a coin, 3+ cups and then turn then upside down. Now get your cat to pick a cup, flip an empty one and ask the cat to switch or not.
You'll see why its first guess is improbable and switching is good.
narrill ยท 1 points ยท Posted at 16:03:42 on May 25, 2016 ยท (Permalink)
The host reveals all but two doors, including the one you picked, and one of those doors contains the prize. So switching will win you the prize if you initially picked wrong, which is a 66% chance with three doors.
pnoozi ยท 1 points ยท Posted at 16:34:47 on May 25, 2016 ยท (Permalink)
It's easier to visualize with more doors
Imagine there were 100 doors, you chose 1, then the host eliminated 98 of them. Unless you got very lucky (unlucky?) and picked the prize to begin with, obviously the door he didn't eliminate contains the prize.
jwktiger ยท 1 points ยท Posted at 16:47:31 on May 25, 2016 ยท (Permalink)
the playing card Monty Hall problem varient is better for understanding that.
suppose you want to pick the Ace of Spades from a deck.
You draw a card from the deck, but don't lock at it. Then the host locks at the rest of the deck and shows you 50 cards that are NOT the Ace of Spades. You now have the choice of the remaining card or the card you choose.
Of course you would flip in that place b/c well there was only a 1/52 chance you were right. There is a 51/52 chance that remaining card is the Ace of Spades.
Another key point is that the object you select is random. The ones the host throws out are NOT random, they are losers selected to throw out.
pjswmkj ยท 1 points ยท Posted at 16:55:19 on May 25, 2016 ยท (Permalink)
Think of it this way: the revealed door is part of your switched pick. Whichever door you originally pick, there is a 2/3 chance that one of the other two doors is the correct one. So pretend that you get to change your pick and can pick both those two other doors. You have a 2/3 chance of being correct, right? That is essentially what it happening: by switching your pick you are essentially just picking two doors, except they don't punish you for the revealed door being picked. There is a 2/3 chance that the switched door is correct.
Sabnitron ยท 1 points ยท Posted at 17:04:16 on May 25, 2016 ยท (Permalink)
If I remember correctly, they go through it pretty well in the first ten minutes of that Kevin Spacey flick 21
mojoshi1 ยท 1 points ยท Posted at 17:05:58 on May 25, 2016 ยท (Permalink)
If you think of each of the doors as having a 1/3 chance of having the prize, then that means that the two doors you didn't pick have a combined 2/3 chance of having the prize behind one of them. Now when the host opens one of those two doors and shows you that it's empty, the last door now has a 2/3 chance of having the prize, since you just found out that it wasn't behind the one he opened. Compare that 2/3 chance with the 1/3 chance you picked the right door first, and it's clear that you have a better chance of winning if you switch.
MedBull ยท 1 points ยท Posted at 17:07:37 on May 25, 2016 ยท (Permalink)
Here is a story about the same principle!
SybariticLegerity ยท 1 points ยท Posted at 17:16:33 on May 25, 2016 ยท (Permalink)
That's really the meat of it. If the host reveals a wrong door every time, then either your door is right or his is. The above fact is still true, which means there's a 66.6% chance you didn't choose the right door.
Leto2Atreides ยท 1 points ยท Posted at 17:24:52 on May 25, 2016 ยท (Permalink)
I heard it best described like this:
You're on a gameshow. The grand prize is hidden behind one of 100 doors. You pick one out of the 100 doors randomly. The host then opens 98 of the doors, revealing no grand prize, and leaving you with two doors; the one you chose, and a single random door the host didn't open.
Which door would you choose now?
[deleted] ยท 1 points ยท Posted at 17:42:11 on May 25, 2016 ยท (Permalink)
The way the game is set up, Monty's proposition is equivalent to him asking whether you want to keep what's behind the door that you chose, or accept whatever is behind both of the doors you didn't choose. Now since at least one of the doors you didn't initially choose will have nothing behind it, Monty can always open such a door before offering you the trade; but he is still offering to let you switch from your first door to both of the doors you didn't pick. Hence it's always better to switch.
PSi_Terran ยท 1 points ยท Posted at 17:52:34 on May 25, 2016 ยท (Permalink)
Someone else might have satisfactorily explained this to you already but imma give a shot anyway.
Okay so you've picked a door. Now there are 3 options.
Option 1: You've picked a door with a goat. The host reveals the other door with the goat, you switch, and you win a car.
Option 2: You've picked the other door with the goat. The host revels a goat, you switch and you win a car.
Option 3: You've picked the door with the car. The host revels either of the goats, you swap and you win a goat. Booo.
Now, 2 out of the 3 options you win the car. That's because the host knows where the goats are and always reveals the one you haven't picked. The only time you lose is when both doors are goats.
A lot of people try to explain it by using 100 doors and opening 99 of them. but I think its better to just look at the options.
arkady48 ยท 1 points ยท Posted at 17:57:45 on May 25, 2016 ยท (Permalink)
Mythbusters actually did an episode where they tested this theory. It was actually really interesting and they explained it very well.
https://www.reddit.com/r/smyths/comments/1pa1pu/s09e21_wheel_of_mythfortune_streamline_edit/
Use the Vimeo link and the password is listed in the thread description. It's the first myth tested.
NickReynders ยท 1 points ยท Posted at 17:58:14 on May 25, 2016 ยท (Permalink)
The easiest way I found to get a grip on this problem is imagine there are 100 doors with 1 "winner" door. You pick 1 door out of them and the host (who knows what's behind each door) then starts systematically opening doors containing no prizes. Now there are only two doors left at the end, the one you picked, and one the host intentionally left closed.
Would you choose the one the host intentionally left closed? or the one you picked?
JonesUCF34 ยท 1 points ยท Posted at 18:00:01 on May 25, 2016 ยท (Permalink)
It pretty much comes down to that fact that before hand you KNEW Monty was going to reveal a door was empty. So the fact that he actually did reveal an empty door didn't give you any more information.
There's a neat probability proof for the problem but I think that's an easy way to explain the intuition behind it.
ThePr1d3 ยท 1 points ยท Posted at 18:05:10 on May 25, 2016 ยท (Permalink)
I think the best way to understand this seemingly non intuitive fact is to look with more numbers.
You have to chose one door between 100. Now The host opens 98 doors aka all of the doors but yours and another one. Now do you switch your choice ?
Lansan1ty ยท 1 points ยท Posted at 18:06:05 on May 25, 2016 ยท (Permalink)
Very simply:
Now that you know that a door has been opened, and he did not reveal the prize, you know that if you picked the wrong door, and switched, you will win.
There were 3 choices:
Door 1 - The Right Door - You picked this, you switch, you lose.
Door 2 - A wrong door - You pick this, you switch, you win.
Door 3 - A wrong door - You pick this, you switch, you win.
You can easily see how many chances of winning you had if you switched, assuming a wrong door is revealed.
CyanPhoenix42 ยท 1 points ยท Posted at 18:07:55 on May 25, 2016 ยท (Permalink)
the other explanation was good, but i like to think about the larger option - so instead of 3 doors, there are 100. then the host reveals 98 of the doors after you choose one, and then asks you if you want to swap. of course you would say yes, because the chances you got the right door the first time is 1/100. the same principal works with the 3 doors.
charizard77 ยท 1 points ยท Posted at 18:08:54 on May 25, 2016 ยท (Permalink)
Think about it like this:
Let's say there are 3 doors. Door 1 is correct, doors 2 and 3 are not.
If you pick door 1 and switch, you will be wrong.
If you pick door 2 and switch, you will be right.
If you pick door 3 and switch, you will be right.
Whereas if you decide not to switch...
If you pick door 1 you are right.
If you pick door 2 you are wrong.
If you pick door 3 you are wrong.
It seems like it should be 50/50 at first, but here you can see that switching gives you a 2/3 chance while staying gives you a 1/3 chance.
ReallyHadToFixThat ยท 1 points ยท Posted at 18:09:55 on May 25, 2016 ยท (Permalink)
When you first picked your door you picked from 3. This means you had a 1/3 chance of picking the correct door.
When the host opens his door that does not change which means the 2/3 probability all transfers to the one remaining door.
Now, had the host opened the door first and then you picked then yes - you would be down to 50-50.
Key points here are that 1) The host knows which door is correct and 2) You pick first.
GrizzzzlyBear ยท 1 points ยท Posted at 18:16:28 on May 25, 2016 ยท (Permalink)
Well there is is very fine example done by WBW on this topic http://waitbutwhy.com/2016/03/the-jellybean-problem.html
Sibraxlis ยท 1 points ยท Posted at 18:24:03 on May 25, 2016 ยท (Permalink)
https://ablestmage.wordpress.com/2013/04/09/5050-is-king-classic-monty-hall-problem-re-addressed-and-re-debunked/
I would argue he's applying statistics inproperly.
c4ptainaw3some ยท 1 points ยท Posted at 19:26:12 on May 25, 2016 ยท (Permalink)*
When you pick the first door you have a 2/3 chance of picking the wrong door. If they opened an incorrect door and then opened your door without giving the option to change you would still be wrong 2 out of 3 times and correct 1 out of 3 times. By changing doors you now have a 1-1/3=2/3 chance of being right.
ctandthefairypatrol ยท 1 points ยท Posted at 20:06:21 on May 25, 2016 ยท (Permalink)
If you pick a goat first (66 percent chance) you will be right 100 percent of the time if you switch.
erdosbaconator ยท 1 points ยท Posted at 20:38:57 on May 25, 2016 ยท (Permalink)
I wrote a simple Matlab code to prove this. I created 1000 cases with random numbers for the prize door and 1000 cases with random numbers for the door chosen. The number of wins when you switch doors is almost twice the number of wins when you stay with your initial choice.
EngiDaBoss ยท 1 points ยท Posted at 20:51:19 on May 25, 2016 ยท (Permalink)
If there were 100 Doors and behind one of them is A Million Dollars and behind the rest of them there are goats. You pick Door No. 42 then door No.25 Is opened to reveal a goat. Your chances of being right were 1/100 but now they are 1/99
Imaginationer ยท 1 points ยท Posted at 21:04:11 on May 25, 2016 ยท (Permalink)
Oh no. Not this again. I've never seen anyone explain at an ELI14 or less. Here's my attempt. (Assume the host MUST open a door after you've selected)
Choice 1: you have a choice between 3 doors, so there's 3 possibilities.
Choice 2. After choosing a door, one of the other doors is always is opened by the host (it's always empty). You can do one of two things
So there are only 6 possible sequences (3x2=6).
Let's just list them out along with their results:
Now, you have no idea whether you selected the correct door or not, so you can't base your decision to STAY or SWITCH on that. Looking at the list of sequences though you see that when you SWITCH, you win 2 of 3 times. If you STAY, you only win 1/3. Try covering up the first "select" part of the sequences and it ends up looking like this.
So would you STAY, or would you SWITCH?
Pancakewagon26 ยท 1 points ยท Posted at 22:26:33 on May 25, 2016 ยท (Permalink)
It's much easier to visualize by adding more doors. So you pick 1 out of 1,000 doors. It's unlikely you've picked the right door. Now every door opens except for one other door.
Which door do you think has the prize behind it?
jmpherso ยท 1 points ยท Posted at 23:00:41 on May 25, 2016 ยท (Permalink)
I've given this explanation in a number of threads now.
It's easiest to think of this way :
Imagine these two scenarios, in one, you start by picking the correct door. In the other, you start by picking the incorrect door.
If there's three doors, obviously you have a 66% chance of picking the wrong door, and a 33% chance of the right door. So let's assume we say "switch doors" every time.
If you pick the correct door, there's two empty doors left. The host opens an (obviously) empty door, and you switch to the other empty door. You've lost. This happens any time you start by picking the correct door, or, 33% of the time.
If you pick the incorrect door, the host opens the only remaining empty door, and the only door left for you to switch to is the correct door. This happens every time you start by picking an incorrect door, or, 66% of the time.
unquietchimp ยท 1 points ยท Posted at 23:08:52 on May 25, 2016 ยท (Permalink)
The best example I heard is to scale it to 100 doors. If you pick one, and the host picks another, and asks if you want to swap to his, your door was 1/100, whereas his door now has 99/100 as one of them has the prize and he picked that specific door.
hypnofed ยท 1 points ยท Posted at 23:11:46 on May 25, 2016 ยท (Permalink)
Here's a better explanation than the ones you've gotten so far.
I have 1,000 doors. Behind one door is a new car. Behind the others is nothing. I invite you to guess which door has the new car. You guess one randomly. That leaves 999 doors. I eliminate 998 of these doors as not having the prize; the prize is either behind the door you chose or the other one I left in contention. Which is more likely: you guessed right the first time randomly out of 1,000 possibilities, or that this other door I led you to has the prize?
[deleted] ยท 1 points ยท Posted at 23:37:32 on May 25, 2016 ยท (Permalink)
It's all in the fact that they only flip the empty door.
Imagine it this way: you select a door, they randomly flip one of the other two, no matter what's behind it. Then, you'd have 3 cases:
1/3 of the time, you select the right door.
1/3 of the time, you select the wrong door and they flip an empty door.
1/3 of the time, you select the wrong door and they flip open the door to the car.
In this scenario, if they flip open the empty door, then it's a 50/50 chance, and is what most people assume is going on. But, in the actual problem, in the 1/3 of the time case where they would reveal the car, they instead also flip open the empty door. So the 1/3 + 1/3 cases become 2/3.
HaplessMagician ยท 1 points ยท Posted at 23:56:14 on May 25, 2016 ยท (Permalink)
The easy way to explain it is with more doors. Lets say there are 5. You are going to pick a door, I open 3 losing doors, you get a chance to switch. Lets assume the prize is in door number 3. If you pick a door and don't switch, you win when you pick 3 and lose when you pick 1, 2, 4, and 5. So you win 20% of the time. But if you pick a door and switch every time, you lose when you pick door 3, but you win when you pick 1, 2, 4, and 5. So you now win 80% of the time.
The key to the problem is if you switch, picking a loser = picking a winner every time. So because there are more losers than winners to start with, you want to bet on your first pick being wrong.
AudioBlood727 ยท 1 points ยท Posted at 00:00:12 on May 26, 2016 ยท (Permalink)
I know others have answered already, but it's much easier to imagine if you expand the number of doors to a million.
[deleted] ยท 1 points ยท Posted at 00:35:28 on May 26, 2016 ยท (Permalink)
I know this has been explained many times but really the best way to think about it is:
Imagine 1,000,000,000 options. One of them is a prize, the rest are nothing. You choose one at random. The chances of that being the prize are basically zero; if you guessed it you're insanely lucky.
The host, who knows which one is the winner, gets rid of all of them but the winner and another.
Would you swap?
If not, you're saying that you believe in your original 1/billion chance which is quite clearly nonsensical.
portableoskker ยท 1 points ยท Posted at 00:49:18 on May 26, 2016 ยท (Permalink)
Engineer reporting in. Easiest way to explain this is by increasing the door count.
Imagine there are 20 doors. You pick door 4. They open every single door but door 4 and door 18, and ask if you want to switch. Well? Of course you do. What are the odds you managed to get it right? (for the record, the average person needs to get to 7 doors before they figure this analogy out. Furthermore, pigeons are not subject to the bias that humans have on the Monty Hall problem).
SultanofStella ยท 1 points ยท Posted at 02:50:52 on May 26, 2016 ยท (Permalink)
You only have a 1/3 chance in getting it right. Therefor 2/3 times you switch doors you will win.
Make a 3x3 table and put an x in the top left, middle, and bottom right squares where x represents the prize. Then play out the scenario and you will see that 2/3 times you switch doors you win the prize.
Treemags ยท 1 points ยท Posted at 03:23:33 on May 26, 2016 ยท (Permalink)
My favorite way to think about it is by writing out the three possibilities: CGG GCG GGC Now without loss of generality assume that I pick door one. Then I have a 1/3 chance of winning if I stay with my original choice (first arrangement) and I have a 2/3 chance of winning if I switch.
ManPumpkin ยท 1 points ยท Posted at 04:31:31 on May 26, 2016 ยท (Permalink)
When you picked there were three doors. 1/3. There are now two doors, 1/2.
Your door has a 33.3% chance while the other door has a 50% chance.
PandaDerZwote ยท 1 points ยท Posted at 07:36:59 on May 26, 2016 ยท (Permalink)
You choose one door at the beginning, there are two outcomes for this:
a) You picked the right door 1/3 chance for that
b) You picked on of the wrong doors 2/3 chance for that
The host eliminates one wrong door, no matter what you picked, you can now choose to either keep your door or swap it, if you keep it, no matter what, you have two outcomes:
a) You picked the right door and kept it, as I said before 1/3 chance
b) You picked a wrong door and kept it, as I said before 2/3 chance
Now you are given the chance to swap no matter what, as one wrong door is eliminated, swapping means you will swap to the right door if you picked one of the wrong doors in the beginning (As you had one of the wrong doors, the other on is opened by the host and you can only swap to the right one) or to the remaining wrong door if you picked the right one at the start (As you had the right one and one wrong one is out, you will get the other wrong door).
This leads to the knowledge that if you change your door, you are guaranteed to get the opposite of what you picked at the start (Wrong -> Right or Right -> Wrong), and since there is a 2/3 chance that you picked a wrong door at the start, there is a 2/3 chance to gain from a swap.
saltinstien ยท 0 points ยท Posted at 15:14:45 on May 25, 2016 ยท (Permalink)*
I don't know if this will help, but it's all about probability being king. If there are three doors, with one prize behind a single one, randomized each time you open one, you can choose a door as many times as you like and you will likely average a 33% success rate. No matter what, (outside of strange luck) having 3 doors gives you a 1/3 chance. So, let's say you choose door #1, which has a 33% chance, just like the others. THEN the game show host opens door #2, which is empty, and allows you to switch if you choose to. What are the odds now? Your door, #1 STILL has 33% odds while door #3 now has a 66% chance. Therefore, it would TECHNICALLY be safer to switch to door #3.
Edit: sorry, looks like door #3 actually has a 66% chance. I couldn't sworn that it was explained to me as 50%, but it's been awhile, and I very likely was remembering it wrong.
CaptainSasquatch ยท 4 points ยท Posted at 15:28:05 on May 25, 2016 ยท (Permalink)
This is incorrect. Door #3 has a 66% chance of containing the prize after Door #2 is revealed to be empty.
saltinstien ยท 2 points ยท Posted at 15:42:36 on May 25, 2016 ยท (Permalink)
Whoops! Sorry about that! I either heard it wrong or remembered it wrong. Edited.
Goddamnit_Clown ยท 2 points ยท Posted at 15:58:38 on May 25, 2016 ยท (Permalink)
Thinking about your chances of missing might be easier. When you chose from lots of doors, you probably already missed.
saltinstien ยท 2 points ยท Posted at 16:01:29 on May 25, 2016 ยท (Permalink)
That's a good take on it, thanks!
Eats_a_lot_of_yogurt ยท 52 points ยท Posted at 16:30:24 on May 25, 2016 ยท (Permalink)*
The last time this problem was posted on reddit, people got hung up on a detail that is essential to this problem, so I'm going to emphasize it:
The host HAS to open a door that does not contain the prize. He's not opening an empty door by accident.
Other people have posted explanations beyond this point, but keep the above fact in mind or else you'll burn a lot of unnecessary fuel trying to figure out why the switch makes sense.
[deleted] ยท 11 points ยท Posted at 18:02:47 on May 25, 2016 ยท (Permalink)
[removed]
YOLO_HASHTAG_SWAG ยท 2 points ยท Posted at 23:48:28 on May 25, 2016 ยท (Permalink)
I included it.
Uhu_ThatsMyShit ยท 2 points ยท Posted at 09:30:46 on May 26, 2016 ยท (Permalink)
For me the distinction is that he HAS to open it and that this was specified even before the candidate chose his first door.
bunnysnack ยท 2 points ยท Posted at 00:22:29 on May 26, 2016 ยท (Permalink)*
Interestingly enough, if you're describing a single situation ("you" on a game show) and Monty chooses and opens a door at random, then it is 50/50 to switch. So merely stating that he opens a losing door isn't enough, because whether he did so randomly or purposefully changes the answer.
Edit: to clarify, I could interpret "he opens one... that doesn't contain the prize" as a rule of the game or as a description of events and the difference matters.
[deleted] ยท 3 points ยท Posted at 21:59:41 on May 25, 2016 ยท (Permalink)
Well, it's obvious that he wouldn't pick the door with the prize behind it, because then the entire thing would fall apart. You'd know which door the prize was behind. It's implied by the rules.
irishsultan ยท 2 points ยท Posted at 22:54:59 on May 25, 2016 ยท (Permalink)
It's implied but not explicitly stated, you could have the host randomly open a door and if it reveals the car then too bad, the contestant can't switch. You can still milk some drama from that outcome if you were really going to televise something like this.
[deleted] ยท 2 points ยท Posted at 12:00:19 on May 26, 2016 ยท (Permalink)
If that happens, then like you said, the contestant can't switch. Therefore that doesn't apply to the Monty Hall problem, because the problem wouldn't exist, the contestant would have just lost.
irishsultan ยท 2 points ยท Posted at 12:13:04 on May 26, 2016 ยท (Permalink)
Right, this is not the Monty Hall problem, this is a variation, but in that variation you do not benefit by switching if the host reveals a goat (and the common explanation of the problem leave out to specify that the host HAS to reveal a goat, most of the time they state that he has revealed a goat (which is different because he could have done that by accident))
[deleted] ยท 1 points ยท Posted at 12:17:12 on May 26, 2016 ยท (Permalink)
But that's not how it works. Even if he does it by accident, the result is still the same. https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3kb29r
overconvergent ยท 1 points ยท Posted at 15:24:16 on May 26, 2016 ยท (Permalink)
No, the result is not the same. Here is some plagiarized Python code for a simulation of this scenario.
Uhu_ThatsMyShit ยท 1 points ยท Posted at 09:31:30 on May 26, 2016 ยท (Permalink)
For me the distinction is that he HAS to open it and that this was specified even before the candidate chose his first door. This was not implied.
[deleted] ยท 1 points ยท Posted at 11:22:17 on May 26, 2016 ยท (Permalink)*
How does the problem even work if he doesn't open it?
Edit: Also, it doesn't have to be specified before the candidate chooses the door. It works even if the candidate isn't aware beforehand.
Uhu_ThatsMyShit ยท 2 points ยท Posted at 13:33:21 on May 26, 2016 ยท (Permalink)
No
You can't allocate the extra 1/3 to the door that's left over in case it wasn't specified beforehand that he was going to have to open a door after the first choice was made. This is in fact crucial.
Faugh ยท 0 points ยท Posted at 22:37:08 on May 25, 2016 ยท (Permalink)
The Monty Hall Problem wouldn't be a "problem" if people didn't explain the solution like fucking idiots.
BenOfTomorrow ยท 3 points ยท Posted at 23:14:52 on May 25, 2016 ยท (Permalink)
It's also very important to know that the problem assumes the host ALWAYS opens a door and offers the switch. In the actual game on Let's Make a Deal, Monty Hall had the option of offering the switch or not, and frequently did not.
hadanish ยท 2 points ยท Posted at 19:15:30 on May 25, 2016 ยท (Permalink)
I never understand why this information is crucial. Can you explain why this point is important?
Eats_a_lot_of_yogurt ยท 4 points ยท Posted at 20:16:19 on May 25, 2016 ยท (Permalink)*
It's important that the host is intentionally choosing an empty door because it's the only way the probability of success from that door collapses onto the last remaining one, instead of being split evenly between your door and the other closed door. The whole problem is easier to explain using 100 doors, like other users have done to describe the problem more generally.
Changing the parameters of the gameshow, there are now 100 doors with 1 prize and 99 duds. I choose a door, the host opens 98 doors and leaves one closed. Imagine the two scenarios where:
a) The host randomly opens 98 of the remaining 99 doors and they all happen to be empty.
b) The host intentionally opens 98 doors he knows won't have the prize.
In situation "a", the host has eliminated 98 doors that aren't winners. However, the probability that the last remaining door has the prize is now 50%, and the chance your first choice has the prize is also 50%. This becomes obvious when you realize that your selecting at random and the host's selecting at random are functionally the same thing. If you decided to randomly open 98 doors and they were all empty, is there any reason to think either of the remaining two doors has a higher chance of containing the prize than the other? Choosing a door to keep closed at the beginning, then opening 98 of the remaining 99 doors would be no different than opening 98 empty doors initially, so why switch doors? If it makes no sense to switch doors when you're the only one randomly opening them, adding in a host makes no difference.
Now look at situation "b." You choose a door at random from a pool of 100. The host intentionally pulls out 98 of the remaining 99 doors which will be empty. In 99 out of 100 situations where you selected a bad door initially, the host is guaranteed to keep the remaining door closed because it's a winner. In 1 out of 100 situations where you had it right the first time, it didn't matter what door he left closed. In other words, it's because the host intentionally opened empty doors that the prize now has a 1% chance of being behind your initial door and a 99% chance of being behind the second.
[deleted] ยท 2 points ยท Posted at 20:06:49 on May 25, 2016 ยท (Permalink)*
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hadanish ยท 1 points ยท Posted at 02:55:02 on May 26, 2016 ยท (Permalink)
Shit man. I first came across this problem 6 years back. I never understood it, though I understood the words. Yours is the most clear, especially that put another way in the last paragraph. That was the missing link in my understanding. I read that extending the scenario to a large number of trials makes it easy to understand, but their way of explaining was not exactly clear to me. Your version of the 3 million trials was perfect. I am saving this comment. Don't delete it.
[deleted] ยท -6 points ยท Posted at 22:18:50 on May 25, 2016 ยท (Permalink)
It's not. It works the same no matter what the host is thinking at the time, or what knowledge they are running under.
jywn4679 ยท 2 points ยท Posted at 00:16:50 on May 26, 2016 ยท (Permalink)
If the host randomly picks a door, and happens to reveal a goat, then switching has a 50/50 chance of winning.
irishsultan ยท 1 points ยท Posted at 22:56:02 on May 25, 2016 ยท (Permalink)
No, it doesn't
[deleted] ยท 0 points ยท Posted at 12:02:02 on May 26, 2016 ยท (Permalink)
Yes, it does.
irishsultan ยท 1 points ยท Posted at 12:07:59 on May 26, 2016 ยท (Permalink)
Notice that in that case the host does think about which doors he opens, if he doesn't think about it at all (and therefore could open the winning door by accident) then that changes the outcome.
[deleted] ยท 0 points ยท Posted at 12:15:50 on May 26, 2016 ยท (Permalink)
Did you read the entire comment? I went over this. You must throw out all results where the randomly picked doors lead to opening the prize winning door on accident, in order to fulfill the conditions of the problem.
irishsultan ยท 1 points ยท Posted at 12:19:18 on May 26, 2016 ยท (Permalink)*
In the Monty Hall problem there are not accidental reveals of cars, so you have don't have to throw those out.
In the Monty Fall problem on the other hand you do have to throw them out, because they can occur but didn't.
edit: I meant cars instead of goats
[deleted] ยท 1 points ยท Posted at 12:20:44 on May 26, 2016 ยท (Permalink)
"goats" referring to bad/empty doors, correct?
The goats are not the prize.
irishsultan ยท 1 points ยท Posted at 12:23:21 on May 26, 2016 ยท (Permalink)
Ah no, I meant cars
[deleted] ยท -1 points ยท Posted at 12:31:26 on May 26, 2016 ยท (Permalink)*
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overconvergent ยท 2 points ยท Posted at 15:43:43 on May 26, 2016 ยท (Permalink)
Just look at a simulation. It's 50/50 if Monty randomly picks one of the two remaining doors.
Danno558 ยท 2 points ยท Posted at 18:13:09 on May 26, 2016 ยท (Permalink)*
Here is a list of all possible outcomes:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 2: Pick L1 - host falls and opens W.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 4: Pick L2 - host falls and opens W.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do you agree that these are literally all of the possibilities? Am I missing any? Or are any of these wrong?
Since we know that a goat door was revealed there are only 4 of the above scenarios that could have possibly happened:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do we disagree on this? Out of the original six scenarios these are the four possible positions that could possibly be true given that a goat door was revealed. Do you disagree with that? What other options could there be?
Of these 4 remaining options, 2 of them switching will result in a win, 2 of them switching will result in a loss. Switching is literally a 50/50 prospect.
If I am incorrect in any of my steps please tell me which step you think I made an error. Do you believe that the original 6 scenarios have different probabilities? Do you believe the 4 possible goat door reveals have a different probability? This is literally the probability tree for the scenario. These are the only possible options.
irishsultan ยท 1 points ยท Posted at 12:53:26 on May 26, 2016 ยท (Permalink)
No, that's simply not true, the state is different, in one case you know the host had to reveal a goat, in the other case you lack that knowledge. That knowledge means you are in a different state.
[deleted] ยท 0 points ยท Posted at 13:05:51 on May 26, 2016 ยท (Permalink)*
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irishsultan ยท 3 points ยท Posted at 13:23:13 on May 26, 2016 ยท (Permalink)
If I know that a coin is biased then it doesn't change the fact that there are still 2 possible outcomes, but it does change how I should bet on it.
Let's go through the different possibilities when the host knowingly reveals a goat:
Now let's see what happens when the host unknowingly opens a door, we can already deduce how likely each of the possible scenarios is:
Now we know that 3 did not happen, because a goat was revealed, but it's also clear that option 2 and option 3 were equally likely before the host opened a door, so if a goat is revealed there are two equally likely possibilities, either I chose a winning door (case 1) or I chose a losing door (case 2)
[deleted] ยท 0 points ยท Posted at 14:14:24 on May 26, 2016 ยท (Permalink)*
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irishsultan ยท 2 points ยท Posted at 14:38:14 on May 26, 2016 ยท (Permalink)
Please read the rest of that post (it in no way depends on my first sentence) and think about every step, try to identify the step where I make an error.
[deleted] ยท -1 points ยท Posted at 19:21:05 on May 26, 2016 ยท (Permalink)
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overconvergent ยท 1 points ยท Posted at 19:43:42 on May 26, 2016 ยท (Permalink)
Your response had nothing to do with irishsultan's post and it is clear you did not read it. irishsultan gave a correct explanation of why the probability in the "Monty Fall" problem is 1/2. You proceeded to give a somewhat incorrect explanation of the gambler's fallacy that had nothing to do with his post. Was a part of his explanation that you had trouble understanding? Have you looked at a computer simulation of this problem yet?
[deleted] ยท -1 points ยท Posted at 19:57:01 on May 26, 2016 ยท (Permalink)
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overconvergent ยท 3 points ยท Posted at 20:12:31 on May 26, 2016 ยท (Permalink)
Since you seem to think that Monty Hall and Monty Fall are identical, it might be time to look at that simulation again.
Their post was correct, so this doesn't matter. If they were incorrect, you should point out exactly where they were incorrect.
What "alternate interpretation" are you talking about?
"explicate"? "problematic theorizing"? This is why you should be in /r/iamverysmart.
I have taught undergrad probability multiple times. I don't need to read an intro stats book for laypeople.
overconvergent ยท 1 points ยท Posted at 17:36:47 on May 26, 2016 ยท (Permalink)
The gambler's fallacy refers to the situation when you already know the probability distribution and you still try to use past events to predict a future independent event. When you do not know the probability distribution, you absolutely should use the previous results to place your bet, since these past results give you information about what the probability might be.
If you know a coin is fair (50:50), then even if you see TTTTT, there is a 50:50 chance that the next coin will be H or T, and you should not use the prior events to guess what the next flip will be. But if you do not know that the coin is fair, then the fact that you just saw TTTTT increases the likelihood of the coin being biased, and you should use this information to guess that the next flip will likely be T.
In any case, this has absolutely nothing to do with the Monty Hall or Monty Fall problems. In the situation where Monty randomly opens one of the two remaining doors and happens to reveal a goat, there is no advantage in switching doors, as a simulation clearly shows.
[deleted] ยท 0 points ยท Posted at 19:48:50 on May 26, 2016 ยท (Permalink)
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overconvergent ยท 1 points ยท Posted at 19:56:09 on May 26, 2016 ยท (Permalink)
What the fuck are you talking about?
This is just word salad at this point.
Again, I have no idea what you are talking about. Are you claiming that if you performed this experiment in the real world, it would turn out differently than in the computer simulation?
Danno558 ยท 2 points ยท Posted at 19:58:28 on May 26, 2016 ยท (Permalink)
This guy belongs on /r/iamverysmart so badly... or he's just trolling at this point.
This has been explained like a dozen times at this point and he's never once pointed out where he thought the error in the math actually falls instead just throwing out this nonsense.
[deleted] ยท -1 points ยท Posted at 20:05:07 on May 26, 2016 ยท (Permalink)
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Danno558 ยท 2 points ยท Posted at 20:10:04 on May 26, 2016 ยท (Permalink)
Will you please just look at my breakdown? Just show me where the error of my logic is. This breakdown should show you without a shadow of a doubt that the Monty Fall is a 50/50 scenario... it literally is the only possible outcome.
Here is a list of all possible outcomes:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 2: Pick L1 - host falls and opens W.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 4: Pick L2 - host falls and opens W.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do you agree that these are literally all of the possibilities? Am I missing any? Or are any of these wrong?
Since we know that a goat door was revealed there are only 4 of the above scenarios that could have possibly happened:
Scenario 1: Pick L1 - host falls and opens L2 . W remains.
Scenario 3: Pick L2 - host falls and opens L1 . W remains.
Scenario 5: Pick W - host falls and opens L1 . L2 remains.
Scenario 6: Pick W - host falls and opens L2 . L1 remains.
Do we disagree on this? Out of the original six scenarios these are the four possible positions that could possibly be true given that a goat door was revealed. Do you disagree with that? What other options could there be?
Of these 4 remaining options, 2 of them switching will result in a win, 2 of them switching will result in a loss. Switching is literally a 50/50 prospect.
If I am incorrect in any of my steps please tell me which step you think I made an error. Do you believe that the original 6 scenarios have different probabilities? Do you believe the 4 possible goat door reveals have a different probability? This is literally the probability tree for the scenario. These are the only possible options.
overconvergent ยท 1 points ยท Posted at 20:07:44 on May 26, 2016 ยท (Permalink)
IT IS NOT IDENTICAL TO MONTY HALL! Just look at a computer simulation. In the Monty Hall problem, there is a 2/3 probability of winning if you switch. In the Monty Fall problem, there is a 1/2 probability of winning if you switch. Do you think the computer simulation is lying? That I'm just getting really, really, really lucky with the random number generator?
How arrogant do you have to be to still insist that you are correct after seeing the simulation?
[deleted] ยท -1 points ยท Posted at 20:12:03 on May 26, 2016 ยท (Permalink)
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overconvergent ยท 2 points ยท Posted at 20:13:14 on May 26, 2016 ยท (Permalink)
Please tell me why you don't trust a computer simulation. Also, this problem has nothing to do with statistics.
[deleted] ยท 0 points ยท Posted at 17:00:55 on May 27, 2016 ยท (Permalink)
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overconvergent ยท 1 points ยท Posted at 17:07:29 on May 27, 2016 ยท (Permalink)
I'm not using the program as a proof. I am well-aware of the mathematical proofs that the probability in the Monty Fall problem is 50%. I am using the computer simulation to try to convince you of the correct answer since you for some reason rejected irishsultan's correct proof.
Do you or do you not agree that the probability is 50% in the Monty Fall problem (where Monty randomly opens one of the two remaining doors and just happens to reveal a goat)? If you do not agree that the probability is 50%, what do you think is wrong with the simulation? Is there something wrong with the code?
Edit: Pynes is not a mathematician. His paper is incorrect and is not accepted by mathematicians.
[deleted] ยท 0 points ยท Posted at 17:14:40 on May 27, 2016 ยท (Permalink)*
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overconvergent ยท 1 points ยท Posted at 17:18:46 on May 27, 2016 ยท (Permalink)
There is no error. As I said, Pynes is not a mathematician. His paper was not reviewed by mathematicians. The paper did not appear in a math journal. His paper is incorrect, and no mathematician accepts his "solution." Unless you can find a problem with the simulation I gave you, the correct answer to the Monty Fall problem is 50%. If you believe the answer is not 50%, what makes you believe that you know more about this basic undergraduate probability problem than everyone with a PhD in the subject?
[deleted] ยท 1 points ยท Posted at 17:33:43 on May 27, 2016 ยท (Permalink)
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overconvergent ยท 1 points ยท Posted at 17:44:28 on May 27, 2016 ยท (Permalink)
Sure. You have already been given a proof that the answer is 50%. Then you were given a computer simulation providing experimental evidence. Those are the counter-arguments. In case you missed it, here is a proof written out in clear English:
You randomly pick one of the 3 doors. There is a 1/3 chance that you pick the door with the car, and a 2/3 chance that you don't.
Suppose you pick the door with the car - recall that this happens 1/3 of the times you play. Monty randomly picks one of the remaining doors and opens it. No matter which of the 2 doors he opens, he reveals a goat. So in 1/3 of all times that you play, you pick the car, and Monty reveals a goat.
Suppose you pick a door without a car - recall that this happens 2/3 of the times you play. Monty randomly picks one of the remaining doors and opens it. He has an equal probability of opening the door with the car and the door with a goat. So in 1/3 (2/3 * 1/2) of the times that you play, you pick a goat and Monty reveals a goat, and in 1/3 (2/3 * 1/2) of the times that you play, you pick a goat and Monty reveals a car.
To recap: In 1/3 of the games, you pick a car and the remaining unopened door is a goat. In 1/3 of the games, you pick a goat and the remaining unopened door is a car. In 1/3 of the games, you pick a goat and Monty accidentally opens the door with the car - we throw out these games because we are not in this situation in the Monty Fall problem. So we are in one of the first two cases, which both have a 1/3 chance of occurring. That is, they have an equal probability of occurring. There is a 50% chance that we are in each of those first two cases.
What about this do you not understand?
Also, you have still not answered my question: Why don't you believe the computer simulation? Is there an error in the code? Is the universe just playing a trick on us by giving us crazy random numbers millions of times in a row?
Danno558 ยท 1 points ยท Posted at 18:05:43 on May 27, 2016 ยท (Permalink)
If you read the paper, the whole thing is going under the assumption that the fall is just a "tease" reveal since there must be a second part to make the offer to switch.
He concludes that if there is actually a chance that Monty could accidentally reveal the prize door that the odds shift to 50/50. The paper is literally just showing that the Monty Hall problem is correct.
Danno558 ยท 1 points ยท Posted at 20:59:16 on May 26, 2016 ยท (Permalink)
You don't have to take his word for it. The very definition of the puzzle says that the host must knowingly reveal.
https://en.wikipedia.org/wiki/Monty_Hall_problem#Standard_assumptions
without the assumptions it falls apart. So you can continue to disagree with us, or assume that the people that developed the problem know what they are talking about.
[deleted] ยท -1 points ยท Posted at 16:55:33 on May 27, 2016 ยท (Permalink)
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Danno558 ยท 0 points ยท Posted at 17:18:24 on May 27, 2016 ยท (Permalink)*
Man, that paper literally says exactly what everyone is telling you. And I quote:
Emphasis mine.
God I love when people supply papers that disprove everything they are saying.
Link to paper https://www.ffri.hr/phil/casopis/abstracts/9_2_3.pdf
Edit: Just read the rest of the paper... apparently he actually believes what you do. I don't see how because it can be shown mathematically incorrect and simulations can show it's 50/50.
[deleted] ยท -1 points ยท Posted at 17:35:28 on May 27, 2016 ยท (Permalink)
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Danno558 ยท 1 points ยท Posted at 18:01:29 on May 27, 2016 ยท (Permalink)
Never mind, he does say it:
There you go. When there is a chance that the host reveals the prize door, the odds go to 50/50. All the rest of his paper are going under the assumption that Monty couldn't reveal the prize door only doing a "tease reveal" since there must be a second part for the switch. That's just cheating though and turns the fall back into the hall.
dryfire ยท 2 points ยท Posted at 21:25:52 on May 25, 2016 ยท (Permalink)*
Exactly! This should be much higher. I have had to correct so many people who miss that when stating the problem.
Monty has to have a 100% chance of choosing a wrong door AND the person playing the game has to know it in order for them to know they should switch doors. That really needs to be emphasized in the problem or else people are just spreading confusion.
Vozor ยท 1 points ยท Posted at 23:02:54 on May 25, 2016 ยท (Permalink)*
The opening of the doors is irrelevant info, which confuses the reader. You get to choose one door or 2 doors where one is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
[deleted] ยท 0 points ยท Posted at 22:07:54 on May 25, 2016 ยท (Permalink)
Obviously the host opens the door with no prize. It wouldn't work otherwise. That's why the detail is "left out".
Even if he opens the empty door on accident, the percentage is still the same. Intent has nothing to do with it. What the host is thinking at the time doesn't change mathematics.
overconvergent ยท 2 points ยท Posted at 23:19:45 on May 25, 2016 ยท (Permalink)
This is not true. The fact that he knowingly opens a door without a car is important. If you run this simulation many times with the host just randomly opening one of the two remaining doors, you will find that it does not matter if you switch.
[deleted] ยท 1 points ยท Posted at 12:01:57 on May 26, 2016 ยท (Permalink)
You are wrong. You are fundamentally misunderstanding why the Monty Hall problem works the way it does. I will try to explain, though I highly doubt this will convince you. Just try to stick with me on this.
To preface this, in order for the conditions of the Monty Hall problem to be met, the host MUST have revealed doors which don't have the prize behind them, because otherwise they'd reveal the door with the prize behind it and you'd know which door is the prize winner, defeating the entire purpose. So by the very structure of the game, this is the way it is.
What doesn't matter is the host being aware of what door is being picked. Lets imagine a scenario where you have a program running the Monty Hall Scenario, and after you chose a door, it randomly reveals the rest of the doors but yours and one other. For the sake of making this easy to understand, lets assume we're using 100 doors instead of just three. So you choose a door, and then the program randomly opens 98 doors. Any time the prize door is revealed, you have to throw that test out, so you'll probably be doing this for a while. From now on we'll assume that every test we do is a functioning one (where the doors randomly opened don't contain the prize door, which would invalidate the scenario).
Eventually you choose a door out of the hundred, the program randomly opens 98 other doors, and just your door and one other are left.
What was the chance of you picking the right door the first time? Obviously 1/100. So, unless you picked the right door (1% chance of that happening) the "host" opening all of the other doors has essentially shown you the correct answer 99% of the time. The host's knowledge has nothing to do with it.
Fundamentally, this is a choice between opening the one door you originally chose, or opening 99 doors.
Let's bump this up a notch. Imagine there are a billion doors. You pick one. The "host" opens 999999998 that aren't your door or the prize door. Unless you have more luck than Fortuna, you didn't pick the right door. At this level, we can just assume you didn't pick the right door. What this means is that the host has opened every door but yours and the prize door. What this means is that the host has just shown you exactly where the prize door is. It doesn't matter what the host is thinking. It doesn't matter if the host knows or not, or is even self aware. It works exactly the same.
Alright, now to return to the original scenario. You have three doors. You pick one. The host randomly opens a door with no prize behind it. You choose the wrong door 2/3rds of the time. 2/3rds of the time, the host has just revealed to you the correct door. If you switch, you will win 2/3rds of the time. Essentially what you're doing is choosing between choosing the one door you originally picked, or choosing two doors.
Intent doesn't randomly change fundamental arithmetic. I can't believe reddit is this bad at math. And I can't believe people are "helping" other people to "understand" how it works by getting them to accept it through the wrong means. Even if you come to the correct solution, if you got there with the wrong methods, you're still wrong. None of you actually understand why the Monty Hall problem works the way it does, even if you accept that it happens.
overconvergent ยท 2 points ยท Posted at 15:13:23 on May 26, 2016 ยท (Permalink)*
I'm a mathematician, you don't have to explain it to me. What you are missing is that it absolutely matters that the host opens a door without a car on purpose.
Unless the host knows which door has a car, he will accidentally open the door with the car almost every time. This is important.
Edit: Here is some Python code that I stole from someone that should show you that it's 50%.
[deleted] ยท 0 points ยท Posted at 17:10:29 on May 26, 2016 ยท (Permalink)*
And if he accidentally opens the door with the correct prize, then it stops being the Monty Hall problem. People are saying that the host must be aware of what door is the prize door in order for the math to work, I'm saying that the math works if the conditions are met (doors other than the picked door and prize door are opened) regardless of whether the "host" has any knowledge. The knowledge allows the problem to work, the knowledge does not change the probability.
Edit: Also
overconvergent ยท 2 points ยท Posted at 17:12:22 on May 26, 2016 ยท (Permalink)*
Please just look at a simulation and stop arguing.
The simulation I linked to accounts for this.
Danno558 ยท 1 points ยท Posted at 17:24:56 on May 26, 2016 ยท (Permalink)
So by your logic, if I asked the host to open the door and revealed a goat, instead of him "falling", then logically the last door suddenly jumps up in probability? That seriously doesn't make any sense... you may recognize this as the Deal or No Deal puzzle.
irishsultan ยท 1 points ยท Posted at 21:30:57 on May 26, 2016 ยท (Permalink)
Yes, that is correct. We've been pointing out the bit of the Monty Hall problem that makes it the Monty Hall problem. Many people are confused the first time they hear this problem and think it's 50/50, it's not. Part of the reason that people tend to think this is probably because their mental model of the problem doesn't actually match the actual problem, look at how many people responded with "now I get it", once it's pointed out that the knowledge of the host matters.
Without this knowledge you don't have the problem with it's standard set of assumptions, as a result you also get a different probability if the knowledge is lacking.
nighserenity ยท 25 points ยท Posted at 16:25:02 on May 25, 2016 ยท (Permalink)*
Sometimes it's difficult to explain in words, here is a table that shows all three scenarios when you pick a door:
Two out of three times when you switch you will win.
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:07:04 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
Drarak0702 ยท 0 points ยท Posted at 11:25:48 on May 26, 2016 ยท (Permalink)
You did put 2 answers in first case, it is
You pick 1 Prize in 1 Host opens 2 Do you win bu opening 3? No
AND
You pick 1 Prize in 1 Host opens 3 Do you win by oprning 2? No
Should go back to 1/2 and 1/2 then...
I am lost again :(
nighserenity ยท 1 points ยท Posted at 15:40:28 on May 26, 2016 ยท (Permalink)
I don't think you should be correcting the logic when you're not grasping it. It's important that the first scenario is an "or" not "and" because it makes the hosts choice irrelevant to the outcome. Just look at the left two columns and ignore the host for a minute. There are only three doors. If you switch, two out of three times you will get the prize.
Drarak0702 ยท 1 points ยท Posted at 18:05:03 on May 26, 2016 ยท (Permalink)
And finally i have undetstood it.
The choice of the host is simply there to allow you changing your choice to the opposite
If you pick the prize and change it you can only change to not picking the prize If you don't pick the prize you will end picking it If you change
This said, you have 1/3 chance to pick the prize and 2/3 to not pick it as first choice If you change it you will reverse the end result, so 1/3 of not winning and 2/3 to get the price.
Beer are always mind opening
Drarak0702 ยท 0 points ยท Posted at 16:28:10 on May 26, 2016 ยท (Permalink)
Was not meant as a correction;
I understand i am wrong, i was just explaining how do I see it
Still lost
Will drink a beer or two looking for wisdom
Oddtail ยท 12 points ยท Posted at 15:26:59 on May 25, 2016 ยท (Permalink)
The funny thing is, the Monty Hall problem's solution is so counterintuitive, a large number of people with scientific background get this one completely wrong. This included Nobel prize-winning physicists. In fact, some of them insisted on the wrong answer even after having been shown proof of the correct one.
L0d0vic0_Settembr1n1 ยท 8 points ยท Posted at 18:55:33 on May 25, 2016 ยท (Permalink)*
Scott Smith, Ph.D, is probably glad he has such a common name so he can always claim that it was another Scott Smith who wrote that condescending letter.
dryfire ยท 3 points ยท Posted at 21:19:39 on May 25, 2016 ยท (Permalink)
The solution is only counter intuitive because you introduce a non-random factor into the middle of a seemingly random problem (Monty has a 100% chance of choosing a wrong door). If Monty is choosing randomly, and he chooses a wrong door then the you are back to having a 50/50 chance with the remaining two doors.
Uhu_ThatsMyShit ยท 2 points ยท Posted at 18:06:40 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
Vozor ยท 1 points ยท Posted at 22:59:43 on May 25, 2016 ยท (Permalink)*
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door and 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
[deleted] ยท 2 points ยท Posted at 23:56:21 on May 25, 2016 ยท (Permalink)
[deleted]
Vozor ยท 1 points ยท Posted at 11:41:58 on May 26, 2016 ยท (Permalink)*
Not at all. It's put in a way that is confusing to the reader, but the second question isn't about a door. The first question asks you to choose one object at random. You have a tiny chance of choosing the correct one. The second round starts. You pick between two sets of objects, the one you picked, and the ones you didn't pick.
The host asks if you want to switch to the other set, with a guarantee of getting the prize - so long as it isn't in the door you already have. Your chance of getting the correct one is now inverse of the original chance, where the first set has 33% chance, the second set has 66% chance of having the prize.
[deleted] ยท 1 points ยท Posted at 15:42:01 on May 26, 2016 ยท (Permalink)
[deleted]
Vozor ยท 1 points ยท Posted at 16:50:23 on May 26, 2016 ยท (Permalink)*
I'm sure we are arguing different points, so I apologize for not making it clear.
The door having nothing behind it is important information. That is true. But the question is posed in a way to make the contestant think he is choosing between one door and one other door. Which would be 50/50 probability
What is happening with the second question is that the contestant is choosing from two sets:
A door
A door, plus another door known to be empty
The important concept is that the first question is not the same as the second question, because it switches from "pick one" to "pick one or multiple."
christina4409 ยท 1 points ยท Posted at 23:01:46 on May 25, 2016 ยท (Permalink)
For me it seems so weird that it's counterintuitive to most people. When I first heard the problem it was obvious to switch.
StephenGostkowskiFan ยท 21 points ยท Posted at 16:13:05 on May 25, 2016 ยท (Permalink)
I never believed this even after reading multiple explanations. It just seems completely wrong.
Finally one day I wrote a Java program to test it out and ran it ~10000 times. Sure as shit it works just like the explanations said.
ninjalink84 ยท 12 points ยท Posted at 16:44:56 on May 25, 2016 ยท (Permalink)
That's the beauty of math. It works whether or not you believe in it.
And I don't mean that to be condescending. The Monty Hall problem sounds completely insane without some deep thought as to why your intuition is wrong in this case. But regardless of intuition, it is demonstrably a 2/3 probability.
Tocoapuffs ยท 6 points ยท Posted at 20:47:46 on May 25, 2016 ยท (Permalink)
I promise the logic is more simple than writing a program to prove it.
Three doors and you choose randomly. There is a 2/3 chance of getting it wrong. The host opens a door that you didn't pick that is the wrong door. If you swap your answer you're now placing your bet that you got your initial guess wrong.
The key is noting that you picked before he opened the door and that he opens a wrong door. This forces the probably of 1/3 as an original guess.
Maybe don't read if you're still confused
Also if he had a chance of opening the correct door, your chances would actually stay the same... Well, if you were willing to swap your answer to the winning door.
StephenGostkowskiFan ยท 1 points ยท Posted at 01:25:52 on May 26, 2016 ยท (Permalink)
I cannot state enough that nothing anyone said would convince me until I tested it haha. It's pure ignorance, I get it, but I needed to see it for myself.
kcazllerraf ยท 2 points ยท Posted at 00:16:33 on May 26, 2016 ยท (Permalink)
Here's the simple chart for it, assume you choose the first door, and the host eliminates a door that both
does not have a car. And
you did not select.
Here are all of the possible outcomes:
as you can see, switching will result in a car 2 out of 3 times, while staying will result in a car 1 out of three times
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:06:50 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
shortcake_minus_cake ยท 28 points ยท Posted at 15:45:06 on May 25, 2016 ยท (Permalink)
Let's say door 1 was the correct door.
You have 1/3 chance of selecting door 1, and when you do, the host will show you one of the two wrong doors so you should stay with your door.
You have 1/3 chance of selecting door 2, and when you do, the host will show you the remaining wrong door so you should switch to the remaining correct door.
You have 1/3 chance of selecting door 3, and when you do, the host will show you the remaining wrong door so you should switch to the remaining correct door.
Notice that in 2 out of 3, scenarios, you should switch doors. Therefore switching doors gives you 66% chance of selecting the right door
guto8797 ยท 3 points ยท Posted at 16:26:19 on May 25, 2016 ยท (Permalink)
I was failing to understand this with all explanations, but yours actually made sense!
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:06:27 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
notapeacock ยท 4 points ยท Posted at 15:26:36 on May 25, 2016 ยท (Permalink)
I HATE THIS ONE. My husband and I have never had more frustrating conversations than about the Monty Hall problem.
roomandcoke ยท 13 points ยท Posted at 16:25:44 on May 25, 2016 ยท (Permalink)
Play the role of host and contestant. One if you hides an object under 3 cups, the other tries to guess where it is located.
Playing the show host really helps make you understand it. As the host, you'll find that the majority of the time (66% of the time), there's only one door you can open because the contestant has already selected one empty door, so you have to reveal the only other empty door.
bunnysnack ยท 8 points ยท Posted at 16:07:29 on May 25, 2016 ยท (Permalink)
Which one of you is on 50/50, and which of you is correct?
notapeacock ยท 2 points ยท Posted at 20:34:03 on May 25, 2016 ยท (Permalink)
I'd rather not say. :) The link /u/Uhu_ThatsMyShit posted was actually super helpful.
[deleted] ยท 5 points ยท Posted at 22:01:42 on May 25, 2016 ยท (Permalink)
So you were the 50/50.
rheus ยท 1 points ยท Posted at 16:35:38 on May 25, 2016 ยท (Permalink)
And why is the door open?
Uhu_ThatsMyShit ยท 2 points ยท Posted at 18:07:15 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
notapeacock ยท 2 points ยท Posted at 20:01:51 on May 25, 2016 ยท (Permalink)
That might be the first helpful thing anyone has said about this.
kcazllerraf ยท 1 points ยท Posted at 00:20:47 on May 26, 2016 ยท (Permalink)
Chart that shit!
Assume you choose the first door, and the host eliminates a door that both 1. does not have a car. and 2. you did not select. Here are all of the possible outcomes:
as you can see, switching will result in a car 2 out of 3 times, while staying will result in a car 1 out of three times
Vozor ยท 0 points ยท Posted at 23:04:42 on May 25, 2016 ยท (Permalink)
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door or 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
Uilamin ยท 0 points ยท Posted at 23:51:03 on May 25, 2016 ยท (Permalink)
The simple explanation is that the host does not change the probability of it NOT being the door you chose by revealing a door.
What you know. 3 doors and 1 has the prize. You choose one randomly with a 33% chance of being right. There is a 66% chance of one of the other two having it. You are then told that the 66% chance is not 2 doors, but actually one. Do you switch for a 66% chance to win?
Dutchwoman ยท 4 points ยท Posted at 15:43:17 on May 25, 2016 ยท (Permalink)
I actually wrote my math thesis paper on this and other math paradoxes! Cool to see it on Reddit today.
yakattack17 ยท 1 points ยท Posted at 19:22:22 on May 25, 2016 ยท (Permalink)
Could you share some other examples of common math paradoxes? These are super interesting!
Dutchwoman ยท 2 points ยท Posted at 20:03:57 on May 25, 2016 ยท (Permalink)
Sure! There is another famous one called the Achilles and the Tortoise. This is the idea of "will you ever catch up to an object?" Let's say you are running after a friend. You are faster than they are and you will eventually run to meet their position. However, in the time that you have run to meet heir position, your friend has since moved ahead a little. So now you must run to meet their new position. However, when you run to meet their new position, they've moved again. So when do you actually over take them? There are YouTube videos to visualize this one!
There is another called the Double Liar Paradox. This is a logic problem. On one side of a card the sentence says, "The sentence on the other side of this card is true." On the other side it says, "The sentence on the other side of this card is false." Can you figure out which is correct?
You can do a quick Google search to find more! Enjoy!
DonkeyTeeth2013 ยท 5 points ยท Posted at 16:16:38 on May 25, 2016 ยท (Permalink)
It's easier to think of when you increase the number of doors. If there are 100 doors, you have a 1% chance to pick the correct door first try. Then all the other doors are removed except yours and one other. Now it seems pretty obvious that there's a 1% chance you'll get it if you stay and a 99% chance you'll get it if you switch.
DeluxeTraffic ยท 2 points ยท Posted at 18:20:19 on May 25, 2016 ยท (Permalink)
I like to think of it using cards. Let's say you are given a deck of 52 cards and you have to pick out the Ace of Spades. So you pick a random card but before it is flipped over someone who knows which card is the Ace of Spades flips over 50 of the cards which aren't the Ace of Spades, leaving two cards, the one which you picked and the one that the person didn't flip over. The card you picked had a 1/52 chance of being the Ace of Spades but this new card has a much higher chance.
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:05:12 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
imp3r10 ยท 3 points ยท Posted at 15:59:36 on May 25, 2016 ยท (Permalink)
I believe this only works if the hosts has to open another door
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:05:03 on May 25, 2016 ยท (Permalink)
Correct!
Judo_John_Malone ยท 3 points ยท Posted at 16:29:56 on May 25, 2016 ยท (Permalink)
I've heard of this numerous times, but I still don't get it.
johnnymo1 ยท 10 points ยท Posted at 19:11:51 on May 25, 2016 ยท (Permalink)
Imagine the situation with a million doors instead. 999,999 have nothing, one has the prize. You pick one, and before revealing what's behind the door, the host opens 999,998 of the remaining doors, revealing nothing behind them. So now all that's left is your door and one other door.
And the question you have to ask is, "Even though there are only two doors left now, is there really any way the chance I chose the correct door in the beginning is 50%?"
[deleted] ยท 1 points ยท Posted at 21:49:40 on May 25, 2016 ยท (Permalink)*
[deleted]
johnnymo1 ยท 2 points ยท Posted at 22:00:35 on May 25, 2016 ยท (Permalink)
60% of the time it's right every time.
Vozor ยท 0 points ยท Posted at 23:05:55 on May 25, 2016 ยท (Permalink)
The opening of the doors is irrelevant info, which confuses the reader. You get to choose between one door and 2 doors, one of which is known to be empty.
The simple explanation is that you get to choose one door or all but one door!
PM_ME_CARROT ยท 4 points ยท Posted at 19:18:39 on May 25, 2016 ยท (Permalink)
Chance of prize behind each door: 1- 33% 2- 33% 3- 33%
You pick one -33% chance you got prize.
Host reveals WHAT HE KNOWS is incorrect door which had 0% of prize. This means the door that's left makes the rest of the total % chance of winning to your 33% door, which is 66%.
Judo_John_Malone ยท 1 points ยท Posted at 00:18:02 on May 26, 2016 ยท (Permalink)
That's beginning to make sense...
[deleted] ยท 7 points ยท Posted at 15:30:16 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 6 points ยท Posted at 16:04:20 on May 25, 2016 ยท (Permalink)*
[deleted]
CaptainSasquatch ยท 1 points ยท Posted at 20:08:07 on May 25, 2016 ยท (Permalink)
It is not relevant to the door you chose, but it is relevant to the remaining door.
[deleted] ยท 2 points ยท Posted at 15:42:38 on May 25, 2016 ยท (Permalink)
[deleted]
fnord_happy ยท 8 points ยท Posted at 16:32:12 on May 25, 2016 ยท (Permalink)
Monty Python
Uhu_ThatsMyShit ยท 1 points ยท Posted at 18:04:38 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j8oo9
Nuns_Love_Guns ยท 1 points ยท Posted at 15:54:48 on May 25, 2016 ยท (Permalink)
i am not a clever man at all but this makes perfect sense to me. like im really not clever at all and i dont understand why people dont get this
rheus ยท 1 points ยท Posted at 16:27:34 on May 25, 2016 ยท (Permalink)
Has there been an experiment on this?
aonome ยท 2 points ยท Posted at 16:53:41 on May 25, 2016 ยท (Permalink)
You can do it in 5 minutes by yourself.
House923 ยท 1 points ยท Posted at 17:05:52 on May 25, 2016 ยท (Permalink)
This is my favorite one for multiple reasons. It is a real brain wrinkler...but also...out of most of these it's the only one where I could see it coming in handy someday.
ChuckCarmichael ยท 1 points ยท Posted at 17:15:23 on May 25, 2016 ยท (Permalink)*
What always makes me mad is that when you bring up this problem on the internet you'll always have some people who'll tell you that this solution is wrong and that it's actually 50/50. It doesn't matter to them that the correct solution is accepted by basically every mathematician around the world, it doesn't matter that it's been proven time and time again that 50/50 is wrong. You can try to explain it as much as you want, they've already decided: they're right, and everybody else is wrong!
Tinderkilla ยท 1 points ยท Posted at 17:40:59 on May 25, 2016 ยท (Permalink)
I was just thinking about this the other day and was wondering if I was misremembering, but you explained it just as expected:)
[deleted] ยท 1 points ยท Posted at 17:50:32 on May 25, 2016 ยท (Permalink)
This was actually a problem in one of my programming courses. We had to write a Monty Hall problem simulator, then add a class to record the statistics after n simulations.
LerrisHarrington ยท 1 points ยท Posted at 17:54:04 on May 25, 2016 ยท (Permalink)
I love this because its so counter intuitive that even PHD's were crying bullshit when it was first proposed.
There is something about the way probability works here that humans just reject. The vast majority of people when given this problem will not switch their choice. Even ones who should know better.
Ron_Jeremy ยท 1 points ยท Posted at 17:56:45 on May 25, 2016 ยท (Permalink)
This one is easier to picture if there are say 100 doors. Still only one has the prize.
You pick one at random. It has a 1:100 chance of being the right one. Now the host eliminates all but two other doors. You now have your original pick and two more; one of which has the prize. Should you stay with your original that had a 1:100 chance or choose one of the new doors that has a 1:2 chance?
arkady48 ยท 1 points ยท Posted at 17:59:09 on May 25, 2016 ยท (Permalink)
For anyone that wants to see this theory tested, mythbusters did an episode and this was one of the myths/theories they tested. Check here
https://www.reddit.com/r/smyths/comments/1pa1pu/s09e21_wheel_of_mythfortune_streamline_edit/
Use the Vimeo link and the password is in the thread description. It's the first myth tested.
Jfrenchy ยท 1 points ยท Posted at 18:09:46 on May 25, 2016 ยท (Permalink)
This is the best explainer I've found on it and it's got James May! https://www.youtube.com/watch?v=tvODuUMLLgM
poobicus ยท 1 points ยท Posted at 18:16:40 on May 25, 2016 ยท (Permalink)
I hate this one. I'll never understand it.
BazeFook ยท 1 points ยท Posted at 18:17:42 on May 25, 2016 ยท (Permalink)*
This comment has been overwritten by an open source script to protect this user's privacy.
bmmy9f ยท 1 points ยท Posted at 18:18:33 on May 25, 2016 ยท (Permalink)*
This doesn't make any sense to me. Wouldn't the odds just change to 50/50 when the empty door is revealed and choosing the initial door would give you a 50% chance? How is this different then this example: You are asked to pick a number for a dice roll, you pick 3. It is then revealed that the dice is actually a 5 sided die. Is it in your best interest to change your pick given the option of 6 is removed?
The answer is no. Your odds were 1 in 6 and they have improved to 1 in 5, the initial odds do no matter since the final roll will be random. Much like the door choice does not matter because the door that is empty will be random. Can someone explain how this is wrong? I really am curious.
Edit: just wrote a program to simulate this, it's 66.6% wtf.
molrobocop ยท 1 points ยท Posted at 18:37:15 on May 25, 2016 ยท (Permalink)
And that's great trivia. But they've never done this on a game show that I can recall.
Kishana ยท 1 points ยท Posted at 18:37:51 on May 25, 2016 ยท (Permalink)
The easiest way to grok this one is to think of it as a logic problem rather than a probability problem.
When you swap doors, you're changing the win state. In order to "win", you have to have picked a losing door to begin with.
In other words, you had 2/3 chance to lose. Now you have a 2/3 chance to win.
savingprivatebrian15 ยท 1 points ยท Posted at 18:41:59 on May 25, 2016 ยท (Permalink)
I did a project for school on this in the 7th grade, even creating a small little game show setup with three doors and a prize that would slide behind each door, allowing for a rapid fire demonstration of the probability of winning when switching and sticking. After explaining why it works (and ending up with a mathematically sound result of like 13/20 wins when switching), he still didn't understand why it worked and gave me a fucking B for the project.
Granted this was for a science class, even though he said our projects could literally be on anything as long as we had some sort of scientific method involved, but still, the teacher should have been able to understand basic math and logic.
shmustache ยท 1 points ยท Posted at 18:42:26 on May 25, 2016 ยท (Permalink)
The only way I have ever been able to wrap my head around this is, when you initially make the pick, there is a 2/3 chance the correct answer is in the group of doors you didn't pick, and a 1/3 chance it's the one you originally pick. If you could, you would pick the two doors together over the one single door. Once the host eliminates a door, there is still a 2/3 chance that the prize is behind one of the doors in the pair. Switching doors isn't just picking between the last two doors, it's picking between a pair of two doors with a 2/3 chance of winning and one door with a 1/3 chance of winning.
luckytaurus ยท 1 points ยท Posted at 18:42:30 on May 25, 2016 ยท (Permalink)
I was thinking about this while watching Deal or No Deal last night. Some chick got all the way to the end with her case and 1 left held by the super sexy model, and she was soooo confident that her case had the million. But I was like, no it can't be because according to this logic (the one with the 3 doors as you explained) the likelihood that she chose the 1 million dollar case was 1/26 or however many there are in total, so when it comes down to it at the very end, you really SHOULD switch and 25/26 times you'll switch cases and win the million. Am I wrong in saying this? Maybe it's a different experiment.
btw, the girl on the show took the deal, gambling 500k is stupid.
CaptainSasquatch ยท 1 points ยท Posted at 20:11:08 on May 25, 2016 ยท (Permalink)
That's actually the "Monty Fall" variant. Since she was randomly revealing cases (she didn't know where the prize was) it was a 50/50 shot that her case and the remaining case would contain the million.
imgonnacallyouretard ยท 1 points ยท Posted at 18:44:26 on May 25, 2016 ยท (Permalink)
Correction: The other two doors have ducks and a goat behind them
PowerfulComputers ยท 1 points ยท Posted at 18:49:43 on May 25, 2016 ยท (Permalink)
I just tried it out:
epicfamilydecals ยท 1 points ยท Posted at 18:51:01 on May 25, 2016 ยท (Permalink)
No offense but I only believe this to be true because the Mythbusters told me so.
nightmareuki ยท 1 points ยท Posted at 19:03:55 on May 25, 2016 ยท (Permalink)
id argue about this just like i do about Cantor set
one_of_fire ยท 1 points ยท Posted at 19:16:00 on May 25, 2016 ยท (Permalink)
People like using the Monty Hall problem as an example of a non-intuitive statistics problem, but I like asking people the following. Suppose there is a family with two children. One of them is a girl who was born on a Tuesday. What is the probability that both children are girls? For a hint, yes, the Tuesday bit does matter, and it's not because of some obscure statistics of people being more likely to be born on certain days. Assume uniform distribution of girls and boys and births per day of the week.
cantdecide930408 ยท 1 points ยท Posted at 19:34:50 on May 25, 2016 ยท (Permalink)
Didn't they test this on mythbusters
amoore109 ยท 1 points ยท Posted at 19:42:09 on May 25, 2016 ยท (Permalink)
I really took this to heart in high school stats class.
"If I'm ever on a game show and this happens, do this!"
Still has yet to happen.
rybl ยท 1 points ยท Posted at 20:13:35 on May 25, 2016 ยท (Permalink)
Wrong. The other two doors contain goats. Check your math and try again.
Hongjohns ยท 1 points ยท Posted at 20:14:26 on May 25, 2016 ยท (Permalink)
I remember my thrusters had an episode on the Monty Hall problem. I remember they had a right which simulated the problem a couple hundred times with the result of winning when switching to be 33.333%. My memory isn't too strong so I don't know if the episode had such a strong result.
Et_tu__Brute ยท 1 points ยท Posted at 20:35:13 on May 25, 2016 ยท (Permalink)
someone want to run this as a program in R and see what the actual numbers are?
MyNameIsZaxer2 ยท 1 points ยท Posted at 20:36:36 on May 25, 2016 ยท (Permalink)
Another fun fact:
If, in the Monty Hall Problem, the game show host opens a random door, instead of using insider knowledge to select a door, your odds do default to 50/50. Think about it this way:
o=your door
x=host door
In all cases, the third doorcontains the car.
Possible outcomes: (host selects a door)
ox- 33%
xo- 33%
-xo 16.5%
x-o 16.5%
Possible outcomes: (door is random)
ox- 16.5%
xo- 16.5%
-xo 16.5%
x-o 16.5%
o-x 16.5% (car is revealed)
-ox 16.5% (car is revealed)
We can eliminate the bottom two outcomes, since we know a car wasn't revealed, but our odds become 50/50 to stay or swap.
This is why Deal or No Deal outcomes are 50/50 to swap your case at the end, because you were selecting randomly instead of exclusively removing non-million-dollar cases
your_mind_aches ยท 1 points ยท Posted at 20:53:23 on May 25, 2016 ยท (Permalink)
66.7%*
Also the other two doors don't have nothing, they have a Zonk. Get your facts right. :P
WarCriminalCat ยท 1 points ยท Posted at 21:05:43 on May 25, 2016 ยท (Permalink)
One of my relationships almost fell apart because of this problem. My boyfriend at the time just refused to believe me this is correct. We broke up like 4 months later for other reasons
cakedestroyer ยท 1 points ยท Posted at 21:06:56 on May 25, 2016 ยท (Permalink)
I've heard and read probably a hundred ways to explain this, but it was your last line that finally made it click.
Thank you so much.
atomiku121 ยท 1 points ยท Posted at 22:23:27 on May 25, 2016 ยท (Permalink)
When I was in highschool, my math teacher had us work it out by mapping out every possible outcome based on the variables of 'which door you picked' and 'which door protects the prize.' I found scenarios neither he nor the textbook accounted for and with my math it suggested the odds returned to 1/2, meaning it meant nothing if you switched.
My stats teacher had no response for it, and I've never found someone who can account for my results. I'm just waiting for some mathmetician to write a paper based on similar math to mine and get a nobel prize or something.
aonome ยท 1 points ยท Posted at 02:26:24 on May 26, 2016 ยท (Permalink)
Your math was wrong. If you write a program with all of the conditions applied and get 1/3 and 2/3 odds.
...
atomiku121 ยท 1 points ยท Posted at 04:45:08 on May 26, 2016 ยท (Permalink)
Oh, I never said it was right, just that I managed to come up with something my math teacher couldn't disprove. Says a lot more about my teacher than it does about me, haha.
Samisacunt ยท 1 points ยท Posted at 22:24:35 on May 25, 2016 ยท (Permalink)
"Always account for variable change"
Vozor ยท 1 points ยท Posted at 22:51:03 on May 25, 2016 ยท (Permalink)*
The opening of the doors is irrelevant info, which confuses the participant. The real trick is that you get to choose one door or all but one door!
RabidMortal ยท 1 points ยท Posted at 23:29:03 on May 25, 2016 ยท (Permalink)
The most intuitively obvious explanation I've heard is this: instead of 3 doors imagine 100 doors. You pick one, the host then opens 98 doors until just two remain. Then changing from your original pick seems obviously correct (at least to me)
tacojoeblow ยท 1 points ยท Posted at 00:01:37 on May 26, 2016 ยท (Permalink)
Good simulator here.
LittleLarryY ยท 1 points ยท Posted at 00:02:17 on May 26, 2016 ยท (Permalink)
We talk about this all the time at work. I wonder if anyone has gone through the old tapes and checked out the real life results.
FloatingR0ck ยท 1 points ยท Posted at 00:04:10 on May 26, 2016 ยท (Permalink)
Its funny seeing math I learned a month ago here .
[deleted] ยท 1 points ยท Posted at 01:00:41 on May 26, 2016 ยท (Permalink)
jesus christ. i read the wiki on this every time it comes up. and i always ask someone to explain how it isnt 50/50. and for years, i have never gotten an answer, just accepted it as a fact. and in that one line, you have made it click in my mind instantly.
darwin2500 ยท 1 points ยท Posted at 01:26:35 on May 26, 2016 ยท (Permalink)
The Monty Hall problem is actually pretty elementary; it's very counter-intuitive, which leads to a lot of confusion, but the math is really pretty straightforward.
If you really want to get confused, try out the Two Envelopes Problem.
THIS_MSG_IS_A_LIE ยท 1 points ยท Posted at 03:03:25 on May 26, 2016 ยท (Permalink)
Didn't a lot of people give Marilyn vos Savant grief over getting this right?
awe778 ยท 1 points ยท Posted at 04:14:58 on May 26, 2016 ยท (Permalink)
Because no sane game show host would open the door to the car, and that's why switching gets that value.
ktkps ยท 1 points ยท Posted at 05:02:35 on May 26, 2016 ยท (Permalink)
according to the top comment it is 63% - don't ask me how..I just go with that number here on for everything involving chance.
Spitfire2k6 ยท 1 points ยท Posted at 09:28:03 on May 26, 2016 ยท (Permalink)
But why does the "other" door get the 33.3 from the "opened" door? Why isn't it split between the "chosen" and the "other" door?
RichtersMask ยท 1 points ยท Posted at 10:01:59 on May 26, 2016 ยท (Permalink)
I like to explain it like this: What if there are a thousand doors? You pick one door at random, and then the gameshow host opens nine hundred and ninety eight doors, leaving one potentially correct, potentially wrong door and the one you chose, every other door is confirmed wrong. Do you switch?
Yes, because your chance was 1/1000 of getting it right with the door you have and, all things being equal, it remains so. Switching increases your chances to 1/2.
sd522527 ยท 0 points ยท Posted at 15:42:42 on May 25, 2016 ยท (Permalink)*
This is a common misconception. In the long term, yes, the odds are 66.6%. However, in this particular instance, without knowing the host's rationale for choosing the door he did, it could be anywhere from 50% to 100%. Still, it never hurts to switch (in the usual version of the game).
Edit: let me show you.
Suppose the host always opens the highest numbered door he can (he might be blocked because you chose it, or because it hides the prize). You pick door 1, he opens door 3. Your chance of winning if you switch? 50%.
Now suppose the host favors the lowest numbered door. Once again, you pick 1, he opens 3. Your chance of winning if you switch? 100%.
Lost4468 ยท 1 points ยท Posted at 16:27:36 on May 25, 2016 ยท (Permalink)
There isn't a rationale, the host always opens a door with nothing behind it. If you picked the correct one it doesn't matter which door the host opens because they're identical. If you didn't then the host only has the option of opening one of them.
sd522527 ยท 1 points ยท Posted at 17:32:38 on May 25, 2016 ยท (Permalink)
Incorrect, see my edit. You are ignoring key information for the particular game you are currently playing: the door you chose, and the door the host chose.
Lost4468 ยท 1 points ยท Posted at 17:46:04 on May 25, 2016 ยท (Permalink)
I see what you're saying, but the problem doesn't cover which door the host will pick when there's two with nothing behind them, so the information is not available to the player.
sd522527 ยท 0 points ยท Posted at 17:58:12 on May 25, 2016 ยท (Permalink)
No my version completely covers that. The subtlety is in saying "you have a 66% chance of winning if you switch!" That is not entirely accurate. Really, if you played the game 1000 times, you'd win by switching 666 times. But for a particular game, that percentage can vary quite a bit based on the host's strategy.
Lost4468 ยท 1 points ยท Posted at 18:06:14 on May 25, 2016 ยท (Permalink)
How does it? It's a 2/3 chance every time if you switch. If I write a program to simulate this and I run it several thousand times and everyone always switches then 2/3 of the plays will win, if I make them all stay then 1/3 will win.
sd522527 ยท 1 points ยท Posted at 19:08:26 on May 25, 2016 ยท (Permalink)
That is not the same as talking about the odds of winning A SPECIFIC GAME. These are two different probabilities. Think about it this way: in my second example of my edit, FOR THAT SPECIFIC GAME, the odds of winning when switching are 100%. So, if you had a thing where you ALWAYS picked door 1, and the game producers had a thing where the ALWAYS put the prize behind door 2, then in that universe, SWITCHING WINS 100% OF THE TIME. When you say "2/3 chance of winning", you are implicitly assuming that each configuration of door choice and prize door is equally likely. Again, a valid assumption, but it DOES matter.
Lost4468 ยท 2 points ยท Posted at 19:16:09 on May 25, 2016 ยท (Permalink)
But you've changed the rules here, you added in new behavior the host has which is not included in the initial problem. You're saying there's possible scenarios where the player can know that switching will give them a 100% chance of winning right? But they could only possibly know that if they had the added benefit of knowing those secret rules on how the host picks when confronted with two empty doors.
sd522527 ยท 1 points ยท Posted at 20:40:26 on May 25, 2016 ยท (Permalink)
Whether the player knows the host's strategy or not does not change the probability. If the host had that strategy, and the player swtiched, they win 100% of the time, regardless.
Lost4468 ยท 2 points ยท Posted at 22:47:33 on May 25, 2016 ยท (Permalink)
Ok I just understood the point of view you're coming at this problem from. I've not seen this type of view represented before in the Monty Hall problem and it's very interesting.
Most people assume that the player is whom we're calculating the probability for, and that the host chooses randomly when both doors are identical. You're instead assuming that the host has some fixed pattern by which it chooses the door to open, which of course reduces and increases the chances of the player.
I've not encountered your viewpoint of the problem before, it's strange because both your viewpoint and the normal viewpoint both lead to the same results but very few people pickup your point of view. I think you've picked up on a psychological viewpoint of the Monty Hall problem that hasn't really been explored.
sd522527 ยท 1 points ยท Posted at 00:55:17 on May 26, 2016 ยท (Permalink)
It is actually detailed quite nicely on the Wikipedia page for this problem. The thing is, this is a poorly defined problem, so there are these implicit assumptions lurking everywhere. Thanks for the stimulating convo!
aonome ยท 1 points ยท Posted at 18:12:11 on May 25, 2016 ยท (Permalink)
Probability of winning and percentage of wins are equivalent here. The host's strategy is to remove an empty door which has not been chosen by the player, that's all there is to it.
sd522527 ยท 0 points ยท Posted at 19:03:15 on May 25, 2016 ยท (Permalink)
No, it's not. Please see my edit, which shows that FOR A SPECIFIC GAME, the host's strategy does matter. Please see the Wikipedia article on this problem if you're having trouble understanding the (subtle) difference; it is explained in great depth there.
aonome ยท 1 points ยท Posted at 19:07:24 on May 25, 2016 ยท (Permalink)
I don't know what to tell you mate, I know the relationship between probability and percentage of outcome better than you do.
sd522527 ยท 0 points ยท Posted at 20:42:07 on May 25, 2016 ยท (Permalink)
I'm sorry you cannot carry on an intellectual conversation. If you'd like to give explicit details about my construction that don't work, that's fine. Hiding behind boasts just wastes my time.
discobob1 ยท 0 points ยท Posted at 16:28:43 on May 25, 2016 ยท (Permalink)
Thank you! I had this exact argument with my Philosophy class in college. Everyone in the class thought I was a moron for arguing that your choice doesn't really matter, in the context of the game. You have no idea WHY the host opened that door. Furthermore, your original choice is 33% accurate. Your second choice is 50% accurate. In other words, you're entirely justified, mathematically in sticking with your door because your second choice is a complete toss-up. If you play the game 30 times? Sure, pick the second door every time. If you play it only once? It's a toss up. The 66% chance for switching doors only comes into play as that 50% second choice gets averaged over time against the 33% first choice. People are confusing averages with one-at-a-time decisions. Averages are only useful for understanding populations, not random draws.
aonome ยท 1 points ยท Posted at 16:55:49 on May 25, 2016 ยท (Permalink)
What? It does matter. You should always pick the most likely door to be correct.
discobob1 ยท 1 points ยท Posted at 17:08:48 on May 25, 2016 ยท (Permalink)*
But the "most likely" to be correct only has meaning when you average many 1st choices and 2nd choices together and only if you make some false assumptions about the nature of the game. In any particular instance, your second choice is 50% accurate whether you stay with your first door or switch. The game isn't really "pick between 3 doors". The game is really "pick between 2 doors." It only appears to be a choice between 3 doors because the host has presented it that way. You do not have a 33% chance of picking the correct door on the first try. You have a 50% chance, because one of the empty doors was effectively off-limits, anyways. You appear to have a choice between 3 doors, but really you only have a choice between the 2 doors that the host does NOT pick. It just so happens that he reveals this fact later. The reason that simulations show a doubling of accuracy for switching is because they make the false assumption that you could choose any of the 3 doors. In reality, you can only choose one of two doors. The host simply changes which door he was going to make "off-limits" based on which door you pick, after the fact.
aonome ยท 2 points ยท Posted at 17:12:10 on May 25, 2016 ยท (Permalink)
Er, the average result is determined by the probability, not the other way around. This is a maths problem, not a scientific experiment.
discobob1 ยท 1 points ยท Posted at 17:26:38 on May 25, 2016 ยท (Permalink)
But the game isn't about your first choice. It's about your second choice. The second choice is always 50/50. The first choice is meaningless.
aonome ยท 2 points ยท Posted at 17:43:59 on May 25, 2016 ยท (Permalink)
No, the second choice is 33/67. That's the whole point of the Monty hall problem.
discobob1 ยท 1 points ยท Posted at 17:53:15 on May 25, 2016 ยท (Permalink)
But it's not. You're assuming that you have a choice between 3 doors. You really only have a choice between 2 doors. Simulations that seek to prove your stance make the false assumption that there are 3 doors, when in reality there are only 2.
aonome ยท 2 points ยท Posted at 18:02:58 on May 25, 2016 ยท (Permalink)
No, that's not how it works. You pick a door and have a third chance of being right. The chance that the money is behind any other door is 2/3.
Now, the host knows which door the money is behind. He purposefully eliminates one of the other two doors which is empty. He eliminated it because it was empty. In other words, whether or not the money is in the 1/3 chance set of doors or 2/3 chance set of doors is irrelevant, an empty door will always be eliminated from the 2/3 set.
This means that the 2/3 set only has one door but the probability has not changed. Again, I will say it so you definitely understand. The host deliberately removed a door that was empty and had not picked and the player was made aware of he fact that these two criteria were the reason for it being removed.
This is why you should switch.
If you do the math you should reach the conclusion that you should switch even though the end result is two doors to choose from. The mathematicians are right and you are wrong.
discobob1 ยท 1 points ยท Posted at 18:14:24 on May 25, 2016 ยท (Permalink)
They're right because they are posing the wrong problem. They are making the assumption that you have a choice between 3 doors. In fact, you only have a choice between 2 doors. You already know beforehand that the host will eliminate one of the empty doors, whether or not you have chosen the door correctly. Doing it before or after your first choice is irrelevant. What if the host eliminated one of the empty doors before your first choice, and then asked you to choose a door? And then he gave you the option to change your mind. Do you switch? It doesn't matter. Either way you have a 50% chance of being right. This is what is happening with 3 doors only the host decides, after your first choice, which door to eliminate, instead of before.
aonome ยท 1 points ยท Posted at 18:23:17 on May 25, 2016 ยท (Permalink)
You're describing two different scenarios. Yes, after the host eliminates the door you have two choices. The key is that you have information because the door was eliminated while you had locked in a door and so if it is empty he can't eliminate it. If you don't pick a door first this is not case and the probability would be different.
f you run a simulation that does exactly what the Monty hall problem describes steo-by-step you will get the result the mathematicians predict. The whole scenario can be done mathematically and it is demonstrable with rigorous proof.
The fact that you think mathematicians who spend every day of their life working to further their understanding of this field are thinking about it wrong is quite funny though.
discobob1 ยท 1 points ยท Posted at 18:58:16 on May 25, 2016 ยท (Permalink)
But it's only the illusion of new information. It's not really new information. You already knew beforehand that he would eliminate an empty door, so your first choice is really between the correct door and one of two empty doors. The reason the simulations behave as you describe is that they feed it the false assumption that you are choosing between three doors. You are not choosing between three doors. You are choosing between two doors.
aonome ยท 1 points ยท Posted at 19:04:39 on May 25, 2016 ยท (Permalink)
No, you are completely wrong. You don't understand what's going on here, i've explained it to you and you are relying in your intuition instead of math.
Please answer this though: do you honestly think that mathematicians that spend their lives studying these paradoxes are mistaken and that you, someone who definitely does not have a background in mathematics, are correct?
Rynyl ยท 894 points ยท Posted at 14:14:33 on May 25, 2016 ยท (Permalink)*
Graham's number
iswas once the largest number used constructively in a math paper. It's literally unimaginably large.As explained by Ron Graham himself:
The Use of Graham's Number. Don't worry, it's surprisingly intuitive.
The magnitude of Graham's Number
As explained by Day9 (because it's really entertaining)
EDIT: Somehow, larger numbers have been used constructively. That blows my mind.
EDIT2: For those who hate watching videos and would rather read
morhe ยท 753 points ยท Posted at 14:25:00 on May 25, 2016 ยท (Permalink)
"Grahamโs Number is a number so big that it would literally collapse your head into a black hole were you fully able to comprehend it. And thatโs not hyperbole โ the informational content of Grahamโs Number is so astronomically large that it exceeds the maximum amount of entropy that could be stored in a brain sized piece of space"
quote stolen from somewhere on the internets
[deleted] ยท 114 points ยท Posted at 15:25:39 on May 25, 2016 ยท (Permalink)
Although true, this fact really really under-eggs it. 3โโโ3 is more than enough to black hole your brain even if your brain were the size of the universe and only contained information. Yet 3โโโ3 is NOTHING compared to 3โโโโ3, which is ABSOLUTELY NOTHING compared to 3โโโโโ3. Don't get me started on 3โโโโโโ3.....
...A long time passes...
...which is pretty much zero compared to Graham's number
marvin ยท 38 points ยท Posted at 17:57:51 on May 25, 2016 ยท (Permalink)
Graham's number to the power of Graham's number is bigger, though. Which is still smaller than the weight of OP's mom.
SMHeenan ยท 19 points ยท Posted at 21:04:44 on May 25, 2016 ยท (Permalink)
It's always so reassuring that, even in a thread dedicated to mathematical theories, it all can be brought back to making fun of OP's mom.
TheOneTrueTrench ยท 1 points ยท Posted at 14:28:52 on May 26, 2016 ยท (Permalink)
Pfft... amateur.
Let ฮ = Graham's Number
ฮ โ ฮ โ ฮ โ ฮ
marvin ยท 5 points ยท Posted at 16:40:09 on May 26, 2016 ยท (Permalink)
Not impressed, this is literally in the bottom percentile of all natural numbers
TheOneTrueTrench ยท 2 points ยท Posted at 18:08:31 on May 26, 2016 ยท (Permalink)
ฮ โ ฮ โ ฮ โ ฮ โ 1
bebewow ยท 6 points ยท Posted at 21:07:35 on May 25, 2016 ยท (Permalink)
What does "โ" mean?
teleksterling ยท 10 points ยท Posted at 21:43:25 on May 25, 2016 ยท (Permalink)
It's Knuth notation for recursive exponentiation. 2โ3 = 222 2โโ3 = a stack of twos with 2โ3 twos in it!
MadlifeIsGod ยท 2 points ยท Posted at 18:28:58 on May 31, 2016 ยท (Permalink)
Not quite, 2โ3 is 23, 2โโ3 is 2โ2โ2, which is 222 .
nโโm is nโnโnโ...โn, with m ns. You're just off by a factor of 1 arrow in your description.
teleksterling ยท 1 points ยท Posted at 21:47:10 on May 31, 2016 ยท (Permalink)
Ah, thanks! I wasn't 100% sure, but wanted to have a go from memory.
Xx_Benis_xX ยท 6 points ยท Posted at 01:35:36 on May 26, 2016 ยท (Permalink)
I think the best intuitive explanation of Graham's number is this: if you had Graham's number of doors, then you would have quite a few doors.
RoadieRich ยท 4 points ยท Posted at 03:16:12 on May 26, 2016 ยท (Permalink)
3โโโ3 is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to numbers the magnitude of 3โโโ3.
Emphursis ยท 2 points ยท Posted at 08:25:47 on May 26, 2016 ยท (Permalink)
What if it was 9's in place of all the 3's? Would I just be astronomically larger?
MadlifeIsGod ยท 2 points ยท Posted at 06:46:46 on May 31, 2016 ยท (Permalink)
I know this is late, but yes it would be absolutely huge. 3โ3 is 27, 3โโ3 is 3โ3โ3, or 3โ27, or 7.6 trillion. 9โ9 is 387 million, so 9โโ9 is 9โ9โ9, or 9โ387 million. I can't get a good answer for what that is, but the number has 369 million digits in it, compared to 13 digits of 3โโ3. Add in another 2 levels and you've got an answer that's just too immensely large to imagine. And that's just 3โโโโ3, which is g0. If you followed through all the way to g64, or Graham's number, using 9s, you can't even imagine how much larger it would be.
jesset77 ยท 2 points ยท Posted at 23:28:43 on May 25, 2016 ยท (Permalink)
I often wonder what size a black hole could get to before DE expansive pressure prevented it from getting any larger. I used to think it was "a hubble volume", but it turns out that the hubble volume is already influenced by gravity so the actual answer would be much larger than that.
But I can't get anybody better at math than me to run this question through the Friedman equations and poop out an answer. xD
[deleted] ยท 2 points ยท Posted at 14:59:11 on May 26, 2016 ยท (Permalink)
Why is this getting downvoted. That's a really cool thought
Supersnazz ยท 326 points ยท Posted at 15:37:25 on May 25, 2016 ยท (Permalink)
What's interesting is that nearly all positive numbers are much bigger than Grahams Number.
karlexceed ยท 23 points ยท Posted at 17:02:54 on May 25, 2016 ยท (Permalink)
Oh you!
[deleted] ยท 48 points ยท Posted at 17:06:39 on May 25, 2016 ยท (Permalink)
there's an infinite amount of positive numbers bigger than graham's number
Dranthe ยท 28 points ยท Posted at 18:51:37 on May 25, 2016 ยท (Permalink)
There's an infinite number of positive numbers between 0 and 1. What's your point?
lazylollylicker ยท 38 points ยท Posted at 19:12:11 on May 25, 2016 ยท (Permalink)
there are infinitely more real numbers in the interval <0,1> then there are positive integers and I love it
[deleted] ยท 3 points ยท Posted at 19:57:26 on May 25, 2016 ยท (Permalink)
How can that be the case
voidsoul22 ยท 24 points ยท Posted at 20:03:35 on May 25, 2016 ยท (Permalink)
You can list the positive numbers: 1, 2, 3, 4,...
You cannot list all the numbers in the interval <0,1>. All these numbers have "0." followed by whatever string of digits (almost all infinite). If you tried to list all those numbers in order (like we did the positive integers), I could foil your dastardly scheme and come up with one you didn't list. I would just pick the first decimal place after the point to be different than the first decimal place of the first number you listed, pick a second decimal place different from that of your second number, pick a different third than your third, and so on forever. My number is not equal to any number on your list, which means your list wasn't complete to begin with, which means the number of numbers in that interval is "uncountable". That is a whole 'nother magnitude of infinity than the countable positive integers.
[deleted] ยท 2 points ยท Posted at 20:19:55 on May 25, 2016 ยท (Permalink)
If we both sat down and started taking turns listing positive numbers, you between 0 and 1 and me positive integers, neither of us would ever finish because both are infinite. I know for every single subsequent positive integer there's another infinite group of positive decimals, but that doesn't mean there are more positive decimals than positive integers because there will always be another positive integer
Mrfish31 ยท 37 points ยท Posted at 20:27:19 on May 25, 2016 ยท (Permalink)
It does though. Some infinities have been proven to be larger than others, the infinity of decimals being larger than the infinity of integers.
It may sound fucky, and that's because it is, but it is absolutely correct.
Supersting ยท 4 points ยท Posted at 22:45:25 on May 25, 2016 ยท (Permalink)
It all sounds fine if you talk about cardinalities, or bijections, instead of sizes of infinity. It all gets weird if you just want to say that one inifinity is bigger than another.
joatmon-snoo ยท 4 points ยท Posted at 04:42:04 on May 26, 2016 ยท (Permalink)
As my set theory professor once said when someone wrote โ on the board: "we're civilized people here, we use well-defined infinities!"
PersonUsingAComputer ยท 3 points ยท Posted at 03:15:35 on May 26, 2016 ยท (Permalink)
The whole point of cardinality is to generalize the notion of "size" to infinite sets. It's not the only possible way to do so, but it's a common and perfectly valid method of talking about the size of a set.
Supersting ยท 1 points ยท Posted at 15:54:41 on May 26, 2016 ยท (Permalink)
I don't argue there - but whilst one infinite set can be bigger than another, I find it's still odd to talk about an infinity being bigger than another. Sets being concrete, infinity just a concept.
dlgn13 ยท 0 points ยท Posted at 21:20:45 on May 26, 2016 ยท (Permalink)
Yep. And you can also talk about measure, but the measure of a countable set is 0, so the reals are still bigger.
[deleted] ยท 15 points ยท Posted at 20:37:39 on May 25, 2016 ยท (Permalink)
Put it this way, for every integer you write (1, 2, 3, 4, ...), I'll get write 1 over that number so: 1/2, 1/3, 1/4 etc
But I also get a while bunch of numbers in between those )eg 2/3, 3/4, etc
Thus I can match every number you get with a number I get, but I get an infinite among more in the middle of each of mine that you don't.
voidsoul22 ยท 8 points ยท Posted at 21:48:08 on May 25, 2016 ยท (Permalink)
Actually, you are describing (positive) rational numbers, and the rational numbers are in a one-to-one correspondence with the positive integers using what's called the "diagonal method". Basically, rational numbers are x/y, where x and y are integers. List all the positive integers in a row, and repeat them in a column. Each intersecting cell is a combination of those headers, and corresponds to a rational number. You can zigzag in such a way that you will hit every rational number, eventually, and you can even calculate when you'd hit a given one first. I don't want to type up something to show you, but you can google it. =P
TLDR: (Positive) Integers are countable. (Positive) Rational numbers are also countable, via the diagonal method. Real numbers in any interval, however, are NOT countable.
[deleted] ยท 1 points ยท Posted at 10:26:59 on May 26, 2016 ยท (Permalink)
In fact, you can include imaginary and negative rational numbers, and draw it so that you have 4 quadrants, one positive real, one negative real, one positive imaginary, one negative imaginary, and spiral out from the centre, hitting every rational number.
thespike323 ยท 2 points ยท Posted at 20:57:18 on May 25, 2016 ยท (Permalink)
That's a brilliant way to explain it, so much simpler than diagonalization. Uncountable vs. countable infinities was always one of my favorite date topics, I'm gonna use this to discuss it from now on.
assdflkj ยท 6 points ยท Posted at 21:45:55 on May 25, 2016 ยท (Permalink)
This still doesn't show the difference between countable and uncountable sets. The same argument applies for the set of rational numbers between 0 and 1, which is countable.
Asterix1806 ยท 3 points ยท Posted at 22:52:23 on May 25, 2016 ยท (Permalink)*
Okay, here's the actual definition of cardinality for you: two sets are of equal cardinality if there exists a bijection between them. For finite sets cardinality is the same thing as the number of its elements. For infinite sets not so much.
A bijection in turn is a function that relates each object of the set of inputs to a unique object in the set of outputs, and each element in the set of outputs is related to an input. In other words, a bijection pairs the objects of two sets together.
Examples of bijections from the reals to the reals are f(x)=x, g(x)=xยณ, or h(x)=1/x when xโ 0 and h(x)=0 when x=0.
A bijection from the integers to integers divisible by two would be n(x)=2x. As this last example demonstrates, true subsets can have the same cardinality as the base set if both sets are infinitely big.
A countably infinite set is one whose cardinality is equal to that of the integers. Whole numbers are countably infinite. So are fractions. Real numbers are not, though.
One characteristic of a countably infinite set, S, is that for all its elements, x, there exists an integer, n, so that a subset of S with n first objects of it will include x.
The point of Cantor's diagonality proof is to show that it's possible to create a real number whose very definition is to not be included in the subset of n first objects for any integer n.
For fractions this kind of infinite goal post moving is of course not possible, as a fraction needs to be expressible as a division of two finite integers.
However, real numbers don't have this restriction. In fact, the completeness axiom gives real numbers freedom to be pretty much whatever they want as long as they are finite in size. This means that it is possible to make a real number that has infinitely many carefully chosen integers to screw up a bijection.
In short, Cantor's diagonal proof works because real numbers can be created using truly infinite goal post moving , and that in turn is possible because of the unique property of the real numbers known as the completeness axiom.
voidsoul22 ยท 2 points ยท Posted at 20:40:05 on May 25, 2016 ยท (Permalink)
It's not so much about whether or not you can create a list. If you could write one integer a second forever (slow at the beginning, incredibly fast once you get up a few digits), you could not only guarantee writing another particular positive integer, you could actually tell me precisely when and where on the list it would show up. There is no such situation with intervals though - as I described, I could easily come up with a number guaranteed to be not on your list, even if you somehow wound up with a complete infinite list.
HughManatee ยท 2 points ยท Posted at 01:49:17 on May 26, 2016 ยท (Permalink)
There's a difference between countably infinite and uncountably infinite. It's confusing and non-intuitive, but that's the way it is.
lazylollylicker ยท 1 points ยท Posted at 22:23:58 on May 25, 2016 ยท (Permalink)
I see where you are comming from, I didn't understand this at all at first too.
the clue is that if you list ALL numbers between 0 and 1 and ALL positive integers, you can still always make a NEW number between 0 and 1, by taking the first deciman of the first number you listed, changing it, and using it as the first decimal of you new number. then proceed with the 2nd decimal, that way you create a new number between 0 and 1 that is different from ALL earlier listed number and thus can't be matched with one of the listed positive integers. then you repeat this process infinitely many times and you have infinitely more numbers between 0 and 1 then positive integers.
maybe this will help: first you list both both the infinite sets and then they are equally big, but then you can make one infinity bigger, while the other infinity can't be made larger.
also YouTube is a great place to learn if you're interested
Supersting ยท 2 points ยท Posted at 22:49:51 on May 25, 2016 ยท (Permalink)
The diagonalisation is correct, but I'm not sure about the hint. You're not making an infinity larger, you're just proving the impossibility of a method to list all real numbers (you list them all, construct one not in the list, so you didn't list them all, but we could list all of the integers if we wanted).
ZigZalgo ยท 1 points ยท Posted at 23:10:08 on May 25, 2016 ยท (Permalink)
When dealing with infinity sizes you do something called mapping. If, for every number in a set, it can be uniquely mapped to another number in another set (and vice-versa), then both sets are said to be the same size (in math it's called being one-to-one I believe) Example: the sets (3,4,5) and (6,7,8). 3 maps to 5 (and vice versa), 4 to 7 and 5 to 8. These sets have the same size.
Now we extend this to the negative integers as one set, and the positive AND negative integers for the other set. We say that every integer in the negative set can be expressed as an equation on the set of all positive and negative integers (I forget the actual mapping equation). Thus both sets have the same size.
When we look at the set of real numbers between 0-1 and all positive integers, there is now way to map them in both directions so one must be larger than the other. In this case, it is the one in which one element from one set has to map to multiple elements in the other set, which is the integers to real numbers.
Shitty explanation I know, but I hope this helps.
decideonanamelater ยท 1 points ยท Posted at 23:44:39 on May 25, 2016 ยท (Permalink)
So what you're talking about is the intuitive concept of how numerous something is, and what he's talking about is the mathematical concept, where an uncountable infinity "has" more numbers in it than a countable infinity. Basically there will never be a perfect metaphor to describe it, but ex: you can create a function that turns numbers in the interval (0,1] into any natural number (the function 1/x works for this), yet you can't write a function that turns natural numbers into the numbers in (0,1] (say you wrote it as 1/x again, any value such as 1/(1.5) would fail, and changing the number in the numerator just switches which values do and don't fail)
christina4409 ยท 1 points ยท Posted at 23:19:38 on May 25, 2016 ยท (Permalink)
Why not just list out all the number you would do and divide them all by infinity? It's not in decimal notation, so you can't do that trick, but you get all the numbers just as well
alanisacowboykiller ยท 1 points ยท Posted at 22:36:50 on May 25, 2016 ยท (Permalink)
I think a more intuitive explanation of what this means would be that while you can theoretically describe any arbitrary integer with a finite sequence of symbols, you cannot do this for arbitrary real numbers between 0 and 1.
If you think of any positive integer, you could theoretically write down its decimal representation. If you think of any rational number, you can write it down as a fraction. We even have ways of representing many irrational numbers, such as square root of 2, pi, etc... you could write down their definition, or maybe an algorithm that will compute their decimal representation up to arbitrary precision.
However, there are more irrational numbers between 0 and 1 (or any real interval with more than one number) than there are ways of representing things finitely. It seems counter-intuitive, and I suppose that's because the set of real numbers is really weird, we just don't think about it that much.
(By ways of representing things finitely I mean finite sequences of symbols chosen from a finite alphabet.)
[deleted] ยท 0 points ยท Posted at 19:31:00 on May 25, 2016 ยท (Permalink)
well saying "nearly all" is silly when there's an infinite amount
Naked_Sweat_Drips ยท 1 points ยท Posted at 19:42:53 on May 25, 2016 ยท (Permalink)
That's the whole point of the original statement I think. "Nearly all" wouldn't mean anything unless there was an infinite amount.
[deleted] ยท 2 points ยท Posted at 20:20:17 on May 25, 2016 ยท (Permalink)
"nearly all" implies an upper bound
iwillnotgetaddicted ยท 4 points ยท Posted at 20:41:28 on May 25, 2016 ยท (Permalink)
it implies the author is funny and capable of making humorous understatements
Lehona ยท 0 points ยท Posted at 23:15:59 on May 25, 2016 ยท (Permalink)
"Nearly all" means there is only a finite amount of exceptions, which is true in this case.
REMagic42 ยท 3 points ยท Posted at 19:07:25 on May 25, 2016 ยท (Permalink)
And the most interesting about that, is that this statement is a precise mathematical statement to make.
Deivore ยท 1 points ยท Posted at 21:44:15 on May 25, 2016 ยท (Permalink)*
Isnt that only true for positive integers? Edit: Apparently not, compact spaces are less infinite than unbounded real intervals.
BOULD ยท 1 points ยท Posted at 23:32:21 on May 25, 2016 ยท (Permalink)
Nearly all positive numbers are greater than any given number.
omaximov ยท 1 points ยท Posted at 19:59:19 on June 1, 2016 ยท (Permalink)
Careful with that. A countable infinity of positive numbers, more accurately
[deleted] ยท 67 points ยท Posted at 14:44:59 on May 25, 2016 ยท (Permalink)*
All that tells me is that no computer with the volume of a human brain can store Graham's number. What is the smallest such computer physically possible? That is, the black hole whose entropy equals that of Graham's number?
Are we looking at a stellar mass black hole? Supermassive galactic nucleus? Observable universe?
edit: Just reacquainted myself with the construction of Graham's number. The answer would be no. No, none of those would be even remotely adequate.
purple_pixie ยท 23 points ยท Posted at 16:22:13 on May 25, 2016 ยท (Permalink)
Very well put. It is a stupidly large number.
prmcd16 ยท 2 points ยท Posted at 22:48:21 on May 25, 2016 ยท (Permalink)*
Think of a quantum computer the volume of a multiverse sized collection of multiverses whose bits are to the Planck volume what the Planck volume is to the computer's volume. Each bit can be in as many states as there are particles in this hypothetical multiverse. Now transform into a photon and whizz around a Planck volume at the speed of light. Each time you make a circuit, add a computer with as much storage as all the ones you have so far. Do this for around about the projected lifespan of the universe. Then get up, go outside, and do something useful with your life, because you haven't even managed to describe the number of digits in the number of digits in the number of digits in Graham's Number.
unampho ยท 8 points ยท Posted at 15:47:29 on May 25, 2016 ยท (Permalink)
room sized computers come back into style
oi_rohe ยท 18 points ยท Posted at 17:38:42 on May 25, 2016 ยท (Permalink)
They're already back in style, every business with a web presence interacts with them constantly, if they don't own at least one outright.
Kapparino1104 ยท 3 points ยท Posted at 17:23:19 on May 25, 2016 ยท (Permalink)
You would literally fill the universe with planck's constant sized atoms, and you are still like, 0.00000000000000000000000000001% away from Graham's number.
jywn4679 ยท 14 points ยท Posted at 17:49:51 on May 25, 2016 ยท (Permalink)
You underestimate Grahams number. You could not possibly write down the number of 0's to make that percentage accurate. You couldn't even write down the number of digits in the number of zeros needed.
[deleted] ยท 2 points ยท Posted at 19:21:23 on May 25, 2016 ยท (Permalink)
You couldn't even write down the number of digits in the number of digits in the number of zeros needed. You couldn't even write down the number of digits in the number of digits in the number of digits....
Heck, you couldn't even write down the number of times we would need to write down "number of digits".
You couldn't even write down the number of digits needed to write down the number of times we would need to write down "number of digits" in your explanation.
Although, if I just kept on going with the pattern in the previous paragraphs, saying that you couldn't write down the number of digits of the number of times needed to write "number of digits needed to write down the number of times needed to write down the number of digits" etc etc etc..., then maybe, just maybe, we can write down the number of paragraphs needed to fully express Graham's Number.
featherfooted ยท 2 points ยท Posted at 20:22:11 on May 25, 2016 ยท (Permalink)
Quite! And since Graham's Number G = g_64, then in a certain sense of your analogy, it would be "64 paragraphs".
rabbitlion ยท 5 points ยท Posted at 16:46:40 on May 25, 2016 ยท (Permalink)
The entropy of Graham's Number is not very large, so if you allow compression it's trivial to store in any computer or your brain.
The_Serious_Account ยท 9 points ยท Posted at 18:14:45 on May 25, 2016 ยท (Permalink)
The fact that we can define it shows it's extremely compressible. The numbers we should worry about are the numbers we literally can't talk about.
Ninja edit: I realize I just talked about them. I, of course, mean a specific one of them.
promisedjoy ยท 3 points ยท Posted at 18:35:29 on May 25, 2016 ยท (Permalink)
What about the smallest positive integer that we can't talk about?
Tysonzero ยท 2 points ยท Posted at 22:51:34 on May 25, 2016 ยท (Permalink)
But you just talked about it. A contradiction.
almightySapling ยท 2 points ยท Posted at 23:38:26 on May 25, 2016 ยท (Permalink)
I can't tell if this is an earnest question or a coy reference to Berry's paradox.
featherfooted ยท 1 points ยท Posted at 18:43:28 on May 25, 2016 ยท (Permalink)
You have discovered the interesting number paradox. The smallest uninteresting number is itself interesting, because it is the smallest uninteresting number.
The_Serious_Account ยท 2 points ยท Posted at 19:57:17 on May 25, 2016 ยท (Permalink)
I do have a degree in computer science and quantum information theory and realized I just unintentionally got myself into pretty deep waters. To rephrase, what's the smallest number so that the definition would collapse the observable universe into a black hole? Well, fuck.
almightySapling ยท 2 points ยท Posted at 20:14:24 on May 25, 2016 ยท (Permalink)
Depends on what you mean by "store".
I mean, if you mean "literally write out all the digits" then sure, but that's true for like... pi.
But I can fully describe pi using clever mathematical notation. For instance, pi = 4 - 4/3 + 4/5 - 4/7 + ... which can be described very very concisely.
Similarly, the construction of graham's number can be described in (relatively) small terms.
thephotoman ยท 2 points ยท Posted at 20:41:50 on May 25, 2016 ยท (Permalink)*
The first number involved in calculating Graham's number is 3 ^ ^ ^ ^ 3. The second number has that many carrots between the threes. The third has the second number of carrots between the threes, and so on until you get to the 64th number. That 64th number is Graham's number.
For the record--to those that don't know--the carrots are not exponentiation. It's Knuth up-arrow notation. 3 (three arrows) 3 is a stupidly big number in and of itself. 3 (one arrow) 3 is 27. 3 (two arrows) 3 is 327. 3 (three arrows) is 3 (two arrows) (3 (two arrows) 3 ), or an exponentiation stack of 327 3's. 3 (four arrows) 3 is 3 (3 three arrows (3 three arrows ( 3 three arrows (... )and you repeat that cycle for 3 ^ ^ ^ 3. And that's not even close to Graham's number!
That is, in and of itself, incomprehensibly large.
So let's turn this around to that black hole, shall we? The Schwarzchild radius of a black hole is r = 2EG/c3, where r is the radius, E is the amount of energy in that radius, and c is the speed of causality, approximately 300,000,000 meters per second.
So when he says "What unit of energy are you using that has E in the Schwarzschild radius formula (r = (2 * energy * universal gravitation constant) / c3) equal to Graham's number?", it doesn't matter. No matter how small of a unit of energy you have, if that amount of energy is at all meaningful, the Schwarzschild radius of the resulting black hole is incomprehensibly larger than the 46,000,000,000 light year radius of the observable universe.
No, seriously.
Let's say you had a photon with a wavelength of light year. Yeah, that means its frequency is 1/31557600 Hz, or 3.16880878 * 10-8. Now, multiply that by Plank's constant (6.626070040ร10-34 kg * m2 * s-1 with some uncertainty), and you get a value that has an order of magnitude of -44. I don't care about that number, and neither should you, gentile reader. Compared to the order of magnitude of a 27-digit tall exponentiation stack of 3's (that first number involved in calculating the number of up arrows in Graham's number), it's nothing at all. Even dividing it by the 300,000,0003 m3*s-3that we get here (that's 3 ^ 24) doesn't save us. Nor does the incredibly small Universal Gravitational constant save us ( 6.674ร10-11 m3kg-2s-2). That still only a number with an order of magnitude of -79.
Fine. So we have G * 10-79 on one side of the equation, where 10-79 has so few digits compared to G that it makes no difference--and that's saying that the unit of energy we're counting Graham's Number of is equal to the energy in a single photon with a wavelength of a light year.
Now let's turn our attention to the radius of that black hole. The diameter of the observable universe is 8.8ร1026 m. That makes its radius 4.4 * 1026 m.
So choose your unit for energy. It doesn't matter. Whatever base unit of energy you choose, if you have Graham's number of it in the size of the observable universe, and you can write down its expression in terms of SI units (or electron volts) in any way, you get a black hole. The order of magnitude of Graham's number is just that big: no matter how small the thing you're counting is, Graham's number of it in the observable universe is a black hole.
jlcooke ยท 1 points ยท Posted at 17:06:28 on May 25, 2016 ยท (Permalink)
log(Grahams Number) =~ 3 ^ ^ ^ 3
Black hole entropy = (c * c * c) * Area / ( 4 * UnivGravConst * h-bar )
So Area =~ 3 ^ ^ ^ 3 * (4) * (6.67408 * 10-11 m3 kg-1 s-2) * (1.05457 * 10โ34 J*s) / (c * c * c)
So yeah, almost exactly equal to 3 ^ ^ ^ 3 ... in what units? Doesn't matter. Seriously, it doesn't.
Edit: Triple carot's ^ don't render as expected in reddit
Edit2: Added spaces to c * c *c ... when will reddit use LaTeX?
[deleted] ยท 5 points ยท Posted at 17:27:48 on May 25, 2016 ยท (Permalink)
That does not seem right to me. Maybe you mean the iterated logarithm? Even then it seems too small.
[deleted] ยท 3 points ยท Posted at 18:58:02 on May 25, 2016 ยท (Permalink)
I recall it being quad carots
thephotoman ยท 1 points ยท Posted at 21:04:57 on May 25, 2016 ยท (Permalink)
g1 is four Knuth up arrows.
And that's g1. Graham's number is g64. For the record, g2 has g1 up arrows between the threes, and g3 has g2 up arrows between the threes. You get the picture. You can't write Graham's Number with Knuth up arrow notation.
santaliqueur ยท 1 points ยท Posted at 01:07:06 on May 26, 2016 ยท (Permalink)
From Wikipedia:
Seems like if you converted all matter in the universe JUST to store Graham's number, each digit in one Planck volume, it still wouldn't be enough.
Bobshayd ยท -3 points ยท Posted at 16:10:59 on May 25, 2016 ยท (Permalink)
No, no, no ANYTHING with the volume of a human brain can store Graham's number. Not even packed atoms with their configurations arranged to match Graham's number.
crh23 ยท 17 points ยท Posted at 14:46:15 on May 25, 2016 ยท (Permalink)
Well, the entropy is clearly not that large, as we can represent it on a piece of paper!
Rynyl ยท 5 points ยท Posted at 14:31:33 on May 25, 2016 ยท (Permalink)
i got you, fam
I didn't post this video in the top thread because I think the one with Ron Graham is better.
Umbrall ยท 8 points ยท Posted at 14:54:15 on May 25, 2016 ยท (Permalink)
Well the fact that we can write it down means it's fairly small. There has to be numbers that are close in magnitude to Graham's number, but admit no clean formula like Graham's number. These numbers could never hope to be described in any way by someone in the universe.
Deathticles ยท 18 points ยท Posted at 15:15:51 on May 25, 2016 ยท (Permalink)
I mean, we can use variables or other non-numerical symbols to represent Graham's number when we write it down (aka I can say that Graham's number = X), but if you were to try to write out each digit in Graham's number for the rest of time, you'd run out of space in the observable universe, even if each digit only took up the space of a single atom.
https://plus.maths.org/content/too-big-write-not-too-big-graham
Umbrall ยท 7 points ยท Posted at 15:51:34 on May 25, 2016 ยท (Permalink)
That's true. The point I'm saying is we can fit the decription of graham's number, as in the proof it appears in, or the 64th iteration of 3 โ x 3 etc. Most numbers the size of graham's number cannot have any kind of succint description like this even fit in the universe, not even considering digits. That we can write down what Graham's number is is a rarity.
fedd_ ยท 2 points ยท Posted at 19:16:43 on May 25, 2016 ยท (Permalink)
Wouldn't it be possible to write such a number in relation to Graham's number? Like Graham's number -1 or -("some fraction of g7") or whatever?
Umbrall ยท 2 points ยท Posted at 19:38:07 on May 25, 2016 ยท (Permalink)
Well you just wrote down what it was, so it definitely can't be in that case. We may certainly be able to write properties though, like saying it's approximately x/y of graham's number
fedd_ ยท 1 points ยท Posted at 20:08:35 on May 25, 2016 ยท (Permalink)
sounds like circular reasoning to me. although i guess I also can't challenge you to tell me a number you can't write down to prove me wrong either ;)
Umbrall ยท 2 points ยท Posted at 21:06:53 on May 25, 2016 ยท (Permalink)
To some degree it is. Pi is a relatively random string, but we've uniquely identified it. So it's not to say that there's anything special about the numbers, only that only so many can be written down finitely.
Look at it like a compression argument. We can't do better than assigning each number a given string. So suppose we're just using english letters and spaces. Then in n of these letters we can only describe 27n total numbers. So if a set of numbers is bigger than 27n, we certainly can't give them all a unique string.
Since Graham's number is so massive, we can't even get close to writing it down, but there has to be at least G - 1 numbers less than it. Since we know we don't have enough nearly space to write out Graham's number in the raw form, we can't have enough space to write out more than a tiny fraction of the numbers less than it since there's not enough possible strings for them. We can have large numbers be possible to write, but this just moves around the tiny fraction.
-Mountain-King- ยท 1 points ยท Posted at 17:42:04 on May 25, 2016 ยท (Permalink)
You'd also run out of time before the heat death of the universe, even if each digit took a nanosecond to write and you started at the beginning of time.
RiOrius ยท 1 points ยท Posted at 19:37:21 on May 25, 2016 ยท (Permalink)
In base ten, sure. In base Graham's Number, I can easily write it out.
marsten ยท 3 points ยท Posted at 17:55:50 on May 25, 2016 ยท (Permalink)*
Even 3โโโโโ3 is vastly larger than the Bekenstein bound for our observable universe. So there is no conceivable way that that number could ever be written down, let alone Graham's number.
That said, it turns out we know the rightmost 500 digits of Graham's number. It ends with a 7 for example.
To me, the fact that we can define and reason about numbers that are so large that they cannot even in principle be written down, is one of the best demonstrations of the power of pure thought.
imgonnacallyouretard ยท 3 points ยท Posted at 18:46:42 on May 25, 2016 ยท (Permalink)
No, Kolmogorov complexity is quite simple for Grahams number - which is exactly why he was able to describe it in a paper!
wegzo ยท 2 points ยท Posted at 16:04:35 on May 25, 2016 ยท (Permalink)
bet i can come up with an even larger number
BritTorrent ยท 7 points ยท Posted at 17:16:17 on May 25, 2016 ยท (Permalink)
Grahams number +1
MontyPythagoras ยท 3 points ยท Posted at 17:42:38 on May 25, 2016 ยท (Permalink)
I checked Peano's axioms, the math works out!
AcademicalSceptic ยท 1 points ยท Posted at 18:31:16 on May 25, 2016 ยท (Permalink)
There is indeed a successor for all x.
green_meklar ยท 2 points ยท Posted at 18:45:26 on May 25, 2016 ยท (Permalink)
There's actually nothing to worry about, because the actual information content of the number is quite small. It can be 'compressed' down to a fairly simple formula, or, more generally speaking, a fairly simple algorithm. I could write you computer code that, if run on a computer with enough RAM, would eventually output all the correct digits of the number and then tell you it was finished; and the code itself would be only a few kilobytes.
Most numbers are not like this. For instance, the average number ranging from G to 2*G (where G is Graham's Number) really does contain some colossal, ungodly amount of information that would collapse the observable universe, and cannot be (uniquely) generated by any concise algorithm. In fact, among all the integers, only an infinitesimally small fraction can be 'compressed' significantly the way Graham's Number can.
Well, actually there is something to worry about. Because it turns out that, although we can easily prove that almost all extremely large numbers contain extremely large amounts of information, it is impossible to prove (using the normal rules of mathematics) that any particular integer contains more than some particular finite amount of information. That is to say, there is a largest finite integer for which the normal rules of mathematics can tell us how much information it really contains, and said integer is much smaller than Graham's Number. (The amount of information it contains would still collapse the observable universe, though.)
StrawberryDiesel ยท 1 points ยท Posted at 16:40:43 on May 25, 2016 ยท (Permalink)
Numberphile, love those guys.
jlcooke ยท 1 points ยท Posted at 16:58:41 on May 25, 2016 ยท (Permalink)
youtube: Numberphile
zacablast3r ยท 1 points ยท Posted at 16:59:19 on May 25, 2016 ยท (Permalink)
Sounds very Douglas Adamsy. Appropriate, considering its towel day.
thecatgoesmoo ยท 1 points ยท Posted at 17:56:35 on May 25, 2016 ยท (Permalink)
Also basically made up
linehan23 ยท 1 points ยท Posted at 17:59:14 on May 25, 2016 ยท (Permalink)
Even if you made each digit a Planck volume (the smallest possible volume) you couldn't fit it into the observable universe
generalgeorge95 ยท 1 points ยท Posted at 18:47:55 on May 25, 2016 ยท (Permalink)
I feel like sometimes math is just fucking with me.
ReliablyFinicky ยท 1 points ยท Posted at 19:06:29 on May 25, 2016 ยท (Permalink)
Let's give /u/jeffdujon credit where it's due by linking the source -- Numberphile.
Fudge89 ยท 1 points ยท Posted at 20:13:27 on May 25, 2016 ยท (Permalink)
Similar to how the number googolplex is impossible to write (physically, dunno about on computers or how that would work). The number of zeros it contains is more than the number of atoms theorized to be in the universe.
scrochum ยท 1 points ยท Posted at 20:35:19 on May 25, 2016 ยท (Permalink)
from the original numberphile video
nissepik ยท 1 points ยท Posted at 23:04:07 on May 25, 2016 ยท (Permalink)
are you guys on some kind of drug or what the fuck
santaliqueur ยท 1 points ยท Posted at 01:03:58 on May 26, 2016 ยท (Permalink)
Stolen from here.
Sleeveharvey ยท 1 points ยท Posted at 01:49:42 on May 26, 2016 ยท (Permalink)
Grahams Number is the Chthulu of numbers...
tritiumosu ยท 102 points ยท Posted at 15:02:39 on May 25, 2016 ยท (Permalink)
Graham's Number is scary as fuck. Reading the Wait but Why post about it really drove home just how mind-bogglingly, stupidly huge things like "infinity" really are.
MysticKirby ยท 16 points ยท Posted at 17:21:11 on May 25, 2016 ยท (Permalink)
That was a great read. I've seen several videos on Youtube about Graham's number, but none have been able to put it into the same sense of scale as this article has.
Fourthdwarf ยท 7 points ยท Posted at 20:02:56 on May 25, 2016 ยท (Permalink)
"Infinity" isn't huge. It transcends size entirely.
To say that if you think you can comprehend it, you can't, is an understatement. It might be true, but it's also true for some finite numbers, like Graham's number.
Saying infinity is big is like saying red is big. The colour red has no edges, as it is a concept, not a thing. Red is occasionally a useful concept when describing something. But red is not a thing.
Putting infinity into the same bucket as finite numbers is as wrong as putting colours and numbers together. Sure, you can colour by numbers, and sure, you can do useful maths with infinity. But you also get some really weird results.
tritiumosu ยท 6 points ยท Posted at 20:32:29 on May 25, 2016 ยท (Permalink)
This is absolutely true - the problem comes from a layperson's incomplete understanding of the scale of things that are finite and measurable.
Learning about large numbers like Graham's Number, TREE(3), etc. gives the average non-academic a profound adjustment to their perception of concepts like infinity when discussing things like religion, space, and so on.
To some extent, it could be compared to what astronauts have experienced with the Overview Effect.
moartoast ยท 1 points ยท Posted at 22:35:27 on May 25, 2016 ยท (Permalink)
You can say that infinitely-sized things are larger than any finite thing. They are big. Their bigness is on a different order, but it's still a measure of bigness.
SlendyIsBehindYou ยท 3 points ยท Posted at 05:34:28 on May 26, 2016 ยท (Permalink)
"Take a minute to realize how not ok this graphic is"
TheSekret ยท 2 points ยท Posted at 20:50:55 on May 25, 2016 ยท (Permalink)
And then you learn about aleph null
moartoast ยท 2 points ยท Posted at 22:33:26 on May 25, 2016 ยท (Permalink)
I find infinities a lot easier to handle than stupendously large numbers. You can describe and reason about "the set of all natural numbers" fairly naturally.
Really Stupendously Huge Numbers are brainbreaking in a different way.
- The Hitchhiker's Guide to the Galaxy
Chameleonpolice ยท 1 points ยท Posted at 22:08:50 on May 25, 2016 ยท (Permalink)
I enjoyed reading that. Thank you!
Actionmaths ยท 1 points ยท Posted at 06:47:11 on May 26, 2016 ยท (Permalink)
Infinity isn't huge, it isn't a number. Saying things like this makes me think you're still of the 7 year old mindset where there is a biggest number and youre calling it Infinity.
exbaddeathgod ยท -2 points ยท Posted at 18:47:43 on May 25, 2016 ยท (Permalink)
I never knew someone could that emotional and use such hyperbole with numbers. Also, why call those intermediate numbers such silly things? Why not use one letter placeholders which is convention in mathematics?
HoechstErbaulich ยท 20 points ยท Posted at 16:19:53 on May 25, 2016 ยท (Permalink)
I would not have expected Day9 in this thread, nice!
[deleted] ยท 7 points ยท Posted at 17:28:14 on May 25, 2016 ยท (Permalink)*
His sex math joke is the best
[edit] link for those that haven't seen it
scrochum ยท 1 points ยท Posted at 20:39:02 on May 25, 2016 ยท (Permalink)
day9 has 2 things; RTS games and math, i expected this topic to be nothing but day9 and numberphile videos
beleg_tal ยท 12 points ยท Posted at 16:41:03 on May 25, 2016 ยท (Permalink)*
FTFY
TREE(3) is bigger, and subcubic graph numbers are even bigger than that :)
BuckRampant ยท 2 points ยท Posted at 23:42:21 on May 25, 2016 ยท (Permalink)
"One... Two.... [CRUNCH]"
I did not expect the owl to be explaining math
Bosck ยท 9 points ยท Posted at 16:34:02 on May 25, 2016 ยท (Permalink)
Wow haven't seen Day9 since WoL. That was a surprise!
MikeBobble ยท 8 points ยท Posted at 15:39:35 on May 25, 2016 ยท (Permalink)
Good bye all your free time: http://waitbutwhy.com/2014/11/1000000-grahams-number.html
[deleted] ยท 2 points ยท Posted at 19:18:09 on May 25, 2016 ยท (Permalink)
He talks about what it would be like to live a Graham's number of years, and how it is simply beyond comprehension.
But couldn't it be argued that any human who was been alive for some period of time, has also been alive for a Graham's number of finite units of time? A really small unit of time, but a finite unit nevertheless?
[deleted] ยท 7 points ยท Posted at 17:27:02 on May 25, 2016 ยท (Permalink)
I love day9
sprankton ยท 6 points ยท Posted at 16:43:07 on May 25, 2016 ยท (Permalink)
Actually, there are a few larger numbers involved in serious mathematical proofs these days. One notable one is TREE(3).
lurgi ยท 5 points ยท Posted at 17:17:39 on May 25, 2016 ยท (Permalink)
Graham's number is an upper bound to a particularly funky math problem. It's not known precisely what the answer is, but we know it's less than Graham's number. For a long time it was suspected that the correct answer was... 6.
We now know that's wrong. It's at least 13.
aaaik ยท 6 points ยท Posted at 15:36:32 on May 25, 2016 ยท (Permalink)
Why are they trying to find a solution to the problem of same-coloured coplanar subgraphs? Does it solve some actual problem, or is it just a "hmmm... I wonder." kind of thing?
chaoticvoid ยท 14 points ยท Posted at 18:07:35 on May 25, 2016 ยท (Permalink)
Most of the time, it's more of a "hmmm... I wonder." That doesn't it won't be useful though. Sometimes the problem ends up being generalized to some other problem, or perhaps the technique used to solve the problem becomes useful for another problem.
Here's a quote from Nobel-prize winning Scientist Richard Feyman that kind of describes his process:
[deleted] ยท 4 points ยท Posted at 16:06:04 on May 25, 2016 ยท (Permalink)
"hard" problems (look up np v p) are all able to be generalized into eachother. Put another way there is a relatively simple way to turn this problem into a problem about visiting all the cities exactly once in the shortest path, or finding the most efficient way to fill a knapsack, etc.
Anthony356 ยท 6 points ยท Posted at 15:48:14 on May 25, 2016 ยท (Permalink)
Beat me to it! Even included the day9 piece on it =D my man
candygram4mongo ยท 5 points ยท Posted at 17:59:14 on May 25, 2016 ยท (Permalink)
I like his Sierpinski Gasket t-shirt.
Alamo44 ยท 4 points ยท Posted at 17:38:17 on May 25, 2016 ยท (Permalink)
Took a class with him at UCSD. This guy is unbelievably smart, but at the same time very approachable. Told us about his friend Erdos the travelling mathematician, his trampoline skills, and how to flip a coin such that it always lands heads.
Not sure if anyone else found this interesting, but I'm all about Graham
b4b ยท 4 points ยท Posted at 22:18:55 on May 25, 2016 ยท (Permalink)
I thought Day9 plays StarCraft Brood War and Hearthstone :D
jlcooke ยท 3 points ยท Posted at 16:58:12 on May 25, 2016 ยท (Permalink)
There have been others larger then big-G - TREE problems etc.
G is still stupid big.
Kruki37 ยท 3 points ยท Posted at 17:06:13 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem
FkIForgotMyPassword ยท 3 points ยท Posted at 17:14:01 on May 25, 2016 ยท (Permalink)
It used to be, but isn't anymore. Not that it makes it any smaller though, obviously. When Knuth's arrow notation isn't enough and you need apply it recursively, you know something's going to be big.
InfectedShadow ยท 2 points ยท Posted at 16:10:47 on May 25, 2016 ยท (Permalink)
What blows my mind: If each digit of Graham's number were written out at the size of a Planck it still would not fit into the observable universe.
chaoticvoid ยท 3 points ยท Posted at 18:12:59 on May 25, 2016 ยท (Permalink)
It's way bigger than that scale. If we also considered the smallest unit of time, then every possible configuration of all the Planck size constants for every Planck second since the beginning of time, would still be dwarfed by G(2), never mind G(64).
polarpigs ยท 2 points ยท Posted at 17:43:54 on May 25, 2016 ยท (Permalink)
I took a discrete math class from Graham! Very mellow and humble guy
linehan23 ยท 2 points ยท Posted at 17:58:05 on May 25, 2016 ยท (Permalink)
If I remember correctly there's been a larger number used now
newdecade1986 ยท 2 points ยท Posted at 18:09:25 on May 25, 2016 ยท (Permalink)
Yeah well I can imagine Graham's number plus one.
[deleted] ยท 2 points ยท Posted at 19:19:17 on May 25, 2016 ยท (Permalink)
G(G(64))
beingforthebenefit ยท 2 points ยท Posted at 19:33:47 on May 25, 2016 ยท (Permalink)
For those who have taken in extremal combinatorics class, this is a pretty normal amount. Every once in a while, one of these coloring algorithms (like Graham's) is applicable. So we'll have a biologist come in asking how to simulate some extremal problem on a computer and we all just hang our heads and explain that it takes a stack of 2's 1/ฮต high, as ฮต tends to zero, iterations for this to work. Not exactly computable.
lynyrd_cohyn ยท 2 points ยท Posted at 20:12:22 on May 25, 2016 ยท (Permalink)
That day9 video is indeed very entertaining, thanks!
Ky1arStern ยท 2 points ยท Posted at 20:21:11 on May 25, 2016 ยท (Permalink)
FTFY
[deleted] ยท 2 points ยท Posted at 20:49:44 on May 25, 2016 ยท (Permalink)
[deleted]
Rynyl ยท 1 points ยท Posted at 21:30:02 on May 25, 2016 ยท (Permalink)
Yes, that would make it bigger, but the point is that Graham's number, at the time it was introduced, was the largest number used in a math paper constructively. It actually has a purpose (surprisingly).
As many have pointed out already, larger numbers have been used since then.
IsakMar ยท 2 points ยท Posted at 20:53:45 on May 25, 2016 ยท (Permalink)
I always thought googelplex was the largest number because mathmatician decided it was, and there was no point in going any further. Man was I (and my math professor) wrong...
6-8-5-7-2-Q-7-2-J-2 ยท 2 points ยท Posted at 21:28:37 on May 25, 2016 ยท (Permalink)
My favourite thing about Graham's Number is that it's the upper limit on the answer the the problem - and the lower limit is 13 (I think). The answer is between 13 and a number so big that knowing every digit would cause your headspace to collapse into a black hole.
sangriadvx ยท 2 points ยท Posted at 21:50:17 on May 25, 2016 ยท (Permalink)
I miss when Day[9] did math stuff.
[deleted] ยท 2 points ยท Posted at 21:59:02 on May 25, 2016 ยท (Permalink)
Here's a trick for those of you that want to make big numbers - and by big I mean absolutely massive. No mere GrahamGraham nonsense here, no we are going so far beyond that that writing GrahamGraham as your largest number is like a child writing 9999999999999999999 as theirs.
We start with a pretty simple concept - repeated application. If f is a function that assigns one number to another, say f(x) = x+1, then we can just write f2 (x) to mean f(f(x)) = f(x+1) = x+2.
Let us use this notion to make an astonishing sequence, defined in the following way:
Define f[1](x) to be 2x, and then define f[n+1](x) to be f[n]x (x).
This gives:
f[1](2) = 4,
f[2](2) = f[1]2 (2) = 2(2(2)) = 8
f[3](2) = f[2]2 (2) = f[2] (8) f[1]8 (8) = 28 * 8 = 2048
Not so impressive? Well we aren't quite done yet. There is one more step, we now make a sequence a1, a2, a3, ...etc. by letting an = f[n](n). If you aren't completely thrown yet, let me calculate a few of these.
a1 = f[1](1) = 2(1) = 2 (Difficult, I know)
a2 = f[2](2) = f[1]2 (2) = 8 (Bear with me, here)
a3 = f[3](3) = f[2]3 (3) = f[2]2 (f[1]3 (3)) = f[2]2 (23 x 3) = f[2]2 (24) = f[2] (f[1]24 (24)) = f[2] (224 x 24) = 224x224 x 224 x 24 ~= 10108 that is, a 1 followed by one hundred million zeroes - take that, googol!).
a4 = f[4](4) = f[3]4 (4) = f[3]3 (f[2]4 (4)) = f[3]3 (f[2]3 (24 x 4))
= f[3]3 (f[2]2 (264 *64)) ~= f[3]3 (f[2]2 (1021 ))
= f[3]3 (f[2] 21021 x 1021) ~= f[3]3 (f[2](101021 ))
=f[3]3 (101021 x 2101021 .) ~= f[3]3 (10101021 )
= f[3]2 (f[2]10101021 (10101021 ) ) ~= f[3]2 (1010...1021 )) (where in the ... we hide about 10101021 10s)
~= f[3](1010...1021 ) (where in the ... we're hiding the 10...1021 10s from last time)
~= 1010...1021 (where in the ... we're hiding the 10...1021 10s from last time)
Let's not go to a5, it may take a while. Suffice to say this gets past Graham's number in about 64 steps, and then a65 = f[65](65) = f[64]65 (65) ~= f[64]64 (Grahams Number) = f[64]63 (f[63]Graham's_Number (Graham's Number)) = ...
So yeah Graham's number pales in comparison to a65, which pales in comparison to a66, which pales...etc. If you want to go even further set b1 = a1, and b[n+1] = aa[n] n. Then b[64] = a(a(a(a(......a(64))...)) where we apply a a(64) times.
Even after all this, we're not one iota closer to the smallest infinity...and there are infinities far, far larger.
Archros ยท 2 points ยท Posted at 22:52:41 on May 25, 2016 ยท (Permalink)
Have you heard about Goodstein's theorem?
Rynyl ยท 1 points ยท Posted at 23:21:42 on May 25, 2016 ยท (Permalink)
I haven't, no. I'm not a mathematician, just an engineer
Archros ยท 2 points ยท Posted at 23:36:04 on May 25, 2016 ยท (Permalink)
Well, here is a general introduction. The wikipedia page is nice too. https://en.wikipedia.org/wiki/Goodstein%27s_theorem
agumonkey ยท 2 points ยท Posted at 23:32:37 on May 25, 2016 ยท (Permalink)
It may run Crysis but it won't compute Graham.
ForteShadesOfJay ยท 2 points ยท Posted at 23:45:46 on May 25, 2016 ยท (Permalink)
After listening to the H.I. podcast because of GCP it's weird clicking on that and seeing Brady. Looks completely different than I pictured him. I knew he had a channel but just never thought to look.
dannystoll84 ยท 2 points ยท Posted at 02:31:27 on May 26, 2016 ยท (Permalink)
I posted this earlier and it was buried, but another fact relating to large numbers that I find absolutely fascinating:
Goodstein's Theorem. Easily one of the weirdest theorems I know, and it at first seems very counterintuitive.
In layman's terms:
When we representing a number in a base (say 99 = 10200 in base 3) we are implicitly representing it as a sum of powers of the base, for instance
99 = 1โข34 + 0โข33 + 2โข32 + 0โข31 + 0โข30
= 34 + 2โข32.
A Goodstein sequence is defined as follows:
Start with any positive number n in any base b_0 > 1, and write out the base b_0 representation for n as a series as above. But don't just do that: every time you see a number greater than to b_0 in one of the exponents, also write that as a power series in b_0, and so on until all the numbers written down are at most b_0. So in our case (n_0 = 99, b_0 = 3) we have
99 = 33+1 + 2โข32.
This is called the hyper-base b_0 representation of n.
So starting with n, we write it in hyper-base b_0. Now comes the cool part: every time you see b_0 in the expansion of n, replace that with b+1. Note that "usually" this will dramatically increase the value represented. After doing this, subtract 1 to obtain a new number n_1, and if n_1 is positive, rewrite the number in hyper-base b_1 = b+1.
So in our example, we have
n_1 = 44+1 + 2โข42 - 1 = 1055
= 44+1 + 42 + 3โข4 + 3
in hyper-base b_1 = 4. We now just repeat this process. For instance, we have
n_2 = 55+1 + 52 + 3โข5 + 2 = 15688,
n_3 = 66+1 + 62 + 3โข6 + 1 = 279991,
et cetera. As you can see, these numbers increase quickly.
On the other hand, Goodstein's theorem states that no matter what our initial base is -- you could start with 1,000,000 in base 2, of you like -- the sequence will eventually terminate, i.e. n_k will equal zero for some finite k.
Somehow, once these numbers get big enough, their structure is exhausted, and they stop increasing, so we then simply subtract 1 until we reach 0.
On the other hand, the time it takes for the sequence to terminate is generally enormous. Indeed, the function giving the number of steps to terminate starting with n_0 in base 2 increases at a very rapid pace. For instance, if we start by writing n_0 = 4 in base b_0 = 2, the sequence takes 3โข2402653211 - 2 steps to reach 0, while if n_0 = 12, the number of steps needed is more than Graham's number.
But the real punchline is that while this theorem is true (according to standard set theory), it cannot be proven using the standard axioms of arithmetic. In a sense, the function described in the above paragraph grows too quickly for first order arithmetic to prove that it is finite for all n (note that it n price the function is finite for each n, by simply writing out the whole sequence, but this is quite different from proving the statement for all n simultaneously.)
RainHappens ยท 2 points ยท Posted at 02:44:47 on May 26, 2016 ยท (Permalink)
Worse yet.
Look at busy beaver numbers. Literally growing faster than any computable function.
B(23) is larger than Graham's number, for instance.
And I saw a paper recently talking about B(7918) (!)
xanthalasajache ยท 2 points ยท Posted at 03:22:29 on May 26, 2016 ยท (Permalink)
How about Graham's NumberGraham'sNumberGraham'sNumberGraham'sNumberGraham'sNumber ?
Rynyl ยท 1 points ยท Posted at 03:59:22 on May 26, 2016 ยท (Permalink)
If you can use it in a peer-reviewed math journal, then yeah, absolutely.
I mean, keeping with the theme, why not G64 โโโโโโ...G64 with G64 up arrows?
this_o_O ยท 2 points ยท Posted at 06:52:46 on May 26, 2016 ยท (Permalink)
That was a rather entertaining read!
ArmadilloFour ยท 2 points ยท Posted at 07:43:57 on May 26, 2016 ยท (Permalink)
I'll be real, those arrows were sort of confusing. But when he wrote out the 327 / 33333333 / 33333333 / and onward (at the 4:10 mark), I let out an audible groan.
God damn. Fuck that number.
TheGoluxNoMereDevice ยท 2 points ยท Posted at 11:42:36 on May 26, 2016 ยท (Permalink)
the best part is the answer to the problem lies somewhere between 26 and Grahams number, so they really got it nailed down tight
idledrone6633 ยท 1 points ยท Posted at 22:30:59 on May 25, 2016 ยท (Permalink)
That notation is only valid in figuring out how many cocks OP's mom has sucked.
Killa-Byte ยท 1 points ยท Posted at 06:41:37 on May 30, 2016 ยท (Permalink)
I wonder how big tree(4) is
h-jay ยท 1 points ยท Posted at 16:05:46 on May 25, 2016 ยท (Permalink)
This made me feel like we're all presumed illiterate. While my 5 year old appreciates YouTube very much, it's my duty to rescue those of us who'd rather read about it.
[deleted] ยท 3 points ยท Posted at 16:47:37 on May 25, 2016 ยท (Permalink)*
Some people prefer videos and learn better from them. I generally prefer to read about things too - and I do appreciate the article post - but there's no reason to be a condescending ass about it.
h-jay ยท -1 points ยท Posted at 17:57:33 on May 25, 2016 ยท (Permalink)
Some amount of condescension is necessary to indicate that it's in nobody's interest for the video-only reality to become the new normal. It is, in a lot of ways, extremely inefficient: in terms of the time needed to produce the content, the bandwidth needed to process and transmit it, and the time needed to receive it. Sure, you can watch at 2x and skip around, but in way too many cases it takes a rather long video to explain something that a few paragraphs would do at most.
isrly_eder ยท 2 points ยท Posted at 17:13:26 on May 25, 2016 ยท (Permalink)
thank you, I hate learning from videos and would rather read. it's so much more efficient!
Rynyl ยท 1 points ยท Posted at 17:59:56 on May 25, 2016 ยท (Permalink)
Fair enough. I'll toss that link on my comment
chubbybrother1 ยท 1 points ยท Posted at 01:28:42 on May 26, 2016 ยท (Permalink)
Downvoted for linking the Day9 explanation. That guy is evil
MartijnCvB ยท 1944 points ยท Posted at 11:19:38 on May 25, 2016 ยท (Permalink)
This equation is a limerick
Edit:
A dozen, a gross and a score
Plus 3 times the square root of 4
Divided by 7
Plus 5 times 11
Is 9 squared and not a bit more.
[deleted] ยท 59 points ยท Posted at 11:44:16 on May 25, 2016 ยท (Permalink)
[deleted]
MartijnCvB ยท 2 points ยท Posted at 11:54:17 on May 25, 2016 ยท (Permalink)
It was on QI a few months ago as well. I already knew it before that though :)
super_aardvark ยท 1 points ยท Posted at 21:25:31 on May 25, 2016 ยท (Permalink)
Wait, what? I thought they retired years ago.
mainstreetmark ยท -1 points ยท Posted at 00:26:36 on May 26, 2016 ยท (Permalink)
Clack died. Now it's the "best of car talk". Or, to use their language:
yvaN_ehT_nioJ ยท 1 points ยท Posted at 23:35:24 on May 25, 2016 ยท (Permalink)
And I heard it this morning on Car Talk thanks to NPR Onetm
The app you can download from your phone's app store that lets you listen to everything from the comedic game show "Wait wait, don't tell me" to the gritty frontline reporting in the new podcast "Embedded," all on the go whenever you want! NPR Onetm
Public radio at your fingertips.
ktkps ยท 377 points ยท Posted at 11:55:34 on May 25, 2016 ยท (Permalink)*
author for that : Leigh Mercer
A light headed limerick:
Edit: more here if you need
Edit 2: From our own backyard: /r/limericks
fff8e7cosmic ยท 540 points ยท Posted at 14:29:52 on May 25, 2016 ยท (Permalink)
There once was a man from Kent
Whose tool was so long that it bent
To save her some trouble
He folded it double
And instead of coming, he went
TheBiggestZander ยท 411 points ยท Posted at 15:59:14 on May 25, 2016 ยท (Permalink)
There was a young lady named Bright
who traveled much faster than light.
She set out one day
in a relative way,
and came back the previous night.
jacob_ewing ยท 45 points ยท Posted at 16:49:43 on May 25, 2016 ยท (Permalink)
There once was a man from Darjeeling,
who boarded a bus bound for Ealing.
He saw on the door,
"Don't spit on the floor!"
so he stood up and spat on the ceiling.
Joald ยท 50 points ยท Posted at 19:18:16 on May 25, 2016 ยท (Permalink)*
There once was a man from Devon,
Whose home was cozy like heaven,
It sat by a lake,
And there he ate steak,
Bush did nine eleven.
oren0 ยท 18 points ยท Posted at 21:01:29 on May 25, 2016 ยท (Permalink)
9/11 jokes are one thing but the tragedy of this post is the terrible meter.
aofhaocv ยท 6 points ยท Posted at 22:33:36 on May 25, 2016 ยท (Permalink)
I fixed it.
DerpDargon ยท 10 points ยท Posted at 23:26:19 on May 25, 2016 ยท (Permalink)
There once was a vampire named Mabel
Who's menstrual cycle was stable
Every full moon
She'd whip out a spoon
And drink herself under the table
Obi-Tron_Kenobi ยท 15 points ยท Posted at 20:01:38 on May 25, 2016 ยท (Permalink)
There one was a man on Reddit
Who tried break lines, but can't get it
He added one space
But it's twice "Enter" in place
He jumped up and just said "forget it."
LonePaladin ยท 3 points ยท Posted at 23:49:44 on May 25, 2016 ยท (Permalink)
With Reddit, you end with a space
Then put one more in the same place
So your lines run together
Like birds of a feather
And you don't put your palm on your face.
(A little clumsy, I'll admit.)
[deleted] ยท 2 points ยท Posted at 21:11:21 on May 25, 2016 ยท (Permalink)*
[deleted]
benwaffle ยท 7 points ยท Posted at 22:06:13 on May 25, 2016 ยท (Permalink)
A sailor who slept in the sun,
Woke to find his fly buttons undone,
He remarked with a smile,
"Good grief, a sun-dial!
And now it's a quarter-past one."
SwordofDionysus ยท 6 points ยท Posted at 23:35:38 on May 25, 2016 ยท (Permalink)
There once was a harlot named Sue
Who filled her vagina with glue,
She said with a grin:
If they'll pay to get in,
Well, they'll pay to get out of it too!
LonePaladin ยท 4 points ยท Posted at 23:44:18 on May 25, 2016 ยท (Permalink)
If you stick a stock of liquor in your locker
Be sure to stick a lock upon your stock
Or some joker who is slicker's
Gonna trick you of your liquor
If you fail to lock your liquor with a lock
gileso ยท 1 points ยท Posted at 01:39:28 on May 26, 2016 ยท (Permalink)
There once was a man called Bob
Who always ate corn on the cob,
He put it in the oven,
It came out in a sudden,
And dropped it all on his nob.
spraykrug ยท 7 points ยท Posted at 19:57:01 on May 25, 2016 ยท (Permalink)
There once was a man from Madras,
who had two great balls of brass,
in stormy weather,
they both clanked together,
and sparks flew out of his ass.
Soringo ยท 4 points ยท Posted at 22:00:54 on May 25, 2016 ยท (Permalink)
There one was a man from Nantucket,
Who always wanked in a bucket,
He woke up one morn,
And he'd lost all his porn,
So he went back to bed and said fuck it.
Mindless_Insanity ยท 2 points ยท Posted at 23:47:57 on May 25, 2016 ยท (Permalink)
There once was a man from Belair, Who was fucking a girl on the stair, The banister broke, So he quickened his stroke, And finished her off in the air,
Edit: I'm the person the reddit limerick was about
THIS_MSG_IS_A_LIE ยท 4 points ยท Posted at 03:10:20 on May 26, 2016 ยท (Permalink)
This bounces off the tongue better:
There once was a man from Madras,
who boasted two great balls of brass,
when in stormy weather
they'd both clank together
and sparks would fly out of his ass.
diarrhea_pockets ยท 7 points ยท Posted at 05:16:13 on May 26, 2016 ยท (Permalink)
A mosquito was heard to exclaim
"A chemist has poisoned my brain!
The cause of my sorrow
Is paradichloro
diphenyltrichloroethane."
[deleted] ยท 1 points ยท Posted at 17:24:44 on May 25, 2016 ยท (Permalink)
[deleted]
Cybraxia ยท 3 points ยท Posted at 21:59:13 on May 25, 2016 ยท (Permalink)
If you want more physics limericks, David Morin's Introduction to Classical Mechanics is excellent.
One of my favourites:
our units are wrong! cried the teacher.
Your church weighs six joules โ what a feature!
And the people inside
Are four hours wide,
And eight gauss away from the preacher!
Dim_Innuendo ยท 1 points ยท Posted at 13:52:24 on May 26, 2016 ยท (Permalink)
There once was a fellow named Fiske,
whose stroke was exceedingly brisk.
So fast was his action,
the Lorenz contraction
diminished his dong to a disk.
bakugandrago18 ยท 1 points ยท Posted at 22:24:51 on May 25, 2016 ยท (Permalink)
A while back I saw a limerick template using variables that was also a limerick.
Dim_Innuendo ยท 1 points ยท Posted at 13:54:22 on May 26, 2016 ยท (Permalink)
A handsome young man from Racine
invented a fucking machine:
both concave and convex
it could fit either sex
(with attachments for those in-between).
Hi_jinks ยท 0 points ยท Posted at 23:59:16 on May 25, 2016 ยท (Permalink)
There once was a man from Nantucket, With a dick so long he could suck it! He said with a grin, Wiping spunk from his chin, "If my ear was a cunt I would fuck it!"
ABCDEFandG ยท 9 points ยท Posted at 16:17:27 on May 25, 2016 ยท (Permalink)
I just realized I love limericks.
rnykal ยท 1 points ยท Posted at 21:17:59 on May 25, 2016 ยท (Permalink)
There was a young man from Belgrave
Who found a dead whore in a cave.
It must have taken pluck,
to have a cold fuck;
But think of the money he saved!
instagramcracker ยท 14 points ยท Posted at 16:58:48 on May 25, 2016 ยท (Permalink)
There once was a man from Peru
Who dreamed he was eating his shoe
He woke with a fright
In the middle of the night
To find that his dream had come true.
Steel_Shield ยท 3 points ยท Posted at 20:37:34 on May 25, 2016 ยท (Permalink)
Wasn't this one in Spongebob?
instagramcracker ยท 1 points ยท Posted at 04:19:20 on May 26, 2016 ยท (Permalink)
Yes sir/ma'am!
Slobotic ยท 22 points ยท Posted at 16:09:54 on May 25, 2016 ยท (Permalink)
There was was a fellow named Paul
Whose prick was incredibly small
He'd get a lay
and fuck her all day
without touching her vaginal wall.
[deleted] ยท 16 points ยท Posted at 18:11:08 on May 25, 2016 ยท (Permalink)*
[deleted]
Slobotic ยท 26 points ยท Posted at 18:18:29 on May 25, 2016 ยท (Permalink)
There once was a user named Spankr
for a limerick he did have a hanker
so I thought one up quick,
and clickity click,
I typed it and sent to the wanker.
ilovemusic_s ยท 2 points ยท Posted at 19:21:58 on May 25, 2016 ยท (Permalink)
There once was a user names slobotic
whom thought a poem robotic
he thought up a rhyme
To sentence his crime
with his keyboard go clickity click
Heroicis ยท 3 points ยท Posted at 23:38:44 on May 25, 2016 ยท (Permalink)
Fuck tha police comin' straight from the underground
Am I doing this right?
ilovemusic_s ยท 1 points ยท Posted at 23:53:09 on May 25, 2016 ยท (Permalink)
Sadly, this is perfect.
Barimen ยท 4 points ยท Posted at 17:22:11 on May 25, 2016 ยท (Permalink)
Ooooh. A Paul plays in my Pathfinder campaign. Gotta save this one for when he rolls a Nat 1. :D
Wiki_pedo ยท 1 points ยท Posted at 22:09:25 on May 25, 2016 ยท (Permalink)
Was it this guy?
Slobotic ยท 1 points ยท Posted at 22:11:48 on May 25, 2016 ยท (Permalink)
My god...
GenestealerUK ยท 7 points ยท Posted at 16:33:52 on May 25, 2016 ยท (Permalink)
oh_no_aliens ยท 2 points ยท Posted at 16:15:16 on May 25, 2016 ยท (Permalink)
Ah. I know this man. We had Yorkshire pudding.
StormRider2407 ยท 5 points ยท Posted at 15:01:52 on May 25, 2016 ยท (Permalink)
There once was a man from Nantucket...
EdricStorm ยท 14 points ยท Posted at 18:10:46 on May 25, 2016 ยท (Permalink)
There once was a man from Nantucket
Whose dick was so long he could suck it
And he said with a grin
As he wiped off his chin
If my ear were a cunt I would fuck it
Enwhyme ยท 11 points ยท Posted at 20:06:15 on May 25, 2016 ยท (Permalink)
A horny young lady named Alice
Used a dynamite stick as a phallus
They found her vagina in North Carolina
And her asshole in Buckingham Pallace
Kid_Truism ยท 8 points ยท Posted at 20:37:35 on May 25, 2016 ยท (Permalink)
there once was woman called jill
used a dynamite stick for a thrill
they found her vagina in north carolina
and bits of her tits in brazil
cousin_franky ยท 1 points ยท Posted at 20:44:44 on May 25, 2016 ยท (Permalink)
I love the 'its' alliteration in the last line, bonus.
Kid_Truism ยท 2 points ยท Posted at 20:50:48 on May 26, 2016 ยท (Permalink)
that's internal rhyme mate not alliteration.
alliteration is when words start with the same sound like lots and lots of lucky lads liking licking ladies.
cousin_franky ยท 1 points ยท Posted at 03:46:51 on May 27, 2016 ยท (Permalink)
Oh cool. Thanks for the explanation! Makes sense.
Kid_Truism ยท 1 points ยท Posted at 15:51:36 on May 27, 2016 ยท (Permalink)
no worries mate! i write rhyming verse and raps so i think about the various facets of poetry and so on quite a lot. :D
ABCDEFandG ยท 1 points ยท Posted at 12:07:38 on May 26, 2016 ยท (Permalink)
that's not an alliteration
CannedWolfMeat ยท 2 points ยท Posted at 18:17:17 on May 25, 2016 ยท (Permalink)
There once was a man from Devon
Who thought that his life was heaven
He ate Cornish ice creams
And watched lots of live streams
Bush did nine-eleven.
Smalz22 ยท 2 points ยท Posted at 15:30:31 on May 25, 2016 ยท (Permalink)
Jack and Jill went up the hill
both with a buck and a quarter
Jill came down with $2.50
What a slut!
[deleted] ยท 2 points ยท Posted at 16:21:21 on May 25, 2016 ยท (Permalink)
OOHHHHHH!!!
oligodendrocytes ยท 1 points ยท Posted at 16:40:03 on May 25, 2016 ยท (Permalink)
I like this one more
saxmaster98 ยท 1 points ยท Posted at 21:30:26 on May 25, 2016 ยท (Permalink)
There once was a man from Nantucket,
Who's cock was so long he could suck it.
He said with a grin,
As he wiped off his chin,
"If my ear were a hole I'd fuck it."
roadrunnuh ยท 1 points ยท Posted at 22:07:04 on May 25, 2016 ยท (Permalink)
Washington?
ktkps ยท 1 points ยท Posted at 05:03:31 on May 26, 2016 ยท (Permalink)
Checks out as per the definition in wiki:
[deleted] ยท 2 points ยท Posted at 16:30:38 on May 25, 2016 ยท (Permalink)
There was an old woman from Ealing
Who had a terrible feeling
She fell on her back
Opened her crack
And pissed all over the ceiling
Kid_Truism ยท 1 points ยท Posted at 20:48:12 on May 25, 2016 ยท (Permalink)
i love that one.
BikerRay ยท 62 points ยท Posted at 17:25:12 on May 25, 2016 ยท (Permalink)
Our chem teacher liked to quote this DDT limerick:
A mosquito was heard to complain
That a chemist had poisoned his brain
The cause of his sorrow
Was paradichloro
Diphenyltrichloroethane.
edgymolotovman ยท 3 points ยท Posted at 02:25:49 on May 26, 2016 ยท (Permalink)
Billy was a chemist's son
Now Billy is no more
For what he thought was H2O
Was H2SO4
EgotisticJesster ยท 44 points ยท Posted at 14:24:50 on May 25, 2016 ยท (Permalink)
I don't get it..
Wyatt915 ยท 7 points ยท Posted at 17:37:45 on May 25, 2016 ยท (Permalink)
I'm with you :/
_Kyu ยท 3 points ยท Posted at 18:52:20 on May 25, 2016 ยท (Permalink)
me either but the rest in the thread were funny
christianpowell416 ยท 3 points ยท Posted at 20:44:36 on May 25, 2016 ยท (Permalink)
What does it mean???
Godd2 ยท 3 points ยท Posted at 21:37:37 on May 25, 2016 ยท (Permalink)
The "correct" answer is desert.
generic-volume ยท 1 points ยท Posted at 10:45:09 on May 26, 2016 ยท (Permalink)
I still don't get it...
Godd2 ยท 2 points ยท Posted at 10:51:26 on May 26, 2016 ยท (Permalink)
It's a trick on the listener of the riddle. You use a couple words that rhyme with beach, and the you describe a desert. The listener then gives an answer of beach, because you've tricked them.
generic-volume ยท 1 points ยท Posted at 01:17:57 on May 27, 2016 ยท (Permalink)
Ahh ok. It still kinda describes a beach though? I think I was largely confused though because I was trying to find something dirty in it given the rest of this thread.
NoticedGenie66 ยท 23 points ยท Posted at 18:24:57 on May 25, 2016 ยท (Permalink)
There once was a poet named Bates
Whose poems weren't always first rate
His first lines weren't bad
But the problem he had
Was that he always tried fitting too many syllables into the last line
[deleted] ยท 4 points ยท Posted at 21:53:03 on May 25, 2016 ยท (Permalink)
Sand isnt soft to the touch! It's coarse and rough, and it gets everywhere.
beenoc ยท 11 points ยท Posted at 16:32:10 on May 25, 2016 ยท (Permalink)
There once was a man from Devon
He thought that his home was heaven
He ate Cornish ice creams
And watched gaming livestreams
George Bush did 9/11
[deleted] ยท 3 points ยท Posted at 17:47:57 on May 25, 2016 ยท (Permalink)
Oh, I need.
Wiki_pedo ยท 3 points ยท Posted at 22:11:25 on May 25, 2016 ยท (Permalink)
There once was a woman from Crewe
Whose limericks stopped at line two
[deleted] ยท 2 points ยท Posted at 17:48:48 on May 25, 2016 ยท (Permalink)
There once was a fellow named Clyde,
Who fell in an outhouse and died,
Along came his brother,
Who fell in another,
And now their interred side-by-side.
bakugandrago18 ยท 2 points ยท Posted at 22:26:50 on May 25, 2016 ยท (Permalink)
Is this a trick question? I feel like an idiot for not getting the real answer.
MartijnCvB ยท 1 points ยท Posted at 11:58:55 on May 25, 2016 ยท (Permalink)
Thank you :) I didn't know that!
WikiWantsYourPics ยท 148 points ยท Posted at 14:11:57 on May 25, 2016 ยท (Permalink)*
The integral t squared dt
from one to the cube root of three
times the cosine
of three pi over nine
is the [natural] log of the cube root of e
Edit: from, not times in line 2. Thanks /u/romkyns !
hborrgg ยท 14 points ยท Posted at 15:25:01 on May 25, 2016 ยท (Permalink)
You could just pronounce it "ln"
Al2718x ยท 14 points ยท Posted at 16:00:15 on May 25, 2016 ยท (Permalink)
Saying "log" is also fine. Mathematicians usually use "log" to mean "natural log" (unless they're talking about log base 2).
hborrgg ยท 4 points ยท Posted at 16:12:54 on May 25, 2016 ยท (Permalink)
That never bugged our professor as much as "lun" though, so we used the latter.
zacharythefirst ยท 4 points ยท Posted at 17:31:37 on May 25, 2016 ยท (Permalink)
just read it as el en
edderiofer ยท 5 points ยท Posted at 18:31:33 on May 25, 2016 ยท (Permalink)
What? It's pronounced "lin", isn't it?
starlitepony ยท 1 points ยท Posted at 23:18:38 on May 25, 2016 ยท (Permalink)
I always say 'lon'
Seraphaestus ยท 2 points ยท Posted at 19:51:33 on May 25, 2016 ยท (Permalink)
I've always seen "log" refer to the log of base 10.
Al2718x ยท 1 points ยท Posted at 00:59:07 on May 26, 2016 ยท (Permalink)
Yeah that's common in high school because of our base 10 number system (1 plus the floor of the base 10 log is the number of decimal digits in a number), but there is nothing special about 10, so very little serious mathematics is done with base 10 logarithms.
beingforthebenefit ยท 1 points ยท Posted at 18:53:52 on May 25, 2016 ยท (Permalink)
log is multivalued though! log(z)=ln(z)+i Arg(z) + 2pi*i*k
Al2718x ยท 1 points ยท Posted at 01:01:29 on May 26, 2016 ยท (Permalink)
Maybe under one definition, but it shouldn't make a difference if you're dealing with real numbers right?
beingforthebenefit ยท 2 points ยท Posted at 01:20:15 on May 26, 2016 ยท (Permalink)
Oh, I was just pointing out another definition of log. It all depends on the context. My attempt at a joke.
If you're in number theory, log(x) means ln(x) and nothing more. If it's basic algebra, log(x) is base 10, if it's complex analysis, log(x) takes on infinitely many numbers (even the image of a real number is a set of infinitely many complex numbers).
ImS0hungry ยท 1 points ยท Posted at 06:26:50 on May 26, 2016 ยท (Permalink)
then what do they say when they actually mean log base 10?
Al2718x ยท 1 points ยท Posted at 13:03:59 on May 26, 2016 ยท (Permalink)
The could say log base 10, but generally, most mathematicians will never have a reason to use log base 10
ImS0hungry ยท 2 points ยท Posted at 14:06:53 on May 26, 2016 ยท (Permalink)
Interesting. I've finally reached a point in my math studies where I use log to mean ln. I'm a C.S. major but the more math I study the more I love it. I'm thinking of double majoring. I'll be starting my sophmore year this fall and will already be taking linear.
062985593 ยท 1 points ยท Posted at 10:33:22 on May 26, 2016 ยท (Permalink)
I always called it "lateral nog".
romkyns ยท 10 points ยท Posted at 15:39:06 on May 25, 2016 ยท (Permalink)
Second line should read "from", not "times". It specifies the limits of the integral.
Here's a slight variation of the same:
Left hand side: http://www.wolframalpha.com/input/?i=integral+t^2+dt+from+1+to+cube+root+3
Right hand side: http://www.wolframalpha.com/input/?i=2%2F3+*+cos%283pi+%2F+9%29+%2B+ln%28cube+root+e%29
bl1y ยท 2 points ยท Posted at 18:22:42 on May 25, 2016 ยท (Permalink)
I learned it as:
WikiWantsYourPics ยท 3 points ยท Posted at 18:26:13 on May 25, 2016 ยท (Permalink)
Z doesn't rhyme with "three" in my accent, so it will stay "t" for me.
bl1y ยท 1 points ยท Posted at 19:36:38 on May 25, 2016 ยท (Permalink)
You can't rhyme "zed" and "thred"?
xereeto ยท 2 points ยท Posted at 01:35:28 on May 26, 2016 ยท (Permalink)
The integral sec y dy
From zero to one sixth of pi
Is log to base e
Of the square root of three
Times the sixty-fourth power of i
139mod70 ยท 4 points ยท Posted at 15:41:09 on May 25, 2016 ยท (Permalink)*
(to the tune of "Pop! goes the Weasel")
X equals negative b
Plus or minus the squaaare root
Of b squared minus four a c
Allll over twoooo aa.
yourmomknowsit ยท 1 points ยท Posted at 22:31:42 on May 25, 2016 ยท (Permalink)
this is a classic that I start to recite out of nowhere sometimes
jesset77 ยท 1 points ยท Posted at 23:21:39 on May 25, 2016 ยท (Permalink)
While it's not the same one, it reminds me of Newton's limerick featured in this ERB episode.
Emm03 ยท 1 points ยท Posted at 01:35:17 on May 26, 2016 ยท (Permalink)
Could also be:
which might flow a little better (although, admittedly, I'm fairly good at math but fairly shitty at poetry)
[deleted] ยท 1 points ยท Posted at 07:29:12 on May 26, 2016 ยท (Permalink)
To make it flow better, you could use "three pi on nine." It's not the most common way of saying it, but I've definitely heard it used. (Mostly by Australians)
quinterbeck ยท 1 points ยท Posted at 15:56:25 on May 25, 2016 ยท (Permalink)
Should be "from one to the cube root of three", not times
[deleted] ยท 17 points ยท Posted at 11:23:49 on May 25, 2016 ยท (Permalink)
[deleted]
MartijnCvB ยท 58 points ยท Posted at 11:25:53 on May 25, 2016 ยท (Permalink)
"And not a bit more"
randomcrocodile ยท 5 points ยท Posted at 13:37:08 on May 25, 2016 ยท (Permalink)
I'd say it's 0=naught (not).
[deleted] ยท 3 points ยท Posted at 13:38:02 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 13:50:56 on May 25, 2016 ยท (Permalink)
But there's no edit sign.
EightBitNacho ยท 6 points ยท Posted at 14:25:56 on May 25, 2016 ยท (Permalink)
If you edit your comment fast enough there won't be one.
Scream26 ยท 3 points ยท Posted at 15:37:48 on May 25, 2016 ยท (Permalink)
There once was a man from Peru,
Who dreamed he was eating his shoe.
He woke with a fright,
In the middle of the night,
To find that his dream had come true.
lunchlady55 ยท 3 points ยท Posted at 16:52:43 on May 25, 2016 ยท (Permalink)
There once was a lady from Bright,
Who could travel much faster than light,
She set out one day,
In a relative way,
And came back on the previous night.
liarandathief ยท 2 points ยท Posted at 11:56:54 on May 25, 2016 ยท (Permalink)
I remember reading this in Omni magazine.
omegaxysgaming ยท 1 points ยท Posted at 15:06:02 on May 25, 2016 ยท (Permalink)
Showed it to my english teacher, "nice".
infosackva ยท 1 points ยท Posted at 15:28:29 on May 25, 2016 ยท (Permalink)
My teacher gave me a nickname because of this limerick
MartijnCvB ยท 1 points ยท Posted at 15:29:25 on May 25, 2016 ยท (Permalink)
What was the nickname? :)
infosackva ยท 2 points ยท Posted at 15:50:21 on May 25, 2016 ยท (Permalink)
"Rapper"
He's this older guy, but genuinely damn brilliant at maths and chess, and he has a reputation for giving nicknames. I'd found this limerick, and no-one in my class was impressed by it, but he was nearby, I told him, he found it very amusing and lo and behold, next time he took the register he said rapper in place of my name.
cocoboco101 ยท 1 points ยท Posted at 15:34:43 on May 25, 2016 ยท (Permalink)
My favorite limerick:
A wonderful bird is the pelican,
His beak can hold more than his belly can;
In his beak, he stores enough food for a week,
But I don't know how in the hell he can.
Sandmaester44 ยท 1 points ยท Posted at 04:11:12 on May 26, 2016 ยท (Permalink)
The meter is a bit off, but it's pretty decent
And in his beak
He stores food for a week
Bobius ยท 1 points ยท Posted at 15:37:23 on May 25, 2016 ยท (Permalink)
This is on my classroom wall!
Presently42 ยท 1 points ยท Posted at 16:09:42 on May 25, 2016 ยท (Permalink)*
Here's one I composed:
The derivative, d/dx
Of a curve, sin(x), shouldn't vex:
It's the slope of the line
Which is tangent to sine
At a given point. See? Not complex!
xereeto ยท 2 points ยท Posted at 01:07:58 on May 27, 2016 ยท (Permalink)
Reddit doesn't use HTML markup... and that's not even valid HTML markup anyway. To make a new line you can either end your line with two spaces followed by a newline
Like this, or use two newlines
Like this
Presently42 ยท 1 points ยท Posted at 01:29:49 on May 27, 2016 ยท (Permalink)
Ah thanks! Couldn't figure it out. And as for my mad html coding skillz, well, I've mostly forgotten them.
xereeto ยท 2 points ยท Posted at 01:38:24 on May 27, 2016 ยท (Permalink)
<br> is a newline. It used to be <br></br> or <br />, but now a single <br> is the standard.
Presently42 ยท 1 points ยท Posted at 01:41:58 on May 27, 2016 ยท (Permalink)
O yeah, I remember now discovering this some where.
Thereminz ยท 1 points ยท Posted at 16:19:29 on May 25, 2016 ยท (Permalink)
Two times three
Is six you see
Farrarzard ยท 1 points ยท Posted at 16:21:45 on May 25, 2016 ยท (Permalink)
Not a limerick, and I can't remember what this equation is for, but b-a/(2k) goes perfectly to shake that by Eminem. It's where Nate Dogg comes in, at 0:53 https://www.youtube.com/watch?v=WrjwGPb0Hvw
loptthetreacherous ยท 1 points ยท Posted at 16:24:12 on May 25, 2016 ยท (Permalink)
Integral t squared dt,
From one to the cubed root of three
Times the cosine
Of three pi over nine
Is the log of the cubed root of e
written out
[deleted] ยท 1 points ยท Posted at 16:41:03 on May 25, 2016 ยท (Permalink)
I would change the last line, since "9" and "squared" are both stressed syllables, which doesn't fit the limerick scheme.
The edit no one asked for:
MartijnCvB ยท 1 points ยท Posted at 16:43:10 on May 25, 2016 ยท (Permalink)
Ah, but I didn't write the limerick... I just copied it. Thanks for the suggestion though :)
guy_from_canada ยท 1 points ยท Posted at 16:45:27 on May 25, 2016 ยท (Permalink)
I think I saw this on QI once!
MartijnCvB ยท 2 points ยท Posted at 16:45:59 on May 25, 2016 ยท (Permalink)
Correct! It was on QI a few months ago ;)
bigdrew510 ยท 1 points ยท Posted at 16:48:19 on May 25, 2016 ยท (Permalink)
Just heard this on car talk this week!
kevtastic ยท 1 points ยท Posted at 16:49:42 on May 25, 2016 ยท (Permalink)
my penis is a limerick
hoodie92 ยท 1 points ยท Posted at 16:54:09 on May 25, 2016 ยท (Permalink)
Reminds me of my favourite educational limerick:
A mosquito was heard to complain
That a chemist had poisoned his brain.
The cause of his sorrow
Was paradichloro-
Diphenyltrichloroethane.
upstateman ยท 1 points ยท Posted at 18:24:18 on May 25, 2016 ยท (Permalink)
There was a man from Peru
Whose limerick ended on line two.
redoubledit ยท 1 points ยท Posted at 18:39:30 on May 25, 2016 ยท (Permalink)
I just fell in love with limericks
Prettygame4Ausername ยท 1 points ยท Posted at 18:54:47 on May 25, 2016 ยท (Permalink)
The integral sec y/dy,
From zero to one sixth of pi,
Is log to the base e,
By the square root of three,
Times the 64th power of i.
Reygle ยท 1 points ยท Posted at 19:30:09 on May 25, 2016 ยท (Permalink)
I also love the show Qi.
MadPat ยท 1 points ยท Posted at 19:52:25 on May 25, 2016 ยท (Permalink)
There once was a product space sizeable,
Whose topology seemed realizable,
for a regular space
with a countable base
is well-known to be always metrizable.
[deleted] ยท 1 points ยท Posted at 20:08:35 on May 25, 2016 ยท (Permalink)
QI
MrSeabody ยท 1 points ยท Posted at 20:24:24 on May 25, 2016 ยท (Permalink)
My personal favorite:
The integral sec y dy
From 0 to 1/6 of pi
Is log to base e
Of the square root of three
Times the sixty-fourth power of i.
Pilchard123 ยท 1 points ยท Posted at 21:27:22 on May 25, 2016 ยท (Permalink)*
There was an Old Person of Chile
Whose conduct was painful and silly
He sat on the stairs
Eating apples and pears
That imprudent Old Person of ChileFiring pips out of his willyMartijnCvB ยท 2 points ยท Posted at 21:31:53 on May 25, 2016 ยท (Permalink)
I get that reference! Alan Davies is great. Silly, but great.
ShinyPants42 ยท 1 points ยท Posted at 00:22:48 on May 26, 2016 ยท (Permalink)
"There once was a woman from Venus whose head was shaped like a"-"Thats enough, Data"
555-voting-system ยท 1 points ยท Posted at 04:33:52 on May 26, 2016 ยท (Permalink)
"Waiter, my butter's writ large in!"
A man was heard to be chargin'
"But I had to write there,
said the waiter, Pierre,
'Cause I couldn't find room in the margin..."
555-voting-system ยท 1 points ยท Posted at 19:22:08 on May 26, 2016 ยท (Permalink)
Also:
Schrรถdinger said that a cat
is alive or it's dead, and that's that.
But Heisenberg said
It's alive and it's dead
And it's state can be seen as a stat!
BlindTiger86 ยท 1 points ยท Posted at 15:16:54 on May 25, 2016 ยท (Permalink)
solve for gross
MartijnCvB ยท 3 points ยท Posted at 15:19:36 on May 25, 2016 ยท (Permalink)
Gross = twelve dozen, AKA 144. https://en.wikipedia.org/wiki/Gross_(unit)
drphillycheesesteak ยท 544 points ยท Posted at 13:40:53 on May 25, 2016 ยท (Permalink)
The Fourier Transform of a Gaussian is another Gaussian.
cthulu0 ยท 376 points ยท Posted at 14:40:26 on May 25, 2016 ยท (Permalink)*
I actually have a patent of an audio signal processing circuit that makes use of that fact. Note: I did not patent the fact that FT(gaussian) = gaussian. You can't patent math.
Edit: In fact if you have an iphone5 or 6, or an ipad or ipod or mac, this patented design is processing your audio. Its not everyday you can say that something you designed is in a hundred million devices.
crossedstaves ยท 77 points ยท Posted at 15:52:24 on May 25, 2016 ยท (Permalink)
Are you sure? I kinda want to try. Like all of math, the concept of math. "A novel method of determining rigorous quantitative relational properties of entities"
Purplociraptor ยท 51 points ยท Posted at 17:27:39 on May 25, 2016 ยท (Permalink)
If Apple can patent round corners, then I think you can patent math.
Harddaysnight1990 ยท 8 points ยท Posted at 22:42:49 on May 25, 2016 ยท (Permalink)
Yeah, but that lawsuit didn't hold up in court, and Apple lost that patent. Really, patents are like contracts. They don't mean much until you take it to court, then they're actually scrutinized.
Thinks_Too_Logically ยท 2 points ยท Posted at 04:05:49 on May 26, 2016 ยท (Permalink)
You can't patent laws of nature. Pretty sure math is in the same vein.
NNNTE ยท 1 points ยท Posted at 00:38:02 on May 26, 2016 ยท (Permalink)
Those were design patents, not utility patents! the requirements for each are a bit different.
[deleted] ยท 14 points ยท Posted at 18:58:32 on May 25, 2016 ยท (Permalink)
The Supreme Court decided this a few years his, more generally about Algorithms. It was mainly due to the insanity of the start up bubble but it applies also to maths. They are still patentable but only under very specific conditions; the new way of doing it is linked to a new physical thing (eg, if it's only possible to utilize this equation in a specific new circuit you invented), or the new algorithm legitimately revolutionizes the field of intended use (eg, you find a new way of adding that makes existing processors execute operations 10x faster). Very few algorithm patents have been granted in the u.s. since then, single digits if I'm not mistaken
mythozoologist ยท 5 points ยท Posted at 23:34:01 on May 25, 2016 ยท (Permalink)
What if I have this sweet middle-out compression algorithm?
guto8797 ยท 53 points ยท Posted at 16:21:01 on May 25, 2016 ยท (Permalink)
Stop giving the finebros new ideqs
DontSayAlot ยท 49 points ยท Posted at 17:47:35 on May 25, 2016 ยท (Permalink)
yeqh it's bqd enough thqt they pqtended the first letter of the qlphqbet.
UNSTABLETON_LIVE ยท 1 points ยท Posted at 20:28:44 on May 25, 2016 ยท (Permalink)
We had to say dickitey because the Kaiser stole our number twenty.
supremecrafters ยท 1 points ยท Posted at 18:53:47 on May 25, 2016 ยท (Permalink)
But you're using it in your username!
kiyoske ยท 5 points ยท Posted at 19:16:09 on May 25, 2016 ยท (Permalink)
You'd probably encounter prior art somewhere.
cthulu0 ยท 1 points ยท Posted at 19:57:53 on May 25, 2016 ยท (Permalink)
What are you smoking? And more importantly, can I have some?
father_kipz ยท 0 points ยท Posted at 18:42:48 on May 25, 2016 ยท (Permalink)
Abstract ideas are not patentable
[deleted] ยท 11 points ยท Posted at 15:50:51 on May 25, 2016 ยท (Permalink)
Wow I'm really curious about this. Can you elaborate.
Katastic_Voyage ยท 8 points ยท Posted at 17:18:31 on May 25, 2016 ยท (Permalink)
Actually, I wonder if you can...
You can certainly mathematical steps. Creative Labs screwed John Carmack by patenting Shadow Volumes. And what is drawing graphics except calculating a bunch of math.
cthulu0 ยท 8 points ยท Posted at 19:50:51 on May 25, 2016 ยท (Permalink)
Well it is established now as of 2016 that you cannot patent abstract ideas. And math is about as abstract as it gets.
Unfortunately inventors get around this loop hole by describing a system that implements the mathematical method. So they technically patenting the embodiment rather than the algorithm.
Unfortunately the patent office is fooled repeatedly by such a trick. Also this Carmack stuff probably happened 2 decades ago before the Supreme Court camed down on these shennanigans.
The patent system is idiotic and needs a serious overhaul if not outright elimination.
Snaperkids ยท 1 points ยท Posted at 02:50:14 on May 26, 2016 ยท (Permalink)
Patents do not need to be eliminated. If someone put forth the resources to develop a concept, then they should have the right to produce it exclusively. However I do agree that it needs a massive overhaul, especially where software is concerned.
cthulu0 ยท 1 points ยท Posted at 14:50:10 on May 26, 2016 ยท (Permalink)
Well European Union has the common sense to disallow software patents because software basically is applied math.
Too bad the US doesn't follow suit. But it won't happen anytime soon. It would require an act of Congress and Congress is full of lawyers. Lawyers would be the ones most hurt by an overhaul of the patent system.
whatisthisicantodd ยท 17 points ยท Posted at 15:28:28 on May 25, 2016 ยท (Permalink)
Hey, cool! What does it do to the audio signal?
(More importantly, can I use it to make music?)
jet_heller ยท 4 points ยท Posted at 15:27:31 on May 25, 2016 ยท (Permalink)
You sound like a person who might work for the Telos Alliance.
cthulu0 ยท 6 points ยท Posted at 20:00:15 on May 25, 2016 ยท (Permalink)
Actually work for Cirrus Logic based here in Austin.
Had to google Telos Alliance. Sounded like a guild in some multiplayer online game :-)
fireatx ยท 1 points ยท Posted at 09:34:06 on May 26, 2016 ยท (Permalink)
Hello fellow Austinite! Got any opportunities for a desperate CS undergrad? ;)
Just kidding (mostly). But really, it's cool to learn about tech companies in our city. I tend to forget how tech-oriented it is here. Also cool to learn about your patent!
cthulu0 ยท 1 points ยท Posted at 14:44:38 on May 26, 2016 ยท (Permalink)
Thank you!
Yes Austin is not nicknamed Silicon Hills for nothing.
jtayl711 ยท 3 points ยท Posted at 17:17:43 on May 25, 2016 ยท (Permalink)
Would you mind elaborating on this? What does your circuit do? I'm very interested in audio processing and just finished taking circuits 2
cthulu0 ยท 3 points ยท Posted at 19:52:46 on May 25, 2016 ยท (Permalink)
Asynchronous sample rate converter. For more detail see my comments to other people who asked something similar.
Ech0ofSan1ty ยท 2 points ยท Posted at 17:36:12 on May 25, 2016 ยท (Permalink)
What does that do for audio signal processing?
cthulu0 ยท 1 points ยท Posted at 19:44:48 on May 25, 2016 ยท (Permalink)
See my replies to other commenters that asked something similar.
zesn ยท 2 points ยท Posted at 18:33:34 on May 25, 2016 ยท (Permalink)
Complete newb about to study electronics with music. Tell me more about this circuit please?
cthulu0 ยท 10 points ยท Posted at 19:43:24 on May 25, 2016 ยท (Permalink)
Asychronous sample rate converter implementation for use on an integrated circuit. Different audio sources use wildly different sample rates. You need to be able to play an audio source data recorded at one sample rate on a system that uses another sample rate. Or you might need to mix different audio sources together which used different sample rates.
rtomek ยท 1 points ยท Posted at 23:21:23 on May 25, 2016 ยท (Permalink)
https://www.google.com/patents/US7298296
kripticblade ยท 1 points ยท Posted at 17:28:09 on May 25, 2016 ยท (Permalink)
I made that.
Lichewitz ยท 1 points ยท Posted at 21:14:08 on May 25, 2016 ยท (Permalink)
That's awesome!
mattenthehat ยท 1 points ยท Posted at 21:49:25 on May 25, 2016 ยท (Permalink)
In your case, it is every day that you can say that! Which kind of mind bogglingly, is also true of a whole lot of engineers, from electronics to cars.
I have a job lined up at Western Digital when I graduate in June, and it's a bit crazy to think that a few years from now hundreds of millions of devices using systems I worked on will be storing billions of dollars worth of data (assuming I do my job well if course).
cthulu0 ยท 1 points ยท Posted at 14:43:08 on May 26, 2016 ยท (Permalink)
Yes you are totally correct of course. In fact that is why we get into engineering: not for the money necessarily ( though you can live very comfortably and even be rich), but rather for the fact that you can creatively design stuff that will benefit millions of people.
Glad to see you are on the verge of starting a promising career.
Zanarkandite ยท 1 points ยท Posted at 21:51:08 on May 25, 2016 ยท (Permalink)
Actually, you can say that every day if you want to.
Im_A_Viking ยท 1 points ยท Posted at 21:53:00 on May 25, 2016 ยท (Permalink)
Cirrus Logic employee spotted.
cthulu0 ยท 2 points ยท Posted at 14:39:38 on May 26, 2016 ยท (Permalink)
:-)
Im_A_Viking ยท 1 points ยท Posted at 17:19:13 on May 26, 2016 ยท (Permalink)
Hire me please ?
physchy ยท 1 points ยท Posted at 21:58:49 on May 25, 2016 ยท (Permalink)
For you? Yes it is every day
gart888 ยท 1 points ยท Posted at 22:47:41 on May 25, 2016 ยท (Permalink)
How rich are you?
cthulu0 ยท 1 points ยท Posted at 14:39:06 on May 26, 2016 ยท (Permalink)
I am squarely in the 1% maybe even 0.1%, but that is not saying much. So are doctors and lawyers and small business owners.
Unfortunately I don't get paid by commission.
gart888 ยท 1 points ยท Posted at 14:46:38 on May 26, 2016 ยท (Permalink)
Top 0.1% would give you an annual income of $1.6M. Congrats!
cthulu0 ยท 1 points ยท Posted at 14:54:54 on May 26, 2016 ยท (Permalink)
Ok I guess I am in the top 0.4%. Still fairly content.
gart888 ยท 2 points ยท Posted at 14:57:18 on May 26, 2016 ยท (Permalink)
I bet. How did you come about inventing/patenting that circuit?
cthulu0 ยท 1 points ยท Posted at 15:28:59 on May 26, 2016 ยท (Permalink)
Hard to answer that question without knowing what your educational background is.
gart888 ยท 2 points ยท Posted at 15:41:30 on May 26, 2016 ยท (Permalink)
I've got a masters degree in applied science.
I'm not asking how /i'd/ go about it though. I'm asking how you did it. Were you working for yourself? Was it a weekend project? Was it a project at a university?
cthulu0 ยท 1 points ยท Posted at 15:57:54 on May 26, 2016 ยท (Permalink)
I was (an still am) working for a company that designs integrated circuits. So though I am the inventor, the company owns the invention. So I obviously did not have to spend my own money on lawyers fees or patent application and maintenace fees. And the invention was for use in a specific product line but was a side project I was working on unbeknownst to my manager.
It took at least a week to show the algorithm would work in MATLAB. It took several months to implement it in actual working silicon. But once that was done and the area was optimized, other managers of other IC projects realized it would benefit their projects also.
Ironically the solution was not fully trusted by our biggest customer (a "fruit" company based in California if you catch my drift). They needed convincing and demanded we show them details. We were apprehensive because they showed a tendency to think that because they were footing the bill, they could co-opt our intellectual property as their own.
kyle1320 ยท 1 points ยท Posted at 23:26:41 on May 25, 2016 ยท (Permalink)
It is if you find enough opportunities.
agumonkey ยท 1 points ยท Posted at 23:30:04 on May 25, 2016 ยท (Permalink)
My name is on a patent but it's both unused, useless and beyond trivial. I like self-repeating equations (quines, exp, ...), this is of much coolness.
cthulu0 ยท 2 points ยท Posted at 14:35:26 on May 26, 2016 ยท (Permalink)
Yes self-reference is cool. I'm a big fan of it. Its what allowed Kurt Godel to formulate his revolutionary incompleteness theorems.
Of the 13 patents I have, I can say the majority of them are either useless and trivial or that I am not particularly proud of them. The gaussian one is only one of two I am really proud of. Unfortunately as an engineer you have to play the patent game to advance in your career.
agumonkey ยท 1 points ยท Posted at 14:51:56 on May 26, 2016 ยท (Permalink)
That's exactly how I got listed in the authors. My adviser wanted to secure the field :)
sbiff ยท 1 points ยท Posted at 23:43:45 on May 25, 2016 ยท (Permalink)
I'd say it everyday regardless.
Mikkelisk ยท 1 points ยท Posted at 01:09:52 on May 26, 2016 ยท (Permalink)
You can say that every day. At least for a few years to come.
CyberneticPanda ยท 1 points ยท Posted at 02:24:44 on May 26, 2016 ยท (Permalink)
I think you can say that every day.
ManPumpkin ยท 1 points ยท Posted at 04:41:27 on May 26, 2016 ยท (Permalink)
You can say it every day though :D
ZanettiJ ยท 1 points ยท Posted at 12:22:45 on May 26, 2016 ยท (Permalink)
WOW, that must be a very very nice thing to achieve.
NicolasGuacamole ยท 1 points ยท Posted at 00:32:51 on August 19, 2016 ยท (Permalink)
Well for you it literally is every day you can say that
mitchell271 ยท 1 points ยท Posted at 18:35:29 on May 25, 2016 ยท (Permalink)
What's it for? I do audio production as a hobby
cthulu0 ยท 5 points ยท Posted at 19:37:09 on May 25, 2016 ยท (Permalink)
Asynchronous sample rate conversion of PCM data on an integrated circuit in an area efficient manner.
GoldenWizard ยท -1 points ยท Posted at 16:49:10 on May 25, 2016 ยท (Permalink)
I patented division by zero.
cthulu0 ยท 1 points ยท Posted at 20:08:38 on May 25, 2016 ยท (Permalink)
Eventhough you are obviously trolling, considering how bad the patent system is, I am surprised nobody does actually have a patent on this.
greenlaser3 ยท 20 points ยท Posted at 17:12:41 on May 25, 2016 ยท (Permalink)
And their widths are related by the Heisenberg uncertainty principle.
Electrical engineering shares a surprising amount of math with quantum physics.
rincon213 ยท 7 points ยท Posted at 19:09:25 on May 25, 2016 ยท (Permalink)
Is it surprising? Electronics basically just push quantum stuffs around
greenlaser3 ยท 5 points ยท Posted at 20:30:07 on May 25, 2016 ยท (Permalink)
I don't see a reason to think that a complicated macroscopic system has to look anything like the underlying quantum mechanics. In fact, quite often the math for macroscopic systems looks nothing like the math for quantum mechanics. For example, diodes exhibit strongly non-linear behaviour even though they're based on quantum mechanics, which is a linear theory.
I think the connection has more to do with the notion of linearity/superposition. It's amazing to me how that idea ties together so many subjects that seem completely unrelated at first glance.
mc8675309 ยท 10 points ยท Posted at 17:50:55 on May 25, 2016 ยท (Permalink)
I've seen that asked on an interview except it was "name an eigenfunction of the Fourier transform."
ben_jl ยท 5 points ยท Posted at 20:03:35 on May 25, 2016 ยท (Permalink)
I'm pretty sure the hyperbolic secant is also an eigenfunction of the FT. Could be wrong though.
mc8675309 ยท 3 points ยท Posted at 20:31:23 on May 25, 2016 ยท (Permalink)
I assume there may be others but the Gaussian is the easiest. If someone demonstrates another I think the interviewer is happy (or I hope they are)
inconspicuous_male ยท 1 points ยท Posted at 02:01:34 on May 26, 2016 ยท (Permalink)
comb is also
TheoryOfSomething ยท 3 points ยท Posted at 22:13:17 on May 25, 2016 ยท (Permalink)*
You're correct. Sech is also an eigenfunction, if you choose the scaling appropriately, namely it has to be Sech[ Sqrt[pi/2] x].
TheoryOfSomething ยท 3 points ยท Posted at 22:15:43 on May 25, 2016 ยท (Permalink)
It's only exactly an eigenfunction if you choose the variance appropriately. If you choose an arbitrary variance then you get back a Gaussian with a different variance than the one you started with, thus its not exactly an eigenfunction.
KrishaCZ ยท 5 points ยท Posted at 16:43:49 on May 25, 2016 ยท (Permalink)
I know some of these words...
inconspicuous_male ยท 6 points ยท Posted at 18:34:48 on May 25, 2016 ยท (Permalink)
If you were to plot a gaussian (a bell curve) with a height of 1, and then draw an infinite number of cosine waves whose height and frequency are the Y and X of the gaussian plot, then add up all of those cosines, you would have the gaussian.
fireball_73 ยท 3 points ยท Posted at 20:38:45 on May 25, 2016 ยท (Permalink)
Are you describing a fourier series or a fourier transform?
inconspicuous_male ยท 1 points ยท Posted at 21:42:59 on May 25, 2016 ยท (Permalink)*
Transform and series since it's a Gaussian!
fireball_73 ยท 1 points ยท Posted at 07:17:41 on May 26, 2016 ยท (Permalink)
Ah yes of course.
Crysist ยท 0 points ยท Posted at 20:14:40 on May 25, 2016 ยท (Permalink)
Just curious, isn't that what the FT does? Split a wave up into an infinite number of waves that add up to the original? Why is the original fact noteworthy?
inconspicuous_male ยท 1 points ยท Posted at 21:44:11 on May 25, 2016 ยท (Permalink)
Because the Fourier transform of most functions is not the original function.
niteman555 ยท 1 points ยท Posted at 01:40:25 on May 26, 2016 ยท (Permalink)
because the fourier transform/series describes the distribution of the amplitudes of the waves with respect to frequency, whereas the original describes the shape with respect to some other variable (for example, time).
Schrockwell ยท 4 points ยท Posted at 15:50:16 on May 25, 2016 ยท (Permalink)
This blew my mind when I first learned it, and at some point I had the necessary knowledge and intuition to have that "ah-ha!" moment, but that's lost now.
The most I can remember is that the FT of a "skinny" Gaussian is a fat one, which I can intuitively understand if I think of the first Gaussian as the amplitude of a signal in the time domain and its FT being the frequency response, i.e. the shorter a pulse gets, the wider the bandwidth it occupies.
niteman555 ยท 3 points ยท Posted at 01:42:17 on May 26, 2016 ยท (Permalink)
You can take it to the extreme and consider the Dirac Delta function, whose Fourier transform is simply 1, and vice-versa. And what is the Dirac Delta, but an infinitely thin Gaussian?
jusjerm ยท 11 points ยท Posted at 16:32:40 on May 25, 2016 ยท (Permalink)
You just dug up an unhappiness I buried long ago
drphillycheesesteak ยท 9 points ยท Posted at 16:47:19 on May 25, 2016 ยท (Permalink)
Fourier is love, Fourier is life... at least until I finish my thesis.
neutron_ ยท 2 points ยท Posted at 19:13:34 on May 25, 2016 ยท (Permalink)
Even after the thesis is complete, you can never stop loving Fourier. Fourier is love. Fourier is life.
inconspicuous_male ยท 2 points ยท Posted at 18:37:06 on May 25, 2016 ยท (Permalink)
Of course the first Fourier comment is from an ImSci student...
drphillycheesesteak ยท 2 points ยท Posted at 18:41:25 on May 25, 2016 ยท (Permalink)
Uh oh, time for a new account.
inconspicuous_male ยท 2 points ยท Posted at 21:44:34 on May 25, 2016 ยท (Permalink)*
I don't know who you are. I just know your r/rit flair.
Although I have an idea...
drphillycheesesteak ยท 1 points ยท Posted at 01:56:06 on May 26, 2016 ยท (Permalink)
http://giphy.com/gifs/qZUqz5qr9wsyA/html5
Whitewolfer ยท 1 points ยท Posted at 18:54:29 on May 25, 2016 ยท (Permalink)
This one is really nifty.
QuintusVS ยท 1 points ยท Posted at 20:54:15 on May 25, 2016 ยท (Permalink)
I understood about 5 words of that sentence...
mokojin ยท 1 points ยท Posted at 23:14:54 on May 25, 2016 ยท (Permalink)
What I found even more interesting is that the Fourier transform of a narrow Gaussian is a wide Gaussian!
Heisenberg's uncertainty relation makes use of this, as the real space and momentum space are connected via the Fourier transform, meaning that you just cannot have arbitrary narrow gaussians for both of them.
(sorry for poor English, studied physics in Germany)
udbluehens ยท 1 points ยท Posted at 02:50:34 on May 26, 2016 ยท (Permalink)
Does it have to do with the fact that a gaussian is created by e, and ex has a slope of ex at every point?
drphillycheesesteak ยท 1 points ยท Posted at 12:29:15 on May 26, 2016 ยท (Permalink)
That property actually does come into play. The derivative of a Gaussian contains another Gaussian term, which is used in the derivation, which you can see here.
[deleted] ยท 0 points ยท Posted at 16:16:24 on May 25, 2016 ยท (Permalink)
[deleted]
Gnzzz ยท 7 points ยท Posted at 16:28:15 on May 25, 2016 ยท (Permalink)*
If I remember correctly, the Fourier transform of the Dirac-Delta is a constant, not another Dirac-Delta. The real part at least, the phase / imaginary part is an exponential of the shift.
PronouncedOiler ยท 6 points ยท Posted at 16:45:53 on May 25, 2016 ยท (Permalink)
Correct! Using the unitary Fourier transform in ordinary frequency, the Fourier Transform of delta(t) is 1.
However, the Gaussian principle is also tangentially related. If you consider a delta function as the limit of a normalized Gaussian as the width goes to 0, the Fourier transform is a Gaussian whose width goes to infinity, (i.e. a constant).
Source: Wikipedia
drphillycheesesteak ยท 3 points ยท Posted at 17:19:45 on May 25, 2016 ยท (Permalink)
Somewhat relevant username
drphillycheesesteak ยท 3 points ยท Posted at 16:46:50 on May 25, 2016 ยท (Permalink)
The Dirac-Comb function is a self transform. That is,
\sum\limits_{i=-\infty}^\infty \delta(x-i)
[deleted] ยท 2592 points ยท Posted at 11:05:17 on May 25, 2016 ยท (Permalink)
ei*pi + 1 = 0
namie_mcnameface ยท 1400 points ยท Posted at 13:33:32 on May 25, 2016 ยท (Permalink)
It's cool until you study the complex plane, then it just makes sense...
ben_jl ยท 380 points ยท Posted at 14:05:56 on May 25, 2016 ยท (Permalink)*
Even more generally, you can derive this solely by considering the definition of exponentiation. The two essential properties of the exponential function are ea * eb = ea+b and (ea)b = eab. When extending to the complex numbers, we want to make sure that ez satisfies these two relations and matches the usual definition when z is real.
From this, you can show that the only definition that fits is ea+i*b = Aea{cos(b)+i*sin(b)}, where A is a constant 1+iB, with B an arbitrary real number. We then choose B=0, and obtain Euler's Relation. No complex plane necessary.
Edit: This also demonstrates that Euler's Identity is ultimately arbitrary, as the value ei*pi is dependent on our choice of B. It only equals -1 when B=0, and we could make it equal any value we want on the unit circle just by changing our choice of B.
[deleted] ยท 217 points ยท Posted at 14:24:58 on May 25, 2016 ยท (Permalink)
[deleted]
ben_jl ยท 61 points ยท Posted at 14:37:09 on May 25, 2016 ยท (Permalink)
Perhaps, but that clouds the (for me, more interesting) fact that the relationship comes from what the exponential does: namely, turning multiplication into addition. The other derivations make it seem almost like a coincidence, at least to me.
SharKCS11 ยท 3 points ยท Posted at 19:58:37 on May 25, 2016 ยท (Permalink)
I first saw it being explained with a complex plane, and it really wasn't very clear. Later I saw it being derived using the Taylor expansion for ex, and it was much easier to understand. But I think one of my math lecturers said that the Taylor expansion method wasn't really a good proof, and only a way to remember the formula.
SilverStar9192 ยท 1 points ยท Posted at 22:07:16 on May 25, 2016 ยท (Permalink)
Thanks for this. I've always thought of the complex plane as a somewhat artificial construct, a useful one to describe certain real-life phenomena like "reactive power" in electricity, but nevertheless a made-up idea. The problem with that was that Euler's relation seemed to make "i" much more fundamental than this, but your explanation points out that it's not really.
mbleslie ยท 5 points ยท Posted at 15:26:26 on May 25, 2016 ยท (Permalink)
but the complex plane only makes sense after you've been told about that sin/cos relationship.
how you go from e(j*w) to cos(w) + j*sin(w) is the amazing part. differential equation is one way. i've heard it can be shown via taylor series as well.
SpiderOnTheInterwebs ยท 7 points ยท Posted at 16:40:04 on May 25, 2016 ยท (Permalink)
Taylor series is how it's always been explained to me. The derivation is actually quite simple.
Odds-Bodkins ยท 2 points ยท Posted at 19:56:28 on May 25, 2016 ยท (Permalink)
I fail to see how he's using differential equations... where are the derivatives?
Anyway, Taylor/Maclaurin for eiw = 1 + iw +(iw)2 /2! + (iw)3 /3! + (iw4) /4! + (iw)5 /5! + ...
= 1 + iw -w2 /2! - iw3 /3! + w4 /4! + iw5 /5! -w6 /6! -iw7 /7! + ...
Taylor for sin(w) = w - w3 /3! + w5 /5! - w7 /7! + ...
Taylor for cos(w) = 1 - w2 /2! + w4 /4! - w6 /6! + ...
Multiply the series for sin by i, add. Get the series for exp.
sluggles ยท 1 points ยท Posted at 17:51:24 on May 25, 2016 ยท (Permalink)
For Taylor series, just plug ix into the Taylor series for the exponential. The even terms for the Taylor series give you the Taylor series for cos(x), the odd terms give you isin(x).
beingforthebenefit ยท 1 points ยท Posted at 18:46:38 on May 25, 2016 ยท (Permalink)
I had an instructor who loved to define ez as cos(z)+i sin(z) and show everything else follows from DeMoivre's formula.
youngeng ยท 1 points ยท Posted at 17:31:59 on May 25, 2016 ยท (Permalink)
by the way, I sometimes find myself deriving trig identities from the Euler formula. Once you're comfortable with j*j=-1 and you know two formulas (sin x, cos x) you can obtain all kinds of stuff. Euler formula and Pascal triangles FTW!
Odds-Bodkins ยท 2 points ยท Posted at 20:00:53 on May 25, 2016 ยท (Permalink)*
I'm missing something, I don't see the differential equations? Do we use d/dx ex = ex along with the properties of exponents he mentioned to construct them?
conceptuality ยท 3 points ยท Posted at 22:34:22 on May 25, 2016 ยท (Permalink)
The second derivative of exp(ix) is -exp(ix). This is the differential equation for a harmonic oscillator (or spring if you like), which admits sinusoidals as solutions.
Odds-Bodkins ยท 1 points ยท Posted at 00:45:38 on May 26, 2016 ยท (Permalink)
I've got you. So that's the "From this, we can show.." bit, solving a second order ODE?
Teblefer ยท 1 points ยท Posted at 21:30:52 on May 25, 2016 ยท (Permalink)
Or just use the Taylor series expansion like the rest of us.
StressOverStrain ยท 1 points ยท Posted at 23:21:28 on May 25, 2016 ยท (Permalink)
Differential equations was the first place I saw it proved. Happily reading along in the textbook about some random concept, "oh and if you just manipulate this and that, you derive this famous equation. But back to solving differential equations..."
tanzWestyy ยท 6 points ยท Posted at 14:45:44 on May 25, 2016 ยท (Permalink)
..my cats name is Mittens
lukesvader ยท 2 points ยท Posted at 20:16:12 on May 25, 2016 ยท (Permalink)
Jeremy's... Iron
[deleted] ยท 4 points ยท Posted at 14:37:50 on May 25, 2016 ยท (Permalink)
Sorry, what are the steps to arrive at the second paragraph?
ben_jl ยท 7 points ยท Posted at 15:03:27 on May 25, 2016 ยท (Permalink)
The majority of the work is done by the condition that the complex exponential f(z) = ez when z is real. Note that this implies that f(z)=eRe{z}g(Im{z}), where g(0)=1. From here, you have to obtain some conditions on g. Specifically, you take derivatives of the relations given by the properties of the exponential, and solve the resulting differential equations for g. The intricacies of that last step are a tad involved for a reddit comment (a lot of symbol formatting I'm not too keen on) - the first chapter of any complex analysis book (or googling 'complex exponential definition') will have the details.
JamEngulfer221 ยท 2 points ยท Posted at 18:58:25 on May 25, 2016 ยท (Permalink)
AlienBlue not supporting superscript/subscript makes maths on reddit very difficult to understand
MysteriousMooseRider ยท 3 points ยท Posted at 15:02:36 on May 25, 2016 ยท (Permalink)
Differental equations. Google Paul's online math notes or wolfram alpha they have good explanations.
Habbeighty-four ยท 3 points ยท Posted at 15:20:06 on May 25, 2016 ยท (Permalink)
No complexity in there at all. No siree.
HEYdontIknowU ยท 3 points ยท Posted at 15:34:07 on May 25, 2016 ยท (Permalink)
I'm just going to have to take your word for it.
[deleted] ยท 2 points ยท Posted at 14:33:11 on May 25, 2016 ยท (Permalink)
Yup all you need is algebra 2 knowledge.
The_JSQuareD ยท 2 points ยท Posted at 17:00:19 on May 25, 2016 ยท (Permalink)
Why do you consider the choice for B=0 to be arbitrary? If we let b=0, we get ea = A ea, thus the only possible choice for A=1, and thus B=0.
yumyumgivemesome ยท 2 points ยท Posted at 17:50:00 on May 25, 2016 ยท (Permalink)
This guy fucks.
naughtydismutase ยท 2 points ยท Posted at 15:46:40 on May 25, 2016 ยท (Permalink)
I like scrambled eggs.
beaverlyknight ยท 1 points ยท Posted at 15:32:36 on May 25, 2016 ยท (Permalink)
The best way (or at least "coolest" way) to see this is using Taylor Series, works out really nicely. You see how cos and sin relate to e, you get Euler's Formula, and then you get Euler's Identity.
zarraha ยท 1 points ยท Posted at 16:48:41 on May 25, 2016 ยท (Permalink)
And because it's arbitrary, it's not as profound as everyone seems to think it is.
[deleted] ยท 1 points ยท Posted at 16:58:38 on May 25, 2016 ยท (Permalink)
3Blue1brown has a great video on this that completely skips the calculus and shows the underlying intuition.
randomguy186 ยท 1 points ยท Posted at 17:03:05 on May 25, 2016 ยท (Permalink)
I'd have to review that proof very carefully to be sure that it's not dependent on that definition.
danhakimi ยท 1 points ยท Posted at 17:34:04 on May 25, 2016 ยท (Permalink)
What? Those properties of exponentiation are obvious in much simpler ways that don't require any knowledge of trigonometry, e, i, calculus, or taylor polynomials.
JesusK ยท 1 points ยท Posted at 19:30:23 on May 25, 2016 ยท (Permalink)
And that kids is were springs come from!
dh363 ยท 1 points ยท Posted at 19:56:25 on May 25, 2016 ยท (Permalink)
The fact that it satisfies these relations while being the only reasonable way to define the exponential function is beautiful though.
CCNezin ยท 1 points ยท Posted at 23:15:08 on May 25, 2016 ยท (Permalink)
I wouldn't say that choice is arbitrary. What about the motivating definition from the addition of taylor series of cos z and i sin z ?
bunnysnack ยท 1 points ยท Posted at 00:50:56 on May 26, 2016 ยท (Permalink)
I've never seen euler's formula including an A=1+Bi where B is arbitrary before, so your edit paragraph does not make any sense to me. I've known Euler's formula to be e^a+ib = e^a (e^cos (b) +i sin (b)). I also don't understand, even if A is included, how adding a complex part (B equals a real non-zero number) can make e^i pi be any number. Would you care to explain?
whitekeyblackstripe ยท 1 points ยท Posted at 02:17:12 on May 26, 2016 ยท (Permalink)
RIP mobile users ๐ญ
IAMA_Printer_AMA ยท 1 points ยท Posted at 03:04:16 on May 26, 2016 ยท (Permalink)
It's comments like these that frustrate me because Alien Blue doesn't do superscript, so I don't know what are exponents and what aren't.
redweasel ยท 1 points ยท Posted at 07:41:38 on May 26, 2016 ยท (Permalink)
This reminds me. While analyzing Spirograph a couple of years ago, I discovered something interesting. Unfortunately the details are now very vague in my mind, but I think it was something like, if you draw any arbitrarily-chosen Spirograph pattern in the complex plane, sized (scaled) such that the outermost-extremal points ("tip" of a "petal" or "loop" or "cusp") lie exactly on the unit circle, then each of those outermost-extremal points is a complex Nth root of 1. For all I know, this could be a well- and long-known result, but it's new to me!. (At the time, I was able to compute, from the numbers of teeth in the "ring" and "moving gear" used to generate the Spirograph pattern, the value of N... and there were some other interesting properties, such as that, in emulating Spirograph in software, using non-integer ring and gear sizes (number-of-teeth being proportional to circumference which can be a real number) is simply equivalent to using very large integers -- the more decimal places, the larger the integers. You can thus very easily generate Spirograph patterns that will entirely fill the circle they occupy, given any specified pen thickness -- but can never truly computer-generate patterns that really entirely fill the circle in the true mathematical sense, because computer numeric precision is limited. To generate a Spirograph pattern that truly fills the circle, you would have to use the exact values of irrational numbers like e and pi.... i.e. infinite numbers of digits...
In the process of all the above, I also independently discovered what turned out to be the well-known relation LCM(a,b) * GCD(a,b) = |ab|.
falco_iii ยท 14 points ยท Posted at 15:50:43 on May 25, 2016 ยท (Permalink)
It is still mind blowing that one equation is so simple & elegant and yet includes the big hitters:
0 - the first real "mathematical concept" - how can you count nothing?
1 - the most basic number.
e - transcendental number - a logarithm found many places in nature.
pi - another transcendental number that everyone knows and loves - again many places in nature.
i - a complex number that loops back to 0 - how do you count something that does not exist?
It also includes the operators =, +, *, ^ exactly once each.
rebirthlington ยท 7 points ยท Posted at 15:02:37 on May 25, 2016 ยท (Permalink)
can you please elaborate / link me to the resources that will allow me to gain this sort of understanding of the complex plane?
ben_jl ยท 6 points ยท Posted at 15:08:38 on May 25, 2016 ยท (Permalink)
Not OP, but I strongly recommend (at least the first chapter of) Visual Complex Analysis by Tristan Needham. You can find a PDF online pretty easily. Its a great first semi-rigorous introduction to complex numbers that gives a lot of intuition for the complex plane.
rebirthlington ยท 3 points ยท Posted at 15:19:32 on May 25, 2016 ยท (Permalink)
Lovely - thank you!
Sprechensiedeustch ยท 2 points ยท Posted at 17:35:44 on May 25, 2016 ยท (Permalink)
A tldr version would be if you imagine a circle with exp(j*theta) describing a unit vector from the origin to any point on this circle with theta being the angle. If theta is pi, then the vector is basically -1. -1 + 1 is 0.
rebirthlington ยท 1 points ยท Posted at 22:15:09 on May 25, 2016 ยท (Permalink)
legend. thnx
ninjalink84 ยท 3 points ยท Posted at 16:39:03 on May 25, 2016 ยท (Permalink)
I think it's even cooler when you understand where it's coming from. The historical significance of the discovery was one of the first steps to understanding the complex numbers as a plane, so rather than looking at what we have now and saying "yes, that just makes sense", I prefer to look at the beauty of the equation from the standpoint that this equation was one of the first steps to extending our understanding of numbers as we know them.
[deleted] ยท 7 points ยท Posted at 17:01:33 on May 25, 2016 ยท (Permalink)
I strongly disagree when people say that this theorem is trivial if you know what it means. I think that this idea is popular because in every text on complex variables the defintion of eix is given as cos (x) + isin (x). But that just buries the real theorem, which is that this definiton allows us to extend the exponential function analytically to the complex plane, with all the expected algebraic properties of exponential function still holding. That part is actually a fairly nontrivial theorem, and in my opinion a pretty surprising result.
[deleted] ยท 1 points ยท Posted at 22:50:39 on May 25, 2016 ยท (Permalink)
This part is actually useful for stuff like phasor analysis
This is what pop science/math blogs spam
snuffleupagus_Rx ยท 3 points ยท Posted at 15:27:17 on May 25, 2016 ยท (Permalink)
That's kind of the truth with most math. Things seem unexpected and clouded in mystery until you understand them. Then they just make sense.
randomguy186 ยท 3 points ยท Posted at 16:59:22 on May 25, 2016 ยท (Permalink)
Of course it just makes sense - it's a mathematical fact, so you can prove it sensibly!
It's still cool that these constants that arose from seemingly disjoint areas of analysis - arithmetic, trigonometry, and exponentiation - are connected in this way. It's a bit like the 9-point circle in geometry. Of course it makes sense - you can even demonstrate its necessity with simple algebra - but it's still cool.
linehan23 ยท 3 points ยท Posted at 17:11:57 on May 25, 2016 ยท (Permalink)
I kind of thought it made sense with Taylor series, what other insight do you get from complex analysis?
redzin ยท 0 points ยท Posted at 17:31:33 on May 25, 2016 ยท (Permalink)
That is the only way it makes sense. The complex plane makes use of Euler's formula from which Euler's Identity can be easily proven, but proving Euler's formula is the difficult part.
Denziloe ยท 0 points ยท Posted at 18:07:46 on May 25, 2016 ยท (Permalink)
No, it isn't. A much more intuitive way to think about it is to use the definition of ex as (1 + x/n)n as n tends to infinity.
So ei*pi is (1 + i*pi/n)n as n tends to infinity.
1 + i*pi/n looks like a rotation of pi/n. Do that n times and you get a rotation of pi, which takes you to -1.
redzin ยท 2 points ยท Posted at 18:34:51 on May 25, 2016 ยท (Permalink)
I'm not sure I understand what that means. If you're talking about the complex plane (which it sounds like you are) then please understand that the only reason the complex plane can be related to complex exponentials is due to Euler's formula, which can be proven. Euler's formula is not a definition.
Denziloe ยท 0 points ยท Posted at 18:38:15 on May 25, 2016 ยท (Permalink)
1 + i*pi/n has nothing to do with exponentials, it's just a complex number. Draw it. For small n it's one nth of the unit circle.
redzin ยท 1 points ยท Posted at 18:46:56 on May 25, 2016 ยท (Permalink)*
But it's not a rotation, it's just a complex number. I get that a rotation of pi get's you to -1 but I don't see any rotations.
Edit: forgot the -
Denziloe ยท 0 points ยท Posted at 19:01:08 on May 25, 2016 ยท (Permalink)
(1 + ipi/n)n is 1 + ipi/n multiplied by itself n times. In the complex plane, multiplications by complex numbers (of size 1) are rotations. So multiplying by 1 + i*pi/n, n times, means rotating by the angle of that complex number, pi/n, n times, which means rotating by pi.
redzin ยท 1 points ยท Posted at 19:15:54 on May 25, 2016 ยท (Permalink)*
That's the part I was missing. Been too long since I did this sort of thing. Also, I've never seen Euler's identity derived this way. Pretty cool.
... one more thing though. The size of 1+i pi/n is not 1, so why does it remain normalized?
Edit: Oh, right. The limit takes care of normalization.
Denziloe ยท 2 points ยท Posted at 19:28:46 on May 25, 2016 ยท (Permalink)
Yep, you've got it. Personally I find this proof infinitely more intuitive and insightful than a power series proof. It actually makes geometric sense. Here's a pretty picture: https://upload.wikimedia.org/wikipedia/commons/0/0e/ExpIPi.gif
redzin ยท 1 points ยท Posted at 19:35:57 on May 25, 2016 ยท (Permalink)
The power series proof gives you Euler's formula though, which is just incredibly useful. But yeah, this is way simpler if you just want the identity.
Denziloe ยท 1 points ยท Posted at 20:16:55 on May 25, 2016 ยท (Permalink)
You can see Euler's formula this way too, just plug in a value other than pi and the same type of argument works. cos@ + isin@ is of course just the point on the unit circle at angle @.
Space-Launch-System ยท 2 points ยท Posted at 15:03:24 on May 25, 2016 ยท (Permalink)
You make it sound so easy. I've been using the complex plane for years and it still doesn't make sense.
slamdunkcommoner ยท 2 points ยท Posted at 17:23:44 on May 25, 2016 ยท (Permalink)
I used to think that this identity (or more generally ei*x = cos x + i sin x) was very arbitrary and obscure, and I couldn't understand why mathematicians would appreciate it so much. Then I learned about analytic continuation and power series and realized how beautiful it was !
redzin ยท 2 points ยท Posted at 17:40:49 on May 25, 2016 ยท (Permalink)*
The idea of the complex plane is based on Euler's formula from which Euler's Identity (OPs equation) can be easily proven (just set x=pi).
Proving Euler's formula is non-trivial though. You need to Taylor expand ex, cos(x) and sin(x), then Euler's formula becomes apparent, but it's certainly not obvious until you see the proof. And even then it's still kinda "magic". Why is Euler's formula true? ... it just is, because it can be proven so.
Dr_Zorand ยท 2 points ยท Posted at 18:27:40 on May 25, 2016 ยท (Permalink)
I don't think exi drawing a circle on a complex plane makes intuitive sense.
Relevant xkcd (especially the alt text).
kyred ยท 2 points ยท Posted at 15:14:04 on May 25, 2016 ยท (Permalink)
What's more fun is ei*pi/2 = i
"i" defines itself.
c3534l ยท 1 points ยท Posted at 16:29:45 on May 25, 2016 ยท (Permalink)
It didn't make sense to people for a very, very long time. They didn't have quite the understanding of things as we do nowadays.
MrJoo ยท 1 points ยท Posted at 18:10:41 on May 25, 2016 ยท (Permalink)
It's cool because it exhibits the three standard operations: addition, multiplication, exponentiation, e & ฯ as the two big constants as well as the multiplicative & additional identities, 1 * 0. All this and nothing extraneous.
Jack-90 ยท 1 points ยท Posted at 18:51:56 on May 25, 2016 ยท (Permalink)
Understanding it made it cooler to me. But hey...
jyonsin ยท 1 points ยท Posted at 19:40:16 on May 25, 2016 ยท (Permalink)
Yo, it's still cool, because it uses the five most important numbers in math. The most beautiful equation.
chiagod ยท 1 points ยท Posted at 22:37:09 on May 25, 2016 ยท (Permalink)
I can see a mathematician, clad in a flamboyant cape, open a closet door from which emerges a most unnatural light....
"Hold my calls. I'm off to study the complex plane!"
JamesEarlDavyJones ยท 1 points ยท Posted at 23:10:36 on May 25, 2016 ยท (Permalink)
Six months ago, I'd have said that you've got some funky notions of complex algebra.
Now, I just finished a graduate leveling class in theory of complex variables, and I'm convinced that I don't understand complex analysis or algebra at all. That class was just brutal, even more so than PDEs.
skysurf3000 ยท 0 points ยท Posted at 14:40:37 on May 25, 2016 ยท (Permalink)
I tend to think of it as just the definition for pi.
ohitsasnaake ยท 1 points ยท Posted at 15:36:26 on May 25, 2016 ยท (Permalink)
Or e, if one defines pi using circles?
AncientHistory ยท 204 points ยท Posted at 11:05:43 on May 25, 2016 ยท (Permalink)
It really is the most elegant equation.
[deleted] ยท 292 points ยท Posted at 11:33:42 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 37 points ยท Posted at 11:44:37 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 87 points ยท Posted at 11:49:09 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 9 points ยท Posted at 11:53:29 on May 25, 2016 ยท (Permalink)
[deleted]
darkfrost47 ยท 11 points ยท Posted at 12:34:25 on May 25, 2016 ยท (Permalink)
For all we know we're in a simulation and having real life sex is just 0s and 1s as well.
JohnnyHendo ยท 4 points ยท Posted at 14:34:12 on May 25, 2016 ยท (Permalink)
So, what your saying is that it's nerdy to have sex? Fuck you cool kids!
[deleted] ยท 2 points ยท Posted at 16:17:39 on May 25, 2016 ยท (Permalink)
01000110 01010101 01000011 01001011 00100000 01011001 01001111 01010101 00100000 01000011 01001111 01001111 01001100 00100000 01001011 01001001 01000100 01010011 00100001 00100001 00100001
DerNicoPico ยท 2 points ยท Posted at 17:29:03 on May 25, 2016 ยท (Permalink)
r/totallynotrobots
JohnnyHendo ยท 1 points ยท Posted at 16:51:00 on May 25, 2016 ยท (Permalink)
HHHHHNNNNNNGGGG!!!!
For some reason, I think that might actually say something if I translated it, but I don't want to translate it.
laz2727 ยท 2 points ยท Posted at 17:51:52 on May 25, 2016 ยท (Permalink)
It's "FUCK YOU COOL KIDS!!!"
Camel_toe_jockey ยท 1 points ยท Posted at 00:49:14 on May 26, 2016 ยท (Permalink)
Next time take the blue pill
ask_me_if_Im_lying ยท 7 points ยท Posted at 12:53:25 on May 25, 2016 ยท (Permalink)
So could Mike Tyhton
Fr0thBeard ยท 1 points ยท Posted at 14:19:18 on May 25, 2016 ยท (Permalink)
As proven by Neil Degrath Thyton.
musicmast ยท 1 points ยท Posted at 14:45:39 on May 25, 2016 ยท (Permalink)
*mathsturbate
DV_shitty_music ยท 1 points ยท Posted at 15:15:06 on May 25, 2016 ยท (Permalink)
Don't forget to keep stiff upper lip!
Rorschach_And_Prozac ยท 1 points ยท Posted at 17:22:06 on May 25, 2016 ยท (Permalink)
How do you think the unthinkable?
With an ithberg
Trogdorocks ยท 1 points ยท Posted at 19:00:57 on May 25, 2016 ยท (Permalink)
Mike Tyson? Do you nibble ears during foreplay?
[deleted] ยท 1 points ยท Posted at 19:18:30 on May 25, 2016 ยท (Permalink)
r/mathurbation
Strangely_quarky ยท 1 points ยท Posted at 01:03:14 on May 26, 2016 ยท (Permalink)
now kith
Narwheagle ยท 4 points ยท Posted at 11:12:57 on May 25, 2016 ยท (Permalink)
Elegant? Why do you say that?
Iโm a relative layman, sureโฆ but I think that the equation might be better characterized as โimpressive.โ
AncientHistory ยท 32 points ยท Posted at 11:18:36 on May 25, 2016 ยท (Permalink)
Euler's Identity unifies several different aspects of mathematics - the natural logarithm, complex numbers (i.e. real and imaginary), and trigonometry (this particular example is a special case of complex analysis, the more general version involves sine and cosine). So you've got several different fields of mathematics all brought together...and it's relevant to all of them.
Narwheagle ยท 6 points ยท Posted at 11:24:43 on May 25, 2016 ยท (Permalink)
The other user who responded to my comment gave a response that was more adequately dumbed-down for me, but Iโm definitely saving this comment so I can revisit it when I understand the concepts better!
I appreciate the explanation. But I must apologize โย it goes waaaay over my (borderline innumerate) head. :P
AncientHistory ยท 6 points ยท Posted at 11:30:56 on May 25, 2016 ยท (Permalink)
S'right. Too many years of math classes at university. Thanks for the gold!
[deleted] ยท 75 points ยท Posted at 11:16:06 on May 25, 2016 ยท (Permalink)*
It is usually considered elegant, or aesthetically pleasing as well. The reason for this is, that it links 5 of the most important constants in math and physics, (0, 1, e, pi, i), with exactly one addition, one multiplication, one power operation and an equality.
edit: Wow my first gold, thank you!
Narwheagle ยท 16 points ยท Posted at 11:20:26 on May 25, 2016 ยท (Permalink)
Ohhhhโฆ
That makes sense. I realized the importance of โe,โ โ๐ ,โย and โiโ, but I definitely missed the significance of โ0โ and โ1,โ along with the nature of the operations used in the equation.
Mark7A ยท 3 points ยท Posted at 15:10:18 on May 25, 2016 ยท (Permalink)
It's funny, at one point the concept of zero didn't exist.
I wonder what people in the future will think of our math.
randomguy186 ยท 3 points ยท Posted at 17:08:47 on May 25, 2016 ยท (Permalink)
I'm pretty convinced that future math historians will marvel at our obsession with limits, and laugh at the gyrations we went through to deny the (to them) obvious existence of infinite and infinitesimal numbers. Limits were required in the 19th century to place analysis on a rigorous mathematical footing, as mathematicians couldn't find a way to make infinitesimals rigorous. However, in the mid-20th century that changed. (Search for non-standard analysis or hyperreal numbers if you want to know more.) The intuitive infinitesimal approach that was used for centuries (even by Newton and Leibniz) can now be treated with as much rigor as you like.
However, we continue to cling to our limits, often accompanied by arguments that infinitesimals aren't "real" - which is exactly the claim that was made about irrationals, negatives, and so-called "imaginary" numbers.
ben_jl ยท 5 points ยท Posted at 13:50:05 on May 25, 2016 ยท (Permalink)
Really, the more impressive fact to mathematicians is the general Euler relation: ei*x = cos(x) + i*sin(x). The Euler Identity is just a special case of this. And not even a particularly interesting one at that; once you understand the relationship between complex exponentiation and the unit circle, its essentially a tautology.
[deleted] ยท 1 points ยท Posted at 14:05:41 on May 25, 2016 ยท (Permalink)
I fully get what you're saying, and I agree that the whole concept of the complex exponential is more impressive. Although I still find the identity quite beautiful on its own, partially for the properties the identity specifically exhibits that I mentioned above.
But of course you are right, the general case is more impressive.
Turtle_78 ยท 1 points ยท Posted at 17:58:43 on May 25, 2016 ยท (Permalink)
Isn't every identity a tautology?
randomguy186 ยท 1 points ยท Posted at 17:03:59 on May 25, 2016 ยท (Permalink)
Yep. The five most significant constants, the three most significant operations, and the one most significant relation.
elee0228 ยท 1 points ยท Posted at 12:23:57 on May 25, 2016 ยท (Permalink)
Make sure you check out the Wikipedia page on Euler's Identity. The entry on the golden ratio is also worth reading.
guthran ยท 3 points ยท Posted at 15:34:04 on May 25, 2016 ยท (Permalink)
except "ei*tau = 1" is even more elegant
stewmberto ยท 1 points ยท Posted at 16:12:21 on May 25, 2016 ยท (Permalink)
Whatever happened to that tau guy anyways?
guthran ยท 1 points ยท Posted at 17:07:35 on May 25, 2016 ยท (Permalink)
he's still tau'ing
randomguy186 ยท 0 points ยท Posted at 17:12:36 on May 25, 2016 ยท (Permalink)
This equation fails to relate the five most important constants of analysis and the three most important operations. It's elegant, but it isn't beautiful.
guthran ยท 0 points ยท Posted at 17:17:51 on May 25, 2016 ยท (Permalink)
I disagree, if you're considering 0 to be the other most important constant and subtraction/addition to be the other most important operation, this equation could be expanded to something like "ei*tau = 1 -/+ 0" and your complaint is now invalid
SLeazyPolarBear ยท 1 points ยท Posted at 16:04:43 on May 25, 2016 ยท (Permalink)
Why?
Elegance in an equation to me seems to be a matter of it simplifying an otherwise complicated concept and doing so in a straight forward easy to use expression.
I don't get whats so elegant about this. It kinda makes a statement about complex numbers.
AncientHistory ยท 2 points ยท Posted at 16:06:55 on May 25, 2016 ยท (Permalink)
I explained this above, but Euler's Identify showcases how several different mathematical systems interact and relate to each other - not just complex numbers, but natural logarithms and complex analysis too.
9tailNate ยท 1 points ยท Posted at 16:20:15 on May 25, 2016 ยท (Permalink)
It is God's signature on His creation.
efurnit ยท 1 points ยท Posted at 17:10:01 on May 25, 2016 ยท (Permalink)
Only if you don't actually study mathematics.
AncientHistory ยท 1 points ยท Posted at 17:16:42 on May 25, 2016 ยท (Permalink)
Engineer: We take what we can use, and leave the rest for the mathematics majors.
efurnit ยท 1 points ยท Posted at 17:57:57 on May 25, 2016 ยท (Permalink)
It's always nice to know that science can never infiltrate the ivory tower of math and art.
AncientHistory ยท 1 points ยท Posted at 17:58:44 on May 25, 2016 ยท (Permalink)
Engineering is obliged to stick to possibilities; science, art, and math are not.
efurnit ยท 1 points ยท Posted at 18:06:44 on May 25, 2016 ยท (Permalink)
Of course. I wouldn't put math and art in the same category as science, though; Math and Art are acts of creation. Everything else is derivative.
Gazorpazorpbear ยท 1 points ยท Posted at 11:12:15 on May 25, 2016 ยท (Permalink)
Truly, such grace.
InappropriateTA ยท 1 points ยท Posted at 14:48:12 on May 25, 2016 ยท (Permalink)
I've typically seen it as:
This way it also includes negative numbers.
[deleted] ยท 1 points ยท Posted at 17:14:15 on May 25, 2016 ยท (Permalink)
eiฯ = 1
is more elegant.
SillyMacey ยท 6 points ยท Posted at 13:59:50 on May 25, 2016 ยท (Permalink)
As beautiful as ei*pi=-1
Coffee-Anon ยท 6 points ยท Posted at 15:27:37 on May 25, 2016 ยท (Permalink)
SOwED ยท 1 points ยท Posted at 18:53:08 on May 25, 2016 ยท (Permalink)
Most would say the other form is more beautiful because it includes e, i, ฯ, 1, and 0.
Mirrorboy17 ยท 120 points ยท Posted at 12:28:25 on May 25, 2016 ยท (Permalink)*
Proof time!
ei*Pi = cos(Pi) + i*sin(Pi)
Sin(Pi) = 0
Cos(Pi) = -1
Hence, eiPi = -1 + 0i = 1 And therefore: eiPi + 1 = 0
QED
Edit: can't be bothered sorting out this italic nonsense
blazingkin ยท 212 points ยท Posted at 12:56:26 on May 25, 2016 ยท (Permalink)*
You skipped the part where you explain how
eix = cos(x) + isin(x)
If anyone is wondering, you use the Taylor Series to get that. (It's a calc 2 subject but only needs calc 1 skills)
kintaroization ยท 50 points ยท Posted at 13:11:29 on May 25, 2016 ยท (Permalink)
Actually no. You use the power series definition of exp
Mirrorboy17 ยท 23 points ยท Posted at 13:16:04 on May 25, 2016 ยท (Permalink)
Taylor Series, that was it - thanks. My mind has got foggy
usernumber36 ยท 51 points ยท Posted at 13:25:29 on May 25, 2016 ยท (Permalink)
nah just use differential equations
sin and cos are the only two solutions where y'' = -y. Which is also true of eix
you therefore obtain:
eix = Acosx + Bsinx
from there you just take the specific case of x=0 to solve for A, i.e.
e0 = Acos0 Bsin0
thus 1 = A
and then to solve for B you can take the first derivative:
ieix = -sinx+Bcosx
and again sub in x=0:
i = B
so you obtain euler's formula overall:
eix = cosx + isinx
then sub in the value pi to get:
eipi = -1
lurking_bishop ยท 13 points ยท Posted at 14:40:55 on May 25, 2016 ยท (Permalink)
Non-trivial information at this level ...
crossedstaves ยท 6 points ยท Posted at 15:22:32 on May 25, 2016 ยท (Permalink)
That is a confusing statement to make. If they're the only two solutions then saying its also true of eix only makes sense if we've already accepted that the two are equivalent, but the the whole point was establish their equivalence. Thus begging the question.
andinuad ยท 2 points ยท Posted at 15:40:35 on May 25, 2016 ยท (Permalink)
They are not the only two solutions. However every solution can be written as a sum of those two solutions (non-trivial result). I.e. C * cos x + D * sin x
For a given initial condition, such as y(0) = 1 and y'(0) = i, the solution has to be unique (also non-trivial result) so therefore since both cos x + i * sinx and exp(ix) solve the equation for that initial condition they must be equivalent due to uniqueness.
[deleted] ยท 2 points ยท Posted at 19:40:56 on May 25, 2016 ยท (Permalink)
So cosx and sinx are an orthogonal basis for the space of solutions to that differential equation? It's cool to realize that linear algebra explains a lot more than just matrices and vectors!
andinuad ยท 1 points ยท Posted at 19:56:19 on May 25, 2016 ยท (Permalink)
As far as I know, orthogonality requires that you define an inner product. Haven't really thought of an inner product in that specific case. A vector space doesn't require an inner product to be defined.
They are certainly a basis for the vector space "solutions to that differential equation".
[deleted] ยท 2 points ยท Posted at 20:15:26 on May 25, 2016 ยท (Permalink)
Found one!.
There was some other argument that I read on /r/math I think, but it wasn't completely rigorous because the usual dot product on Rn doesn't extend to Rinfinity. But the gist of it was to take the coefficients of each from its Taylor polynomial. Then, since cosx is even and sinx is odd, the 'dot product' would be zero. Dunno how to rigourize that, but it'd be nice to cause I thought that argument was neat.
OHHHHHHH. and this is why Fourier decomposition is a thing!
crossedstaves ยท 1 points ยท Posted at 16:44:22 on May 25, 2016 ยท (Permalink)
Yeah, my intended point was just that establishing the equivalence was sort of the important part, and glossing over it was a (non-trivial result) or related doesn't really accomplish the goal and certainly no better than using a taylor series expansion would.
[deleted] ยท 1 points ยท Posted at 16:57:54 on May 25, 2016 ยท (Permalink)
[deleted]
crossedstaves ยท 2 points ยท Posted at 17:02:35 on May 25, 2016 ยท (Permalink)
I think you have to establish that sin and cos solutions are linearly independent, which isn't hard, and then i think you have to prove that sin and cos span the solution space. Once you do that you can express any solution, such as eix as a linear combination of sin and cos.
But i'm not actually super robust at these forms of rigorous mathematical analysis being more of a physics type person, and off the top of my head I don't know how you prove the spanning.
usernumber36 ยท 1 points ยท Posted at 08:56:08 on May 26, 2016 ยท (Permalink)
I said this to someone else, but there's some theorem in solving second order dfferential equations that the general solution is equal to a linear combination of two specific solutions or somehting. Can't ever remember the name of it or the exact particulars
Anaract ยท 3 points ยท Posted at 16:05:55 on May 25, 2016 ยท (Permalink)
I had an interview recently where I was asked to solve for the square root of i.
Mind was blown for about 20 seconds, then I started going through Euler's and it was pretty simple. Interesting, though. Certainly wasn't expecting that
GuyBelowMeDoesntLift ยท 2 points ยท Posted at 14:34:28 on May 25, 2016 ยท (Permalink)
Oh shit that's super cool
JackandFred ยท 2 points ยท Posted at 15:17:55 on May 25, 2016 ยท (Permalink)
Oh god is all coming back to me, I thought I'd forgot all of differential equations
mammablaster ยท 2 points ยท Posted at 15:30:05 on May 25, 2016 ยท (Permalink)
There should be more threads like this. I enjoy this so much
RUacronym ยท 1 points ยท Posted at 16:28:03 on May 25, 2016 ยท (Permalink)
Wow thank you. This was surprisingly easy to follow (for those who understand the math I guess)
BloodFartTheQueefer ยท 1 points ยท Posted at 16:51:25 on May 25, 2016 ยท (Permalink)
I like this proof more than the series expansion thing. Awesome!
endershadow98 ยท 1 points ยท Posted at 19:37:33 on May 25, 2016 ยท (Permalink)*
So the derivative of ix is idx?
EDIT: of course it is. i is a constant and not a variable.
usernumber36 ยท 2 points ยท Posted at 08:49:46 on May 26, 2016 ยท (Permalink)
derivative of eix is i.eix
exactly the same as the derivative of ekx = k.ekx
endershadow98 ยท 1 points ยท Posted at 19:49:24 on May 26, 2016 ยท (Permalink)
I realize that now that I 'remembered' that i is a constant
SharKCS11 ยท 1 points ยท Posted at 20:01:03 on May 25, 2016 ยท (Permalink)
Damn, this was the first time I've seen it explained like this. I love it. But is it factual that y''=-y can ONLY be solved by sine and cosine?
usernumber36 ยท 1 points ยท Posted at 08:50:48 on May 26, 2016 ยท (Permalink)
there's some theorem in differential equations that says the general solution to a second order DE like this is a linear combination of two independent specific solutions or something.
I wish I remembered that theorem. Someone mathsy help?
ben_jl ยท 2 points ยท Posted at 14:16:35 on May 25, 2016 ยท (Permalink)
You don't even need Taylor Series! In fact, that method misses the essential point, and makes the result seem like a pure coincidence. Euler's relation, fundamentally, is the only sensible extension of the exponential function to the complex numbers. No calculus necessary.
skysurf3000 ยท 2 points ยท Posted at 14:41:05 on May 25, 2016 ยท (Permalink)
That's the definition of sin and cos!
DropMySpaghetti ยท 1 points ยท Posted at 14:49:04 on May 25, 2016 ยท (Permalink)
Mmm, spicy summations.
FloppyTheUnderdog ยท 1 points ยท Posted at 15:23:55 on May 25, 2016 ยท (Permalink)
Well, it really depends how you define cos and sin.
Most calculus courses define them as such: cos(x) := Re(eix) sin(x) := Im(eix)
Or like this (which is pretty much the same as above): cos(x) := 1/2(eix + e-ix) sin(x) : = 1/(2i))(eix - e-ix)
Hence eix = cos(x) + i*sin(x) does not have to be "proven".
So it follows directly by definition.
The real question is: Why is sin(pi) = 0 and cos(pi) = -1 ?
The thing is: that is how calculus classes define pi! (Kinda...) pi/2 is the root of cos in the interval [0,2]. And that is kinda annoying to show that it exists and all...
Or another way to look at pi is: We show that: |eix| = 1 for all x (not that easy to show, I believe...)
and that it is periodic (and maybe properties...). We then define 2*pi to be the length of the period ("circumference"). Then it is easy to see why eipi = -1
So it's all not that easy, actually.
Bobius ยท 1 points ยท Posted at 15:36:52 on May 25, 2016 ยท (Permalink)
Another fun way.
Use the quotient rule with f(x) = cos(x)+isin(x) aand g(x)=ei*x
Find that [f(x)/g(x)]' is 0, so f(x)/g(x)=a constant
Use f(0)=1 to see the constant = 1
Easy!
IAmTheAg ยท 1 points ยท Posted at 17:29:35 on May 25, 2016 ยท (Permalink)
Let's just watch this nice bald man explain it
DenebVegaAltair ยท 1 points ยท Posted at 18:35:01 on May 25, 2016 ยท (Permalink)
That's because Taylor series suck.
Mirrorboy17 ยท 0 points ยท Posted at 13:00:29 on May 25, 2016 ยท (Permalink)
I know, thanks - just wasn't going to attempt that on my phone
ZachofArc ยท 0 points ยท Posted at 13:46:00 on May 25, 2016 ยท (Permalink)
Or just know it as Euler's identity.
-___-_-_-- ยท 6 points ยท Posted at 15:08:08 on May 25, 2016 ยท (Permalink)
Without this italic nonsense:
Godtiermasturbator ยท 2 points ยท Posted at 14:34:49 on May 25, 2016 ยท (Permalink)
Is QED like the mic drop of acronyms?
The_Mr_Sheepington ยท 1 points ยท Posted at 15:11:07 on May 25, 2016 ยท (Permalink)
sees "Hence, eiPi = -1 + 0i = 1 And therefore: eiPi + 1 = 0" well 'scuse me sir you appear to have a little bit of a smudge on your screen lemme ru--- wow what is this symbol is it magic will it take me to narnia will it make the world forget the prequels?
YellowishWhite ยท 1 points ยท Posted at 17:32:45 on May 25, 2016 ยท (Permalink)
You want to put a \ before every *
\ tells reddit to ignore any special properties of the next character. See the source of this comment for an example.
youav97 ยท 1 points ยท Posted at 19:03:54 on May 25, 2016 ยท (Permalink)
What does this QED mean? Quantum electrodynamics?
hbgoddard ยท 2 points ยท Posted at 04:40:15 on May 26, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Q.E.D.
It basically means "my proof is finished."
[deleted] ยท 1 points ยท Posted at 22:55:38 on May 25, 2016 ยท (Permalink)
I'm sticking with witchcraft as an explanation
thegaysamosa ยท 1 points ยท Posted at 05:25:04 on May 26, 2016 ยท (Permalink)
FTFY
eix = cos(x) + i sin(x)
ei * pi = cos(ฯ) + i sin(ฯ)
cos(ฯ) = -1 ; sin(ฯ) = 0
ei * pi = (-1) + i(0) = -1
griggsy92 ยท -1 points ยท Posted at 14:20:22 on May 25, 2016 ยท (Permalink)
Notice me sin(Pi)!
[deleted] ยท 95 points ยท Posted at 13:28:01 on May 25, 2016 ยท (Permalink)
ei*tau = 1
Cast off the false idol that is pi. Praise be to the one true god that is tau!
Cilph ยท 27 points ยท Posted at 16:00:42 on May 25, 2016 ยท (Permalink)*
We've gone full circle now.
EDIT: I feel like too few people got the joke.
bunker_man ยท 29 points ยท Posted at 13:36:33 on May 25, 2016 ยท (Permalink)
Well, at least tau would stop the stupid pie jokes.
adruven ยท 79 points ยท Posted at 14:03:42 on May 25, 2016 ยท (Permalink)
Nah, they'll just double.
Fr0thBeard ยท 6 points ยท Posted at 14:20:34 on May 25, 2016 ยท (Permalink)
Not in the Middle East. Did you not hear they're enforcing a Tau-A-Ban?
conairh ยท 5 points ยท Posted at 14:01:13 on May 25, 2016 ยท (Permalink)
But tau?
OmegaSilent ยท 6 points ยท Posted at 14:51:46 on May 25, 2016 ยท (Permalink)
It tautally would.
phraps ยท 5 points ยท Posted at 15:21:02 on May 25, 2016 ยท (Permalink)
What, are you just gonna throw in the tau-el that quickly?
c00yt825 ยท 10 points ยท Posted at 13:42:53 on May 25, 2016 ยท (Permalink)
Heresy! Burn the infidel!
Quuantix ยท 1 points ยท Posted at 15:04:22 on May 25, 2016 ยท (Permalink)
Are you one of Pythagoras' followers?
itz4mna ยท 1 points ยท Posted at 19:07:05 on May 25, 2016 ยท (Permalink)
Nope, this is the Inquisition and you'll have to come with me I'm afraid. Consorting with xenos is heresy against the Emperor.
Quuantix ยท 1 points ยท Posted at 12:28:10 on May 26, 2016 ยท (Permalink)
heresy, burn them at the stake
ObeseMoreece ยท 2 points ยท Posted at 20:34:19 on May 25, 2016 ยท (Permalink)
You stick your filthy fucking tau up your heretic ass
do_you_smoke_paul ยท 1 points ยท Posted at 14:22:53 on May 25, 2016 ยท (Permalink)
But it's one of the biggest causes of dementia and movement disorders
phyphor ยท 1 points ยท Posted at 14:45:55 on May 25, 2016 ยท (Permalink)
Surely: eZiฯ = 1
Dunan ยท 1 points ยท Posted at 14:00:58 on May 25, 2016 ยท (Permalink)
Supposedly the ancient Egyptians approximated pi as 255/81, which is (2^8 - 1)/9^2, so an approximation for tau is 2^9/9^2, which is a palindrome.
(Can you say "palindrome" for mathematical expressions?)
falconhead6 ยท 1 points ยท Posted at 14:09:20 on May 25, 2016 ยท (Permalink)
It is for the greater good
[deleted] ยท 1 points ยท Posted at 16:30:58 on May 25, 2016 ยท (Permalink)
for the greater good
setfire3 ยท 1 points ยท Posted at 17:09:01 on May 25, 2016 ยท (Permalink)
in fairness, ei*pi + 1 = 0 combines the 5 universal constants together.
as for ei*tau = 1, it is missing the universal constant 0
[deleted] ยท 6 points ยท Posted at 17:18:11 on May 25, 2016 ยท (Permalink)
There ya go.
jatheist ยท 2 points ยท Posted at 19:06:18 on May 25, 2016 ยท (Permalink)
Thank you! It always bugged me that people were so excited about the zero being in the equation. All it means is that ei pi = -1.
Serialk ยท 1 points ยท Posted at 22:11:25 on May 25, 2016 ยท (Permalink)
Besides, the 0 is kind of "already there" since it's i*sin(tau) = 0 in the expansion
MacrosInHisSleep ยท 2 points ยท Posted at 17:53:03 on May 25, 2016 ยท (Permalink)
0 is always there.
BlackBloke ยท 0 points ยท Posted at 13:52:31 on May 25, 2016 ยท (Permalink)
You should write a +0 in there to be extra correct.
BerryPi ยท 0 points ยท Posted at 13:59:04 on May 25, 2016 ยท (Permalink)
Wars have been started for less.
PI VULT!
jfb1337 ยท -1 points ยท Posted at 15:21:34 on May 25, 2016 ยท (Permalink)
That's not as special because e0 = 1 too, whereas there is no real number that gives -1 when exponentiated.
[deleted] ยท 0 points ยท Posted at 15:50:22 on May 25, 2016 ยท (Permalink)
What do you mean not as special? It is just another (better) way to express the relationship described through Euler's identity.
[deleted] ยท 6 points ยท Posted at 12:57:47 on May 25, 2016 ยท (Permalink)
If you mark it as a code then you can reddit will probably show the equation.
PM_PIC_4_COMPLIMENTS ยท 3 points ยท Posted at 11:21:11 on May 25, 2016 ยท (Permalink)
/r/oddlysatisfying
mtomny ยท 3 points ยท Posted at 11:47:28 on May 25, 2016 ยท (Permalink)
I'm too lazy to figure out how to google this, can someone explain what I'm looking at?
leDippah ยท 3 points ยท Posted at 12:54:15 on May 25, 2016 ยท (Permalink)
Because I'm to lazy to explain, read this
ChipsHanden ยท 2 points ยท Posted at 16:11:22 on May 25, 2016 ยท (Permalink)*
I just read the wikipedia article and I cannot for the life of me discern why everyone is literally jizzing at the sight of an equation.
When you multiply some fancy numbers you get 0-1? How that revelation can be described as "filled with cosmic beauty" is beyond me. Mathematicians are weird.
[deleted] ยท -1 points ยท Posted at 11:50:35 on May 25, 2016 ยท (Permalink)*
[deleted]
nonotevenonce ยท 1 points ยท Posted at 12:00:04 on May 25, 2016 ยท (Permalink)
Not
good
enough
NotSorryIfIOffendYou ยท 0 points ยท Posted at 12:25:54 on May 25, 2016 ยท (Permalink)
You can google Euler's identity.
[deleted] ยท 1 points ยท Posted at 13:24:00 on May 25, 2016 ยท (Permalink)
[deleted]
elyisgreat ยท 1 points ยท Posted at 14:25:13 on May 25, 2016 ยท (Permalink)
I've never understood how this works with logs though. For example I know that ln(1)=0. But if eฯi=1...
jfb1337 ยท 2 points ยท Posted at 15:24:55 on May 25, 2016 ยท (Permalink)
The complex logarithm is really a multivalued function, like the inverse trigonometric functions. So you add on 2*pi*i*n where n is in Z, or just take the principle value where -pi < Im(log(z)) <= pi
[deleted] ยท 1 points ยท Posted at 14:28:25 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=F_0yfvm0UoU
https://www.youtube.com/watch?v=-dhHrg-KbJ0 (my favorite)
donuthazard ยท 1 points ยท Posted at 14:40:19 on May 25, 2016 ยท (Permalink)
One of my favorites too :)
MrDysprosium ยท 1 points ยท Posted at 15:10:24 on May 25, 2016 ยท (Permalink)
Eli5?
cboski ยท 1 points ยท Posted at 15:27:04 on May 25, 2016 ยท (Permalink)
Thanks to the law of cosines right?
mammablaster ยท 1 points ยท Posted at 15:27:39 on May 25, 2016 ยท (Permalink)
The reason I like this so much is that two irrational numbers, which means that they have an infinite amount of decimal, combined with an imaginary number can form a negative integer. It's one of those things that really fascinated me in math class.
Beliriel ยท 1 points ยท Posted at 15:31:17 on May 25, 2016 ยท (Permalink)
This boggled my mind for so fucking long, I even complained to the professor that it doesn't make sense. Turns out instead of a plus, I mistakenly wrote a minus on my notes.
pisslord ยท 1 points ยท Posted at 15:46:56 on May 25, 2016 ยท (Permalink)
Im so used to using j now
[deleted] ยท 1 points ยท Posted at 15:51:21 on May 25, 2016 ยท (Permalink)
Me too actually. But I thought sticking to the general default makes sense here.
SilentHorizon ยท 1 points ยท Posted at 15:51:49 on May 25, 2016 ยท (Permalink)
I like phrasing it "ii=ei*pi ". That way it sort of rhymes.
atakomu ยท 1 points ยท Posted at 16:28:44 on May 25, 2016 ยท (Permalink)
It's even more fascinating when you think about what are e i and pi. Pi is some number we invented to be able to calculate pi. i is another one we invented to be able to get roots of negative numbers and we mostly use e to do differential calculus. But all those numbers together are in this nice equation.
Math is probably one of the things that is transcended over to the aliens and we could "talk" about it with them.
Kadenb12 ยท 1 points ยท Posted at 16:30:04 on May 25, 2016 ยท (Permalink)
Came here for this. Great Kahn Academy video on this. He gets truly anxious about solving it.
phrocks254 ยท 1 points ยท Posted at 16:34:10 on May 25, 2016 ยท (Permalink)
If you learn phasor analysis, the magic is gone.
pm8k ยท 1 points ยท Posted at 16:56:07 on May 25, 2016 ยท (Permalink)
If you change it to e-i*pi , you can add in the negative sign to get one more symbol in there
DizeazedFly ยท 1 points ยท Posted at 16:59:36 on May 25, 2016 ยท (Permalink)
I prefer the square root. That way you get an entire equation without numbers
randomguy186 ยท 1 points ยท Posted at 17:01:35 on May 25, 2016 ยท (Permalink)
I knew this would be in this thread!
I'm actually a bit more impressed with the general equation this derives from:
exi = cos x + i * sin x
I've often wondered what Euler thought when he stumbled upon this - was it impressive to him? Or was it merely Yet Another Deep Connection?
SaggiSponge ยท 1 points ยท Posted at 17:05:10 on May 25, 2016 ยท (Permalink)
ei*tau =1
[deleted] ยท 1 points ยท Posted at 17:12:07 on May 25, 2016 ยท (Permalink)
I prefer
eiฯ = 1
Bohnanza ยท 1 points ยท Posted at 17:23:13 on May 25, 2016 ยท (Permalink)
Found Euler
mrspockinator ยท 1 points ยท Posted at 17:43:02 on May 25, 2016 ยท (Permalink)
I love this fact so much I got it as a tattoo!
Monte07 ยท 1 points ยท Posted at 17:44:39 on May 25, 2016 ยท (Permalink)
I used to think that math was no fun, I couldn't see how it was done. But now Euler's my hero, since ei*pi + 1 = 0.
Oh, math poetry.
John_Q_Deist ยท 1 points ยท Posted at 17:53:43 on May 25, 2016 ยท (Permalink)
It's always about the oil. Always.
dat_asshai ยท 1 points ยท Posted at 17:58:33 on May 25, 2016 ยท (Permalink)
Even better, you can use this to prove i ^ i is a real number!
-1 = Exp[i*pi] (Take sqrt of both sides) i = Exp[i*pi/2] (Raise each side to ith power) i ^ i = Exp[-pi/2] ~ 0.208
BosslikeBehavoir ยท 1 points ยท Posted at 17:58:35 on May 25, 2016 ยท (Permalink)
So in that sense, we can just say that ei*pi is equal to -1.
ThePr1d3 ยท 1 points ยท Posted at 18:00:52 on May 25, 2016 ยท (Permalink)
Captain obvious to explain me what is cool here ? :(
ythl ยท 1 points ยท Posted at 18:01:47 on May 25, 2016 ยท (Permalink)
I discovered this by accident playing with my Ti-83. I was just messing around with the baked in constants, and when I tried epi * i, and saw "-1" I was baffled and amazed. I showed my high school math teacher and he attributed it to a glitch in the calculator.
munchbunny ยท 1 points ยท Posted at 18:07:07 on May 25, 2016 ยท (Permalink)
A single equation that makes much of trigonometry trivial. It's awesome because a lot of things that are really complex to do with trigonometry just sort of fall out when you approach it using Euler's theorem.
bitch_nigga ยท 1 points ยท Posted at 18:11:52 on May 25, 2016 ยท (Permalink)
Notice how what you've written consists of the 5 most important numbers in mathematics: e, i, pi, 1 and 0.
That makes it much cooler, imo
ThisUsernameIsMyName ยท 1 points ยท Posted at 18:19:33 on May 25, 2016 ยท (Permalink)
Thats Euler's identity?
gods_fear_me ยท 1 points ยท Posted at 18:28:50 on May 25, 2016 ยท (Permalink)
English plz
lthornton20 ยท 1 points ยท Posted at 18:57:26 on May 25, 2016 ยท (Permalink)
So is it safe to assume that ei*pi = -1 ?
AinTunez ยท 1 points ยท Posted at 19:01:04 on May 25, 2016 ยท (Permalink)
In better format for geeks like me: eฯi + 1 = 0
Johnputer ยท 1 points ยท Posted at 19:02:06 on May 25, 2016 ยท (Permalink)
This. The equation contains the 5 most important numbers in mathematics.
SillyFlyGuy ยท 1 points ยท Posted at 19:12:09 on May 25, 2016 ยท (Permalink)
Can we get a picture or something? I don't math good enough to make sense of this.
jaredjeya ยท 1 points ยท Posted at 19:17:39 on May 25, 2016 ยท (Permalink)
eiฯ = 1
CRISPR ยท 1 points ยท Posted at 19:33:53 on May 25, 2016 ยท (Permalink)
Finally, correct answer
[deleted] ยท 1 points ยท Posted at 19:36:29 on May 25, 2016 ยท (Permalink)
Every single time this question is asked holy rip.
wasdo ยท 1399 points ยท Posted at 12:05:17 on May 25, 2016 ยท (Permalink)*
22/7 is
muchmore close to the actual value of pi than 3.14 is.edit: okay, okay, I get it.
[deleted] ยท 722 points ยท Posted at 12:38:28 on May 25, 2016 ยท (Permalink)
[deleted]
poktanju ยท 653 points ยท Posted at 14:20:02 on May 25, 2016 ยท (Permalink)
22/7 and 3.14 are both about 0.05% off, 355/113 is less than 0.00001% off.
sheepyowl ยท 35 points ยท Posted at 14:39:51 on May 25, 2016 ยท (Permalink)
How off is pi
Baeward ยท 86 points ยท Posted at 14:41:46 on May 25, 2016 ยท (Permalink)
Depends how many days you left it out
DoctorBr0 ยท 20 points ยท Posted at 18:10:33 on May 25, 2016 ยท (Permalink)
pi/1 is pretty close.
RGBLaser ยท 36 points ยท Posted at 15:23:59 on May 25, 2016 ยท (Permalink)
It's off the hook ๐ Math is cool!
[deleted] ยท 9 points ยท Posted at 16:57:27 on May 25, 2016 ยท (Permalink)
I was about to say that if you're remembering 6 digits anyway, you might as well just go to the 5th digit of pi. Then you're off by less than .00001. ...but then I saw the % sign!
BLAZINGSORCERER199 ยท 7 points ยท Posted at 16:45:57 on May 25, 2016 ยท (Permalink)
Why don't we just use 355/113 as standard instead of 3.14 then ?
I've always used 3.14 since sixth grade.
poktanju ยท 8 points ยท Posted at 16:52:16 on May 25, 2016 ยท (Permalink)
Harder to remember and not as easy to use in a typical calculator, I assume. It's hundredths of a percent difference in any case.
HamsterBoo ยท 5 points ยท Posted at 17:35:48 on May 25, 2016 ยท (Permalink)
Because its only about 10 times as accurate as 3.14159, which is the same number of digits and much easier to remember.
absentbird ยท 5 points ยท Posted at 20:07:55 on May 25, 2016 ยท (Permalink)
Only off by an order of magnitude? Well never mind then.
sangriadvx ยท 5 points ยท Posted at 21:46:34 on May 25, 2016 ยท (Permalink)
"Close enough." - math.
[deleted] ยท 5 points ยท Posted at 22:34:30 on May 25, 2016 ยท (Permalink)
[deleted]
Swiggety666 ยท 3 points ยท Posted at 23:44:31 on May 25, 2016 ยท (Permalink)
The mathematician just write ฯ
casey12141 ยท 1 points ยท Posted at 22:50:25 on May 25, 2016 ยท (Permalink)
The only time you'll ever care about the tiny fractions of error between them, you'll be doing computational solutions anyway. So just use the simplest thing.
LedditHiveMind ยท 2 points ยท Posted at 18:42:47 on May 25, 2016 ยท (Permalink)
ELI5 why do different circumferences and diameters result in numbers closer to pi? What is 'real' pi?
Lobo2ffs ยท 2 points ยท Posted at 19:48:12 on May 25, 2016 ยท (Permalink)
The others aren't perfect circles, pi is for a circle and it's an irrational number which can't be expressed as a fraction (whole number in integer numerator and denominator).
For example, if you have a regular hexagon where each angle is (360/6) = 60ยบ and each side is the same length, then "pi" = circumference/diameter is 3. As you increase it to a bigger regular n-gon, you get closer and closer to the real value of pi.
There are many formulas for calculating pi, here are some http://mathworld.wolfram.com/PiFormulas.html
Zavant ยท 2 points ยท Posted at 20:03:51 on May 25, 2016 ยท (Permalink)
I think you meant to say, that 22/7 and 3.14 are off by 0.005%. It's impossible for 3.14 to be off by 0.05%, as the two first digits of pi are 1 and 4. If it was off by .05%, the actual digits of pi would be either 3.09 or 3.19.
[deleted] ยท 1 points ยท Posted at 10:13:18 on May 26, 2016 ยท (Permalink)
pi99.95%, or pi\0.9995 = 3.1400. So yeah, it's 0.5%.
Zavant ยท 1 points ยท Posted at 10:28:32 on May 26, 2016 ยท (Permalink)
Ah well apparently i'm bad at noticing the % thing, even though i wrote it myself. I was thinking about the digits themselves and not a percentage difference. Oh well.
atrain728 ยท 2 points ยท Posted at 17:37:34 on May 25, 2016 ยท (Permalink)
But requires you to memorize 6 digits. Compare to 3.14159
[deleted] ยท 3 points ยท Posted at 19:39:29 on May 25, 2016 ยท (Permalink)*
[deleted]
Vanity_Blade ยท 1 points ยท Posted at 20:22:52 on May 25, 2016 ยท (Permalink)
MATH!
[deleted] ยท 1 points ยท Posted at 10:12:33 on May 26, 2016 ยท (Permalink)
And 355/112 gives 3.141593 (rounded), so an extra figure.
[deleted] ยท 1 points ยท Posted at 23:39:57 on May 25, 2016 ยท (Permalink)
31415926535897932384/10000000000000000000 is even MORE accurate!!!!
CrazyKirby97 ยท -13 points ยท Posted at 15:45:11 on May 25, 2016 ยท (Permalink)*
TIL the calculators people pay 100 dollars for are
shit.decent calculators.poktanju ยท 4 points ยท Posted at 15:56:09 on May 25, 2016 ยท (Permalink)
What do you mean?
CrazyKirby97 ยท -9 points ยท Posted at 16:25:58 on May 25, 2016 ยท (Permalink)
They use a less accurate version of pi.
[deleted] ยท 16 points ยท Posted at 16:47:50 on May 25, 2016 ยท (Permalink)
I've never seen a calculator that used 3.14 for pi. Much less a $100 one.
tim0901 ยท 10 points ยท Posted at 16:55:43 on May 25, 2016 ยท (Permalink)
My ยฃ15 casio uses 3.1415926535898 as pi, so I doubt a $100 calculator is going to use anything less accurate
KirbyElder ยท 8 points ยท Posted at 16:27:38 on May 25, 2016 ยท (Permalink)
My ยฃ15 calculator has pi to 3.141592
FrostyBeav ยท 1 points ยท Posted at 17:50:36 on May 25, 2016 ยท (Permalink)
My HP 48SX always just carried the pi symbol through the answer. That was annoying at times so I usually just typed in 3.14159 by hand (because that's oh so accurate).
Superboy309 ยท 4 points ยท Posted at 18:15:06 on May 25, 2016 ยท (Permalink)*
My ti-84 plus uses 3.1415926535898, it also does integrals, derivatives and graphing, which are all very important things that a $20 calculator wont do.
edit: did a dumb
Thraol ยท 3 points ยท Posted at 20:30:38 on May 25, 2016 ยท (Permalink)
Not to be pedantic or anything, but there's an extra "4" in that number that shouldn't be there (3.14159265
435898).Superboy309 ยท 2 points ยท Posted at 20:53:21 on May 25, 2016 ยท (Permalink)
You are correct, I had to view pi in 2 parts and it rounded the 3.
Insertnamesz ยท 2 points ยท Posted at 19:16:00 on May 25, 2016 ยท (Permalink)
What's your point? All computers with finite bit storage must use numbers that have a finite size/precision, aka approximations when it comes to irrationals.
IAm_From_2045_AMA ยท 52 points ยท Posted at 14:50:26 on May 25, 2016 ยท (Permalink)
3141592653589793/1000000000000000 is actually phenomenally accurate.
SleestakJack ยท 24 points ยท Posted at 15:09:12 on May 25, 2016 ยท (Permalink)
Thank you for stopping on a digit where the next digit isn't 5 or higher. Whenever anyone rattles off an approximation of pi, and i know the next digit is a 7, I really want to tell them, "Well, if you're going to stop there, then your last digit is off..."
IAm_From_2045_AMA ยท 9 points ยท Posted at 15:12:38 on May 25, 2016 ยท (Permalink)
That irks me too, I actually wanted to stop on the last 5 of "535" but then realized it would round up, and then just kept going until the next number no longer rounded it up, which turned out to be another five digits. No problem, random citizen!
SleestakJack ยท 2 points ยท Posted at 15:18:53 on May 25, 2016 ยท (Permalink)
You bet...
Ahem.
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348283421170679...
???
mattsprofile ยท 5 points ยท Posted at 16:09:45 on May 25, 2016 ยท (Permalink)
Well they're rattling off digits. If they say "I don't know any more digits" then obviously they wouldn't round up the last one because they don't know what the next one is. They know there's another digit, they said all of the other digits up until that point, which is what they were trying to do. What's the problem? You're just being fussy.
SleestakJack ยท 5 points ยท Posted at 16:15:11 on May 25, 2016 ยท (Permalink)
I'm someone who's memorized around 100 digits of pi. I did it in middle school and 28 years later it's still stuck in my head.
What part of this doesn't scream "fussy?"
Tocoapuffs ยท 2 points ยท Posted at 20:36:47 on May 25, 2016 ยท (Permalink)
Not wrong. Truncated.
Sideshowcomedy ยท 1 points ยท Posted at 18:13:28 on May 25, 2016 ยท (Permalink)
Have you ever actually said this, because that's a sad math fact.
Kayyam ยท -1 points ยท Posted at 15:33:21 on May 25, 2016 ยท (Permalink)
I don't get it. The same logic that make you round up at 7 makes you round down at 3, so why is the last digit off when it's a 7 and not a when it's a 3 ?
[deleted] ยท 1 points ยท Posted at 15:37:19 on May 25, 2016 ยท (Permalink)
[deleted]
Kayyam ยท 9 points ยท Posted at 16:06:54 on May 25, 2016 ยท (Permalink)
You just rounded down.
[deleted] ยท -2 points ยท Posted at 16:15:51 on May 25, 2016 ยท (Permalink)
[deleted]
Kayyam ยท 7 points ยท Posted at 16:23:17 on May 25, 2016 ยท (Permalink)
I mean, you had an initial number, now you have a new rounded one and it happens that it's inferior to the initial one. I don't think it's a matter of perspective.
Insanitypenguinz ยท 1 points ยท Posted at 15:54:28 on May 25, 2016 ยท (Permalink)
Not as accurate as : 2646693125139304345/ 842468587426513207
Source
xeow ยท 9 points ยท Posted at 16:58:53 on May 25, 2016 ยท (Permalink)
Indeed! 355/113 has fairly high accuracy and very high efficiency.
Onceuponaban ยท 2 points ยท Posted at 17:51:52 on May 25, 2016 ยท (Permalink)
What is the difference between accuracy and efficiency?
xeow ยท 1 points ยท Posted at 19:54:30 on May 25, 2016 ยท (Permalink)
Accuracy here is how close the computed ratio is to the real value of ฯ. In the code, I defined accuracy as 1 โ error, where error is defined as the absolute value of ratio and target (the target being ฯ in this case).
Efficiency here is how much information is packed into the digits for the level of accuracy. If two ratios are equally accurate, the one with fewer digits is more efficient. In the code, I defined the efficiency as
-log10(error) / ((1+log10(numerator)) + (1+log10(denominator))). There might be better ways to rate the ratios, but that's what I used.fyi1183 ยท 3 points ยท Posted at 17:38:22 on May 25, 2016 ยท (Permalink)
In general, the trick to getting surprisingly accurate rational approximations of irrational numbers is to cut off the continued fraction. This is where the examples for pi come from.
Neat fact: using continued fractions, if your denominator happens to be k, you get accuracy better than O(1/kยฒ).
Bmandk ยท 2 points ยท Posted at 17:30:17 on May 25, 2016 ยท (Permalink)
But what about 710/226??? /s
thelegendarymudkip ยท 2 points ยท Posted at 17:35:07 on May 25, 2016 ยท (Permalink)
As is 3141592653589793238462643383279502884197169399375/1000000000000000000000000000000000000000000000000.
RedAnonym ยท 1 points ยท Posted at 19:51:28 on May 25, 2016 ยท (Permalink)
Add 1,0 to make 50 digits at least. Fuckin normies.
bowser0000 ยท 2 points ยท Posted at 18:05:07 on May 25, 2016 ยท (Permalink)
/u/355over113
scstraus ยท 2 points ยท Posted at 19:28:35 on May 25, 2016 ยท (Permalink)
Yeah, but the operation is almost as long as the number of digits of pi it gets you, and then you have to actually do the operation to get the digits. Better just to memorize the digits. I memorized the first 25 as a kid and it didn't take me very long.
355over113 ยท 2 points ยท Posted at 22:31:26 on May 25, 2016 ยท (Permalink)
Hey, my username's relevant again!
bathrobehero ยท 1 points ยท Posted at 14:43:42 on May 25, 2016 ยท (Permalink)
Best one yet.
BCMike ยท 1 points ยท Posted at 15:49:22 on May 25, 2016 ยท (Permalink)
Take the first three odd numbers
Double them up, like so:
Take the last three, and divide by the first:
bathrobehero ยท 1 points ยท Posted at 16:15:18 on May 25, 2016 ยท (Permalink)
Neat, though to me it's easier to remember 355 and 113.
It's easy to visualize also, 55 and 11 surrounded by threes.
jorellh ยท 1 points ยท Posted at 15:06:15 on May 25, 2016 ยท (Permalink)
Shush Ramanujan
jacob_ewing ยท 1 points ยท Posted at 16:58:40 on May 25, 2016 ยท (Permalink)
314159265358979/100000000000000 is way better though.
SteveIzHxC ยท 1 points ยท Posted at 18:17:42 on May 25, 2016 ยท (Permalink)
See also
http://www.wolframalpha.com/input/?i=Table%5BRationalize%5BPi,s%5D,%7Bs,%7B0.1,0.01,0.001,0.0001,0.00001,0.000001,0.0000001%7D%7D%5D
iamonlyoneman ยท 1 points ยท Posted at 18:19:14 on May 25, 2016 ยท (Permalink)
as someone who is not great with fractions, I'll just stick to 3.14ish, thanks
ReekRhymesWithWeak ยท 1 points ยท Posted at 18:33:50 on May 25, 2016 ยท (Permalink)
28023 / 8920 is another nice one
imgonnacallyouretard ยท 1 points ยท Posted at 18:42:59 on May 25, 2016 ยท (Permalink)
Yeah but ฯ/1 is way better
weareallthere ยท 1 points ยท Posted at 20:47:10 on May 25, 2016 ยท (Permalink)
Or 710 / 226
xanthalasajache ยท 1 points ยท Posted at 03:20:27 on May 26, 2016 ยท (Permalink)
pi/1 is more accurate
xanthalasajache ยท 1 points ยท Posted at 03:20:41 on May 26, 2016 ยท (Permalink)
pi/1 is more accurate
xanthalasajache ยท 1 points ยท Posted at 03:20:46 on May 26, 2016 ยท (Permalink)
pi/1 is more accurate
aldesuda ยท 0 points ยท Posted at 16:25:31 on May 25, 2016 ยท (Permalink)
And easy to remember, since from the bottom, it goes 1-1-3-3-5-5.
Lyress ยท 928 points ยท Posted at 14:01:36 on May 25, 2016 ยท (Permalink)*
So 22nd of july is the real Pi day?
Moobs_like_Jagger ยท 462 points ยท Posted at 15:56:12 on May 25, 2016 ยท (Permalink)*
In America, it's Duodecember 7th
A date which will live in infamy... in the future
EDIT: I get it, duodecim is "12." But the numbers of the months don't match up with their names now, and maybe in the future there will be a bunch of silly month-names in between December and Duodecember, like "Drumpf" or "Half-Life 3."
bl1y ยท 10 points ยท Posted at 18:30:30 on May 25, 2016 ยท (Permalink)
Duodec is 12, not 22. Don't you remember the children's rhyme?
datorangeguy ยท 2 points ยท Posted at 22:26:56 on May 25, 2016 ยท (Permalink)
But it shouldn't be 22, it should be twenty. The tenth month isn't December, remember?
bl1y ยท 1 points ยท Posted at 00:18:11 on May 26, 2016 ยท (Permalink)
... that
... that's not right
datorangeguy ยท 2 points ยท Posted at 00:19:36 on May 26, 2016 ยท (Permalink)
Bamboozled!
hairetikos ยท 6 points ยท Posted at 17:43:34 on May 25, 2016 ยท (Permalink)
Like duodecimal? That's how they mark books in libraries.
nephelokokkygia ยท 5 points ยท Posted at 18:12:48 on May 25, 2016 ยท (Permalink)*
You're thinking of Dewey Decimal. Duodecimal is a size of book page that's made by folding each printed sheet into twelve leaves.
sangriadvx ยท 3 points ยท Posted at 21:44:47 on May 25, 2016 ยท (Permalink)
You're thinking of duodecimo. Duodecimal is the first part of the small intestines.
[deleted] ยท 2 points ยท Posted at 08:12:10 on May 26, 2016 ยท (Permalink)
You're thinking of the duodenum . Duodecimal is that guy from the X-files.
Fit_Shaced ยท 2 points ยท Posted at 19:27:54 on May 25, 2016 ยท (Permalink)
This reads exactly like something the Cybernetic Ghost of Christmas Past from the Future would say.
ThePr1d3 ยท 2 points ยท Posted at 18:01:39 on May 25, 2016 ยท (Permalink)
Isn't duodecember 24 ?
Poops_McYolo ยท 1 points ยท Posted at 18:33:17 on May 25, 2016 ยท (Permalink)
The 7th of Toyotathon courtesy of G. W. Bush
super_aardvark ยท 1 points ยท Posted at 21:33:34 on May 25, 2016 ยท (Permalink)
In the Year of the Whopper.
CRISPR ยท 1 points ยท Posted at 19:37:57 on May 25, 2016 ยท (Permalink)
I wonder how is the weather in Duodecember
[deleted] ยท 1 points ยท Posted at 20:52:28 on May 25, 2016 ยท (Permalink)
Or the 7th of ... wait
PMmeYourSins ยท 1 points ยท Posted at 22:52:54 on May 25, 2016 ยท (Permalink)
Shouldn't it be Vigicember?
DoubleFried ยท 22 points ยท Posted at 16:06:20 on May 25, 2016 ยท (Permalink)
It's Pi Approximation Day.
epiphone_fan1 ยท 4 points ยท Posted at 17:00:22 on May 25, 2016 ยท (Permalink)
"It celebrates failure?" "Not failure, Utah-raptor! Approximations of success"
ghtuy ยท 2 points ยท Posted at 19:19:23 on May 25, 2016 ยท (Permalink)
I want a t shirt that says "Failure is just success rounded down, my friend."
jsmooth7 ยท 4 points ยท Posted at 18:28:15 on May 25, 2016 ยท (Permalink)
And it's celebrated by eating cake, because it's approximately pie.
TheWolfXCIX ยท 74 points ยท Posted at 14:38:14 on May 25, 2016 ยท (Permalink)
[deleted] ยท 83 points ยท Posted at 14:44:44 on May 25, 2016 ยท (Permalink)
twenty tooth
pm_me_gnus ยท 4 points ยท Posted at 17:08:50 on May 25, 2016 ยท (Permalink)
Pretty much, yeah. I eat pie all day on Jul 22, and right now I'm down about a dozen teeth.
marpro15 ยท 2 points ยท Posted at 14:57:26 on May 25, 2016 ยท (Permalink)
what? how?
[deleted] ยท -1 points ยท Posted at 18:38:09 on May 25, 2016 ยท (Permalink)
It's written 22/7 in backwards countries.
marpro15 ยท 1 points ยท Posted at 19:02:49 on May 25, 2016 ยท (Permalink)
i was talking about the th thing
tinverse ยท 3 points ยท Posted at 16:01:27 on May 25, 2016 ยท (Permalink)
No, weren't you paying attention? Smarch 113th is Pi day.
2close2see ยท 3 points ยท Posted at 16:06:32 on May 25, 2016 ยท (Permalink)
Or the 7th day of the 22nd month if you're American.
[deleted] ยท 4 points ยท Posted at 15:53:48 on May 25, 2016 ยท (Permalink)
Well, the 22th of July is the day the right-wing psychopath Anders Behring Breivik killed 77 people in and around Oslo.
So I have a feeling this day wouldn't be very popular in Norway.
eeeebbs ยท 3 points ยท Posted at 17:32:20 on May 25, 2016 ยท (Permalink)
It's also my birthday :):
twbk ยท 2 points ยท Posted at 16:45:04 on May 25, 2016 ยท (Permalink)
My thought too. I think we'll stick to 3.14, or the third of dodecember or whatever the fourteenth month is called.
Source: Am Norwegian. From Oslo.
almightybob1 ยท 3 points ยท Posted at 14:57:12 on May 25, 2016 ยท (Permalink)
[deleted] ยท 0 points ยท Posted at 15:31:57 on May 25, 2016 ยท (Permalink)
what? how?
popedarren ยท 1 points ยท Posted at 16:06:50 on May 25, 2016 ยท (Permalink)
It was an edit. It once said, "22th," and now it says, "22nd."
Lyress ยท 1 points ยท Posted at 17:42:33 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j3woh
realog173 ยท 4 points ยท Posted at 15:50:12 on May 25, 2016 ยท (Permalink)
No, it'd be the Twentytwomber 7th.
jmwbb ยท 3 points ยท Posted at 14:44:01 on May 25, 2016 ยท (Permalink)
Lyress ยท 9 points ยท Posted at 14:45:09 on May 25, 2016 ยท (Permalink)
Corrected, my bad. English is not my native.
marpro15 ยท 2 points ยท Posted at 14:57:23 on May 25, 2016 ยท (Permalink)
what? how?
jmwbb ยท 4 points ยท Posted at 15:01:24 on May 25, 2016 ยท (Permalink)
He edited, it said 22th before
marpro15 ยท 5 points ยท Posted at 15:06:03 on May 25, 2016 ยท (Permalink)
ow okay, i was confused, it seemed like you were correcting it to 22th
Zecym ยท 4 points ยท Posted at 14:55:08 on May 25, 2016 ยท (Permalink)
Not here in the land of the free, 'Murica
10TAisME ยท 1 points ยท Posted at 14:51:02 on May 25, 2016 ยท (Permalink)
22nd
NeverBeenStung ยท 1 points ยท Posted at 15:20:51 on May 25, 2016 ยท (Permalink)
No but the 22nd is
Herr_Doktore ยท 1 points ยท Posted at 15:26:18 on May 25, 2016 ยท (Permalink)
We should all celebrate by eating more pie.
Ioseb ยท 1 points ยท Posted at 15:56:08 on May 25, 2016 ยท (Permalink)
As someone from a part in Europe, yes.
pnasmaster ยท 1 points ยท Posted at 15:57:20 on May 25, 2016 ยท (Permalink)
No the 355th day of the month of Graxspoth is the real Pi day. Standard Galactic Federation time of course.
rainbow_party ยท 1 points ยท Posted at 16:08:19 on May 25, 2016 ยท (Permalink)
Pi approximation day. You're supposed to eat Boston Cream Pie.
happilyworking ยท 1 points ยท Posted at 16:22:50 on May 25, 2016 ยท (Permalink)
Don't tell the yanks that
kingbobofyourhouse ยท 1 points ยท Posted at 16:36:00 on May 25, 2016 ยท (Permalink)
I think you mean the 7th of Gurbuarember.
MrJohz ยท 1 points ยท Posted at 16:37:32 on May 25, 2016 ยท (Permalink)
And the Brits have been trying to tell you this for years now.
ILIEKDEERS ยท 1 points ยท Posted at 17:03:38 on May 25, 2016 ยท (Permalink)
Only if you aren't using a freedom calendar.
RickHalkyon ยท 1 points ยท Posted at 17:18:12 on May 25, 2016 ยท (Permalink)
checks whether next July or next March is closer
Yessir, that's true. Ask me again in August.
hubife13 ยท 1 points ยท Posted at 17:30:01 on May 25, 2016 ยท (Permalink)
No because America is the only country in the world.
Ron_Jeremy ยท 1 points ยท Posted at 17:53:26 on May 25, 2016 ยท (Permalink)
Maybe in countries that haven't been freedom'd yet
Lyress ยท 1 points ยท Posted at 18:01:57 on May 25, 2016 ยท (Permalink)
So about 99% of the world's countries?
Ron_Jeremy ยท 1 points ยท Posted at 18:42:59 on May 25, 2016 ยท (Permalink)
YET
BenAreLamb ยท 1 points ยท Posted at 17:55:28 on May 25, 2016 ยท (Permalink)
Not in America! mm/dd/yyyy
letsgolakers24 ยท 1 points ยท Posted at 18:28:00 on May 25, 2016 ยท (Permalink)
Not in freedom countries
[deleted] ยท 1 points ยท Posted at 18:29:46 on May 25, 2016 ยท (Permalink)
what are you. Not american?
Lyress ยท 1 points ยท Posted at 19:35:34 on May 25, 2016 ยท (Permalink)
Actually
hsuresh ยท 1 points ยท Posted at 18:57:55 on May 25, 2016 ยท (Permalink)
Approximately. 0.05% off precisely.
jaltair9 ยท 1 points ยท Posted at 19:27:36 on May 25, 2016 ยท (Permalink)
Except in America.
JackAceHole ยท 1 points ยท Posted at 19:41:02 on May 25, 2016 ยท (Permalink)
Only outside the US
deusset ยท 1 points ยท Posted at 20:21:11 on May 25, 2016 ยท (Permalink)
Can you make this a thing? I think we should make this a thing.
SnakeMan448 ยท 1 points ยท Posted at 21:18:20 on May 25, 2016 ยท (Permalink)
What about the 22nd of February?
Vinny_Gambini ยท 1 points ยท Posted at 02:06:19 on May 26, 2016 ยท (Permalink)
Isn't that Febtober 7?
PallBear ยท 0 points ยท Posted at 15:43:42 on May 25, 2016 ยท (Permalink)
Found the European
Lyress ยท 1 points ยท Posted at 17:41:15 on May 25, 2016 ยท (Permalink)
No, just not american
poktanju ยท 21 points ยท Posted at 14:17:14 on May 25, 2016 ยท (Permalink)
22/7 is off by 0.04%, 3.14 by 0.05%.
Pandamana ยท 5 points ยท Posted at 18:42:30 on May 25, 2016 ยท (Permalink)
MUCH MORE CLOSE
[deleted] ยท 4 points ยท Posted at 15:05:51 on May 25, 2016 ยท (Permalink)
I just use the Pi button on my calculator
peanutbuttersucks ยท 8 points ยท Posted at 16:25:05 on May 25, 2016 ยท (Permalink)
I had a math teacher once whose answer key for a test was done using 3.14. I used the pi button on my calculator for calculations and she marked half my test wrong. I had to sit down with her and basically re-type each question into my calculator to show her why my answers were slightly different... :/
jusjerm ยท 7 points ยท Posted at 16:31:30 on May 25, 2016 ยท (Permalink)
It is possible that you were instructed to use 3.14 as an approximation in the test directions. My time as a teacher assured me that words written in bold between tests questions might as well be invisible.
This is (maddeningly) done because certain standardized tests ALSO tell you to use the 3.14 approximation rather than pi
NotGloomp ยท 3 points ยท Posted at 21:02:37 on May 25, 2016 ยท (Permalink)
At some point you just have got to put a margin.
FloatingGhost ยท 5 points ยท Posted at 15:20:07 on May 25, 2016 ยท (Permalink)
I actually memorized 22/7 back in year 6 (age.. 10), or as far as a crappy little calculator could display
3.1428571 And the sqrt was 1.7728105 if i recall
NewbornMuse ยท 6 points ยท Posted at 15:47:57 on May 25, 2016 ยท (Permalink)
It's actually 142857 repeating. Boom, memorized all of them! For more cool info, check the comment chain on 1/7 further up.
FolkSong ยท 1 points ยท Posted at 17:27:03 on May 25, 2016 ยท (Permalink)
Why did you memorize 22/7 and not pi?
FloatingGhost ยท 1 points ยท Posted at 19:04:31 on May 25, 2016 ยท (Permalink)
because we didn't have access to a pi button on the calculators and the best estimate I had to go by was 22/7
This is how I spent junior school. 10/10.
[deleted] ยท 1 points ยท Posted at 19:09:35 on May 25, 2016 ยท (Permalink)
[deleted]
FloatingGhost ยท 1 points ยท Posted at 19:32:58 on May 25, 2016 ยท (Permalink)
Because I didn't have access to a value of pi!
And I had nothing better to do.
FolkSong ยท 1 points ยท Posted at 20:47:53 on May 25, 2016 ยท (Permalink)
You should have just worked it out once with a series expansion!
Just kidding, I realize you were 10.
superpastaaisle ยท 3 points ยท Posted at 16:11:35 on May 25, 2016 ยท (Permalink)
If you can memorize 3.14 adding two digits is reasonable. 3.1416 (3.14159) will probably cover all situations outside of space travel to sufficient accuracy.
veggiesama ยท 3 points ยท Posted at 16:26:59 on May 25, 2016 ยท (Permalink)
I had a middle school teacher who told me something like that ("Pi is pretty close to 22/7! Neat, huh?") and I forgot about half of that ("Pi is
pretty close to22/7!"), so when high school rolled around I had a hard time figuring out why everyone thought pi was such a big deal. It's just a dumb magic fraction, right? Nooope.SteveIzHxC ยท 3 points ยท Posted at 18:12:46 on May 25, 2016 ยท (Permalink)
Much more close? I'll give you more close, though.
3.14 underestimates pi by 0.0507%
22/7 overestimates pi by 0.0402%
pokemonpasta ยท 2 points ยท Posted at 15:24:12 on May 25, 2016 ยท (Permalink)
I usually go 3.141592 in calculations
Vaxtin ยท 1 points ยท Posted at 15:35:37 on May 25, 2016 ยท (Permalink)
The cube root of 31 is very accurate as well.
chamuth ยท 1 points ยท Posted at 15:39:13 on May 25, 2016 ยท (Permalink)
The cube root of 31 is actually really close also
-KR- ยท 1 points ยท Posted at 16:15:23 on May 25, 2016 ยท (Permalink)
Also 19/7 is very close to e.
And 10/7 to sqrt(2)
CaptainMelonHead ยท 1 points ยท Posted at 16:16:29 on May 25, 2016 ยท (Permalink)
ฯ/1
jimmythefrenchfry ยท 1 points ยท Posted at 16:17:19 on May 25, 2016 ยท (Permalink)
brilliant!
[deleted] ยท 1 points ยท Posted at 17:07:16 on May 25, 2016 ยท (Permalink)
pi/1 usually does me
-HeisenBird- ยท 1 points ยท Posted at 17:13:46 on May 25, 2016 ยท (Permalink)
311/3 is even closer
avenlanzer ยท 1 points ยท Posted at 19:27:51 on May 25, 2016 ยท (Permalink)
3 โ31
dogfish83 ยท 1 points ยท Posted at 17:51:05 on May 25, 2016 ยท (Permalink)
I eat pi 22/7.
ythl ยท 1 points ยท Posted at 18:03:46 on May 25, 2016 ยท (Permalink)
And even more surprisingly, 22/7 is closer to the actual value of pi than pi itself is.
zeekar ยท 1 points ยท Posted at 18:40:13 on May 25, 2016 ยท (Permalink)
vs.
that's a difference of 0.000328164322443314... so I'm not sold on the "much" part. On the other hand,
which is quite close enough for most purposes.
jimeoptimusprime ยท 1 points ยท Posted at 18:46:42 on May 25, 2016 ยท (Permalink)*
The fastest known algorithm for calculating the value of pi uses an infinite sum. The more terms you include, the better the approximation, essentially. Including the first two terms of the sum is enough to get an approximation with a relative error of just 0.0000000000000000000000000001 percent.
Edit: Clarification
manickthoughts ยท 1 points ยท Posted at 19:34:35 on May 25, 2016 ยท (Permalink)
Not by Price is Right rules!
Bhizzle64 ยท 1 points ยท Posted at 20:05:43 on May 25, 2016 ยท (Permalink)
I remember one time when I was bored in math class I created a fraction that was equivalent to pi up to the tenth digit.
derangerd ยท 1 points ยท Posted at 20:25:19 on May 25, 2016 ยท (Permalink)
Much more seems a bit of an exaggeration. Not that I don't appreciate this fact.
heystevieray ยท 1 points ยท Posted at 20:33:23 on May 25, 2016 ยท (Permalink)
666/212 is even closer. Number of the beast/boiling pt of water in Fahrenheit = pi
wolfgangdieter ยท 1 points ยท Posted at 21:31:30 on May 25, 2016 ยท (Permalink)
The number of seconds in a non-leap year / 107 is closer.
And if you don't mind waiting and counting it is very easy to remember.
Meulentje11 ยท 1 points ยท Posted at 21:39:12 on May 25, 2016 ยท (Permalink)
31415926535/10000000000 is also very accurate.
jonnyiw ยท 1 points ยท Posted at 22:14:31 on May 25, 2016 ยท (Permalink)
The cube root of 31 works pretty well too.
Layek7 ยท 1 points ยท Posted at 22:45:11 on May 25, 2016 ยท (Permalink)
The cube root of 31 is another cool approximation of pi!
daxmendax099 ยท 1 points ยท Posted at 00:03:53 on May 26, 2016 ยท (Permalink)
We should celebrate 22/7 as #PiDay (and 3.14 as #PiApproximationDay) as it's less approximate and more close to value of Pi!
Actionmaths ยท 1 points ยท Posted at 06:44:06 on May 26, 2016 ยท (Permalink)
You still can't say more close.
thestickystickman ยท 1 points ยท Posted at 07:54:46 on May 26, 2016 ยท (Permalink)
So is literally any number in the range of pi +/- (pi - 3.14).
kyleqead ยท 1 points ยท Posted at 17:57:32 on May 25, 2016 ยท (Permalink)
314159265358979323846/00000000000000000000 is a pretty good frakshun approximation too.
Vaxtin ยท 1 points ยท Posted at 19:39:03 on May 25, 2016 ยท (Permalink)
Divided by 0?
kyleqead ยท 1 points ยท Posted at 20:54:48 on May 25, 2016 ยท (Permalink)
put a one in front of them
jakefromstatefarm10 ยท -2 points ยท Posted at 14:14:57 on May 25, 2016 ยท (Permalink)
It's not that much closer.
ShadowWolf92 ยท -1 points ยท Posted at 14:48:52 on May 25, 2016 ยท (Permalink)
Using numerology to count the people i sent to heaven, produces more digits than 22 divided by seven
wu_niversity ยท 2 points ยท Posted at 17:35:53 on May 25, 2016 ยท (Permalink)
Not a lot of Immortal Technique fans around here?
ShadowWolf92 ยท 1 points ยท Posted at 17:36:55 on May 25, 2016 ยท (Permalink)
Guess not :)
[deleted] ยท -3 points ยท Posted at 14:02:35 on May 25, 2016 ยท (Permalink)
[deleted]
demonicpigg ยท 11 points ยท Posted at 14:25:48 on May 25, 2016 ยท (Permalink)
It becomes a bit awkward when you realize that's 22/6.
Dont_Be_So_Rambo ยท 4684 points ยท Posted at 12:39:52 on May 25, 2016 ยท (Permalink)
You can divide by 0 when no one is watching.
Mathmage530 ยท 1153 points ยท Posted at 12:52:37 on May 25, 2016 ยท (Permalink)
No!
theodore33 ยท 1039 points ยท Posted at 14:07:05 on May 25, 2016 ยท (Permalink)
you cant
source: am imprisoned
HEYdontIknowU ยท 33 points ยท Posted at 15:37:28 on May 25, 2016 ยท (Permalink)
That is good to know they take this so seriously.
Do you have any friends in prison, or are they all imaginary?
theodore33 ยท 44 points ยท Posted at 15:56:10 on May 25, 2016 ยท (Permalink)
I have many close friends in prison.
In fact, we're indivisible
HEYdontIknowU ยท 10 points ยท Posted at 15:57:18 on May 25, 2016 ยท (Permalink)
With liberty and justice for all.
theodore33 ยท 12 points ยท Posted at 15:58:01 on May 25, 2016 ยท (Permalink)
Justice yes.
Liberty, not so much.
adeebchowdhury ยท 1 points ยท Posted at 11:13:08 on May 26, 2016 ยท (Permalink)
Goddamn
columbus8myhw ยท 1 points ยท Posted at 12:26:28 on May 26, 2016 ยท (Permalink)
I'd square them if not for all the negativity
Yuki-no-Kage ยท 4 points ยท Posted at 16:56:08 on May 25, 2016 ยท (Permalink)
Someone is watching. Source: Foucault
Bambooshka ยท 2 points ยท Posted at 17:32:14 on May 25, 2016 ยท (Permalink)
Or are they? WE'LL NEVER KNOW!!! Guess I'd better act as if someone is watching just in case.
setfire3 ยท 3 points ยท Posted at 17:06:56 on May 25, 2016 ยท (Permalink)
I can't get myself to, every time i tried to, Oak's voice keeps echoing in my head.
BiffManly ยท 2 points ยท Posted at 17:24:48 on May 25, 2016 ยท (Permalink)
That was for ripping the tag off that mattress. The zero thing was fine.
BenAreLamb ยท 2 points ยท Posted at 17:50:17 on May 25, 2016 ยท (Permalink)
You can use Reddit in prison?
den3erw ยท 1 points ยท Posted at 15:28:11 on May 25, 2016 ยท (Permalink)
because you think no one is watching you in your solitary cell
pmoney757 ยท 1 points ยท Posted at 19:45:06 on May 25, 2016 ยท (Permalink)
How are you on reddit?
icywindflashed ยท 11 points ยท Posted at 14:23:17 on May 25, 2016 ยท (Permalink)
How big is "No!"?
Peregrine7 ยท 22 points ยท Posted at 14:42:41 on May 25, 2016 ยท (Permalink)
1x2x3x4....
...
...(No-1)xNo
pokemonpasta ยท 1 points ยท Posted at 15:14:40 on May 25, 2016 ยท (Permalink)
You're not wrong
Guckaugen ยท 2 points ยท Posted at 15:00:30 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial
Mathmage530 ยท -1 points ยท Posted at 14:33:47 on May 25, 2016 ยท (Permalink)
About tree fiddy
139mod70 ยท 5 points ยท Posted at 15:41:35 on May 25, 2016 ยท (Permalink)
N0! = N
bleedRnge ยท 2 points ยท Posted at 18:11:33 on May 25, 2016 ยท (Permalink)
Beat me to it!
NinjaRobotPilot ยท 3 points ยท Posted at 22:02:04 on May 25, 2016 ยท (Permalink)
What the hell is Aleph null factorial?!
PM_Me_SFW_Pictures ยท 1 points ยท Posted at 15:09:44 on May 25, 2016 ยท (Permalink)
/r/suprisefactorial
Swate- ยท 2 points ยท Posted at 21:57:42 on May 25, 2016 ยท (Permalink)
/r/unexpectedfactorial my friend
PM_Me_SFW_Pictures ยท 1 points ยท Posted at 23:24:14 on May 25, 2016 ยท (Permalink)
Thanks, forgot the name
dontthrowmeinabox ยท 1 points ยท Posted at 15:15:35 on May 25, 2016 ยท (Permalink)
....one else was in the room where it happened.
frugalNOTcheap ยท 1 points ยท Posted at 15:36:26 on May 25, 2016 ยท (Permalink)
I just did
cwf82 ยท 1 points ยท Posted at 16:10:58 on May 25, 2016 ยท (Permalink)
C.N. can!
BrofessorBroDown ยท 1 points ยท Posted at 16:48:17 on May 25, 2016 ยท (Permalink)
This is a tough one because you didn't give us the value of N. But o!=o so No!= N
[deleted] ยท 1 points ยท Posted at 16:55:15 on May 25, 2016 ยท (Permalink)
So dividing by 0 is the same as No! (no factorial)?
drinks_antifreeze ยท 1 points ยท Posted at 18:01:31 on May 25, 2016 ยท (Permalink)
No factorial?
blore40 ยท 1 points ยท Posted at 21:20:11 on May 25, 2016 ยท (Permalink)
No! is 1 just like 0! is 1.
redweasel ยท 1 points ยท Posted at 07:10:12 on May 26, 2016 ยท (Permalink)
No factorial?
ixora7 ยท 1 points ยท Posted at 09:38:24 on May 26, 2016 ยท (Permalink)
is u kill
bigalssupra ยท 710 points ยท Posted at 14:06:16 on May 25, 2016 ยท (Permalink)
I divided by zero once. It was pretty cool at first but then the room started to spin and my hands got all clammy. I had to call my friend over, I told him what I did and he was real dissapointed but of course interested in what it was like.
michaelberry2 ยท 26 points ยท Posted at 17:13:13 on May 25, 2016 ยท (Permalink)
I divided by zero once too.
Unfortunately, I lost an arm and a leg, and my little brother went missing as well...
Frenchfry_55 ยท 6 points ยท Posted at 17:33:46 on May 25, 2016 ยท (Permalink)
Gasp that's forbidden alchemy
GoldenWizard ยท 34 points ยท Posted at 16:41:08 on May 25, 2016 ยท (Permalink)
Divided? I think you mean divode, the past tense of divide.
leolego2 ยท 7 points ยท Posted at 18:38:42 on May 25, 2016 ยท (Permalink)
damn that's a stupid past tense
drpinkcream ยท 2 points ยท Posted at 20:39:58 on May 25, 2016 ยท (Permalink)
And once you divode the number becomes divod.
wafflefighter69 ยท -5 points ยท Posted at 17:19:21 on May 25, 2016 ยท (Permalink)
You ask divided to seem like you don't know what he's trying to say
pethuman ยท 5 points ยท Posted at 16:42:26 on May 25, 2016 ยท (Permalink)
you should probably see a doctor to make sure your liver is still on the left side of your body. last time my friend did this, he ended up in a parallel universe where everyone's internal organs were reversed.
drpinkcream ยท 1 points ยท Posted at 20:41:05 on May 25, 2016 ยท (Permalink)
You're gonna laugh.
kampamaneetti ยท 3 points ยท Posted at 19:50:00 on May 25, 2016 ยท (Permalink)
Are you sure you didn't just take acid by accident instead?
iSmear ยท 3 points ยท Posted at 19:50:49 on May 25, 2016 ยท (Permalink)
May I interest you in /r/fifthworldproblems ?
AnonZak ยท 3 points ยท Posted at 22:09:34 on May 25, 2016 ยท (Permalink)
You made a crucial mistake when you attempted to go at it yourself. I wrote a program to constantly divide by zero in my stead. I'm still trying to close the portal to hell...
quintinn ยท 1 points ยท Posted at 18:17:05 on May 25, 2016 ยท (Permalink)
I think you just jerked off with sriracha and claimed to divide by zero.
MaxCrack ยท 1 points ยท Posted at 18:31:07 on May 25, 2016 ยท (Permalink)
I divided by 0 once and proved that 1 = 2.
LOLNOEP ยท 1 points ยท Posted at 18:36:30 on May 25, 2016 ยท (Permalink)
moms spaghetti
All_Fallible ยท 1 points ยท Posted at 18:47:07 on May 25, 2016 ยท (Permalink)
Sounds a lot like that time I smoked salvia
adamrsb48 ยท 1 points ยท Posted at 20:12:40 on May 25, 2016 ยท (Permalink)
That's PCP, son. I told you not to do it once, and I'll do it again.
Don't do drugs, kids.
zmemetime ยท 1 points ยท Posted at 03:19:50 on May 26, 2016 ยท (Permalink)
I did that once too, I saw imaginary numbers.
Blewedup ยท 0 points ยท Posted at 17:18:41 on May 25, 2016 ยท (Permalink)
isn't dividing by zero essentially doing nothing?
i mean, if i have a pie and i divide it zero times i have done nothing to the pie.
therefore, dividing by zero is the math equivalent sleep. or rest. or something like that.
popejubal ยท 11 points ยท Posted at 17:26:52 on May 25, 2016 ยท (Permalink)
Nope. Take a pie and cut it into one piece. That means you now still have that same lie. Dividing by one (or multiplying by one) is the math equivalent of sleep.
Dividing by zero is asking to cut the pie into zero pieces. No matter how many times you cut, you will still have not-zero pieces. Dividing by zero is bad and doesn't work and is bad.
Blewedup ยท 1 points ยท Posted at 16:25:59 on May 26, 2016 ยท (Permalink)
i don't think you're being zen enough about this one.
to divide by zero is to do no math on the pie. the pie is better off, and so is the mathematician.
popejubal ยท 1 points ยท Posted at 17:46:32 on May 26, 2016 ยท (Permalink)
Dividing by zero is performing an operation, though. It's not about being Zen - it's about understanding what the operations mean at a fundamental level. Dividing (or multiplying) by one is doing no math on the pie. That's why 1 is the multiplicative identity.
Here is a nice explanation of why dividing by zero is a problem: http://www.freemathhelp.com/division-by-zero.html
[deleted] ยท 0 points ยท Posted at 19:38:26 on May 25, 2016 ยท (Permalink)
[deleted]
popejubal ยท 8 points ยท Posted at 19:40:56 on May 25, 2016 ยท (Permalink)
That's not multiplying or dividing, though. That's subtracting. You can subtract any number you want.
PacificBrim ยท 3 points ยท Posted at 20:45:04 on May 25, 2016 ยท (Permalink)
Nah.. You have to send it into another dimension
agoel007 ยท 295 points ยท Posted at 14:04:23 on May 25, 2016 ยท (Permalink)
I can't believe you've done this!
dogbreath101 ยท 9 points ยท Posted at 17:13:25 on May 25, 2016 ยท (Permalink)
[https://www.youtube.com/watch?v=_X6VoFBCE9k](ah fuck)
_Kyu ยท 7 points ยท Posted at 18:53:48 on May 25, 2016 ยท (Permalink)
[text](https://www.linkhere.com)
GMY0da ยท 1 points ยท Posted at 21:03:00 on May 25, 2016 ยท (Permalink)
Bravo!
kangarooseatbelt ยท 5 points ยท Posted at 15:44:46 on May 25, 2016 ยท (Permalink)
Mathematicians hate him!
The_MoistMaker ยท 2 points ยท Posted at 18:39:07 on May 25, 2016 ยท (Permalink)
Ah fuck!
Cuillin ยท 2 points ยท Posted at 19:10:08 on May 25, 2016 ยท (Permalink)
Ah fuck!
bowser0000 ยท 1 points ยท Posted at 18:05:40 on May 25, 2016 ยท (Permalink)
Ah fuck, I can't believe you've done this
killingit12 ยท 23 points ยท Posted at 15:13:13 on May 25, 2016 ยท (Permalink)
Had an argument with my mate about dividing by zero, he was convinced it equaled infinite, I was like wtf mate, we're both doing a degree in astrophysics, you should know this :/
jywn4679 ยท 19 points ยท Posted at 15:35:19 on May 25, 2016 ยท (Permalink)
In some contexts 1/0 is really just infinity.
killingit12 ยท 15 points ยท Posted at 15:38:59 on May 25, 2016 ยท (Permalink)
No, the limit tends to infinity
jywn4679 ยท 13 points ยท Posted at 15:41:34 on May 25, 2016 ยท (Permalink)
In the real numbers the limit doesn't even tend to infinity, it doesn't exist. In other number systems though 1/0=infinity. An example is the extended complex plane.
Santi871 ยท 7 points ยท Posted at 16:05:11 on May 25, 2016 ยท (Permalink)
The limit doesn't exist strictly speaking, but approaching from the left will make it tend towards -infinity and from the right +infinity, so you can say approaching from either side will tend towards positive or negative infinity.
SorrowOverlord ยท 2 points ยท Posted at 21:49:22 on May 25, 2016 ยท (Permalink)
On the extended complex plane there's only 1 infinity.
kogasapls ยท 1 points ยท Posted at 20:21:09 on May 25, 2016 ยท (Permalink)
It tends to infinity, the limit doesn't exist. The limit itself doesn't tend to anything, strictly speaking, but both of those are true. Some people are fine with saying the limit is infinity.
jywn4679 ยท 1 points ยท Posted at 22:05:59 on May 25, 2016 ยท (Permalink)
It doesn't tend to infinity, as it can be positive or negative.
In some number systems division by 0 is well defined, and there 1/0=infinity. No limits needed.
kogasapls ยท 1 points ยท Posted at 22:17:59 on May 25, 2016 ยท (Permalink)
Oh, you're right. I thought the argument was over whether the limit exists at infinity or does not exist, but the limit as x approaches 0 of 1/x doesn't exist.
functor7 ยท 4 points ยท Posted at 18:01:43 on May 25, 2016 ยท (Permalink)
Doing it the right way, you can. Mathematicians do it all the time, it's just that arithmetic with infinity has a lot of special cases so it's harder to teach to nonmathematicians.
q3w3e3 ยท 1 points ยท Posted at 16:47:39 on May 25, 2016 ยท (Permalink)
It depends on where you approach from.
Pure_Reason ยท 2 points ยท Posted at 20:39:48 on May 25, 2016 ยท (Permalink)
I suck at math, but I would think it would just be zero. 1/2 (1 divided into two parts) is .5. 1/1 (1 divided into one part) is 1. So 1 divided into 0 parts seems like it should be 0. Where does the tricky part come in?
jywn4679 ยท 1 points ยท Posted at 22:04:49 on May 25, 2016 ยท (Permalink)
If 1/0=0, then 1=0*0=0, so 1=0 which is false.
[deleted] ยท 2 points ยท Posted at 15:41:56 on May 25, 2016 ยท (Permalink)*
[deleted]
jywn4679 ยท 6 points ยท Posted at 15:42:53 on May 25, 2016 ยท (Permalink)
False. It is define in some contexts, like the extended complex plane.
[deleted] ยท 0 points ยท Posted at 16:36:01 on May 25, 2016 ยท (Permalink)
0/0 could be the set of all real numbers.
jywn4679 ยท 3 points ยท Posted at 16:37:02 on May 25, 2016 ยท (Permalink)
0/0 is not defined in any context I know of. However it is true that as an indeterminate form is can be any real number.
Adarain ยท 12 points ยท Posted at 16:39:58 on May 25, 2016 ยท (Permalink)
The nice thing about math is that it's really hard to break. You can define 1/0 to be whatever you please and then see what happens. For example, if I define 1/0 = q (a number I just invented), then what is q+1? Let's see...
q+1 = 1/0 + 1/1
Well, that is a bit unfortunate, we can't really sum those up... though... we allow division by 0 now, right? And it ought to work like any other division, so let me just expand that...
1/0 + (10)/(10) = 1/0 + 0/0 = (1+0)/0 = q
So q+1 = q, and the same proof can be extended to any q+x for x =/= q.
What about q+q? That's easy, 1/0 + 1/0 = 2(1/0) = 2q
So q behaves like we'd expect when we add it to multiples of itself.
If you play around a bit more, you'll find that our q acts just like 1 did before, and 1 (and any non-q multiple of it) acts like 0 did before. So we just created two parallel number systems that can be converted in between by dividing by 0. Neat, huh? (Also, I wonder whether this has any other neat properties that I missed. I haven't really experimented with this very in-depth)
edderiofer ยท 6 points ยท Posted at 18:27:17 on May 25, 2016 ยท (Permalink)
Nah. Look:
If 1/0 = q, then:
1 = q*0
= q*(2*0)
= 2(q*0)
= 2.
Thus, 1 = 2, if "division by zero" works exactly the way any other division should work.
casey12141 ยท 5 points ยท Posted at 19:00:53 on May 25, 2016 ยท (Permalink)
Yup, even if you only look at logical inconsistencies in q and not real numbers, you can show that anything involving q breaks communitiviy and distributivity.
The nice thing about math is that it's really hard to break.The awful thing about math is that it's really easy to break and have everything look like it still works on the surface.
[deleted] ยท 1 points ยท Posted at 19:43:42 on May 25, 2016 ยท (Permalink)
[deleted]
SirSooth ยท 3 points ยท Posted at 19:53:08 on May 25, 2016 ยท (Permalink)
It came from the 0. 2 times 0 is 0.
[deleted] ยท 1 points ยท Posted at 20:03:52 on May 25, 2016 ยท (Permalink)
[deleted]
edderiofer ยท 3 points ยท Posted at 20:41:55 on May 25, 2016 ยท (Permalink)
No, you wouldn't. 2*0 = 0, so wherever a 0 appears, you can replace it with 2*0 and the equation will always hold.
[deleted] ยท 1 points ยท Posted at 05:34:29 on May 26, 2016 ยท (Permalink)
[deleted]
edderiofer ยท 1 points ยท Posted at 06:54:45 on May 26, 2016 ยท (Permalink)
But 2*0 = 0, so you've proven that 1/q = 2/q. That is to say, 1 = 2.
[deleted] ยท 0 points ยท Posted at 07:01:54 on May 26, 2016 ยท (Permalink)
[deleted]
edderiofer ยท 1 points ยท Posted at 07:04:46 on May 26, 2016 ยท (Permalink)
And yet you're not going to state your point?
My point is that if you allow division by zero, you get into a contradiction.
theyellowmeteor ยท 0 points ยท Posted at 20:49:11 on May 25, 2016 ยท (Permalink)
q*0 = 1 * (0/0)
Am I correct in assuming you're a bit presumptuous for equating an undeterminate with 1?
edderiofer ยท 3 points ยท Posted at 20:54:41 on May 25, 2016 ยท (Permalink)
Not really. I'm only assuming the "facts" that /u/Adarain has given (in addition to, of course, a few axioms of arithmetic); namely that there exists some number q equal to 1/0, and division by 0 works "exactly the way any other division should"; that is, if a/c = b, then a = bc.
If you're going to call me "presumptuous" because division by 0 doesn't work "exactly the way any other division should", then you're merely stating my conclusion, so your comment is useless.
SorrowOverlord ยท 0 points ยท Posted at 21:51:39 on May 25, 2016 ยท (Permalink)
Division by zero isn't invertable then, no problem. Or you could at the rule "you can't multiply by 0" in your system if you want to get creative.
edderiofer ยท 2 points ยท Posted at 22:26:59 on May 25, 2016 ยท (Permalink)
Or we could just add the rule "you can't divide by 0". Oh wait...
Anyway, multiplying by 0 is useful and intuitive. If I have 9 people, each with $0 in their bank account, then they have in total 9*0 = $0. It's dividing by 0 that isn't. "If I divide $100 between 0 people, how much does each person (who doesn't exist, since there are 0 people, but must exist for anyone to "get" anything) get?"
If we wish to go deeper into theory, we must have multiplication by zero in order for the real numbers to be a field (which has nice properties). Division by zero instead wouldn't allow such nice properties.
SorrowOverlord ยท 0 points ยท Posted at 06:56:57 on May 26, 2016 ยท (Permalink)
We could do that too. There isn't a math police that enforce a particular set of rules, you can work in any system you want.
edderiofer ยท 2 points ยท Posted at 06:59:19 on May 26, 2016 ยท (Permalink)
So long as it's consistent.
But the main reasons we work in the "don't divide by zero" system are that it reflects real life, and that it lets the real numbers be a field. This is far better than your "don't multiply by zero" system.
Tobl4 ยท 2 points ยท Posted at 17:46:27 on May 25, 2016 ยท (Permalink)
Nice, and q/0 should be q2 if I'm not mistaken?
casey12141 ยท 1 points ยท Posted at 18:50:44 on May 25, 2016 ยท (Permalink)
But look what happens when you abuse the fact that q+x = q for any real number x != q:
So I don't think this checks out as a closed field. You could obtain any scaling of q that you wanted for q/0 by swapping out other numbers for the 2 and 1 there.
Tobl4 ยท 1 points ยท Posted at 22:01:26 on May 25, 2016 ยท (Permalink)*
Now I'm wondering, can we just introduce the q down there? Because in that case it seems like it would also be true that
which is contrary to our original definition.
Edit: Actually, wouldn't q2 just be q?
casey12141 ยท 2 points ยท Posted at 22:28:16 on May 25, 2016 ยท (Permalink)
Yeah, everything you just said is correct in the sense that, given the rules the guy above defined, you can correctly derive these (all contradictory) results.
This is because he mistakenly thought that because nothing immediately broke when trying to do a few quick algebraic examples on 1/0, that treating 1/0 as a valid mathematical construct is an ok and "non-math-breaking" thing to do, when it in fact is not. These contradictory results are exactly why 1/0 is not defined in the real number system. Actually any one of them is sufficient to prove that we "broke math" by assigning a distinct real value to 1/0.
If this stuff is interesting to you, you should look into topology. Awesome field of math. Here's a little pdf of notes from a CSU class: http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf
casey12141 ยท 2 points ยท Posted at 18:40:13 on May 25, 2016 ยท (Permalink)
It's not really a parallel number system though, is it? I don't think it even qualifies as a field, because it's not distributive:
The letter q is starting to look really strange...
Alejandro_Last_Name ยท 2 points ยท Posted at 23:36:36 on May 25, 2016 ยท (Permalink)
I wrote this above:
For binary logic a->b is exactly the same as b/a if you assume division by 0 gives you 1. (You only get false for 1->0)
I created an entire class of algebraic objects around this idea called implication rings.
Now you have some incredibly wacky axioms you have to define to make things nice and neat and I don't really want to pore through my dissertation to enumerate them.
Of course these things aren't rings at all but I got them pretty darn close.
casey12141 ยท 2 points ยท Posted at 01:04:35 on May 26, 2016 ยท (Permalink)
Haha I'm an idiot, I read that as "if you assume 1/0 gives you 1", and I thought "man, I swear 0->0 is 1 but 0/0 is undefined..." until I reread what you said.
That's really neat though. How did you come up with the idea, was there a real application, maybe computer related? Out of curiosity's sake, is there a specific interesting yet accessible axiom you'd like to share? I'm an undergrad just getting into math and I've been dying to take topology, so I'm drooling when I see someone with something interesting to say lol.
Alejandro_Last_Name ยท 2 points ยท Posted at 01:22:19 on May 26, 2016 ยท (Permalink)
I'll PM you the relevant portion of paper tomorrow.
Honestly I don't know precisely what good these algebras are. I'm a teaching mathematician so I really just shelved the idea. The real key is understanding the homomorphisms between them. Perhaps there could be applications in logic, unfortunately I'm not an expert in that.
A lot of topology you can sort of self teach, basic topological proofs are incredibly good for building a good abstract mindset.
If you ever need advice drop me a line.
casey12141 ยท 2 points ยท Posted at 01:40:33 on May 26, 2016 ยท (Permalink)
Awesome :) I'm a computer engineering student so whenever I hear "binary logic" I perk up a little. I found a pretty awesome old little topology book abandoned in the attic of my college's main building so I've been able to tide myself over for now.
[deleted] ยท 4 points ยท Posted at 15:35:00 on May 25, 2016 ยท (Permalink)*
[removed]
aonome ยท 1 points ยท Posted at 15:43:14 on May 25, 2016 ยท (Permalink)
What are you talking about?
lapishelper ยท 1 points ยท Posted at 18:15:26 on May 25, 2016 ยท (Permalink)*
he probably means that if you divide a number by any number and it gets smaller and smaller it gets closer to infinity. For example if you divide 1 by 0.1 you get 10, if you divide 1 by 0.01 you get 100, and so on...
edit: On many calculators or even computational engines, if you input something like 1/0 you will get infinity, or close to infinity. For example on Wolfram alpha you will get close to infinity
2nd edit: And after many years I've actually found something that will prove that it is never actually infinity (The more you know) :P https://www.quora.com/Is-1-0-infinity
aonome ยท 1 points ยท Posted at 18:25:07 on May 25, 2016 ยท (Permalink)
It seemed like he was agreeing that you can't divide by zero in standard arithmetic but it didnt make much sense is all.
kogasapls ยท 1 points ยท Posted at 20:23:07 on May 25, 2016 ยท (Permalink)
That's not "close to infinity," it's "complex infinity."
the_real_gorrik ยท 12 points ยท Posted at 13:31:01 on May 25, 2016 ยท (Permalink)
You're a monster!
jorellh ยท 25 points ยท Posted at 15:04:14 on May 25, 2016 ยท (Permalink)
Send him to l'hopital
asdfqwertyfghj ยท 1 points ยท Posted at 15:37:29 on May 25, 2016 ยท (Permalink)
Ah my favorite la hospital's rule.
ICanSmellYourBl00d ยท 3 points ยท Posted at 14:36:00 on May 25, 2016 ยท (Permalink)
http://iwastesomuchtime.com/on/?i=2778
qubedView ยท 3 points ยท Posted at 15:25:47 on May 25, 2016 ยท (Permalink)
Math is always watching.
nadarko ยท 2 points ยท Posted at 15:16:11 on May 25, 2016 ยท (Permalink)
You broke maths Brady, stop that.
functor7 ยท 2 points ยท Posted at 18:02:41 on May 25, 2016 ยท (Permalink)
This is actually true, doing it the right way, you can divide by zero. Mathematicians do it all the time, it's just that arithmetic with infinity has a lot of special cases so it's harder to teach to nonmathematicians.
LordEnigma ยท 2 points ยท Posted at 18:11:53 on May 25, 2016 ยท (Permalink)
Instructions unclear: Winston Churchill is now a carrot.
T_at ยท 2 points ยท Posted at 18:16:39 on May 25, 2016 ยท (Permalink)
I've heard that Schroedinger's cat does it pretty much all the time.
Boopdelahoop ยท 2 points ยท Posted at 14:32:14 on May 25, 2016 ยท (Permalink)
MATHEMATICIANS HATE HIM
TerminalReddit ยท 1 points ยท Posted at 15:19:30 on May 25, 2016 ยท (Permalink)
It actually solves every math problem in earth. Not a joke either.
Iammackers ยท 1 points ยท Posted at 15:51:16 on May 25, 2016 ยท (Permalink)
My meteorology professor did it once with an entire class watching and it worked.
SilverHammerMan ยท 1 points ยท Posted at 15:52:42 on May 25, 2016 ยท (Permalink)
Don't be so Rambo.
omgwtfamidoinghere ยท 1 points ยท Posted at 16:02:57 on May 25, 2016 ยท (Permalink)
You will get stuck in an infinite loop on a mechanical calculator just like the Song That Never Ends. https://youtu.be/443B6f_4n6k
Zmirburger ยท 1 points ยท Posted at 16:05:26 on May 25, 2016 ยท (Permalink)
this reminds me of a funny story. 4 years ago, i wanted to try acid for the first time, so i called up a buddy who gave me a pack, and told me to ONLY EAT ONE first and test it out, and soon you can increase your dosage, forgetting to tell me how long it would take to kick in. so i got back home, took one, and waited 5 mins, nothing happened. took another, waited 5 minutes, still nothing. i told myself fuck it, ill take another two. another 5 minutes passed and i was like fuck maybe im immune to acid. so i ended up googling how long it would take to kick in, and i got the answer, it was 30 minutes! so i decided to divide 30 by 4, coz i was guessin it would take 1/4 of the time to kick in coz i took 4! i took out my calculator, missed the 3, typed in 0/4 instead, pressed equals and
Banzai51 ยท 1 points ยท Posted at 16:12:08 on May 25, 2016 ยท (Permalink)
In nature we call these black holes. :P
Zolden ยท 1 points ยท Posted at 16:23:24 on May 25, 2016 ยท (Permalink)
I once divided by O, and notging happened, but everyone was under impression, that I perfirmed division by 0. One lady even passed out.
c3534l ยท 1 points ยท Posted at 16:28:50 on May 25, 2016 ยท (Permalink)
I had a finance professor yesterday assert that you can't divide by zero because the answer is infinity and infinity is impossible. Then he went on to reason about a formula where he divided by zero and argued the solution to that one part was "some impossibly big number." These are the people running our stock markets...
kevie3drinks ยท 1 points ยท Posted at 16:40:34 on May 25, 2016 ยท (Permalink)
so that's what my teenage son is doing in the bathroom all the time.
xxAkirhaxx ยท 1 points ยท Posted at 16:49:50 on May 25, 2016 ยท (Permalink)
I mean, as long as no one is watching so that no one could determine who did it.
zarraha ยท 1 points ยท Posted at 16:54:55 on May 25, 2016 ยท (Permalink)
I divided by zero once. Then I wrote down an equation which was false, and used regular algebra rules to turn it into another equation which was also false, and then wrote down 1 = 0, which is false.
dot-pixis ยท 1 points ยท Posted at 17:08:08 on May 25, 2016 ยท (Permalink)
eli5 - if the question is x รท 0, why is the answer not "remainder x"?
Purplociraptor ยท 1 points ยท Posted at 17:28:41 on May 25, 2016 ยท (Permalink)
I divide by 0 all the time. The answer is "I get to keep it all"
ThatGuyWhoEngineers ยท 1 points ยท Posted at 17:46:39 on May 25, 2016 ยท (Permalink)
Unless your into people watching you...
PsychoticLime ยท 1 points ยท Posted at 17:53:47 on May 25, 2016 ยท (Permalink)
You just have to do it really really fast so that the Intergalactic Police can't spot you
onzie9 ยท 1 points ยท Posted at 17:55:25 on May 25, 2016 ยท (Permalink)
Division by 0 is actually perfectly possible in some areas of math. We usually dress it up, though, depending on the application. Localization is a fancy way to divide; while localization at 0 (dividing by 0) isn't wildly useful, it doesn't necessarily break anything, either.
DukePPUk ยท 1 points ยท Posted at 17:55:43 on May 25, 2016 ยท (Permalink)
Provided you're not a pure mathematician, and that you know what you're doing, you can divide by 0 quite easily. You just have to make sure you're dividing 0 by 0.
It's how differential and integral calculus work.
BosslikeBehavoir ยท 1 points ยท Posted at 17:59:17 on May 25, 2016 ยท (Permalink)
UNDEFINED UNDEFINED UNDEFINED - like your mother's waist, OP.
Joll19 ยท 1 points ยท Posted at 18:00:53 on May 25, 2016 ยท (Permalink)
You can divide by 0!
MrSirManDudeGuy ยท 1 points ยท Posted at 18:08:14 on May 25, 2016 ยท (Permalink)
A friend of mine once tried to turn in a math assignment he didn't do by burning a large hole in the middle of his paper with a lighter and pretending that he tried to divide by zero.
[deleted] ยท 1 points ยท Posted at 18:25:38 on May 25, 2016 ยท (Permalink)
Don't do it! You will awake the Old Ones!!
There are things man aren't meant to know!
You will doom us all!!!!
Nerf190 ยท 1 points ยท Posted at 18:26:33 on May 25, 2016 ยท (Permalink)
Since there seem to be people good at math here, isn't x-0 always just equal to one? I haven't done math in a long time but I thought this was true.
casey12141 ยท 1 points ยท Posted at 21:25:58 on May 25, 2016 ยท (Permalink)
x-0 is indeed 1 for all real numbers x. How does that cause problems? Even if you think of x-0 as 1 / x0, which I'm assuming is what is causing you confusion, that still evaluates to 1/1 = 1.
This might help give some intuition for exponentiation by 0: https://betterexplained.com/articles/understanding-exponents-why-does-00-1/
Nerf190 ยท 1 points ยท Posted at 07:57:49 on May 26, 2016 ยท (Permalink)
It doesn't cause problems, just the way he worded the answer made me think it was impossible to divide by 0
casey12141 ยท 1 points ยท Posted at 12:09:02 on May 26, 2016 ยท (Permalink)
It is. 1 / x-0 =/= 1/0. The former equals 1, the latter is undefined.
E_Penfold ยท 1 points ยท Posted at 19:10:13 on May 25, 2016 ยท (Permalink)
Only Chuck Norris can do that.
socialtrouble ยท 1 points ยท Posted at 19:17:45 on May 25, 2016 ยท (Permalink)
Don't be so rambo
BeyonceIsBetter ยท 1 points ยท Posted at 19:18:23 on May 25, 2016 ยท (Permalink)
I think you're wrong but don't know enough about math to prove it
nesfor ยท 1 points ยท Posted at 19:27:02 on May 25, 2016 ยท (Permalink)
And it looks like this
btor_sixty ยท 1 points ยท Posted at 19:33:25 on May 25, 2016 ยท (Permalink)
Why do i feel like this should have been a chapter in Sideways stories of Wayside School... if it wasn't already?? It's been too long.
angel0devil ยท 1 points ยท Posted at 19:34:29 on May 25, 2016 ยท (Permalink)
You do know each time you do that one more person will vote for Trump.
off-and-on ยท 1 points ยท Posted at 19:45:41 on May 25, 2016 ยท (Permalink)
But Santa is always watching
ninja-neer ยท 1 points ยท Posted at 19:54:02 on May 25, 2016 ยท (Permalink)
I divided by zero once, but I got that 1=2.
DosAqueous ยท 1 points ยท Posted at 20:05:30 on May 25, 2016 ยท (Permalink)
My calc professor had a very bad burn scar covering about half his face and started off the semester by telling us the story of how he got it. He said he was a young boy doing math homework in his basement and tried to divide by zero.
therealKimbo ยท 1 points ยท Posted at 20:14:15 on May 25, 2016 ยท (Permalink)
the relativity fanboys sure do it a lot. you get all kinds of awesome stuff like black holes. they get "infinities" somehow. even as a school kid I learned you can't divide by zero. it isn't infinity, it is undefined
[deleted] ยท 1 points ยท Posted at 21:00:41 on May 25, 2016 ยท (Permalink)
If I had 6 pieces of pizza divided by 0 people wouldn't I just have 6 pieces of pizza? I've never understood why X/0 isn't X. I know it isn't, but it doesn't make sense.
terrible_f ยท 1 points ยท Posted at 21:22:29 on May 25, 2016 ยท (Permalink)
Thanks Obama.
[deleted] ยท 1 points ยท Posted at 21:25:10 on May 25, 2016 ยท (Permalink)
L'Hospital agrees with you, but also that you can divide by infinity, only if you take the derivatives.
henningbaer ยท 1 points ยท Posted at 21:27:10 on May 25, 2016 ยท (Permalink)
just brace for the incoming raptor attack.
fishtape ยท 1 points ยท Posted at 21:27:14 on May 25, 2016 ยท (Permalink)
If you divide N zero times you still have N. If you divide N one time you have two pieces. Hence N/0=N, and N/1=2. Everyone knows this! ;)
heyitzdavid ยท 1 points ยท Posted at 21:30:11 on May 25, 2016 ยท (Permalink)
You actually get โ when you divide by zero (if you take the limit).
i.e. If you take 1/0.1 you get 10, 1/0.01 you get 100, 1/0.001 you get 1000, and so on.
Take a decimal so (infinitesimally) close to zero, like 0.000....0001, and you're gonna get a HUGE number. That's why dividing by zero technically gives you infinity.
b4b ยท 1 points ยท Posted at 21:56:10 on May 25, 2016 ยท (Permalink)
Don't drink and derive!
labdog ยท 1 points ยท Posted at 22:24:43 on May 25, 2016 ยท (Permalink)
You can divide by 0 in JavaScript. The result is Infinity or (-Infinity) depending on sign of the number divided by 0. I think it may even give correct results with very small signed numbers used as "positive and negative almost zero". And you can do it even when everyone is watching. This is possible because JavaScript just assumes the result of division by zero is equal the result of division by "positive almost zero". With this assumption the operation (and estimated answer) is correct. It behaves pretty nicely with estimating limits. And it's pretty intuitive that numbers exceeding maximum or minimum variable value are substituted by Infinity and (-Infinity). Statements made with such notation are almost obviously true. If you divide by a number sufficiently close to zero - the result will surely overflow the variable. This overflow is really a nice feature to have. In computer programs there a limits to any value. If you apply Infinity values to comparisons - you end up with the limit values. So you get pretty deterministic operation without hardcore math involved.
spacedrgn ยท 1 points ยท Posted at 22:45:05 on May 25, 2016 ยท (Permalink)
I remember seeing a story where someone's calculator went wild when divided by zero, and I think I found it: http://www.iflscience.com/technology/retro-mechanical-calculator-freaks-out-if-you-try-divide-zero
[deleted] ยท 1 points ยท Posted at 23:27:15 on May 25, 2016 ยท (Permalink)
can someone explain not being able to divide by zero to me
the splitting among zero friends doesn't make sense to me, as you'd have zero left over, like multiplication
i mean I'm not disagreeing obviously i just don't get it lmao
Alejandro_Last_Name ยท 1 points ยท Posted at 23:30:27 on May 25, 2016 ยท (Permalink)
For binary logic a->b is exactly the same as b/a if you assume division by 0 gives you 1.
I created an entire class of algebraic objects around this idea called implication rings.
agumonkey ยท 1 points ยท Posted at 23:33:09 on May 25, 2016 ยท (Permalink)
You can tape it for later too https://www.youtube.com/watch?v=443B6f_4n6k
Mindless_Insanity ยท 1 points ยท Posted at 00:05:26 on May 26, 2016 ยท (Permalink)
1/0 = infinity. Zero is simply infinity-1. In this way you can perform all mathematical operations involving zero and infinity with no information loss.
askold9 ยท 1 points ยท Posted at 02:24:04 on May 26, 2016 ยท (Permalink)
When I divide by zero I try to LIMIT myself
[deleted] ยท 1 points ยท Posted at 03:30:51 on May 26, 2016 ยท (Permalink)
Dividing by zero makes me better at my job actually
_____D34DP00L_____ ยท 1 points ยท Posted at 05:54:51 on May 26, 2016 ยท (Permalink)
Late to the party, but you actually need to divide by zero in some cases when finding limitations in the case that x approaches infinity - keep in mind this does not mean dividing by zero equals infinity. Also, you don't actually write down you are dividing by zero because that is illegal and wrong - but you have to mentally do it to find the limitation.
mepwwn ยท 1 points ยท Posted at 23:56:37 on May 26, 2016 ยท (Permalink)
Mathematicians hate him
Killa-Byte ยท 1 points ยท Posted at 06:31:51 on May 30, 2016 ยท (Permalink)
Killa-Byte ยท 1 points ยท Posted at 06:31:58 on May 30, 2016 ยท (Permalink)
sorry i tried to divide by 0
arainzady4 ยท 13615 points ยท Posted at 11:12:03 on May 25, 2016 ยท (Permalink)
Not only does 12+1=11+2, but the letters "twelve plus one" rearrange to give you "eleven plus two"
prpolly ยท 4425 points ยท Posted at 11:54:17 on May 25, 2016 ยท (Permalink)
YOU'RE A WITCH!!!
da_deman ยท 1321 points ยท Posted at 12:17:16 on May 25, 2016 ยท (Permalink)
And what do we do with witches?
Bruss48 ยท 2023 points ยท Posted at 12:44:26 on May 25, 2016 ยท (Permalink)
Build a bridge outta 'er!
fast_cherry_bomb ยท 947 points ยท Posted at 13:30:28 on May 25, 2016 ยท (Permalink)
Ahh, but can you not also make bridges out of stone?
frickindeal ยท 816 points ยท Posted at 13:59:35 on May 25, 2016 ยท (Permalink)
A DUCK!
fast_cherry_bomb ยท 552 points ยท Posted at 14:09:21 on May 25, 2016 ยท (Permalink)
Exactly! So, logically...
jallenrt ยท 620 points ยท Posted at 14:12:26 on May 25, 2016 ยท (Permalink)
If the equation weighs the same as a DUCK...
j-purch ยท 575 points ยท Posted at 14:17:41 on May 25, 2016 ยท (Permalink)
SHE'S A WITCH!
fast_cherry_bomb ยท 463 points ยท Posted at 14:32:27 on May 25, 2016 ยท (Permalink)
We shall use my largest scales.
dingboodle ยท 17 points ยท Posted at 16:01:10 on May 25, 2016 ยท (Permalink)
I love that Reddit can go from 0 to Monty Python in less than 2 comments regardless of what the original comment was about. Hmm maybe that's my math fact to contribute.
198jazzy349 ยท 6 points ยท Posted at 18:00:19 on May 25, 2016 ยท (Permalink)*
This theorem needs a name.
The Reddit Witch Duck Theorem
any comment thread can go from zero to monty python in no fewer than 2 comments.
Edit:speeling.
dingboodle ยท 1 points ยท Posted at 18:04:15 on May 25, 2016 ยท (Permalink)
I like it! Although *theorem if we're going to publish the article.
198jazzy349 ยท 3 points ยท Posted at 18:15:01 on May 25, 2016 ยท (Permalink)
Dammit I can't speel. 0/2
Soulicitor ยท 1 points ยท Posted at 23:18:14 on May 25, 2016 ยท (Permalink)
Monty Python and the Whorey Karma
Haenep ยท 2 points ยท Posted at 18:12:31 on May 25, 2016 ยท (Permalink)
It's absolutely amazing! Did you ever play the game? It's amazing!
NorrinR ยท 10 points ยท Posted at 15:11:44 on May 25, 2016 ยท (Permalink)
It's a fair cop.
[deleted] ยท 13 points ยท Posted at 14:43:16 on May 25, 2016 ยท (Permalink)
If she floats in the water, then she is a witch. If she sinks in the water and drowns, then she is not a witch.
deadfermata ยท 14 points ยท Posted at 14:52:34 on May 25, 2016 ยท (Permalink)
But...but I wanna...siiiing
readytodo ยท 8 points ยท Posted at 17:10:18 on May 25, 2016 ยท (Permalink)
She's got Huge Tracts of Land
circuital14 ยท 1 points ยท Posted at 19:10:40 on May 25, 2016 ยท (Permalink)
Burn the witch
We know where you live
eshansingh ยท 4 points ยท Posted at 16:23:16 on May 25, 2016 ยท (Permalink)
we did it reddit
DW241 ยท 5 points ยท Posted at 17:19:25 on May 25, 2016 ยท (Permalink)
You just have to know these things when you're a king, you know
A_SPICY_NIPPLE ยท 3 points ยท Posted at 14:58:45 on May 25, 2016 ยท (Permalink)
So are we burning someone or what
american16 ยท 8 points ยท Posted at 15:07:24 on May 25, 2016 ยท (Permalink)
It's from Monty Python and the Holy Grail.
Bainsyboy ยท 3 points ยท Posted at 15:29:27 on May 25, 2016 ยท (Permalink)
br0wens ยท 3 points ยท Posted at 15:29:52 on May 25, 2016 ยท (Permalink)
I love Reddit.
manly_lumberjack ยท 2 points ยท Posted at 15:15:26 on May 25, 2016 ยท (Permalink)
She's ugly!
PressureChief ยท 2 points ยท Posted at 18:17:58 on May 25, 2016 ยท (Permalink)
I brought my floating small rocks.
jobblejosh ยท 2 points ยท Posted at 18:55:57 on May 25, 2016 ยท (Permalink)
It's a fair cop!
RochesterJosh ยท 2 points ยท Posted at 19:26:57 on May 25, 2016 ยท (Permalink)
This. Right here. Read the whole chain hoping someone would drop this line. You did not disappoint.
elgost ยท 22 points ยท Posted at 14:40:20 on May 25, 2016 ยท (Permalink)
BURN HER!
DesertTripper ยท 1 points ยท Posted at 00:42:24 on May 26, 2016 ยท (Permalink)
But she's got HUUUUGE... tracts of land!
steven6162 ยท 4 points ยท Posted at 18:03:33 on May 25, 2016 ยท (Permalink)
She turned me to a newt!.......I got better.
Urabutbl ยท 3 points ยท Posted at 16:37:24 on May 25, 2016 ยท (Permalink)
It's a fair cop...
Sardonnicus ยท 2 points ยท Posted at 17:04:38 on May 25, 2016 ยท (Permalink)
Don't you think it's a bit early to go imposing roles on it??
mbelf ยท 2 points ยท Posted at 18:53:41 on May 25, 2016 ยท (Permalink)
And therefore...
fugly16 ยท 2 points ยท Posted at 19:42:47 on May 25, 2016 ยท (Permalink)
Burn her anyway, Burrrrnnnnnn!
h2ogie ยท 1 points ยท Posted at 19:36:53 on May 25, 2016 ยท (Permalink)
It's a fair cop
thestickystickman ยท 1 points ยท Posted at 07:18:48 on May 26, 2016 ยท (Permalink)
A WITCH!
XXVIIMAN ยท 3 points ยท Posted at 14:21:18 on May 25, 2016 ยท (Permalink)
Then duck rearranges to spell equation!
DawnsBreaker45 ยท 3 points ยท Posted at 21:59:12 on May 25, 2016 ยท (Permalink)
BURN 'ER
DuckDuckBoson ยท 1 points ยท Posted at 15:23:28 on May 25, 2016 ยท (Permalink)
/r/TheyDidTheDuckMath
phantompowered ยท 4 points ยท Posted at 15:30:30 on May 25, 2016 ยท (Permalink)
And who are you, so wise in the ways of science?
CrazyKirby97 ยท 2 points ยท Posted at 15:37:03 on May 25, 2016 ยท (Permalink)
But a good bridge is shaped like a parabola, and only two types of old ladies can pull off a parabola. Retired Russian Olympians and WITCHES.
[deleted] ยท 2 points ยท Posted at 22:43:05 on May 25, 2016 ยท (Permalink)
Ahhh... VERY SMALL ROCKS
Mindless_Insanity ยท 1 points ยท Posted at 23:52:26 on May 25, 2016 ยท (Permalink)
So, get her stoned?
solsquinox ยท 2 points ยท Posted at 15:14:43 on May 25, 2016 ยท (Permalink)
I heard that you could build it 1 metre higher by using 6.3 extra witches
PurpleDotExe ยท 1 points ยท Posted at 16:18:37 on May 25, 2016 ยท (Permalink)
YOU MUST CONSTRUCT ADDITIONAL WITCHES
BeastftMiddleEast ยท 1 points ยท Posted at 17:51:58 on May 25, 2016 ยท (Permalink)
And... Make her pay for it!
jamaicanhopscotch ยท 16 points ยท Posted at 15:02:52 on May 25, 2016 ยท (Permalink)
We knowwwwww where you liveeeeeeee
DukeSC2 ยท 7 points ยท Posted at 15:33:30 on May 25, 2016 ยท (Permalink)
Woo, I was hoping for a Radiohead reference.
jamaicanhopscotch ยท 2 points ยท Posted at 16:02:50 on May 25, 2016 ยท (Permalink)
I was hoping someone would get a Radiohead reference!
observedlife ยท 2 points ยท Posted at 18:28:53 on May 25, 2016 ยท (Permalink)
Found a radiohead fan out in the wild!
hollowheaded ยท 7 points ยท Posted at 16:34:51 on May 25, 2016 ยท (Permalink)
Not sure, let's ask Radiohead.
PungentBallSweat ยท 7 points ยท Posted at 14:33:19 on May 25, 2016 ยท (Permalink)
Burn them
SerDancelot ยท 6 points ยท Posted at 18:53:27 on May 25, 2016 ยท (Permalink)
If she floats she'll burn.
Mr_Zaroc ยท 15 points ยท Posted at 12:33:23 on May 25, 2016 ยท (Permalink)
We accept them as our new overlord?
I mean thinking logically, we have little chance against someone who can use magic, when we on the otherhand only can use pitchforks and torches
Sinetan ยท 6 points ยท Posted at 12:57:37 on May 25, 2016 ยท (Permalink)
What's the airspeed velocity of an unladen swallow?
IanMalkaviac ยท 2 points ยท Posted at 17:12:36 on May 25, 2016 ยท (Permalink)
It depends do you mean a European or an African swallow
Mark7A ยท 1 points ยท Posted at 15:12:41 on May 25, 2016 ยท (Permalink)
A duck?
brannana ยท 1 points ยท Posted at 15:08:44 on May 25, 2016 ยท (Permalink)
But we have the advantage of numbers! Think WWII Eastern Front.
Mr_Zaroc ยท 2 points ยท Posted at 15:12:53 on May 25, 2016 ยท (Permalink)
FTFY
[deleted] ยท 3 points ยท Posted at 14:05:51 on May 25, 2016 ยท (Permalink)
We lick 'em
PatrickBecerra ยท 2 points ยท Posted at 14:36:10 on May 25, 2016 ยท (Permalink)
I too enjoy John Cena in comedies starring women.
Bluesberry12345 ยท 3 points ยท Posted at 14:12:19 on May 25, 2016 ยท (Permalink)
-------E?
arsenale ยท 3 points ยท Posted at 14:49:34 on May 25, 2016 ยท (Permalink)
Burn the with! With witches!
hau5prYd ยท 3 points ยท Posted at 18:48:17 on May 25, 2016 ยท (Permalink)
Burn the witch?
keenly_disinterested ยท 2 points ยท Posted at 14:52:55 on May 25, 2016 ยท (Permalink)
Use her as a floatation device in the event of a water landing?
Redhavok ยท 1 points ยท Posted at 14:45:18 on May 25, 2016 ยท (Permalink)
make lemonade
Jarnagua ยท 1 points ยท Posted at 15:04:43 on May 25, 2016 ยท (Permalink)
Evaporate salt in them?
you_got_fragged ยท 1 points ยท Posted at 15:10:30 on May 25, 2016 ยท (Permalink)
poison their water supply
eddie_koala ยท 1 points ยท Posted at 15:23:59 on May 25, 2016 ยท (Permalink)
Nominate them for president of the U.S?
Mormoran ยท 1 points ยท Posted at 15:56:50 on May 25, 2016 ยท (Permalink)
Fuck 'em right in the pussy!
No? Isn't that... ? Oh... Ok
jameskcubed ยท 1 points ยท Posted at 16:09:03 on May 25, 2016 ยท (Permalink)
MORE WITCHES!
[deleted] ยท 1 points ยท Posted at 16:13:27 on May 25, 2016 ยท (Permalink)
Burn the witch
PapillonsRevenge ยท 1 points ยท Posted at 17:25:02 on May 25, 2016 ยท (Permalink)
Not today! - wait, no that's not eight...
Clockeycrincrank ยท 1 points ยท Posted at 19:15:18 on May 25, 2016 ยท (Permalink)
Witches get stitches.
efeustula ยท 1 points ยท Posted at 19:33:36 on May 25, 2016 ยท (Permalink)
To shreds you say...
mdpatelz ยท 1 points ยท Posted at 20:13:09 on May 25, 2016 ยท (Permalink)
Not today
BlueThumbtack08 ยท 1 points ยท Posted at 20:25:07 on May 25, 2016 ยท (Permalink)
https://youtu.be/fvozYm3S-kw
Burn the witch!
Hempsterball ยท 1 points ยท Posted at 22:09:47 on May 25, 2016 ยท (Permalink)
Upon what do we burn witches?
Blessing727 ยท 1 points ยท Posted at 23:06:11 on May 25, 2016 ยท (Permalink)
Ask thom yorke
littlecar ยท 1 points ยท Posted at 07:01:41 on May 26, 2016 ยท (Permalink)
Nominate them for president.
wilks33 ยท 1 points ยท Posted at 13:05:05 on May 25, 2016 ยท (Permalink)
MORE WITCHES
kkehoe5 ยท 0 points ยท Posted at 13:00:18 on May 25, 2016 ยท (Permalink)
"Not today"
dirty_penguin ยท 324 points ยท Posted at 12:17:39 on May 25, 2016 ยท (Permalink)
SHE TURNED ME INTO A NEWT!!!!
Loserblast ยท 301 points ยท Posted at 12:40:16 on May 25, 2016 ยท (Permalink)
I got better....
a_lil_husky ยท 4 points ยท Posted at 14:57:47 on May 25, 2016 ยท (Permalink)
Burn her anyways!
teldra ยท 5 points ยท Posted at 14:41:00 on May 25, 2016 ยท (Permalink)
A newt?!?
smixton ยท 1 points ยท Posted at 15:58:13 on May 25, 2016 ยท (Permalink)*
You must have gotten better.
Fuckeddit ยท 1 points ยท Posted at 21:22:23 on May 25, 2016 ยท (Permalink)
So if she....floats....SHES....A WITCH!
[deleted] ยท 1 points ยท Posted at 13:28:14 on May 25, 2016 ยท (Permalink)
I got better
fratzcatsfw ยท 3 points ยท Posted at 13:38:05 on May 25, 2016 ยท (Permalink)
Harry!
ryantrip ยท 2 points ยท Posted at 15:53:20 on May 25, 2016 ยท (Permalink)
But I'm just Harry!
jeremyrey ยท 2 points ยท Posted at 17:27:57 on May 25, 2016 ยท (Permalink)
Burn the witch!
barnenail ยท 1 points ยท Posted at 18:54:33 on May 25, 2016 ยท (Permalink)
this is, no doubt, a low flying panic attack
Sir_Ein ยท 2 points ยท Posted at 17:50:41 on May 25, 2016 ยท (Permalink)
"You're a wizard, Harry!"
sheawey ยท 2 points ยท Posted at 19:37:45 on May 25, 2016 ยท (Permalink)
Burn the Witch!
tman1015 ยท 2 points ยท Posted at 20:51:30 on May 25, 2016 ยท (Permalink)
I love all of these Holy Grail references.
ckowkay ยท 2 points ยท Posted at 22:11:46 on May 25, 2016 ยท (Permalink)
a batterwitch
thirdGEARchirp ยท 2 points ยท Posted at 04:26:02 on May 26, 2016 ยท (Permalink)
burn her, burn the witch!!!
PSPHAXXOR ยท 1 points ยท Posted at 14:25:13 on May 25, 2016 ยท (Permalink)
Flashlights OFF!
ObsidianG ยท 1 points ยท Posted at 14:31:56 on May 25, 2016 ยท (Permalink)
You have Triskaidekaphobia.
noobiepoobie ยท 1 points ยท Posted at 14:41:35 on May 25, 2016 ยท (Permalink)
HARRY!!!
Garrett_Dark ยท 1 points ยท Posted at 16:28:24 on May 25, 2016 ยท (Permalink)
I think they prefer to be called "Mathemagicians".
neuromorph ยท 1 points ยท Posted at 17:53:08 on May 25, 2016 ยท (Permalink)
Warlock
bcyost ยท 1 points ยท Posted at 18:26:04 on May 25, 2016 ยท (Permalink)
...hermione
simplytwo ยท 1 points ยท Posted at 14:16:23 on May 25, 2016 ยท (Permalink)
I wish I had reddit gold to give you, because this comment made 1) my day and 2) me laugh out loud.
Thementalrapist ยท 0 points ยท Posted at 15:19:35 on May 25, 2016 ยท (Permalink)
My favorite fact is if you call it maths you're a pretentious twat.
Dunan ยท 1284 points ยท Posted at 13:51:24 on May 25, 2016 ยท (Permalink)
And if you count the number of letters in each of those phrases, you get the number of letters that the phrases describe.
prpolly ยท 446 points ยท Posted at 14:25:26 on May 25, 2016 ยท (Permalink)
Holy. Crap. This goes deep.
SLOPPYMYSECONDS ยท 100 points ยท Posted at 15:03:12 on May 25, 2016 ยท (Permalink)
Illuminati confirmed
banfromallsubreddits ยท 18 points ยท Posted at 15:15:26 on May 25, 2016 ยท (Permalink)
Triskaidekanati confirmed.
Machtung7 ยท 3 points ยท Posted at 15:55:14 on May 25, 2016 ยท (Permalink)
Do you play MtG or do you just happen to know about Triskaideka?
MrMeltJr ยท 6 points ยท Posted at 16:34:01 on May 25, 2016 ยท (Permalink)
Triskaidekaphobia is an actual thing, it's an irrational fear of the number 13. WotC didn't come up with the word.
Machtung7 ยท 2 points ยท Posted at 17:12:03 on May 25, 2016 ยท (Permalink)
I understand that, but I had never heard the term until the card. I haven't researched all that much Greek so it was a new word for me. I was just wondering where u/banfromallsubreddits had heard the term from originally.
MrMeltJr ยท 4 points ยท Posted at 18:02:39 on May 25, 2016 ยท (Permalink)
Ah, ok.
Plafi ยท 4 points ยท Posted at 15:57:55 on May 25, 2016 ยท (Permalink)
it means 13
Dunan ยท 2 points ยท Posted at 16:40:58 on May 25, 2016 ยท (Permalink)
It's just Greek. I know nothing about MtG but this is the kind of word that you can easily figure out: tris kai deka = three and ten.
oi_rohe ยท 7 points ยท Posted at 17:14:50 on May 25, 2016 ยท (Permalink)
Not only this, but the second digit of 13 is 3, EXACTLY THE NUMBER OF SIDES IN A TRIANGLE!
PLUS, it's the second digit, and if we add the first digit, 1, to 2 for the second digit, THREE AGAIN!
SLOPPYMYSECONDS ยท 1 points ยท Posted at 19:52:16 on May 25, 2016 ยท (Permalink)
Oh my lord! I think we're on to something here.
darkshadow17 ยท 1 points ยท Posted at 20:12:57 on May 25, 2016 ยท (Permalink)
Half life 3 confirmed
Dunan ยท 2 points ยท Posted at 15:32:43 on May 25, 2016 ยท (Permalink)
Ah, you see the connection with the sum of the digits of the year of the Illuminati's founding, '76. How could you possibly have known I was a member of-- wait, the Illuminati are a myth. They disbanded long ago. If they existed. Which we don't. ...I mean, they don't. Shhhhh.
PerInception ยท 17 points ยท Posted at 15:13:56 on May 25, 2016 ยท (Permalink)
I feel like we might have just stumbled onto the key to the unified theory of everything.
gods_fear_me ยท 5 points ยท Posted at 18:26:50 on May 25, 2016 ยท (Permalink)
42
JackAceHole ยท 5 points ยท Posted at 19:14:07 on May 25, 2016 ยท (Permalink)
AND THIRTY-ONE PLUS TWENTY-FOUR IS EQUAL TO THIRTY-FOUR PLUS TWENTY-ONE!!
loyallemons ยท 3 points ยท Posted at 19:50:51 on May 25, 2016 ยท (Permalink)
Illuminati confirmed
TheSling ยท 3 points ยท Posted at 21:44:43 on May 25, 2016 ยท (Permalink)
This is like some inception shit right there.
ipslne ยท 2 points ยท Posted at 17:28:24 on May 25, 2016 ยท (Permalink)
huh.
It's real.
Sploitspiller ยท 2 points ยท Posted at 19:16:03 on May 25, 2016 ยท (Permalink)
And 9 + 11 = NYC + $20 bill = George W Bush!!!
Dylanxfrogman ยท 2 points ยท Posted at 19:34:57 on May 25, 2016 ยท (Permalink)
Who's willing to dig?
RedIsBlackDragon ยท 2 points ยท Posted at 20:57:59 on May 25, 2016 ยท (Permalink)
...guess what 11+12 is
GiveMeNotTheBoots ยท 2 points ยท Posted at 21:53:52 on May 25, 2016 ยท (Permalink)
We must go deeper.
'Snap!' goes the latex glove...
wickedsteve ยท 11 points ยท Posted at 15:13:29 on May 25, 2016 ยท (Permalink)
Spoiler alert: it's 13! I did the math.
[deleted] ยท 17 points ยท Posted at 15:27:13 on May 25, 2016 ยท (Permalink)*
[removed]
wickedsteve ยท 6 points ยท Posted at 16:10:29 on May 25, 2016 ยท (Permalink)
Yes, it's 6,227,020,800!
GiveItHereBoss ยท 9 points ยท Posted at 16:36:13 on May 25, 2016 ยท (Permalink)
oh fuck.
[deleted] ยท 3 points ยท Posted at 18:19:48 on May 25, 2016 ยท (Permalink)
Error-Overflow.
IMMEDIATE EDIT: I'm going to try to solve this. Check back in a few hours.
vizzmay ยท 4 points ยท Posted at 16:05:02 on May 25, 2016 ยท (Permalink)
/r/expectedfactorial
[deleted] ยท 1 points ยท Posted at 02:46:18 on May 26, 2016 ยท (Permalink)
/r/unexpectedfactorial
RobinsEggTea ยท 1 points ยท Posted at 17:54:55 on May 25, 2016 ยท (Permalink)
No. 26 letters in both phrases. Is 12 letters, 11 letters, 2 letters and 1 letter.
craptrick ยท 7 points ยท Posted at 14:50:43 on May 25, 2016 ยท (Permalink)
Holy shit, mother f*cker! You're blowing my mind here!
SirAlexH ยท 2 points ยท Posted at 15:45:07 on May 25, 2016 ยท (Permalink)
No wei
ChickenF622 ยท 2 points ยท Posted at 16:36:32 on May 25, 2016 ยท (Permalink)
/r/tautology
ixora7 ยท 2 points ยท Posted at 09:16:10 on May 26, 2016 ยท (Permalink)
Now that's just voodoo.
a_casserole ยท 1 points ยท Posted at 15:44:50 on May 25, 2016 ยท (Permalink)
Did you actually count them? :0
Guikle ยท 12 points ยท Posted at 16:18:07 on May 25, 2016 ยท (Permalink)
It's literally 6 words....
a_casserole ยท 2 points ยท Posted at 19:43:27 on May 25, 2016 ยท (Permalink)
But who would think to do that
eric1894 ยท 2 points ยท Posted at 19:52:29 on May 25, 2016 ยท (Permalink)
/u/Dunan
a_casserole ยท 3 points ยท Posted at 19:54:46 on May 25, 2016 ยท (Permalink)
My guy
Dunan ยท 2 points ยท Posted at 20:12:45 on May 25, 2016 ยท (Permalink)
Wasn't there a guy in the movie City Slickers who could the number of letters in phrases effortlessly? I hope it was the Jon Lovitz character. That guy is always hilarious.
Tocoapuffs ยท 2 points ยท Posted at 20:31:05 on May 25, 2016 ยท (Permalink)
Did you actually count them? :0
Dunan ยท 1 points ยท Posted at 21:59:31 on May 25, 2016 ยท (Permalink)
It looked for a moment like the phrase might happen to have 13 letters, and I thought "eleven plus two", let's see, 6, then 4, then 3; it works! And since "twelve plus one" has the exact same letters (only in a different order) it has to work too. ^_;
xanthalasajache ยท 1 points ยท Posted at 03:25:23 on May 26, 2016 ยท (Permalink)
5 4 3 = 5 4 3
Opandemonium ยท 2732 points ยท Posted at 14:27:48 on May 25, 2016 ยท (Permalink)
I've always thought 12 and 11 were the most magical of numbers. The 11 multiplication trick...time is divided into 12 months, 12 hours, I was 11 the first time I hid a body, and 12 the first time I killed a man in cold blood.
AmyzonWarrior ยท 1286 points ยท Posted at 14:52:59 on May 25, 2016 ยท (Permalink)
...Ted Cruz?
pemboo ยท 44 points ยท Posted at 17:18:37 on May 25, 2016 ยท (Permalink)
12 signs of the zodiac
LMM01 ยท 17 points ยท Posted at 18:11:16 on May 25, 2016 ยท (Permalink)
Number 11 will kill you!
asj29 ยท 19 points ยท Posted at 17:04:50 on May 25, 2016 ยท (Permalink)
Z O D I A C
DJCzerny ยท 10 points ยท Posted at 17:09:56 on May 25, 2016 ยท (Permalink)
In 1998 Ted Cruz killed a woman and ate her body
iamonlyoneman ยท 7 points ยท Posted at 18:17:43 on May 25, 2016 ยท (Permalink)
so, when did you stop beating your wife?
[deleted] ยท 4 points ยท Posted at 19:39:35 on May 25, 2016 ยท (Permalink)
Hillary has killed more people than Cruz
[deleted] ยท 2 points ยท Posted at 20:30:06 on May 25, 2016 ยท (Permalink)
Oh
senorswank ยท 1 points ยท Posted at 01:48:45 on May 26, 2016 ยท (Permalink)
Someone told me he was Lucifer. I'm an Artiest so can he just be a total piece of garbage to me?
The14thNoah ยท -6 points ยท Posted at 17:45:00 on May 25, 2016 ยท (Permalink)
Talk about a joke that should have been taken out back and shot awhile ago....
[deleted] ยท 17 points ยท Posted at 19:08:26 on May 25, 2016 ยท (Permalink)
Someone call Ted Cruz.
I hear he's good at that sort of thing.
DaddyDinosaur ยท 55 points ยท Posted at 15:22:35 on May 25, 2016 ยท (Permalink)
Someone give this man 12 gold
SKR47CH ยท 217 points ยท Posted at 15:27:21 on May 25, 2016 ยท (Permalink)
He got 12-11 gold. That's enough, i guess.
Lucarcas ยท 12 points ยท Posted at 15:34:05 on May 25, 2016 ยท (Permalink)
What did you do between hiding the body and killing the man?
Antsache ยท 56 points ยท Posted at 15:39:21 on May 25, 2016 ยท (Permalink)
Had a birthday party, clearly.
a_casserole ยท 5 points ยท Posted at 15:45:32 on May 25, 2016 ยท (Permalink)
Looool
richardec ยท 2 points ยท Posted at 16:16:08 on May 25, 2016 ยท (Permalink)
But nobody came ๐
TheHynusofTime ยท 5 points ยท Posted at 16:40:12 on May 25, 2016 ยท (Permalink)
Twelve people were supposed to be there, but eleven of them didn't show up.
Which just left himself.
nighthawk648 ยท 5 points ยท Posted at 15:42:30 on May 25, 2016 ยท (Permalink)
Time traveled or figured it out rather. How would he hide a body if he didn't kill anyone? This guy ain't no joke so it's not like he hide a body his friend killed, no he figured out time travel and covered up his own murder.
turtlemix_69 ยท 5 points ยท Posted at 16:02:56 on May 25, 2016 ยท (Permalink)
Could've been an accident. He was 12 when he killed a man in "cold-blood". Never said it was his first kill.
abc123shutthefuckup ยท 2 points ยท Posted at 19:17:08 on May 25, 2016 ยท (Permalink)
Or maybe he did an apprenticeship or something and part of his training was hiding a body for his master
turtlemix_69 ยท 1 points ยท Posted at 19:52:01 on May 25, 2016 ยท (Permalink)
Like a really low level dark brotherhood quest
schmeasy ยท 3 points ยท Posted at 16:56:00 on May 25, 2016 ยท (Permalink)
If you hid a (presumably) dead body before you killed a man, then you were an accomplice. 11 year old plus 1 other killer = 12.
yenwood ยท 2 points ยท Posted at 18:45:22 on May 25, 2016 ยท (Permalink)
magic
Opandemonium ยท 1 points ยท Posted at 00:22:16 on May 26, 2016 ยท (Permalink)
Math!
YELLING_IN_YOUR_HEAD ยท 6 points ยท Posted at 15:39:39 on May 25, 2016 ยท (Permalink)
This seems like the opening paragraph of a book I'd settle in to savor. Bravo.
collin_sic ยท 5 points ยท Posted at 19:23:15 on May 25, 2016 ยท (Permalink)
Go read Apt Pupil by Steven King.
RochesterJosh ยท 3 points ยท Posted at 19:27:48 on May 25, 2016 ยท (Permalink)
Wait... so that means you just stumbled across an already dead body at 11. Somehow that makes this a cooler story...
Snailic ยท 2 points ยท Posted at 17:09:03 on May 25, 2016 ยท (Permalink)
That's because Time is Base-60 aka Sexagesimal, created in 3000 B.C.E. by the Sumerians.
Autocoprophage ยท 1 points ยท Posted at 20:37:50 on May 25, 2016 ยท (Permalink)
The Sumerians created time? Ancient Aliens was right!
[deleted] ยท 2 points ยท Posted at 20:51:28 on May 25, 2016 ยท (Permalink)
Wait ... what?
Jogsta ยท 1 points ยท Posted at 16:14:16 on May 25, 2016 ยท (Permalink)
...and that's a magic numberrrrrrrrr.
ceylonaire ยท 1 points ยท Posted at 17:31:19 on May 25, 2016 ยท (Permalink)
Damn!
kitchenperks ยท 1 points ยท Posted at 17:33:57 on May 25, 2016 ยท (Permalink)
ra's al ghul?
[deleted] ยท 1 points ยท Posted at 18:22:30 on May 25, 2016 ยท (Permalink)
[deleted]
BrianThePainter ยท 1 points ยท Posted at 00:32:04 on May 26, 2016 ยท (Permalink)
Also magical because they stealthily avoid the name policy of basically all other numbers, in that they somehow avoided becoming oneteen and twoteen.
Opandemonium ยท 1 points ยท Posted at 01:55:28 on May 26, 2016 ยท (Permalink)
My love of them has just grown exponentially.
redweasel ยท 1 points ยท Posted at 06:42:08 on May 26, 2016 ยท (Permalink)
A friend once designed a base-12 digital clock. It used the standard 7-segment LED digit displays, and he had to invent glyphs for the eleventh and twelfth digits, i.e. those coming between "9" and "10," base 12. I found his solution to be genius: for the eleventh digit he illuminated the bottom horizontal bar and entire upper half of the 7-segment cell, and for the twelfth digit he illuminated just the middle and bottom horizontal bars. The genius part was that if you tilted your head to the left :-) these were literally a tiny "10" and "11", coming right after "9," exactly as they should.
PM_ME_YOUR_MESMER ยท 1 points ยท Posted at 16:32:05 on May 25, 2016 ยท (Permalink)
That escalated far too quickly
straight_oughta_nyc ยท -1 points ยท Posted at 17:39:17 on May 25, 2016 ยท (Permalink)
and when you turned 13, discovered that 3 inch stick between your legs has the power to give you pleasure, repeatedly, the blood letting ceased. right?
Opandemonium ยท 1 points ยท Posted at 00:21:17 on May 26, 2016 ยท (Permalink)
I started bleeding from my naughty no no place and a woman was born.
SgtFinnish ยท 69 points ยท Posted at 12:54:21 on May 25, 2016 ยท (Permalink)
You can actually do this with any two numbers. Go ahead, try it out!
tcatron565 ยท 29 points ยท Posted at 16:30:06 on May 25, 2016 ยท (Permalink)
7+1=6+2
"Seven plus one" becomes "Sev plus eno..ne"
You're right!
[deleted] ยท 2 points ยท Posted at 20:48:44 on May 25, 2016 ยท (Permalink)
I guess the lesson here is that just because we can do it, doesn't mean we should do it.
RagingAcid ยท 42 points ยท Posted at 13:06:08 on May 25, 2016 ยท (Permalink)
Oh.
Redtox ยท 6 points ยท Posted at 16:48:51 on May 25, 2016 ยท (Permalink)
Please teach me how to arrange the letters in "seven plus one" into "six plus two".
SgtFinnish ยท 1 points ยท Posted at 16:52:30 on May 25, 2016 ยท (Permalink)
Creatively!
Harvey_Rabbit ยท 8 points ยท Posted at 14:44:42 on May 25, 2016 ยท (Permalink)
That's what I was thinking 16 + 9 = 19 + 6 72 + 21 = 71 + 22
Brio_ ยท 3 points ยท Posted at 15:00:46 on May 25, 2016 ยท (Permalink)
Well, yeah, all you're doing is rearranging the numbers. It's basically saying 1+2 == 2+1
16+9 == 10+6+9
red_eye_rob ยท 8 points ยท Posted at 15:17:35 on May 25, 2016 ยท (Permalink)
Even if you're right, that's still one plus one plus two plus one, not one plus two plus one plus one.
Brio_ ยท 2 points ยท Posted at 15:39:16 on May 25, 2016 ยท (Permalink)
What do you mean even if I'm right?
Of course I'm right, it's simple math.
I'm not sure what you're even talking about. This whole thing is just about switching the ones places.
Lorenzo_Matterhorn ยท 6 points ยท Posted at 16:25:23 on May 25, 2016 ยท (Permalink)
That was a reference to the movie Clue.
red_eye_rob ยท 1 points ยท Posted at 15:47:36 on May 25, 2016 ยท (Permalink)
it's a quote
Yamatjac ยท 3 points ยท Posted at 16:17:11 on May 25, 2016 ยท (Permalink)
Yea but dude.
Eleven plus two can be rearranged to make Twelve plus one.
Can you do that with your 1+2 == 2+1? Pls.
korpsart ยท 2 points ยท Posted at 17:45:14 on May 25, 2016 ยท (Permalink)
You can do this with any language too. Go ahead, try it out!
korpsart ยท 1 points ยท Posted at 17:48:20 on May 25, 2016 ยท (Permalink)
"doce mas uno" equals "once mas duo"
dandroid126 ยท 2 points ยท Posted at 17:49:48 on May 25, 2016 ยท (Permalink)
Need to do a proof by induction.
Dernom ยท 4 points ยท Posted at 14:13:48 on May 25, 2016 ยท (Permalink)
Not with 13+4
DoWhile ยท 50 points ยท Posted at 14:29:44 on May 25, 2016 ยท (Permalink)
13+4=4+13, but the letters "thirteen plus four" rearrange to give you "four plus thirteen"
a_monkeys_head ยท 15 points ยท Posted at 14:35:55 on May 25, 2016 ยท (Permalink)
genius
MonsterOG ยท 2 points ยท Posted at 14:51:43 on May 25, 2016 ยท (Permalink)
username checks out
Dernom ยท 3 points ยท Posted at 14:51:36 on May 25, 2016 ยท (Permalink)
But that's not what OPs comment said, it said to take 12+1 and swap the 2 in 12 with the lone 1, so in the case of 13+4 you swap the 3 and the 4 to make 14+3. And you can't rearrange "thirteen plus four" to "fourteen plus three"
Brio_ ยท 7 points ยท Posted at 14:58:58 on May 25, 2016 ยท (Permalink)
You gotta say it with an accent. Fourteen plus thir.
you_got_fragged ยท -4 points ยท Posted at 15:12:31 on May 25, 2016 ยท (Permalink)
whoosh
TheActualAWdeV ยท 10 points ยท Posted at 14:37:30 on May 25, 2016 ยท (Permalink)
That's not really a math fact. That's a minor quirk of english.
navinohradech ยท 3 points ยท Posted at 19:14:59 on May 25, 2016 ยท (Permalink)
Yeah this is like saying "the Arabic numeral for 7 is real pretty!" is a math fact
Dr_Legacy ยท 0 points ยท Posted at 21:11:16 on May 25, 2016 ยท (Permalink)
It's certainly a quirk of language, but it is also a property of a set.
TheActualAWdeV ยท 1 points ยท Posted at 13:24:44 on May 26, 2016 ยท (Permalink)
But it's not a math-specific thing. It's just english.
Math is sometimes called the universal language. If this 'fact' relies on a single language then it's not much of a math fact.
Dr_Legacy ยท 1 points ยท Posted at 14:56:28 on May 26, 2016 ยท (Permalink)
Well, sure, it's a fact about a set with a very particular definition.
Here are more general formulations that avoid your objection.
"let {A} be the set of integers whose numeric and named representations in (given language) both participate in anagrammatic arithmetic"
Similarly, "let {E} be the set of integer arithmetic equations whose numeric and (given-language)-named representations both exhibit anagrammatic arithmetic"
I leave the definition of 'anagrammatic arithmetic' as an exercise, but the concept isn't tied to one language: http://www.thefreelibrary.com/Anagram+arithmetic.-a0256685601 google "anagrammatic arithmetic" for more.
cyfermax ยท 1 points ยท Posted at 14:44:35 on May 25, 2016 ยท (Permalink)
I got snarky when I read this, I was all "Hah! What if we say 'twelve ADD one'..." but it still works...damn you.
arsenale ยท 1 points ยท Posted at 14:48:58 on May 25, 2016 ยท (Permalink)
Dodici piรน uno = undici piรน due
Nothing to rearrange here, so math isn't a universal language.
Kadaver_NL ยท 1 points ยท Posted at 15:14:27 on May 25, 2016 ยท (Permalink)
So 9/11 happened the 1st of december? Whoa...
Dudeguy2121ICW ยท 1 points ยท Posted at 15:22:00 on May 25, 2016 ยท (Permalink)
Once y cuatro = catorce y uno
cboski ยท 1 points ยท Posted at 15:26:21 on May 25, 2016 ยท (Permalink)
On mobile but start at 0:33. http://youtu.be/a2FWtELWUS0
ectish ยท 1 points ยท Posted at 15:27:22 on May 25, 2016 ยท (Permalink)
Will Shortz??
elee0228 ยท 1 points ยท Posted at 15:35:27 on May 25, 2016 ยท (Permalink)
I learned a slightly different version:
ELEVEN + TWO - ONE = TWELVE
[deleted] ยท 1 points ยท Posted at 16:10:16 on May 25, 2016 ยท (Permalink)
And "Elven pulse tow"
dzhsck ยท 1 points ยท Posted at 16:20:11 on May 25, 2016 ยท (Permalink)
Also 12x12 = 144, 21x21 = 441, 13x13 = 169, 31x31 = 961.
heyworlditsme ยท 1 points ยท Posted at 16:35:33 on May 25, 2016 ยท (Permalink)
you're a wizard harry
DemonicSquid ยท 1 points ยท Posted at 16:39:28 on May 25, 2016 ยท (Permalink)
Nigel Tufnel: The numbers all go to eleven. Look, right across the board, eleven, eleven, eleven and... Marty DiBergi: Oh, I see. And most amps go up to ten? Nigel Tufnel: Exactly. Marty DiBergi: Does that mean it's louder? Is it any louder? Nigel Tufnel: Well, it's one louder, isn't it? It's not ten. You see, most blokes, you know, will be playing at ten. You're on ten here, all the way up, all the way up, all the way up, you're on ten on your guitar. Where can you go from there? Where? Marty DiBergi: I don't know. Nigel Tufnel: Nowhere. Exactly. What we do is, if we need that extra push over the cliff, you know what we do? Marty DiBergi: Put it up to eleven. Nigel Tufnel: Eleven. Exactly. One louder. Marty DiBergi: Why don't you just make ten louder and make ten be the top number and make that a little louder? Nigel Tufnel: [pause] These go to eleven.
[deleted] ยท 1 points ยท Posted at 17:39:08 on May 25, 2016 ยท (Permalink)
MIND BLOWN
vesomortex ยท 1 points ยท Posted at 18:28:43 on May 25, 2016 ยท (Permalink)
That's actually called an aptagram
Zwoelfenbein ยท 1 points ยท Posted at 18:48:03 on May 25, 2016 ยท (Permalink)
Doesn't work in German though
CRISPR ยท 1 points ยท Posted at 19:17:13 on May 25, 2016 ยท (Permalink)
And that beats Euler's formula on reddit, ladies and gentlemen
Glynn36 ยท 1 points ยท Posted at 19:20:48 on May 25, 2016 ยท (Permalink)
If you spell the number 2 and rearrange the letters they also spell wot.
donosaur66 ยท 1 points ยท Posted at 20:08:30 on May 25, 2016 ยท (Permalink)
And both have 13 letters. Boom.
SenorBeef ยท 1 points ยท Posted at 21:19:43 on May 25, 2016 ยท (Permalink)
I bet someone was really high and was testing all sorts of anagram combinations to come up with that.
Jerzeem ยท 1 points ยท Posted at 21:23:55 on May 25, 2016 ยท (Permalink)
This would be less fascinating if the names of some our numbers weren't stupid. Let me explain what I mean. We have the names of the digits, right? One, two, three, four, five, six, seven, eight, nine, ten (and zero.) Then we have place values, ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc.
For numbers that have place values of ones, you just use the digit name. For numbers that have place values of hundred and higher, you the digit and place value (one hundred, two thousand, three million.)
But we have special names for the numbers with ten as their place value: twenty, thirty, forty, etc instead of two ten, three ten, four ten. And even more special names for the numbers between ten and twenty: eleven, twelve, thirteen, etc.
If we called the eleven, "one ten one," (and called the other special numbers similar things) a lot of math would become somewhat clearer when it's being taught (if more verbose.)
But then 12+1 = 11+2 would just be written as, "one ten two plus one equals one ten one plus two." And that makes the fact that the letters are the same less interesting...
vendetta2115 ยท 1 points ยท Posted at 21:47:12 on May 25, 2016 ยท (Permalink)
Is that you, Hofstadter?
TheThompsonator ยท 1 points ยท Posted at 22:09:18 on May 25, 2016 ยท (Permalink)
That's numberwang and wordwang...all in one!.
TatteredMonk ยท 1 points ยท Posted at 22:53:08 on May 25, 2016 ยท (Permalink)
Why is the 12+1 thing special? Its like saying 5+1=4+2
seanfish ยท 1 points ยท Posted at 22:57:33 on May 25, 2016 ยท (Permalink)
Respect to the top comment but this is the least factual maths fact there is. It's only true in English.
If it turned out to be true in every language I would convert to whatever religion that would be.
TheBlackBear ยท 1 points ยท Posted at 23:11:42 on May 25, 2016 ยท (Permalink)
Does this mean English is the One True Language?
[deleted] ยท 0 points ยท Posted at 12:54:31 on May 25, 2016 ยท (Permalink)
[deleted]
javilla ยท 0 points ยท Posted at 15:11:38 on May 25, 2016 ยท (Permalink)
Fun fact: The same goes for 1+2=2+1
j-r-m-b-v-n ยท 33 points ยท Posted at 19:29:04 on May 25, 2016 ยท (Permalink)
This is what you get when you track the relative positions of Earth and Venus over an 8 year period
a_flying_walrus ยท 662 points ยท Posted at 13:38:54 on May 25, 2016 ยท (Permalink)
The Banach-Tarski Paradox
You can cut a sphere up into pieces, and then reassemble those pieces to get two spheres which are exactly the same as the first sphere.
It sounds impossible, but the following analogy might help:
Imagine you have a dictionary where every string of letters is a word, so the dictionary lists all strings of letters. So AAAA is a word, WXYZ is a word, even ZZZZZZZZ.........Z is a word. Now because the dictionary list all possible words, it also lists BAAAA, BWXYZ, BZZZZZZZZ.........Z, CAAAA, CWXYZ, and so on.
So, if we take all the words that begin with the letter B, we can remove the first B from all of those words then we will have a list of all the words in the original dictionary.
If we do this 26 times, we'll get 26 copies of our original dictionary, plus A,B,...,Z left over.
Infinity is weird.
[deleted] ยท 54 points ยท Posted at 15:33:38 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 16 points ยท Posted at 16:12:33 on May 25, 2016 ยท (Permalink)
Choice is only weird in the case of infinite sets. Finite choice is perfectly well behaved and provable from ZF
johnnymo1 ยท 5 points ยท Posted at 19:04:07 on May 25, 2016 ยท (Permalink)
But its negation is just as weird, if not weirder. Vector spaces with no bases, products of non-empty sets which are empty...
thosethatwere ยท 1 points ยท Posted at 16:21:58 on May 25, 2016 ยท (Permalink)
Hmm, I think axiom is choice is what solves it, to me it's the property of infinite sets to be divided into two and still be the same size that's weird.
atomant30 ยท 19 points ยท Posted at 15:47:47 on May 25, 2016 ยท (Permalink)
thosethatwere ยท 15 points ยท Posted at 16:20:53 on May 25, 2016 ยท (Permalink)
Infinity is weird:
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
[deleted] ยท 1 points ยท Posted at 16:31:29 on May 25, 2016 ยท (Permalink)
Does this one work the same with subtraction?
karlexceed ยท 2 points ยท Posted at 17:36:46 on May 25, 2016 ยท (Permalink)
I don't think so... But this stuff gets really counter-intuitive.
In my mind, infinity-infinity=0 but then if I have an infinite set of items and remove an infinite number of the items in that set, I would still be left with an infinite set by definition... I think.
[deleted] ยท 5 points ยท Posted at 17:45:46 on May 25, 2016 ยท (Permalink)
Here's the thing though, infinity isn't a number. You can't do arithmetic with it.
Not exactly. That's true for some infinite sets (in fact, it's true for an infinite number of infinite sets).
Let's say you have the set of all integers. Now remove the set of all even numbers. You're left with the set of all odd numbers which is still infinite.
But what if I have the set of all even numbers and I remove all even numbers from the set? It's still an infinite set removed from an infinite set, but now the set you're left with has size 0.
Now let's say we have the set of all natural numbers. Our next set is the set of all natural numbers, and then we add -1 to the start of it. Now if we remove everything in the first set from the second, we're left with a set of 1 term: -1.
Basically, infinity isn't a number and you have to define what type of infinity you're looking at when you do stuff with it.
karlexceed ยท 0 points ยท Posted at 19:26:41 on May 25, 2016 ยท (Permalink)
Yeah, an infinite set of size one... Haha. That's what is so frustrating about the concept of infinite things.
[deleted] ยท 2 points ยท Posted at 19:57:50 on May 25, 2016 ยท (Permalink)
The thing is after removing an infinite amount of values (all natural numbers) from that set (all natural numbers and -1), it's no longer infinite. It has a size one so it, by definition, is no longer an infinite set.
karlexceed ยท -1 points ยท Posted at 20:48:13 on May 25, 2016 ยท (Permalink)
So, how much in can an infin ite if an infin can fin ite?
Lol, sorry. I'll see myself out.
Dr-K-G ยท 1 points ยท Posted at 17:23:06 on May 25, 2016 ยท (Permalink)
What do you mean?
[deleted] ยท 3 points ยท Posted at 17:32:50 on May 25, 2016 ยท (Permalink)
If there are an infinite number of rooms in the hotel and each room is full, one guest leaves and the manager moves every guest down a room. Is the hotel still full?
Dr-K-G ยท 2 points ยท Posted at 17:35:37 on May 25, 2016 ยท (Permalink)
Yes that works.
auntfaintly ยท 9 points ยท Posted at 15:49:09 on May 25, 2016 ยท (Permalink)
My professor in college gave the most beautiful and elegant proof of this.
RealSarcasmBot ยท 38 points ยท Posted at 16:28:24 on May 25, 2016 ยท (Permalink)
Did he take a bowling ball and make two?
Because to someone who is physically minded anything but that just shows that maths can't be used to precisely predict this universe. (duhh)
visor841 ยท 19 points ยท Posted at 16:46:12 on May 25, 2016 ยท (Permalink)
It means that you can do things in math that you can't in real life. Not necessarily the other way around.
RealSarcasmBot ยท 3 points ยท Posted at 17:09:25 on May 25, 2016 ยท (Permalink)
oi_rohe ยท 3 points ยท Posted at 17:44:18 on May 25, 2016 ยท (Permalink)
Which is why my graduate dissertation is a mathematical approximation of fucking OP's mom
mythozoologist ยท 1 points ยท Posted at 00:20:11 on May 26, 2016 ยท (Permalink)
Are you really fucking anyone if your electrons never touch? "Oh baby your electromagnetic field is so tight."
StatikDynamik ยท 12 points ยท Posted at 19:02:48 on May 25, 2016 ยท (Permalink)
A bowling ball does not have an infinite series of points, so therefore it is not a true sphere. In fact, nothing in the universe is a true sphere. This theorem has nothing to do with what can be done in the physical universe. But when you think about it in terms of purely mathematical objects, it's actually pretty clear that it is true and isn't quite as counter-intuitive as it originally seems. It's only counter-intuitive when dealing with physical objects because it can't actually be used with them.
Turtle_78 ยท 2 points ยท Posted at 20:57:17 on May 25, 2016 ยท (Permalink)
That makes so much more sense.
thephotoman ยท 2 points ยท Posted at 21:42:24 on May 25, 2016 ยท (Permalink)
More correctly, you can't break anything up into an infinite series of points. The problem is not the unreality of spheres, but the unreality of points, particularly infinitely small ones. The fact that the Plank volume is the smallest meaningful space possible pretty much rules out mathematical points.
StatikDynamik ยท 1 points ยท Posted at 21:46:00 on May 25, 2016 ยท (Permalink)
It does, but it also breaks down before that with atoms. Breaking an object down smaller than that fundamentally changes what it is. It's probably fortunate that this isn't possible in real life though. Life is complicated enough already without duplication glitches.
[deleted] ยท 1 points ยท Posted at 02:09:57 on May 26, 2016 ยท (Permalink)
Fucking thank you. This is the sentence that helped my poor brain stop falling apart. The concept of a "true sphere" being an "infinite set of points" and this paradox using this concept of a true sphere was completely lost to me, but knowing this makes the whole thing a lot easier to digest conceptually.
auntfaintly ยท 3 points ยท Posted at 16:47:51 on May 25, 2016 ยท (Permalink)
Well we did all yell "demonstration!" at the end but it was a joke.
Unfortunately a bowling ball is not a mathematical sphere.
I'm sorry math failed to predict the future for you and make you a second bowling ball.
Tysonzero ยท 1 points ยท Posted at 22:55:33 on May 25, 2016 ยท (Permalink)
It doesn't show that at all. Just because you CAN do strange things in math doesn't mean that you cannot limit yourself to a certain subset of math and describe all physical things without any weirdness.
crappymathematician ยท 1 points ยท Posted at 23:39:28 on May 25, 2016 ยท (Permalink)
Of course it can't. It's not meant to.
[deleted] ยท 69 points ยท Posted at 14:53:34 on May 25, 2016 ยท (Permalink)
I really don't like it when people call it a paradox. It's un-intuitive, that doesn't make it a paradox.
canIborrowAfellaying ยท 37 points ยท Posted at 15:27:29 on May 25, 2016 ยท (Permalink)
It's called a paradox because of the naive notions of measure beforehand made it a paradox, if we allow for the axiom of choice then it fixes the paradox. This is further complicated by the fact that die-hard set theorists look at the axiom of choice with extreme suspicion.
actual_factual_bear ยท 2 points ยท Posted at 16:39:53 on May 25, 2016 ยท (Permalink)
say wha???
canIborrowAfellaying ยท 6 points ยท Posted at 16:45:18 on May 25, 2016 ยท (Permalink)
An implication of the axiom of choice is that every set is well-ordered. This means we can well order the real numbers, but it's been shown we can never explicitly give an example of such an ordering. The axiom of choice is a Pandora's box of logic. The day is saved by the fact if we extend our usual axioms to include the axiom of choice then if we arrive at a contradiction then it would have been there regardless of the axiom of choice being there, so it is nice in some respects, pathological in others.
drive_by_whooshing ยท -3 points ยท Posted at 16:59:44 on May 25, 2016 ยท (Permalink)
whoosh!
Diagonaldenker ยท 9 points ยท Posted at 17:22:42 on May 25, 2016 ยท (Permalink)
Ah yes, the famous Banach Tarsky unintuitivity.
Dude13371337 ยท 15 points ยท Posted at 15:10:20 on May 25, 2016 ยท (Permalink)
Same for all paradoxes.
pemboo ยท 9 points ยท Posted at 17:22:35 on May 25, 2016 ยท (Permalink)
Most paradoxes*
I.E. the ones worth discussing, because the real paradoxes are boring
ableman ยท -1 points ยท Posted at 18:39:14 on May 25, 2016 ยท (Permalink)
There are no real paradoxes. Or they all are.
Nastapoka ยท 2 points ยท Posted at 19:09:24 on May 25, 2016 ยท (Permalink)
Paradox literally means "against popular opinion". Para = against, doxa = popular opinion
Magical_Gravy ยท 4 points ยท Posted at 16:49:56 on May 25, 2016 ยท (Permalink)
That's what a paradox is.
[deleted] ยท -1 points ยท Posted at 17:29:31 on May 25, 2016 ยท (Permalink)
A paradox is something that is simultaneously true and false, a self contradicting statement. The Banach Tarski result is a theorem that is simply true in the framework of ZFC - which almost all mathematicians work under.
phoenixrawr ยท 4 points ยท Posted at 17:42:27 on May 25, 2016 ยท (Permalink)
Paradoxes don't have to be both true and false. The important part of a paradox is that you start with logical premises and reach a seemingly illogical conclusion. The conclusion can be perfectly valid and still be a paradox. Look at something like Simpson's Paradox - nothing about this is "simultaneously true and false," but it's a paradox nonetheless because the conclusion doesn't appear to make sense given the premises.
Magical_Gravy ยท 3 points ยท Posted at 17:43:48 on May 25, 2016 ยท (Permalink)
That's an oxymoron. A paradox is different.
dh363 ยท 1 points ยท Posted at 20:06:08 on May 25, 2016 ยท (Permalink)
Paradoxes are not precisely defined, and one of its technically correct uses is something that is true but just seems false or unintuitive.
dh363 ยท 1 points ยท Posted at 20:03:57 on May 25, 2016 ยท (Permalink)
Paradox means seemingly contradictory or senseless but logically true and sound, so this is actually one of the few things people call paradoxes that actually is one.
QueerandLoathinginTO ยท 1 points ยท Posted at 21:28:23 on May 25, 2016 ยท (Permalink)
Isn't something being unintuitive exactly what makes it a paradox? A paradox is an apparent but not actual contradiction.
971365 ยท 6 points ยท Posted at 15:42:40 on May 25, 2016 ยท (Permalink)
And the new spheres can make newer spheres? Forever and ever?
joshthewaster ยท 8 points ยท Posted at 16:05:43 on May 25, 2016 ยท (Permalink)
Yes. The second is identical to the first. And so on.
971365 ยท 1 points ยท Posted at 16:14:55 on May 25, 2016 ยท (Permalink)
Infinity is weird..
natziel ยท 14 points ยท Posted at 15:44:02 on May 25, 2016 ยท (Permalink)
It really doesn't have anything to do with infinity. The pieces of the sphere (which are finite in number) have 0 measure (in this case, the measure is 3 dimensional volume), so it doesn't make sense to reassemble them into a shape with nonzero measure, hence the contradiction. Or you can explain the contradiction by rejecting the axiom of choice, lol.
Another example of measure theory is when you have a real number line from a to b. Suppose you pick a random number between a and b. There is a 100% chance that you pick an irrational number, because the Lebesgue measure (the length of an interval) of rationals is 0 (as with any other countable set), and the Lebesgue measure of [a, b] is a-b. So the probability of selecting an irrational is (L([a, b]) - 0)/L([a, b]), or 1. The probability is exactly 1, not 99.9999% or anything like that. Pretty neat.
[deleted] ยท 25 points ยท Posted at 16:12:20 on May 25, 2016 ยท (Permalink)
None of the pieces will have zero measure. They all have either positive measure or nonexistent measure. Banach Tarski works by the existence of nonmeasurable sets, and that has everything to do with infinity. Choice is only weird in the case of infinite sets. Finite choice is perfectly well behaved and provable from ZF
ThePopeShitsInHisHat ยท 4 points ยท Posted at 16:40:18 on May 25, 2016 ยท (Permalink)
I'd say it really has to do with infinity. The point of measure theory (very roughly speaking) is to say how "big" sets are, and as you've said that's tied with their cardinality (e.g. countable -> measure 0). Without a proper understanding of infinity and set theory even the definition of measure (or of real numbers for what it's worth!) wouldn't make much sense.
Maybe my point of view is a bit skewed because that's my area of interest though!
isrly_eder ยท 4 points ยท Posted at 17:34:05 on May 25, 2016 ยท (Permalink)
this made me anxious and sweaty.
can you explain in layperson's terms how exactly there's a literal 0 chance of picking a rational number? does this have anything to do with cardinalities of infinity?
natziel ยท 3 points ยท Posted at 18:23:45 on May 25, 2016 ยท (Permalink)
So, you understand that if you have the set of numbers between 0 and 4, your probability of picking a number less than or equal to 1 is 1/4, because (1-0)/(4-0) = 1/4. More generally, the probability of selecting a number in a subinterval within an interval is the quotient of their lengths.
So, the probability of selecting a rational would be the length of the rationals over the length of the reals. So, all that's left is to show that the length of the rationals is 0.
Because the rationals are countable, you can enumerate them such that Q = Union({q_i}, i = 1, i -> infinity). Pardon the notation. Since the length of each {q_i} is 0, the sum of the lengths is 0, so L(Q) = 0.
So, the probability of picking a rational is 0. Ergo, the probability of picking an irrational is 1-0.
BananGunnar ยท 1 points ยท Posted at 05:41:58 on May 26, 2016 ยท (Permalink)
There is 0 chance of picking any one number. There is an infinite amount of real numbers between any two reals a and b. If you pick at random from that interval the probability of, say c, being picked is 1/infinity which is zero. Any time you pick any number at random and actually get a number back is fucking spectacular given that there was literally zero chance for that number to be picked
dh363 ยท 2 points ยท Posted at 20:08:03 on May 25, 2016 ยท (Permalink)
So it has everything to do with infinity because the whole reason the axiom of choice gives you this weird is if you accept infinite choice. The axiom of choice on finite sets doesn't lead to anything weird.
PM_ME_CARROT ยท 2 points ยท Posted at 19:22:03 on May 25, 2016 ยท (Permalink)
It's something that, in theory, happens when infinity "is allowed to occur", so it's misleading to use terms like "cut up spheres" which are physical terms. It's not something that's physically possible.
needuhLee ยท 1 points ยท Posted at 16:38:25 on May 25, 2016 ยท (Permalink)
It has to do with the fact that we can break up a sphere into non-measurable sets, so that rotation is not volume invariant.
Dr-K-G ยท 1 points ยท Posted at 17:23:49 on May 25, 2016 ยท (Permalink)
Rotation is still volume invariant it's just that those pieces are so ugly that they can't be assigned a volume.
needuhLee ยท 1 points ยท Posted at 17:59:56 on May 25, 2016 ยท (Permalink)
Right yea, that's what I meant by mentioning non-measurable sets. I guess it would be better to say volume is not relevant so it doesn't prevent this unintuitive behavior from happening as it normally would.
thatspunny ยท 1 points ยท Posted at 16:44:08 on May 25, 2016 ยท (Permalink)
Well, except you're cutting the sphere into a finite number of pieces, so its a little more complicated than that.
MagicBandAid ยท 1 points ยท Posted at 17:43:18 on May 25, 2016 ยท (Permalink)
That's a countably infinite set.
memcginn ยท 1 points ยท Posted at 18:03:42 on May 25, 2016 ยท (Permalink)
Did you know that BANACH TARSKI anagrams to BANACH TARSKI BANACH TARSKI?
franklywang ยท 1 points ยท Posted at 18:09:25 on May 25, 2016 ยท (Permalink)
The axiom of choice is obviously true, the well-ordering principal is obviously false, and who knows about Zorn's lemma??
PointyOintment ยท 1 points ยท Posted at 18:31:58 on May 25, 2016 ยท (Permalink)
Not a sphere. A ball.
Also, it becomes extremely obvious and not at all counterintuitive when you consider it this way: Take a ball (a solid). Represent it as an infinitely dense point cloud. Select half of the points by some method that results in the selected points being distributed uniformly throughout the ball. Move the selected points as a group to another location. You now have two infinitely dense point clouds the same shape and size of the original.
FreddeCheese ยท 1 points ยท Posted at 18:35:33 on May 25, 2016 ยท (Permalink)
If anyone wants to see the actual maths behind it, this is probably the easiest complete proof.
Aesahaetr ยท 1 points ยท Posted at 18:48:18 on May 25, 2016 ยท (Permalink)
Which led to the famous joke:
What's an anagram of Banach-Tarski?
Banach-Tarski Banach-Tarski.
_Magnolia_ ยท 1 points ยท Posted at 18:57:34 on May 25, 2016 ยท (Permalink)
A friend of mine explained this to me and I just. I don't even know I mean it's just so weird.
Eliphion ยท 1 points ยท Posted at 18:58:45 on May 25, 2016 ยท (Permalink)
Okay I get your dictionary analogy, and how infinity works.... I just don't see how that applies to one sphere being cut into pieces and then reassembled into two spheres exactly the same as the first. I don't see what that has to do with infinity. Spheres have finite volumes and dimensions. And if it were some sort of infinity example, wouldn't you say you could cut up one sphere into pieces that could be made into an infinite number of other spheres of the same size as the first?
Can you explain? I'm not seeing it...
DCdictator ยท 1 points ยท Posted at 19:18:37 on May 25, 2016 ยท (Permalink)
lol, my answers were also basically that infinite is weird.
Mr-ButterMilk ยท 1 points ยท Posted at 19:19:17 on May 25, 2016 ยท (Permalink)
This reminded me of that anagram of Banach-Tarski : Banach-Tarski Banach-Tarski
beingforthebenefit ยท 1 points ยท Posted at 19:36:00 on May 25, 2016 ยท (Permalink)
My favorite math joke:
What's an anagram for Banach-Tarski?
Banach-Tarski Banach-Tarski.
nosliw_rm ยท 1 points ยท Posted at 21:14:18 on May 25, 2016 ยท (Permalink)
I loved the video in this and wish there were more like it or a sub for videos like it
wazup000 ยท 1 points ยท Posted at 21:24:50 on May 25, 2016 ยท (Permalink)
Pair the dictionary metaphor with the fact that circles and spheres are of an irrational circumference and surface area respectively, and you can put together how a sphere can be copied.
trey3rd ยท 1 points ยท Posted at 21:30:30 on May 25, 2016 ยท (Permalink)
How does removing the first a from aaaa make that a word in the dictionary? Am I missing a step?
TheSimon98 ยท 1 points ยท Posted at 21:36:35 on May 25, 2016 ยท (Permalink)
Is Banach-Tarski Banach-Tarski an anagram for Banach-Tarski then?
Mareldamus ยท 1 points ยท Posted at 21:37:03 on May 25, 2016 ยท (Permalink)
Thank you Michael Stevens
cloughie ยท 1 points ยท Posted at 22:11:09 on May 25, 2016 ยท (Permalink)
Wouldn't you have a list of all the original words, minus one letter (the B?)
b4b ยท 1 points ยท Posted at 22:25:20 on May 25, 2016 ยท (Permalink)
What you wrote does not make sense. If you take out the first later of "BAAAA" and get "AAAA" you will never get "AAAAA" (5 letters "A"), you basically only get words that are 1 letter shorter.
I dont know why you are getting upvoted, I guess a wikipedia link + random nonsense, makes the nonsense legitimate.
rollybison ยท 1 points ยท Posted at 22:28:14 on May 25, 2016 ยท (Permalink)
I read that as The Banach-Tarski Pokedex
sluggles ยท 1 points ยท Posted at 23:17:14 on May 25, 2016 ยท (Permalink)
So, your analogy isn't exactly what's going on. If you replace A through Z with 0 through 9, then what you're essentially saying is take the numbers 1.something, subtract 1 to get .something, and multiply by 10, and you get all the numbers from 0 to 9 again. Multiplying by 10 doesn't preserve volume. The paradox is that you can break a sphere into pieces, and then put the pieces back together in a way that only uses rotations and translations (which preserve length and volume) and the two spheres have the same volume as the original. The resolution of the paradox is measure theory. The idea is that you have to break up the sphere into sets that have no volume. So you have a set with volume V, then several other sets (the pieces) which can have no volume, and then a set with volume V' where V != V'.
theniceguytroll ยท 1 points ยท Posted at 23:24:50 on May 25, 2016 ยท (Permalink)
I, too, watch Vsauce.
rump_truck ยท 1 points ยท Posted at 01:30:23 on May 26, 2016 ยท (Permalink)
I've heard it several times before, but this is the first explanation that really clicked! Like the first time I heard of Cantor diagonals. I guess with infinity, everything comes down to mapping like this.
imtn ยท 1 points ยท Posted at 02:14:11 on May 26, 2016 ยท (Permalink)
The last time I read about this, I realized that it was because the sphere used for that paradox is infinitely dense.
Ol_No_Name ยท 1 points ยท Posted at 03:01:39 on May 26, 2016 ยท (Permalink)
Vsauce video on the paradox https://www.youtube.com/watch?v=s86-Z-CbaHA
SonOfaFlynn ยท 1 points ยท Posted at 04:23:27 on May 26, 2016 ยท (Permalink)
This is is one of my favorite results
superiority ยท 1 points ยท Posted at 06:44:58 on May 26, 2016 ยท (Permalink)
Crucially, into finitely many pieces (in finitely many operations). Otherwise someone might just think it's not much different than applying f(x) = 2x to [0,1].
Nlelith ยท 1 points ยท Posted at 09:40:34 on May 26, 2016 ยท (Permalink)
The really astounding thing about the Banach-Tarski Paradox is, that even though it deals with "infinities", it staes that you actually carve the sphere into a finite amount of pieces to double it.
[deleted] ยท 1 points ยท Posted at 13:46:31 on May 26, 2016 ยท (Permalink)
That is ... a really bad analogy. Furthermore, Banach-Tarski is only valid if you accept the axiom of choice.
omaximov ยท 1 points ยท Posted at 20:00:43 on June 1, 2016 ยท (Permalink)
Do you need all the words to be finitely long?
Supersting ยท 1 points ยท Posted at 16:24:24 on May 25, 2016 ยท (Permalink)
Warning, requires Axiom of Choice to function...
AngelTC ยท 1 points ยท Posted at 16:57:17 on May 25, 2016 ยท (Permalink)
Not really tho, the usual proof uses AC but it has been shown that the theorem requires weaker axioms
Supersting ยท 1 points ยท Posted at 22:39:04 on May 25, 2016 ยท (Permalink)
Okay, my point being that B-T isn't a "fact" like many of the other comments are. It requires more than our standard assumptions in ZF (but yeah, sure, people are mostly fine with AC nowadays, and the facts on this page all rely on axioms too, so aren't really facts at all, because they are based on underlying assumptions and oh my god nothing is true anymore).
theGiogi ยท 0 points ยท Posted at 15:26:07 on May 25, 2016 ยท (Permalink)
This should be higher up. It's not a paradox though.
canyoutriforce ยท 2869 points ยท Posted at 11:18:02 on May 25, 2016 ยท (Permalink)*
There are 52! ways to shuffle a deck of cards.
80658175170943878571660636856403766975289505440883277824000000000000 ways.
How big is that number?
Start by picking your favorite spot on the equator. You shuffle the deck of cards once every second. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.
Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time youโve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits havenโt even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still wonโt do it. There are still more than 5.385e67 seconds remaining. Youโre just about a third of the way done.
NotSorryIfIOffendYou ยท 868 points ยท Posted at 12:28:38 on May 25, 2016 ยท (Permalink)
To put it otherwise if someone makes you a wager where they shuffle two decks and if the cards are in the same order they get to kill you and if not you get a dollar you play that game until you're richer than Bill Gates.
phreakmonkey ยท 880 points ยท Posted at 14:43:10 on May 25, 2016 ยท (Permalink)
If someone bets you they can shit wooden nickels, it's probably because they have a technique for shitting wooden nickles.
[deleted] ยท 30 points ยท Posted at 20:23:05 on May 25, 2016 ยท (Permalink)
PunxsatownyPhil ยท 3 points ยท Posted at 21:37:54 on May 25, 2016 ยท (Permalink)
Guys and Dolls! I was thinking of the same thing.
ForeskinFondler ยท 1 points ยท Posted at 22:40:31 on May 25, 2016 ยท (Permalink)
"Daddy! I've got cider in my ear"
I was thinking the exact same thing.
LonePaladin ยท 17 points ยท Posted at 00:17:35 on May 26, 2016 ยท (Permalink)
I saw this exchange in a bar once:
barrtender ยท 10 points ยท Posted at 05:56:02 on May 26, 2016 ยท (Permalink)
I heard an extended version.
LonePaladin ยท 2 points ยท Posted at 08:11:57 on May 26, 2016 ยท (Permalink)
Oh, that's not right.
4floorsofwhores ยท 27 points ยท Posted at 18:09:05 on May 25, 2016 ยท (Permalink)
It's a safer bet they just want to shit on your floor.
d-scott ยท 22 points ยท Posted at 18:33:06 on May 25, 2016 ยท (Permalink)
Ah, just a standard run of the mill turd. You win i guess, see ya later
NotSorryIfIOffendYou ยท 7 points ยท Posted at 15:27:37 on May 25, 2016 ยท (Permalink)
As long as I can assure the shuffles are random I'd take the bet for a paperclip let alone a dollar
motherfuckingriot ยท 18 points ยท Posted at 17:52:11 on May 25, 2016 ยท (Permalink)
Then you can trade that paper clip for a fish shaped pen in vancouver.
coollegolas ยท 9 points ยท Posted at 17:53:18 on May 25, 2016 ยท (Permalink)
But how long does it take to trade up to a house?
motherfuckingriot ยท 19 points ยท Posted at 18:03:42 on May 25, 2016 ยท (Permalink)
Why on earth would you trade the fish pen?
coollegolas ยท 6 points ยท Posted at 19:00:40 on May 25, 2016 ยท (Permalink)
Well, what if someone wanted a fish pen and they were willing to give you a hand-sculpted doorknob?
motherfuckingriot ยท 3 points ยท Posted at 19:06:54 on May 25, 2016 ยท (Permalink)
Hand sculpted you say?
coollegolas ยท 2 points ยท Posted at 19:15:58 on May 25, 2016 ยท (Permalink)
Yes, but you need to come to Seattle.
WikiWantsYourPics ยท 181 points ยท Posted at 14:05:42 on May 25, 2016 ยท (Permalink)
ASSUMING that the shuffle is truly random, that's a great deal.
Even if the shuffle is even quite reasonably good, it's a good deal.
The_null-A ยท 12 points ยท Posted at 15:13:16 on May 25, 2016 ยท (Permalink)
It's also proved that you have to shuffle only 7 times to have a reasonably good random shuffle.
Demonstration is however quite complex.
TribeWars ยท 1 points ยท Posted at 15:35:02 on May 26, 2016 ยท (Permalink)
if you do a perfect shuffle
The_null-A ยท 1 points ยท Posted at 17:55:58 on May 26, 2016 ยท (Permalink)
A reasonably good shuffle. It allows for some 2-3 cards inserted between the two on the other side.
TribeWars ยท 1 points ยท Posted at 18:04:56 on May 26, 2016 ยท (Permalink)
Guess I was slightly misinformed
WebStudentSteve ยท 9 points ยท Posted at 14:50:22 on May 25, 2016 ยท (Permalink)
Hand shuffles are never truly random. Many people don't cut between shuffles and the top card will always be in the top 10% of the deck afterwards, it really limits the shuffle. Same reason why when you play poker with friends better cards end up showing more often later in the game (lower card values are folded first putting them lower in the deck).
mr_ewe ยท 3 points ยท Posted at 16:13:44 on May 25, 2016 ยท (Permalink)
I just watched a YouTube video about this a few days ago.
7 bridge shuffles is sufficiently random.
Or 1 minute of scrambling cards on the table top.
CaptchaInTheRye ยท 3 points ยท Posted at 15:32:13 on May 25, 2016 ยท (Permalink)
That isn't true for card games like hold'em where lots of cards are folded and burned from all around a physical table, where the first cards don't necessarily go to the bottom of the deck when retrieved.
mathbandit ยท 2 points ยท Posted at 16:54:14 on May 25, 2016 ยท (Permalink)
As others have said, 7 rifle shuffles gives a sufficiently random deck.
aegluc ยท 1 points ยท Posted at 15:07:25 on May 25, 2016 ยท (Permalink)
interesting. can anyone confirm ?
WebStudentSteve ยท 4 points ยท Posted at 15:09:23 on May 25, 2016 ยท (Permalink)
You can confirm for yourself, take a deck of cards and add one card that has a different color back to the top. Shuffle the deck a few times (try to do it the way you normally would) and see where the card you put on top ends up. It will never, ever be on the bottom if you did the test honestly, and usually in the top 10%. Showing that hand shuffles are not random.
aegluc ยท 1 points ยท Posted at 17:42:12 on May 25, 2016 ยท (Permalink)
will try this ! Cool fact
mathbandit ยท 1 points ยท Posted at 12:09:34 on May 26, 2016 ยท (Permalink)
Assuming you are shuffling perfectly (One card from Side A, one from Side B, one from Side A, etc) and do just five rifle shuffles, the card that started on top can end up anywhere from Slot 1 to Slot 32.
Again, once you do 7 rifle shuffles, it has proven to be mathematically random.
Miniminotaur ยท -10 points ยท Posted at 15:03:43 on May 25, 2016 ยท (Permalink)
But wouldn't chaos theory play a part..there's always a possibility that they will be the same.
joshthewaster ยท 6 points ยท Posted at 15:09:47 on May 25, 2016 ยท (Permalink)
That's not really what chaos theory deals with in a mathematical sense. But yes, you could get extremely unlucky. The odds of that are small. Really really really really small.
WikiWantsYourPics ยท 6 points ยท Posted at 15:39:52 on May 25, 2016 ยท (Permalink)
That's not what chaos theory says. Chaos theory describes systems where an arbitrarily small perturbation in the starting conditions can yield arbitrarily large changes in final conditions; and also describes attractors and suchlike systems.
It doesn't say anything that would lead you to conclude that two independent card shuffles are more likely to come out the same than you would expect by chance alone.
Miniminotaur ยท 1 points ยท Posted at 22:24:07 on May 25, 2016 ยท (Permalink)
So which theory is it that concludes anything could happen at any time.? Isn't there an infinitesimal chance that the cards could just disappear also? I remember reading about if you were to spend all your time pushing against a wall, there's a chance, at one point, you may push through it..
Plsdontreadthis ยท 2 points ยท Posted at 00:38:11 on May 26, 2016 ยท (Permalink)
That last part is called quantum tunneling, and it is incredibly rare on a macroscopic level.
Unless you just mean breaking a hole in the wall.
BarqsDew ยท 495 points ยท Posted at 13:53:44 on May 25, 2016 ยท (Permalink)
Where >they< shuffle the decks? Yeah, no thanks dude!
IAm_From_2045_AMA ยท 36 points ยท Posted at 14:42:50 on May 25, 2016 ยท (Permalink)
I see magicians shuffle that way so often, I never knew it was fake :o
BarqsDew ยท 48 points ยท Posted at 15:39:22 on May 25, 2016 ยท (Permalink)
It's not always fake, and that's not the only false shuffle out there. There's a false shuffle for just about every real shuffle.
IICVX ยท 6 points ยท Posted at 18:41:11 on May 25, 2016 ยท (Permalink)
also aside from false shuffles there's perfect shuffles, which are 100% predictable.
BarqsDew ยท 2 points ยท Posted at 19:00:10 on May 25, 2016 ยท (Permalink)
True. Those can be a bit harder to perform reliably, though.
BangedYourMum ยท 7 points ยท Posted at 15:34:25 on May 25, 2016 ยท (Permalink)
only sometimes it is it all depends on the trick
AAAAAAAHHH ยท 2 points ยท Posted at 14:47:06 on May 25, 2016 ยท (Permalink)
The first way sounds more impressive.
NotSorryIfIOffendYou ยท 1 points ยท Posted at 15:26:07 on May 25, 2016 ยท (Permalink)
Ok cool you go trying to stack paper to the sun while I cruise in my Bugatti.
culb77 ยท 1 points ยท Posted at 15:45:36 on May 25, 2016 ยท (Permalink)
Ricky Jay would take that bet. Of course, he's not actually shuffling....
TheLonelyPillow ยท 1 points ยท Posted at 16:25:28 on May 25, 2016 ยท (Permalink)
Who would make that wager? It's not like you could ever possibly get the same combo if you truly shuffled them.
mmazurr ยท 1 points ยท Posted at 20:05:47 on May 25, 2016 ยท (Permalink)
I would assume they have some kind of trick up their sleeve and are trying to get me to agree to my own death. Not falling for that.
Inane_newt ยท 1 points ยท Posted at 20:58:04 on May 25, 2016 ยท (Permalink)
Same order or matching the order of any previous shuffle.
Still going to have more money than Bill Gates Moneybefore you die.
Though not more than (Bill Gates Money)!
r4ndpaulsbrilloballs ยท 1 points ยท Posted at 23:10:08 on May 25, 2016 ยท (Permalink)
That's assuming a fair and random shuffle.
If there's one law I've learned about the universe it's this:
There's no such thing as a fair game in nature.
devman0 ยท 1 points ยท Posted at 23:48:47 on May 25, 2016 ยท (Permalink)
You know what they say. Every well shuffled deck of cards is unique from every other well shuffled deck of cards in history.
owiseone23 ยท 1 points ยท Posted at 01:51:30 on May 26, 2016 ยท (Permalink)
Maybe mathematically, but first of all decks don't start in a random order, and second, people don't shuffle randomly so the chances are still slim, but not ridiculous.
Mackiato ยท 1 points ยท Posted at 04:46:53 on May 26, 2016 ยท (Permalink)
But after 50 times or something you'd be at like 63% risk of dying
NotSorryIfIOffendYou ยท 1 points ยท Posted at 04:49:26 on May 26, 2016 ยท (Permalink)*
I know you're getting meta but that's a rule of thumb and the term "arbitrarily large," which is relevant there is meant to be vague enough to imply whichever number is big enough to make the statement true. 50 makes this work for most real life probabilities but definitely not something as minuscule as what we're talking here.
What their equation meant is that if something has a 1/x chance in happening and you do it x times the percent chance it happens will be 63%
UCanJustBuyLabCoats ยท 1 points ยท Posted at 08:13:48 on May 26, 2016 ยท (Permalink)
But to do that, that person would have to be Bill Gates!
be_my_plaything ยท 1 points ยท Posted at 08:44:35 on May 26, 2016 ยท (Permalink)
(sighs) I'd probably be the 806581751709438785716606368564037669752895054408832778239999999999999th person they'd tried it on that day.
TribeWars ยท 1 points ยท Posted at 15:34:32 on May 26, 2016 ยท (Permalink)
yeah, but he might not shuffle it sufficiently
Dernom ยท 1 points ยท Posted at 14:19:35 on May 25, 2016 ยท (Permalink)
Only about 100'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000 times richer
๐๏ธ TheLoneWolf156 ยท 889 points ยท Posted at 11:21:48 on May 25, 2016 ยท (Permalink)
Isn't that from VSauce?
[deleted] ยท 327 points ยท Posted at 12:26:21 on May 25, 2016 ยท (Permalink)
[deleted]
velion0223 ยท 8 points ยท Posted at 15:24:58 on May 25, 2016 ยท (Permalink)
There are a couple of places I've heard that. I learned something very similar to that from my Stats teacher in highschool before I ever saw it on Vsause. That is a mindbogglingly large number that actually influences our everyday life.
Fuckshit77 ยท 1 points ยท Posted at 22:55:44 on May 25, 2016 ยท (Permalink)
Look up Graham's number, it is more digits than there are atoms in the universe.
Umbrius ยท 2 points ยท Posted at 21:39:13 on May 25, 2016 ยท (Permalink)
The explanation after that one is even better to me. Dealing yourself 5 cards, and every royal flush you deal, buy a lottery ticket.
Every winning lottery ticket add a grain of sand to the grand canyon.
When the grand canyon is full take 1 oz from Mt. Everest.
After Everest is gone. Repeat 256 more times to get to 52! in time spent
Denascite ยท 56 points ยท Posted at 13:02:39 on May 25, 2016 ยท (Permalink)
http://czep.net/weblog/52cards.html
I first read it here...don't know which one was first though
Deasy_ ยท 11 points ยท Posted at 13:58:30 on May 25, 2016 ยท (Permalink)*
That was first, I remember finding that out then seeing the VSauce video uploaded like a week later!
EDIT: I'm not saying VSauce copied it, just pointing out the coincidence for me in learning of the fact then VSauce uploaded the video talking about it
aaronclements ยท 18 points ยท Posted at 14:12:28 on May 25, 2016 ยท (Permalink)
Czep's was first, and VSauce gave him full credit in the video, even referencing his site, czep.net.
PointyOintment ยท 2 points ยท Posted at 18:13:14 on May 25, 2016 ยท (Permalink)
That one was first.
Drendude ยท 1 points ยท Posted at 22:23:40 on May 25, 2016 ยท (Permalink)
I saw it ages before the VSauce. Like, years.
DoctorWaluigiTime ยท 13 points ยท Posted at 14:18:10 on May 25, 2016 ยท (Permalink)
It's also from every single math-related thread.
esneT ยท 0 points ยท Posted at 17:10:45 on May 25, 2016 ยท (Permalink)
Op's comment is quite literally a transcription of vsauce's video
charlesgegethor ยท 5 points ยท Posted at 15:57:45 on May 25, 2016 ยท (Permalink)
That fact has been around long before Vsauce.
RequiredReading ยท 3 points ยท Posted at 15:21:13 on May 25, 2016 ยท (Permalink)
It's a pretty old and very popular math related fact, but yes, Vsauce also recently covered it.
mattsprofile ยท 3 points ยท Posted at 16:27:50 on May 25, 2016 ยท (Permalink)
This is an example of something that is so blatantly the work of a single person (or group) but yet people for some reason don't feel the need to cite that one person. I understand if you don't cite someone if you coincidentally happen to come to the same solution as them. But that is not the case here. Nobody else is just going to happen to come up with the conclusion that you need to start walking around the earth and removing drops of water from the Pacific Ocean and then stacking sheets of paper to the moon and filling the ocean back up and reaching the sun then unstacking the papers and repeating thousands of times.
In order to even recite the fact with as much accuracy as done here, you'd need to look it up anyway! So he didn't even pull it out of memory and say "I don't remember who came up with this." He found a source for this fact which is not common knowledge and then didn't cite the source that he just found.
mattfloyd ยท 4 points ยท Posted at 16:42:43 on May 25, 2016 ยท (Permalink)
Vsauce gave the original creator full credit. /u/canyoutriforce is just some dude on the Internet reciting a math fact. Just like most other people in here.
[deleted] ยท 4 points ยท Posted at 13:49:49 on May 25, 2016 ยท (Permalink)
This here:
https://www.youtube.com/watch?v=ME1XNMjXjZU
Amazing stuff! really helps to have the visualizations for those not mathematically inclined like myself.
JuanDeLasNieves_ ยท 1 points ยท Posted at 15:08:57 on May 25, 2016 ยท (Permalink)
Why is that dude making a BvS Lex Luthor impression while explaining this
[deleted] ยท 2 points ยท Posted at 14:34:35 on May 25, 2016 ยท (Permalink)
It was also featured on QI
Stickyballs96 ยท 2 points ยท Posted at 17:13:59 on May 25, 2016 ยท (Permalink)
Vsauce didn't invent math concepts no
adruven ยท 1 points ยท Posted at 14:13:08 on May 25, 2016 ยท (Permalink)
Also from here.
PM_ME_YOUR_MESMER ยท 1 points ยท Posted at 16:35:47 on May 25, 2016 ยท (Permalink)
I read that in Michael's voice. It's weird. He just popped into my head from the bottom of my vision and started talking.
goldpeaktea314 ยท 1 points ยท Posted at 17:05:17 on May 25, 2016 ยท (Permalink)
I also posted this same thing on a similar thread 8 days ago.
Saldar1234 ยท 1 points ยท Posted at 22:04:09 on May 25, 2016 ยท (Permalink)
Funny enough I said that I was facsinated by supertasks and cited a source of information: a vsauce video and got downvoted for it. This guy quotes a vsauce video verbatim giving no credit whatsoever and gets 1900+ upvotes.
I love reddit.
BoogsterSU2 ยท 1 points ยท Posted at 01:48:06 on May 26, 2016 ยท (Permalink)
"Hey, Vsauce! Michael here."
SWAG_M4STER ยท 1 points ยท Posted at 06:58:19 on May 26, 2016 ยท (Permalink)
AND THANKS FOR WATCHING
Master_Of_Knowledge ยท -1 points ยท Posted at 17:29:38 on May 25, 2016 ยท (Permalink)
Math* you limey bastard
Xydos ยท 48 points ยท Posted at 13:57:59 on May 25, 2016 ยท (Permalink)
Really? That's all I have to do? Brb.
cnho1997 ยท 13 points ยท Posted at 18:35:54 on May 25, 2016 ยท (Permalink)
RemindMe! 8.063 * 1067 seconds
Ervin_Pepper ยท 230 points ยท Posted at 12:01:07 on May 25, 2016 ยท (Permalink)*
People never fully comprehend the almighty power of putting ! at the end of a number. Like, you've got the number 100. That's a normal sized number, not too big. But look what happens when I put an ! at the end. Rounding up to one significant figure it becomes 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(That's 1 followed by 158 zeroes for the curious)
[deleted] ยท 75 points ยท Posted at 14:18:08 on May 25, 2016 ยท (Permalink)
10 unquinquagintillion
[deleted] ยท 66 points ยท Posted at 14:58:02 on May 25, 2016 ยท (Permalink)
I see you have been playing AdVenture Capitalist
cwf82 ยท 6 points ยท Posted at 17:32:41 on May 25, 2016 ยท (Permalink)
All I know about large numbers (I.e. beyond quadrillion) comes from AdCap
dpavlicko ยท 4 points ยท Posted at 19:05:39 on May 25, 2016 ยท (Permalink)
I genuinely feel like after you hit quadrillion the third time that game is just about number naming conventions
TheBoysNotQuiteRight ยท 3 points ยท Posted at 17:26:43 on May 25, 2016 ยท (Permalink)
Just don't play that word in Scrabble.
syrne ยท 2 points ยท Posted at 17:40:20 on May 25, 2016 ยท (Permalink)
Too long to fit on the board :(
[deleted] ยท 1 points ยท Posted at 00:59:30 on May 26, 2016 ยท (Permalink)
I have... but I only know because I looked it up
Sharpie_Buttsalot ยท 15 points ยท Posted at 14:46:06 on May 25, 2016 ยท (Permalink)
Adventure Capitalist as educational tool
christian-mann ยท 39 points ยท Posted at 13:13:00 on May 25, 2016 ยท (Permalink)
No? 100 factorial is 9.332 x 10157.
Ervin_Pepper ยท 48 points ยท Posted at 13:16:14 on May 25, 2016 ยท (Permalink)
Rounded up to 1 sig fig, probably should have stated that in my comment. Edited it now
JackFlynt ยท 46 points ยท Posted at 13:39:54 on May 25, 2016 ยท (Permalink)
While I am impressed by that number I am wounded by your treatment of poor, innocent significant figures :P
ccfreak2k ยท 2 points ยท Posted at 15:52:58 on May 25, 2016 ยท (Permalink)
What's a couple of powers of ten between friends?
Crazyblazy395 ยท 1 points ยท Posted at 15:07:45 on May 25, 2016 ยท (Permalink)
(1*102 )! does only have one sig fig... I think....
cachow6 ยท 8 points ยท Posted at 15:21:58 on May 25, 2016 ยท (Permalink)
In this case 100 or 1*102 is not a measurement, it is an exact number, so it has an infinite number of significant figures.
Crazyblazy395 ยท 2 points ยท Posted at 18:21:21 on May 25, 2016 ยท (Permalink)
Bahhhhh, get out of here with your science and knowledge!
JackFlynt ยท 3 points ยท Posted at 22:23:46 on May 25, 2016 ยท (Permalink)
I was going more for the fact that 9.332...*10X rounded to one significant figure is 9*10X . Rounding it to 10*10X or 1*10X+1 is... well, less correct, and as my old maths teacher would say, is a crime worthy of being sent to Maths Prison.
Not that it's overly important, of course, it's just the idea of rounding up to a significant figure is weird in my head.
jelloey ยท 3 points ยท Posted at 15:49:00 on May 25, 2016 ยท (Permalink)
Rounded to one sig fig is 9ร10157 , not 1ร10158
lordanubis79 ยท 9 points ยท Posted at 14:24:53 on May 25, 2016 ยท (Permalink)
Should've been rounded down, not up
[deleted] ยท -1 points ยท Posted at 15:13:02 on May 25, 2016 ยท (Permalink)*
[deleted]
dafuqwhatyousayin ยท 1 points ยท Posted at 15:28:33 on May 25, 2016 ยท (Permalink)
??? you can round to 9 x 10157
lordanubis79 ยท 0 points ยท Posted at 15:45:56 on May 25, 2016 ยท (Permalink)
I have a very high level of knowledge in scientific fields and I'm currently working on a mathematical paper that may change the world, I think I can round numbers
9.3 is closer to 9 than to 10, as simple as that
_kst_ ยท 2 points ยท Posted at 02:31:54 on May 26, 2016 ยท (Permalink)
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
[deleted] ยท 4 points ยท Posted at 15:34:54 on May 25, 2016 ยท (Permalink)
Here's another powerful operator.
https://en.wikipedia.org/wiki/Knuth's_up-arrow_notation
Pm_me_any_dragon ยท 2 points ยท Posted at 16:45:23 on May 25, 2016 ยท (Permalink)
Gotta love me some up arrow
AManHasSpoken ยท 1 points ยท Posted at 20:49:27 on May 25, 2016 ยท (Permalink)
Reddit's favorite operator
Pm_me_any_dragon ยท 1 points ยท Posted at 20:55:40 on May 25, 2016 ยท (Permalink)
didnt even notice that one...
sweet catch
Spikinou ยท 2 points ยท Posted at 15:07:29 on May 25, 2016 ยท (Permalink)
How do you call "!" orally ? Like 52 X ?
NeedsMoreShawarma ยท 14 points ยท Posted at 15:41:02 on May 25, 2016 ยท (Permalink)
! is "factorial". So 52! would be called "Fifty Two Factorial".
SoberIRL ยท 1 points ยท Posted at 18:07:13 on May 25, 2016 ยท (Permalink)
Dumb question:
Can you do other operations with the factorial? Like: 55! or 5!! or (5!)!
NeedsMoreShawarma ยท 2 points ยท Posted at 18:13:48 on May 25, 2016 ยท (Permalink)
Don't see why not, typing "5^5!" into Google seems to perform that calculation, as well as (5!)!. Not sure about 5!! haha
SoberIRL ยท 2 points ยท Posted at 18:39:10 on May 25, 2016 ยท (Permalink)
Part of me just wants to have another reason to chuckle when I see "omg!!!" or something. Like, "hey, depending on your values for o, m, and g, that's probably a danged big number."
jonmcfluffy ยท 1 points ยท Posted at 19:41:58 on May 25, 2016 ยท (Permalink)
i assume it would end up doing (5!)!
so 5!! would be 6.689503e+198
actually yeah, putting in 5!! as a google search brings that one up.
Seraphaestus ยท 1 points ยท Posted at 20:01:21 on May 25, 2016 ยท (Permalink)
Factorials are numbers just like anything else so you can do anything you can do to a number. For example, 5! = 120; 55! is just 5120. 5!! is 120!. (5!)! is also 120!.
_kst_ ยท 1 points ยท Posted at 02:35:54 on May 26, 2016 ยท (Permalink)
You should still say it loudly:
FIFTY TWO FACTORIAL
JackSpyder ยท 13 points ยท Posted at 16:32:30 on May 25, 2016 ยท (Permalink)
You just say it much louder.
PanchDog ยท 1 points ยท Posted at 16:21:27 on May 25, 2016 ยท (Permalink)
That isn't 158 zeros you have there, for the curious. Can anyone else please confirm?
DemonCipher13 ยท 1 points ยท Posted at 18:39:28 on May 25, 2016 ยท (Permalink)
I wonder how awkward it must have been to be sitting at your office desk, typing "0", with a gaze that could set a stack of papers aflame, all-the-while counting every single one. "...101...102...103..."
You da real MVP.
SillyFlyGuy ยท 1 points ยท Posted at 19:16:07 on May 25, 2016 ยท (Permalink)
I put it at the end of all my sentences! That way people hear me and know I'm serious!
nnyx ยท 1 points ยท Posted at 19:28:45 on May 25, 2016 ยท (Permalink)
I think it's less that people don't understand factorials (although I'm sure plenty of people don't) and more no one understands numbers that are even remotely close to that big.
Even imagining what 1000 of something looks like is hard without breaking it into smaller pieces.
Once you get past a million or so, in most peoples minds, it only registers as "really big number".
[deleted] ยท 1 points ยท Posted at 20:42:25 on May 25, 2016 ยท (Permalink)
That is 10158, just to give a perspective there are ~1080 atoms in the observable universe.
DrBubbles ยท 1 points ยท Posted at 20:47:28 on May 25, 2016 ยท (Permalink)
I always think numbers look more impressive with the commas.
Behold.
100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Styrak ยท 1 points ยท Posted at 21:49:12 on May 25, 2016 ยท (Permalink)
(100!)!
PMmeYourSins ยท 1 points ยท Posted at 22:50:15 on May 25, 2016 ยท (Permalink)
But this has 156 zeroes.
kyune ยท 1 points ยท Posted at 06:26:32 on May 26, 2016 ยท (Permalink)*
Factorials are difficult to relate to--even if you're familiar with binary powers (2x), conceptually making the jump to factorials is difficult to understand without a math background. And even if you did, you quickly end up with numbers that are practically unintelligible without crafted stories and analogies.
rasmusvedel ยท 1 points ยท Posted at 07:55:14 on May 26, 2016 ยท (Permalink)
A significant figure is the first digit after a zero and every subsequent digit, as I was taught.
You, sir, have a lot more significant figures.
1 x 10158 seems about right though.
klod42 ยท 1 points ยท Posted at 10:29:43 on May 26, 2016 ยท (Permalink)
One of my professors used to say "Exponential growth is intuitively ungraspable" (I can't translate it better). Factorial grows even faster. We can't even really comprehend how fast the number grows when you keep adding zeroes to it, let alone factorial.
100! is far more than number of atoms in observable universe. Many, many orders of magnitude larger. To my knowledge, no physical size exists that would be described by such a number. But it's still less than number of ways to shuffle a double deck of cards.
saab121 ยท 1 points ยท Posted at 13:47:59 on May 26, 2016 ยท (Permalink)
I only count 156
pokemonpasta ยท 0 points ยท Posted at 15:16:59 on May 25, 2016 ยท (Permalink)
bigger than googol then
JTswift ยท 214 points ยท Posted at 14:12:22 on May 25, 2016 ยท (Permalink)
I know 52! is a big number (as you typed), but this one is just really hard to fathom.
Steps around the world, drops in the Pacific Ocean, then pieces of paper to the sun. It's all so absurd that it kind of fails in its intent, in my opinion. It's almost like trying to imagine infinity.
Carl_GordonJenkins ยท 67 points ยท Posted at 15:00:33 on May 25, 2016 ยท (Permalink)
I like this one better:
If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles.
JTswift ยท 5 points ยท Posted at 15:02:55 on May 25, 2016 ยท (Permalink)*
So, each person can shuffle a trillion packs of cards at a time?
How many hands do these imaginary people have?!?
Striderrs ยท 37 points ยท Posted at 15:22:20 on May 25, 2016 ยท (Permalink)
Two trillion.
SKR47CH ยท 9 points ยท Posted at 15:42:49 on May 25, 2016 ยท (Permalink)
Math checks out. sorta..
burgerga ยท 1 points ยท Posted at 22:01:15 on May 25, 2016 ยท (Permalink)
Just change it to a trillion of these galaxies and only one deck per person and you'd have the same thing
Crully ยท 0 points ยท Posted at 17:47:10 on May 25, 2016 ยท (Permalink)*
Is that the total shuffles for the number, or does that take into account the fact that working with random numbers you would hit a collision before you get to the final number.
Sorry not a mathematician, what I mean is on a smaller scale if you had to pick a random number between 1 and 1000, you wouldn't need 1000 goes to get a number two times.
Edit: Why I'm downvoted, I'm just asking a question because I didn't understand the above post, this is the AskReddit sub right?
xiaodown ยท 16 points ยท Posted at 15:29:42 on May 25, 2016 ยท (Permalink)*
Yeah, it's easier to say something like: if you shuffled a deck of cards randomly a billion times a second since the beginning of the universe, you'd still today only be a little over a third of the way through the possible combinations.
Another fun math fact involving powers: when we ran out of IPv4 addresses, and came up with IPv6, we really fixed the problem. IPv4 addresses are a 32 bit number, and IPv6 addresses are a
64 bit128 bit (oops) number. This means that there are 4.3 billion IPv4 addresses in total, but there are more IPv6 addresses than there are atoms in the observable universe.Teo222 ยท 10 points ยท Posted at 16:38:10 on May 25, 2016 ยท (Permalink)
Actually we fixed it by 25 orders of magnitude more than you think. It's 128 bit..
Pm_me_any_dragon ยท 6 points ยท Posted at 16:50:59 on May 25, 2016 ยท (Permalink)
And we still dont get uniqueones from our isp.
I hate dealing with port forwarding.
You could easily give each user a 32 bit segment and still have no problem at all, fitting all devices
shinyM ยท 4 points ยท Posted at 16:59:22 on May 25, 2016 ยท (Permalink)
I was trying to explain this to co-workers who didn't quite understand the magnitude. They just believed that the number of addresses went up by a power of 6.
I explained to them like this:
Our current IPv4 internet has 232 addresses -- including the ones already reserved. IPv6 has 2128 addresses. an IPv4 /30 block (1 network address, 1 broadcast address, 2 usable addresses) is akin to an IPv6 /126 address.
So -- an IPv6 /96 block is the size of our current IPv4 internet.
a /95 block is 2 IPv4 internets. a /94 block is 4 IPv4 internets [...] a /64 block is is 232 IPv4 internets. Meaning that if every single IP address in an IPv4 block had its own separate, full IPv4 internet -- that's the number of addresses you'd have.
... and then their heads would explode when we advised that we were designating /48 blocks to our enterprise customers. :)
I think we'll have enough addresses for a little while...
ThellraAK ยท 1 points ยท Posted at 17:01:16 on May 25, 2016 ยท (Permalink)
https://xkcd.com/865/
Is saying nanobots a few microns large could only devour half of the earth though.
ChipsHanden ยท 1 points ยท Posted at 17:28:25 on May 25, 2016 ยท (Permalink)
Yeah, but when IPv4 first came around, engineers across the globe would tout "you'll never need more addresses than this. This is good."
Then, whaddaya know, we ran out of IPv4 addresses ahaha. Now this isn't to say we're poised to build and connect more devices than there are atoms in the observable universe, but virtualization is only getting more popular. It may not be within our lifetime, but we will run out of IPv6 addresses as well.
xiaodown ยท 2 points ยท Posted at 21:09:32 on May 25, 2016 ยท (Permalink)
Every virtualized system will require at least multiple atoms to track its state. That's not going to be what does us in. What does us in is people handing out /32's to ISPs and hosting companies, probably.
sirdaveyboy ยท 6 points ยท Posted at 16:04:18 on May 25, 2016 ยท (Permalink)
I thought he was just being flamboyant with the exclamation point. I was an English major.
amazondrone ยท 2 points ยท Posted at 18:57:53 on May 25, 2016 ยท (Permalink)
Gotta be careful with those exclamation marks after numbers!
/r/unexpectedfactorial
IsThisMeta ยท 5 points ยท Posted at 15:21:48 on May 25, 2016 ยท (Permalink)
It did a good job of giving me an idea of the immense scale, kinda like that black hole video floating around reddit
statdance ยท 10 points ยท Posted at 14:55:26 on May 25, 2016 ยท (Permalink)
That's the point?
DigitalChocobo ยท 1 points ยท Posted at 04:38:35 on May 26, 2016 ยท (Permalink)
I think the point of the explanation is to explain how big the number is, not make the reader lose track of it.
T3C_Illuzion ยท 2 points ยท Posted at 14:56:24 on May 25, 2016 ยท (Permalink)
I believe that is kind of the point. The number is almost too big to comprehend.
JTswift ยท 4 points ยท Posted at 15:01:02 on May 25, 2016 ยท (Permalink)
Ok, let me try and explain the point I was going for.
That example is too tough to imagine. Therefore, it makes me even question if the math is correct (because I'm not going to do the math myself).
If the example is at least somewhat relatable, then I can begin to imagine it and really comprehend the size of the number.
T3C_Illuzion ยท 2 points ยท Posted at 15:05:26 on May 25, 2016 ยท (Permalink)
That's a good point which I had not considered. In any case it is a fun example, if a little hard to understand.
AudioBlood727 ยท 2 points ยท Posted at 15:18:10 on May 25, 2016 ยท (Permalink)
The point is that there is no way to represent this number in a way that makes sense to you. I've read, can't remember where, that numbers above 1 million are basically impossible for the human brain to actually conceptualize so we just generally imagine it. Assuming that's a low ball estimate and we can really imagine a million millions (also known as 1 trillion) then you would still need a trillion trillions. Times a trillion trillions. Times a trillion trillions(almost, a bit shy).
What I'm saying is that there is no way to make this description make sense because it its orders of magnitudes larger than our ability to even comprehend a number. To make this understandable would require cutting it up into steps less than a million, which would be a 16 part process that would get confusing very quickly because, again, the numbers just stop meaning anything to you.
creepyeyes ยท 3 points ยท Posted at 15:35:12 on May 25, 2016 ยท (Permalink)
You could make it make sense just by using concrete measurements like time and distance alone. I don't know how many drops of water are in the Pacific ocean, a drop of water is a subjective unit of measure and the Pacific borders other bodies of water
AudioBlood727 ยท 1 points ยท Posted at 15:59:51 on May 25, 2016 ยท (Permalink)
The problem is those numbers wont mean anything to you. As another reply stated "1 million seconds is 11 days. 1 billion seconds is 31 years." As you can see, moving up an order of magnitude makes a big difference. Now you need to move up another 19 times. The numbers are just too big to do anything meaningful which is, again, the whole point.
JTswift ยท 3 points ยท Posted at 15:39:46 on May 25, 2016 ยท (Permalink)
1 million seconds is 11 days. 1 billion seconds is 31 years.
SKR47CH ยท 1 points ยท Posted at 15:45:16 on May 25, 2016 ยท (Permalink)
Do trillion.
ChrisOfTheReddit ยท 1 points ยท Posted at 16:08:33 on May 25, 2016 ยท (Permalink)
31,689 Years
SKR47CH ยท 1 points ยท Posted at 16:24:45 on May 25, 2016 ยท (Permalink)
That's very exact. Or are you rounding up.
ChrisOfTheReddit ยท 1 points ยท Posted at 17:07:07 on May 25, 2016 ยท (Permalink)
https://www.wolframalpha.com/input/?i=1+trillion+seconds
JTswift ยท 1 points ยท Posted at 17:13:54 on May 25, 2016 ยท (Permalink)
1 trillion seconds is 32,000 years.
Denroll ยท 1 points ยท Posted at 17:12:17 on May 25, 2016 ยท (Permalink)
Tell me about it. I had a good start going, then the moon slammed into my stack of paper and knocked it over. That's bullshit!
youngeng ยท 1 points ยท Posted at 17:35:47 on May 25, 2016 ยท (Permalink)
Check out https://en.wikipedia.org/wiki/Graham%27s_number. It's mind-boggling.
JTswift ยท 1 points ยท Posted at 17:48:55 on May 25, 2016 ยท (Permalink)
Bleh.
modestexhibitionist ยท 1 points ยท Posted at 18:29:07 on May 25, 2016 ยท (Permalink)
Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.
NotRoryWilliams ยท 1 points ยท Posted at 18:38:10 on May 25, 2016 ยท (Permalink)
I've heard it put more simply, just that it's a statistical near certainty that no two shuffles have ever been the same.
I've interpreted this to imply that shuffling isn't really that important, and when I deal at poker night I typically just cut it once, fold it into itself, and cut it again. That adds enough uncertainty and I'm pretty sure that the odds of ever seeing the same deal come out of two deals in a night, or even in the course of our three month tournaments, are astronomical.
ATXBeermaker ยท 1 points ยท Posted at 18:41:21 on May 25, 2016 ยท (Permalink)
Another way to think about it is to consider the fact that every time you shuffle a deck of cards there is a nearly 100% chance that the resulting order is completely unique in human history, assuming a legit, random shuffling.
[deleted] ยท 1 points ยท Posted at 03:09:32 on May 26, 2016 ยท (Permalink)
It's from VSauce
mainsworth ยท 0 points ยท Posted at 15:43:00 on May 25, 2016 ยท (Permalink)
It's like trying to imagine how fat your mom is.
JTswift ยท 1 points ยท Posted at 17:14:21 on May 25, 2016 ยท (Permalink)
That's what I mean....it's an absurd number.
mainsworth ยท 1 points ยท Posted at 17:47:37 on May 25, 2016 ยท (Permalink)
Because like, how does she do it? 57 with that figure?
ktkps ยท 5 points ยท Posted at 12:17:01 on May 25, 2016 ยท (Permalink)
Gimme a visual cue to imagine this
JackFlynt ยท 21 points ยท Posted at 13:46:25 on May 25, 2016 ยท (Permalink)
Let's say there are 7 billion people on Earth. Now, for each person, you make a tiny model of the Earth, complete with 7 billion tiny model people. This is the second iteration of "people" and it contains about 4.9E19 model people. But that's not enough, so in every model, you add 7 billion even tinier Earths, with their own people. That's the third iteration.
It takes SEVEN ITERATIONS to get to a number of people that's larger than 52!. Almost exactly 10 times larger, in fact. This isn't a very good cue, I suppose, but it's a really difficult number to visualise however you go about it.
necrow ยท 16 points ยท Posted at 13:57:16 on May 25, 2016 ยท (Permalink)
I like this so much better than the original. Ive always hated that one cause it adds so many unnecessary steps and details.
[deleted] ยท 2 points ยท Posted at 14:38:55 on May 25, 2016 ยท (Permalink)
The number of possible outcomes is approximately the same (1068) as the number of atoms in our galaxy.
A_Wizzerd ยท 0 points ยท Posted at 13:48:08 on May 25, 2016 ยท (Permalink)
Ok, this is the planet earth.
Start by picking your favorite spot on the equator. You shuffle the deck of cards once every second. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. After you complete your round the world trip, remove one drop of water from the Pacific Ocean.
Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time youโve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits havenโt even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers.
So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still wonโt do it. There are still more than 5.385e67 seconds remaining. Youโre just about a third of the way done.
ktkps ยท 1 points ยท Posted at 06:21:15 on May 26, 2016 ยท (Permalink)
you mean as long as one DBZ saga?
A_Wizzerd ยท 1 points ยท Posted at 08:04:43 on May 26, 2016 ยท (Permalink)
Almost
Kildragoth ยท 12 points ยท Posted at 11:56:14 on May 25, 2016 ยท (Permalink)
If we had a road to the sun and we got in a car travelling at 65mph toward the sun we'd burn up before we got there. But if we couldn't burn from it we'd die of radiation poisoning. But say space relating things couldn't kill us we'd still die of old age.
avocadoclock ยท 2 points ยท Posted at 14:46:43 on May 25, 2016 ยท (Permalink)
This thread is for math facts, not science facts!
ArthurJason ยท 3 points ยท Posted at 19:14:27 on May 25, 2016 ยท (Permalink)
I honestly couldn't believe it, because it sounded so absurd. I fired up Wolfram Alpha to proof your calculation.
We shuffle the deck every second. So the ammount of seconds it takes us to go around the earth will be equal to the number of times we shuffled the deck. We move with the speed v of 1m/1billion years. Our distance s is the length of the equator. Formula is t=v/s, which leaves us with 1.2638057ร1024 shuffles for "running" the whole distance once.
Every time we do that, we remove one water droplet from the pacific ocean. We assume that one water droplet has a volume of 50ยตl (0.05ml), I couldn't find a value on Wolfram Alpha for that. To get the number of times we have to remove a droplet, we take the voulme of the pacific and divide it by the volume of a water droplet, which leaves us with 1.32ร1025 number of times to empty the ocean.
Last but not least we put papers on top of each other for every time we emptied the ocean. To get the number of papers we need we divide the distance from sun to earth by the thickness of paper. This leaves us with 1.492ร1015 papers.
Because we have to complete one task to take a step in the next one we mulitply the value of every task. This leaves us with 2.488ร1064 shuffles after building the tower once. If we do that one thousand times more now, we will end up with 2.488ร1067. Because this was just one third of the whole way, we also multiply by 3.
Our final equation gives us 7.465ร1067 shuffles, which is still around 0.5*1067 off to the ammount of possible combinations of 51! = 8.066ร1067.
Wow, this was indeed a very cool, yet totaly arbitrary fact!
c0me_at_me_br0 ยท 10 points ยท Posted at 11:22:53 on May 25, 2016 ยท (Permalink)
Holy fuck.
Sacamato ยท 4 points ยท Posted at 15:14:33 on May 25, 2016 ยท (Permalink)
And then after you've completed a thousand stacks of paper to the sun, take another lap around Black Mountain!
I see you in the wild all the time, man.
c0me_at_me_br0 ยท 2 points ยท Posted at 15:22:04 on May 25, 2016 ยท (Permalink)
Oh god no. Never.
And yes, I do venture outside of the collective running subs quite often.
thehighschoolgeek ยท 4 points ยท Posted at 12:29:16 on May 25, 2016 ยท (Permalink)
Vsauce!
blue_nebula ยท 3 points ยท Posted at 14:40:52 on May 25, 2016 ยท (Permalink)
What number does Vsauce! make?
thehighschoolgeek ยท 2 points ยท Posted at 15:14:24 on May 25, 2016 ยท (Permalink)
Vsauce! =A ton load of awesomeness
Bandin03 ยท 2 points ยท Posted at 17:18:42 on May 25, 2016 ยท (Permalink)
Converting Vsauce from base 36 to base 10 comes up with 1921986590!
I don't know how to calculate how many digits would be in that number though.
blue_nebula ยท 1 points ยท Posted at 22:00:19 on May 25, 2016 ยท (Permalink)
Obviously a fuck-ton
chengiz ยท 2 points ยท Posted at 14:47:23 on May 25, 2016 ยท (Permalink)
Well walk faster dammit.
SlaveAmbient ยท 2 points ยท Posted at 15:43:12 on May 25, 2016 ยท (Permalink)
My nose just started bleeding
Flater420 ยท 2 points ยท Posted at 08:17:38 on May 26, 2016 ยท (Permalink)
I always liked QI's illustration of the number better:
[deleted] ยท 1 points ยท Posted at 14:17:00 on May 25, 2016 ยท (Permalink)
that's 80 unvigintillion
zicronblade ยท 1 points ยท Posted at 14:27:35 on May 25, 2016 ยท (Permalink)
Yeah, but there are 60! ways to shuffle my modern deck, and they all leave me land flooded.
enderarchmage ยท 1 points ยท Posted at 18:24:03 on May 25, 2016 ยท (Permalink)
highfive
Harvey_Rabbit ยท 1 points ยท Posted at 14:57:53 on May 25, 2016 ยท (Permalink)
Similarly,I like to demonstrate how many possible bingo cards there are. ((15x14x13x12x11)5)/11 = 552446474061128648601600000
tacosaladchupacabra ยท 1 points ยท Posted at 15:03:12 on May 25, 2016 ยท (Permalink)
I tried this, but the sun kept burning down my paper stack
Tarantio ยท 1 points ยท Posted at 15:11:17 on May 25, 2016 ยท (Permalink)
This means that every time you shuffle a deck of cards, that order has never existed before in the universe.
Even if everyone who ever lived had each shuffled a deck of cards once a second for the entire age of the universe, the odds would be against a single replicated order.
AichSmize ยท 1 points ยท Posted at 15:19:48 on May 25, 2016 ยท (Permalink)
Slightly different:
Take one step every billion years.
Every time you go around the world, buy a lottery ticket.
Whenever the lottery wins the grand prize, drop one grain of sand in the Grand Canyon (USA).
Whenever the Grand Canyon fills up, empty it and remove one gram of mass from Mount Everest.
When Everest is flattened, rebuild it.
Do that 36 times and you have reached 52! years.
DrivingPark ยท 1 points ยท Posted at 15:30:24 on May 25, 2016 ยท (Permalink)
I bet my favorite spot on the equator is better than yours.
mermaidrampage ยท 1 points ยท Posted at 15:30:49 on May 25, 2016 ยท (Permalink)
Damn. Reminds me of the Built to Spill song "Randy Describes Eternity"
https://www.youtube.com/watch?v=Kb1RlzyWHm4
WhiskeyOnASunday93 ยท 1 points ยท Posted at 15:45:50 on May 25, 2016 ยท (Permalink)
Fuck
crossedstaves ยท 1 points ยท Posted at 15:45:53 on May 25, 2016 ยท (Permalink)*
Yeah, but i'm not playing a game where suit matters, so honestly I don't care about how the unique arrangement of suits. So for all 13 card values we have what 4! ways of arranging them in the deck and we compound those to be 13*4! ways to permute the deck into equivalent states. Well that gets me down to about 2.5*1065 nearly three orders of magnitude. That's still a lot to worry about, so well maybe all I'm a lazy black players and all I care about is face cards. so let's say 10,J,Q,K,A. Then 2-9 can be permuted freely so that's another 8! . Now I'm down to like 6*1060 . Which is still a whole mess of ways to assemble cards. Its gone down by a factor of like 10,000,000 but I'm still in a losing battle.
Anyway... I didn't have any point at all.
anamericandude ยท 1 points ยท Posted at 15:52:34 on May 25, 2016 ยท (Permalink)
In other words it's fucking incredible for me to pick up 7 2 3 times in a row
Trosso ยท 1 points ยท Posted at 15:57:32 on May 25, 2016 ยท (Permalink)
suddenly i understand what eternity means.
DocJawbone ยท 1 points ยท Posted at 16:04:02 on May 25, 2016 ยท (Permalink)
I just feel like you'd have trouble with paper too near to the sun.
aslum ยท 1 points ยท Posted at 16:05:00 on May 25, 2016 ยท (Permalink)
This reminds me of the song Randy Describes Eternity by Built to Spill
KingKidd ยท 1 points ยท Posted at 16:05:03 on May 25, 2016 ยท (Permalink)
Question: can you empty one ocean without emptying all of them? They're all connected.
Free_Rick_Sanchez55 ยท 1 points ยท Posted at 16:05:28 on May 25, 2016 ยท (Permalink)
Ok, settle down Michael
BallisticSnowman ยท 1 points ยท Posted at 16:10:31 on May 25, 2016 ยท (Permalink)
Wow
eltoro ยท 1 points ยท Posted at 16:13:10 on May 25, 2016 ยท (Permalink)
In effect, you can say with fairly high confidence that no two decks of cards in the world are in the same order if they have been shuffled.
Dannyprecise ยท 1 points ยท Posted at 16:30:26 on May 25, 2016 ยท (Permalink)
Mother fucker, this is sorcery.
toddbbot ยท 1 points ยท Posted at 16:37:40 on May 25, 2016 ยท (Permalink)
I've posted this before in similar threads but:
The possible permutations of a deck of cards (52!) is roughly equal to the number of atoms in the Milky Way galaxy.
52! = 8 x 1067
mass of Milky Way = 6 x 1045 g
atoms/g (~75% hydrogen) ~ 1 x 1023
atoms in Milky Way ~ 6 x 1068
Pyran ยท 1 points ยท Posted at 16:41:52 on May 25, 2016 ยท (Permalink)
Or put another way, every time you shuffle a deck of cards you put them in an order that has never before been seen anywhere in the history of the universe.
merlin401 ยท 1 points ยท Posted at 16:42:05 on May 25, 2016 ยท (Permalink)
This is obvious, but still a cool fact: When you shuffle the deck of cards and deal, it is almost certain that a deck of cards has ever existed in that order before or ever will again.
AmishElectricity49 ยท 1 points ยท Posted at 16:49:43 on May 25, 2016 ยท (Permalink)
I thought the stack of paper was to the moon not the sun but I may be wrong.
klseu8 ยท 1 points ยท Posted at 16:51:48 on May 25, 2016 ยท (Permalink)
this is a really confabulated explanation
Kryonixc ยท 1 points ยท Posted at 16:58:52 on May 25, 2016 ยท (Permalink)
So what are the chances to shuffle a deck of cards 52! times in a row getting the same result every single time? Did I break math?
ticktockaudemars ยท 1 points ยท Posted at 17:03:46 on May 25, 2016 ยท (Permalink)
I read this like an Old Spice Commerical.
reddixmadix ยท 1 points ยท Posted at 17:06:28 on May 25, 2016 ยท (Permalink)
If i remember Numberphile correctly, this number is bigger than the number of particles in the universe, or something like that.
iamreddy44 ยท 1 points ยท Posted at 17:10:37 on May 25, 2016 ยท (Permalink)
I don't like it , it's not really intuitive so I tried to come up with my own.
If every planet in the entire universe had as much grains of sand as the Earth ,
and in each of these grains lived 7 billion people which can shuffle a deck every second ,
they would need to shuffle from the Big Bang until now to come up with the nr of possible permutations.
Hope I didn't mess any calculations.
asgeorge ยท 1 points ยท Posted at 17:16:43 on May 25, 2016 ยท (Permalink)
How would you pass the remaining 2/3rds of the time?
Start by dealing yourself 5 random cards. Once every billion years.
When you finally deal yourself a royal flush, buy yourself a lottery ticket.
If the ticket wins the lottery, throw a single grain of sand into the Grand Canyon.
As soon as the Grand Canyon is completely filled with sand, remove one ounce (28g) of rock from Mt. Everest.
Empty the Grand Canyon and start again. Repeat until Mt. Everest has been leveled.
Then put Mt. Everest back together and do this whole thing 256 times and the remaining time will have been spent.
[deleted] ยท 1 points ยท Posted at 17:23:43 on May 25, 2016 ยท (Permalink)
For anyone who doesn't know, 52! means 52x51x50x49 and so on until you get to 1. It's not just 52 but said with more enthusiasm
SOAR21 ยท 1 points ยท Posted at 17:26:27 on May 25, 2016 ยท (Permalink)
So, it's statistically probable that of all the truly random shuffles in history of all the 52-card decks from anywhere in the world are unique?
darksingularity1 ยท 1 points ยท Posted at 17:27:56 on May 25, 2016 ยท (Permalink)
Too bad the sun is going to go out after like 4 or 5 of those steps.
LeonardSmallsJr ยท 1 points ยท Posted at 18:03:51 on May 25, 2016 ยท (Permalink)
Combining this with thedeejus post above, if you were to actually do all of this (shuffling cards every second while slowly circling the Earth, draining the Pacific, and stacking paper toward the sun 3000 times), the probability of reshuffling at any time back to a deck like new (unshuffled) is approximately 63%.
My mind is blowing up today.
drinks_antifreeze ยท 1 points ยท Posted at 18:05:40 on May 25, 2016 ยท (Permalink)
Christ.
_JustAnAwfulPerson ยท 1 points ยท Posted at 18:24:09 on May 25, 2016 ยท (Permalink)
I watch VSauce too
MrTheoRiZE ยท 1 points ยท Posted at 18:41:59 on May 25, 2016 ยท (Permalink)
Nothing is anything and we're all going to die, comes to mind.
Haighstrom ยท 1 points ยท Posted at 18:48:34 on May 25, 2016 ยท (Permalink)
What is "one drop"? That's not a unit!
Bumble217 ยท 1 points ยท Posted at 18:49:49 on May 25, 2016 ยท (Permalink)
Saved for later. I am going to blow someones mind with this when I get home. Thanks!
DlProgan ยท 1 points ยท Posted at 18:56:31 on May 25, 2016 ยท (Permalink)
That makes me wonder what kind of example the guys would come up with to picture how many type of Magic The Gathering decks and shuffles you could play with (the game got ~15.000 different cards).
WG95 ยท 1 points ยท Posted at 18:57:55 on May 25, 2016 ยท (Permalink)
r/expectedfactorial
maz-o ยท 1 points ยท Posted at 19:05:43 on May 25, 2016 ยท (Permalink)
but where is he putting all the drops?
HadYouKen ยท 1 points ยท Posted at 19:21:25 on May 25, 2016 ยท (Permalink)
Shit I got this question wrong on my discrete mathematics final. Now I'm worried for my grade
beingforthebenefit ยท 1 points ยท Posted at 19:23:55 on May 25, 2016 ยท (Permalink)
59! is approximately the number of atoms in the observable universe.
avenlanzer ยท 1 points ยท Posted at 19:32:15 on May 25, 2016 ยท (Permalink)
But the distance from he earth to the sun will change in that time.
[deleted] ยท 1 points ยท Posted at 19:38:31 on May 25, 2016 ยท (Permalink)
Why one step every billion years?
PublicAccount1234 ยท 1 points ยท Posted at 19:55:06 on May 25, 2016 ยท (Permalink)
I think you're going to need to walk faster to manage to walk the equator and not drown.
FishDawgX ยท 1 points ยท Posted at 19:57:57 on May 25, 2016 ยท (Permalink)
My favorite algorithm (on a computer) for shuffling a deck of cards is fairly simple and produces a truly random order where every one of the 52! possible orders is possible and equally likely.
(Linear time complexity and the shuffle is done in place with no extra storage space.)
superbungalow ยท 1 points ยท Posted at 21:10:57 on May 25, 2016 ยท (Permalink)
What timer? You never established a timer?
Roftastic ยท 1 points ยท Posted at 21:24:58 on May 25, 2016 ยท (Permalink)
Reading that just made me nauseous.
colbymg ยท 1 points ยท Posted at 22:03:37 on May 25, 2016 ยท (Permalink)
at that speed, plate techtonics would play a larger role in your travels than walking ;)
tojoso ยท 1 points ยท Posted at 22:07:55 on May 25, 2016 ยท (Permalink)
I've heard it put this way: for any given shuffle of a deck of cards, it is more likely than not that it is the first time the cards have been shuffled into that order.
Chameleonpolice ยท 1 points ยท Posted at 22:11:09 on May 25, 2016 ยท (Permalink)
Sorry I just read about graham's number so 52! No longer scares me
grammascookies ยท 1 points ยท Posted at 22:17:44 on May 25, 2016 ยท (Permalink)
Wow that's insane. I remember hearing that there is an extremely high chance that when you shuffle a deck of cards, that that combination has never been made before. Interesting stuff!
TILtonarwhal ยท 1 points ยท Posted at 22:37:31 on May 25, 2016 ยท (Permalink)
So it's pretty safe to say that nobody has ever shuffled a deck of cards the same way that any deck of cards has been before.
(obviously this doesn't include intentional stacking of the deck in a certain way such as in ascending order and by suit or something like that)
Jonners_chester ยท 1 points ยท Posted at 22:46:58 on May 25, 2016 ยท (Permalink)
Are there any two decks of cards that have truly been shuffled in the same order then?
KypDurron ยท 1 points ยท Posted at 23:05:05 on May 25, 2016 ยท (Permalink)
What if we don't have one?
[deleted] ยท 1 points ยท Posted at 23:06:02 on May 25, 2016 ยท (Permalink)
The way I came up with to explain it to someone is that if you made a path equal in length to that number (in metres) then the diameter of the whole observable universe would be a tiny, insignificant blip on that line
cezane279 ยท 1 points ยท Posted at 23:35:46 on May 25, 2016 ยท (Permalink)
Vsauce!
Trofont ยท 1 points ยท Posted at 01:20:44 on May 26, 2016 ยท (Permalink)
The version I heard: A trillion galaxies, each with a trillion stars, each with a trillion planets, each with a trillion people, each with a 1000 decks of cards, each shuffling every deck every second since the dawn of time. There would still be combinations that never existed.
0kZ ยท 1 points ยท Posted at 02:41:06 on May 26, 2016 ยท (Permalink)
Did you c/c this ? http://czep.net/weblog/52cards.html
udbluehens ยท 1 points ยท Posted at 03:01:29 on May 26, 2016 ยท (Permalink)
See, you know how I know that's a small number, because you can still point out physical things as analogies. The real big numbers you can barely do that with the number of operations involved, and the really big numbers it stops completely.
ernesto_shaves ยท 1 points ยท Posted at 03:13:01 on May 26, 2016 ยท (Permalink)
And still only a 63% chance you have it in a sequence that has been done before.
upstateman ยท 1 points ยท Posted at 05:06:07 on May 26, 2016 ยท (Permalink)
I am a bit confused by this. Are we doing one shuffle per second? Or one order? The number of random shuffles to have a 99% chance of getting all possibilities is a lot bigger than the number of possibilities.
And is the Pacific re-filling from the other oceans?
gp133 ยท 1 points ยท Posted at 06:50:43 on May 26, 2016 ยท (Permalink)
That is the most intricate way I have ever seen to explain how big a really big number is. I really enjoyed that!
MrFisterrr ยท 1 points ยท Posted at 08:47:40 on May 26, 2016 ยท (Permalink)
This is what I imagine hell would be like
greezeh ยท 1 points ยท Posted at 10:16:53 on May 26, 2016 ยท (Permalink)
I saw a different way of explaining this on Q.I. If you give a billion packs of cards to a billion different people on a billion different planets and get them to shuffle them at 15,000 per minute since the beginning of time. Then we'd only just be repeating shuffles. Something like that. I don't remember exactly but its a crazy thing to think about.
PewPewLaserss ยท 1 points ยท Posted at 10:51:31 on May 26, 2016 ยท (Permalink)
Vsauce ;)
PewPewLaserss ยท 1 points ยท Posted at 10:51:31 on May 26, 2016 ยท (Permalink)
Vsauce ;)
MickletheDillPickle ยท 1 points ยท Posted at 00:16:27 on May 27, 2016 ยท (Permalink)
I saw this on a Vsauce video, I find this so interesting! Math is so fun.
gamingonion ยท 1 points ยท Posted at 14:04:09 on May 25, 2016 ยท (Permalink)
At least give credit
BeardFace5 ยท 0 points ยท Posted at 13:49:11 on May 25, 2016 ยท (Permalink)
Wait, why are we walking so slow?
MAADcitykid ยท 0 points ยท Posted at 15:30:43 on May 25, 2016 ยท (Permalink)
What a terrible and unrelatable example
FetchFrosh ยท 447 points ยท Posted at 11:33:58 on May 25, 2016 ยท (Permalink)
I don't know if this counts as a math fact, but it's my favorite math puzzle. I guess the fact would be the solution. Anyway, it would be the Konigsburg Bridge Problem.
It's an interesting mathematics puzzle that laid the foundation for graph theory. I remember going through it once in school for reasons that I can't quite remember now.
The problem from the outset is pretty simple. You have four landmasses with a series of seven bridges between them, pictured here. Now, what you need to do is find a path that will cross each bridge exactly once. Try it out for a minute and see how you do.
Now that you're back, you're probably telling me that it's impossible. Well, you're right. So now, the question is, why? Why can you not cross each of the bridges exactly once? I'll give you some hints if you need them, but try and figure it out.
Hint #1: Draw the landmasses as nodes and the bridges as lines between them. If you don't know what I mean by that, here's an example.
Hint #2: Add one bridge and try to find a route that will go across all eight of these bridges. Give it a minute and you'll be able to find a path
Hint #3: Count how many bridges each island has. What do you notice about the numbers? What changes when the eighth bridge was added in Hint #2
Hint #4: Other than the start and end point, when you cross a bridge to get to an island, you must also cross one to leave. What does this mean for each non-endpoint bridge?
Solution: In order to cross all of the bridges between any number of landmasses exactly once, you must have exactly 0 or 2 landmasses which have an odd number of bridges. The reason for this is that each time you enter a new landmass, you must also leave it to go to the next one, meaning that you will cross an even number of bridges each time. The exception is the start and endpoints. In those cases you either don't have to enter or don't have to leave. If you have two landmasses with an odd number, you will start and finish in different places. If you have none, you can start and finish anywhere.
sjf13 ยท 509 points ยท Posted at 14:55:14 on May 25, 2016 ยท (Permalink)*
Well, I can do it if I circumnavigate the globe to get to the final bridge.
see?
Schrockwell ยท 251 points ยท Posted at 15:44:38 on May 25, 2016 ยท (Permalink)
Well, then that's only 3 landmasses.
That satisfies the condition for the solution. :)
tdug ยท 29 points ยท Posted at 17:16:11 on May 25, 2016 ยท (Permalink)
You could swim across a river once.
Sssiiiddd ยท 2 points ยท Posted at 00:43:28 on May 26, 2016 ยท (Permalink)
Or jump really far...
QuintusVS ยท 1 points ยท Posted at 11:47:48 on May 27, 2016 ยท (Permalink)
Doesn't have to be a big river, could just be a creak.
Cgdb10 ยท 1 points ยท Posted at 23:12:30 on May 25, 2016 ยท (Permalink)
I'm a great swimmer
Potatospazm54321 ยท 12 points ยท Posted at 16:39:43 on May 25, 2016 ยท (Permalink)
Okay Pacman
sjf13 ยท 7 points ยท Posted at 17:24:14 on May 25, 2016 ยท (Permalink)
waka waka
WeaponsGradeHumanity ยท 23 points ยท Posted at 15:56:06 on May 25, 2016 ยท (Permalink)
Lol, check out this guy - he thinks the world is a globe!
sjf13 ยท 21 points ยท Posted at 16:14:24 on May 25, 2016 ยท (Permalink)
Don't be silly. This solution works just as well on a cylinder.
AsterJ ยท 3 points ยท Posted at 18:38:13 on May 25, 2016 ยท (Permalink)
That's something you'd cover in a topology class, along with doing the same thing on a donut / cylinder.
Meatslinger ยท 2 points ยท Posted at 18:43:48 on May 25, 2016 ยท (Permalink)
Now you're thinking in 3D!
imgonnacallyouretard ยท 2 points ยท Posted at 18:51:38 on May 25, 2016 ยท (Permalink)
Unfortunately the real problem states you must be walking in Konigsberg :(
Moikepdx ยท 2 points ยท Posted at 20:39:31 on May 25, 2016 ยท (Permalink)
This guy is going places.
dwapb ยท 3 points ยท Posted at 15:14:56 on May 25, 2016 ยท (Permalink)
brilliant!
Et_tu__Brute ยท 1 points ยท Posted at 20:49:08 on May 25, 2016 ยท (Permalink)
I mean, you could also go up around the headwaters of your river system or take a ferry, steal a canoe or a number of other things that destroy the spirit of the question.
Randomd0g ยท 1 points ยท Posted at 23:21:33 on May 25, 2016 ยท (Permalink)
Fairly easy. You just have to utilise the half A press and then travel to parallel universes.
Extramrdo ยท 1 points ยท Posted at 02:45:59 on May 26, 2016 ยท (Permalink)
A portal gun would also work, as would
stretching your hand out really far to reach the middle of a bridge, then doing the same from the other sidechopping off your limbs one by one and tossing them across the bridges. If you're strong, you could bend one of the bridges so it points back at the land mass you just tried to leave.[deleted] ยท 1 points ยท Posted at 13:47:33 on May 26, 2016 ยท (Permalink)
edgy
Prod_Is_For_Testing ยท 1 points ยท Posted at 18:34:51 on May 25, 2016 ยท (Permalink)
I think you win
sjf13 ยท 1 points ยท Posted at 18:39:58 on May 25, 2016 ยท (Permalink)
By the way, working in IT, your username is making me twitch.
Prod_Is_For_Testing ยท 2 points ยท Posted at 18:41:19 on May 25, 2016 ยท (Permalink)
By the way, I'm a software developer. MWAHAHAHA
valeyard89 ยท 78 points ยท Posted at 14:39:33 on May 25, 2016 ยท (Permalink)
I tried walking the bridges when I was in Koeninsburg (Kaliningrad). But there's only 4 bridges remaining, so you can do it.
palordrolap ยท 6 points ยท Posted at 22:06:57 on May 25, 2016 ยท (Permalink)
If I remember rightly, there was only a very tiny window of time where Kรถnigsburg had the seven particular bridges that Euler was thinking about.
This provides an alternative solution: "Wait for someone to build another bridge, or else destroy one, so we can start again!"
[deleted] ยท 35 points ยท Posted at 15:39:10 on May 25, 2016 ยท (Permalink)
I'm an engineer and I can get 6/7 so I'll call it an empirical approximation of your problem.
ThalanirIII ยท 1 points ยท Posted at 17:36:10 on May 25, 2016 ยท (Permalink)
except its a real-life problem - e.g.quick delivery times for a postal service, where petrol consumption adds up when you're being inneficient. None of your engineering approximations over here. Its an application of Eulerian graphs as a part of decision or discrete maths, which has a lot of applications.
mikronaut ยท 19 points ยท Posted at 14:27:03 on May 25, 2016 ยท (Permalink)
I just studied this in discreet math
TyeDyeShirtKid ยท 26 points ยท Posted at 15:51:13 on May 25, 2016 ยท (Permalink)
If it's discreet math you probably shouldn't be telling us about it.
roh8880 ยท 7 points ยท Posted at 16:42:06 on May 25, 2016 ยท (Permalink)
The first rule of discreet math is that you do not talk about discreet math.
mattenthehat ยท 2 points ยท Posted at 22:52:26 on May 25, 2016 ยท (Permalink)
Because people call you a nerd and ask you to leave.
MisterJose ยท 30 points ยท Posted at 15:27:20 on May 25, 2016 ยท (Permalink)
Discreet math? whispers "Psst. Two plus two is four."
Tavyr ยท 9 points ยท Posted at 15:09:02 on May 25, 2016 ยท (Permalink)
If anyone wants the technical graph theory definition of the theorem: "A connected, undirected graph has an Eulerian cycle if and only if every vertex has even degree."
ThalanirIII ยท 5 points ยท Posted at 17:37:34 on May 25, 2016 ยท (Permalink)*
Where an Eulerian cycle is one which crosses each node and returns to its start point without returning over the crossed edges.
There's also semi-Eulerian
cyclesgraphs with 2 odd-degree nodes, in which you must start at one odd node and finish at the other.edit - semi-eulerian graphs, not cycles
Tavyr ยท 2 points ยท Posted at 17:55:20 on May 25, 2016 ยท (Permalink)
Would a semi-Eulerian cycle just be an Eulerian path?
ThalanirIII ยท 1 points ยท Posted at 18:09:08 on May 25, 2016 ยท (Permalink)
In that it isn't a cycle I suppose, but I was taught that you'd describe the entire graph as eulerian/semi-eulerian if its possible to make a eulerian/semi-eulerian route. e.g this graph is semi-eulerian. Your wording made me confuse myself, so I've corrected the original.
Wingul-The-Nova ยท 4 points ยท Posted at 14:04:42 on May 25, 2016 ยท (Permalink)
Well, I figured out why it was impossible. But the rest of the solution was all a little above my problem solving ability.
[deleted] ยท 5 points ยท Posted at 16:15:24 on May 25, 2016 ยท (Permalink)
My favorite math puzzle/problem is this:
Two pastors, of two small villages, meet on a Sunday on the road between their villages. One tells the other: "There were so few people in church today, once again." The other says: "In my church too. Only 3 people were in church today! Let me give you a little quiz about the age of the three people who were in church. If you multiply their ages, you'll get 2450. But if you add their ages, you'll get the height of the church in your village!" The other pastor says he will try to figure it out, and they leave. On the next Sunday, they meet again at the same place. The one who tried to solve the problem says: "I tried and tried, but I can't seem to figure it out." The other says: "Sorry, you couldn't solve that, I forgot to give you one hint. The oldest of the 3 people is younger than our bishop." So then he could solve the puzzle.
Question: How old are the 3 people who were in church? How high is the second pastor's church? And, how old is the bishop?
I love this puzzle because at the first look it seems unsolvable, but if you think about it and find out, then it's actually pretty easy.
FirstRyder ยท 2 points ยท Posted at 17:18:27 on May 25, 2016 ยท (Permalink)
The best I could do was a range of ages for the bishop. Unless there's some minimum or maximum height for a church that I don't know about.
[deleted] ยท 6 points ยท Posted at 18:13:03 on May 25, 2016 ยท (Permalink)*
No minimum or maximum height. I'll type the solution out later!
Edit:
Solution: First, find out the possible ages for the 3 people. For that, it's easiest to split 2450 into its prime numbers: 2*5*5*7*7 = 2450 Combine them, and the possible ages are:
2 + 5 + 245 = 252
2 + 7 + 175 = 184
2 + 25 + 49 = 76
2 + 35 + 35 = 72
5 + 5 + 98 = 108
5 + 7 + 70 = 82
5 + 10 + 49 = 64
5 + 14 + 35 = 54
7 + 7 + 50 = 64
7 + 10 + 35 = 52
7 + 14 + 25 = 56
As 1 is also a possibility, also:
1 + 1 + 2450 = 2452
1 + 2 + 1225 = 1228
1 + 5 + 490 = 496
1 + 7 + 350 = 358
1 + 10 + 245 = 256
1 + 14 + 175 = 190
1 + 25 + 98 = 134
1 + 35 + 70 = 106
1 + 49 + 50 = 100
But now, the important part is, that the pastor couldn't solve the problem with this much info. He knows how high his church is, but it still wasn't possible for him to find the solution. And as there's only one sum which comes up twice, 64, that must be the height of his church, as these are the only options for which the puzzle is unsolvable for him. So, possible are 5+10+49=64, or 7+7+50=64. And, as he knew which of the two is the right answer after being told that the oldest (who is 49 or 50) is younger than the bishop, the bishop must therefore be 50, and the right answer must be 5, 10, and 49 years old.
FirstRyder ยท 2 points ยท Posted at 03:59:25 on May 26, 2016 ยท (Permalink)
Ah, of course, I forgot that while I have no idea a church can be, the other pastor is obviously able to check how high his own is even if he doesn't know it off hand.
triangularfox ยท 1 points ยท Posted at 03:30:09 on May 26, 2016 ยท (Permalink)
Brilliant!
4_out_of_5_people ยท 1 points ยท Posted at 20:16:32 on May 25, 2016 ยท (Permalink)
I tried solving this and was totally stumped right of the bat. If the product of their ages is 2450 then the average age is 816. As a full disclosure, I am the worlds dumbest person when it comes to math so it's probably me. It's been years and years since I had to do any math. I had to look up the word 'product'.
[deleted] ยท 1 points ยท Posted at 20:55:09 on May 25, 2016 ยท (Permalink)
They can't be 816, because if you multiply 816*816*816, you get a way higher number than 2450. For the average (or rather, if all 3 were the same age), it would not have to be 2450/3, but rather the third root of 2450. That's about 13. And if you calculate 13*13*13 = 2197, so that's about right, and they could be all about 13 years old. But, easier solution to get to the actual possible ages, is by using prime numbers of 2450. Solution is in the other comment!
I also couldn't solve this problem by myself, when I heard it for the first time. :D I was sure it couldn't be solved, but I found it very interesting and clever after someone told me the answer.
Raffo7777 ยท 5 points ยท Posted at 17:01:50 on May 25, 2016 ยท (Permalink)
I still could not figure out the answer to this after an hour of trying :( would someone eli5 it for me please?
Cheers!
[deleted] ยท 7 points ยท Posted at 15:09:18 on May 25, 2016 ยท (Permalink)*
Euler-nt this back in Discrete Math nerd!!!!
Pestilence86 ยท 3 points ยท Posted at 16:00:03 on May 25, 2016 ยท (Permalink)
I started thinking about what bridge (and what direction) to cross first and quickly found out the 3 surrounding masses all have 3 bridges entering, so if i enter on one, i have to exit on the second, leaving the third (and second entering) a dead end, which would be fine if my journey ended there, but i would need to go to the other landmass after. So the first move had to be entering the center mass. The second move again can not go onto any of the surrounding masses with 3 bridges, except the one i just came from (because it only has 2 unused bridges left) so i would have to go back to that one, and the third move was gonna be leaving it again over the last bridge, but that leads me to one of the masses from the beginning that i wouldn't be able to go onto because the number of bridges would always lead to one of them turning into a dead end before i can reach the last landmass.
jorellh ยท 2 points ยท Posted at 15:15:05 on May 25, 2016 ยท (Permalink)
Spiral in works
drinks_antifreeze ยท 2 points ยท Posted at 18:10:32 on May 25, 2016 ยท (Permalink)
Didn't this problem also inspire the creation of topology?
jman31500 ยท 2 points ยท Posted at 19:45:59 on May 25, 2016 ยท (Permalink)
I didn't see this part, and spent half an hour on this
lazyl ยท 2 points ยท Posted at 20:22:30 on May 25, 2016 ยท (Permalink)
Not having looked at any of your hints this is my explanation.
Only the starting and ending landmasses (which could be the same) can be connected to an odd number of bridges. All other land masses must be connected to an even number of bridges. This is obvious when you consider that every time you enter a landmass it will be via a bridge you haven't used yet. Then you must leave by a second bridge which you also haven't used yet. This means those bridges must always come in pairs, i.e. there must be an even number. In this diagram all four landmasses have an odd number of bridges and so such a path is impossible.
Theriegs ยท 2 points ยท Posted at 23:06:16 on May 25, 2016 ยท (Permalink)
Fuck me. I didn't read all of your post, so I didn't see the part where you said it's impossible. Spent a good 20 minutes trying everything thinking "THERE HAS TO BE A WAY".
pwalters64 ยท 2 points ยท Posted at 14:49:11 on May 25, 2016 ยท (Permalink)
So after trying this many many times, isn't the answer quite simple?
There is an odd number of bridges, and an even number of land.
So you would have to walk over one once more in order to evenly cross. Right?
[deleted] ยท 2 points ยท Posted at 15:55:54 on May 25, 2016 ยท (Permalink)
It doesn't have to do with even lands and odd bridges. Imagine 2 lands, and 7 bridges, and it works. Because you don't need to end where you started.
_NW_ ยท 1 points ยท Posted at 18:36:01 on May 25, 2016 ยท (Permalink)
Any location with an odd number of routes to it must either be a starting point or an ending point. One start point plus one end point means that you can have no more than two locations with an odd number of routes to it.
pokemonpasta ยท 1 points ยท Posted at 15:23:03 on May 25, 2016 ยท (Permalink)
Isn't there also a thing where if you have 1 landmass with odd number of bridges, you have a specific startpoint or endooint?
PersonUsingAComputer ยท 1 points ยท Posted at 16:49:22 on May 25, 2016 ยท (Permalink)
If you have two landmasses with an odd number of bridges, there will be a path but those two must be your starting and ending points. It's not possible to have only one landmass with an odd number of bridges leading to it. Each bridge has 2 endpoints, so the total number of bridge endpoints must be even no matter what your map looks like. If you try to make exactly 1 landmass have an odd number of bridge endpoints, there's no way the total number of bridge endpoints could end up being even.
infosackva ยท 1 points ยท Posted at 15:36:08 on May 25, 2016 ยท (Permalink)
Isn't this just the handshake lemma?
[deleted] ยท 1 points ยท Posted at 16:27:46 on May 25, 2016 ยท (Permalink)
I did a presentation on this problem a couple months ago. It's a lot more fun to talk about than a lot of other math centered things
beeeel ยท 1 points ยท Posted at 16:57:44 on May 25, 2016 ยท (Permalink)
You're slightly wrong on the solution- it's possible to do it if 1 landmass has an odd number of bridges (eg: remove the left hand to bridges), and then one end of the path has to be on that landmass.
It's a nice problem though, I remember studying it in decision maths at school.
Gingevere ยท 1 points ยท Posted at 17:10:29 on May 25, 2016 ยท (Permalink)
Just so people don't waste their time.
This problem has no solution.
graaahh ยท 1 points ยท Posted at 17:16:45 on May 25, 2016 ยท (Permalink)
I wonder if it's possible in higher dimensions.
Baggotry ยท 1 points ยท Posted at 18:33:02 on May 25, 2016 ยท (Permalink)
I remember this from graph theory.
jrr6415sun ยท 1 points ยท Posted at 21:21:32 on May 25, 2016 ยท (Permalink)
i played professor layton games too.
nevus_bock ยท 1 points ยท Posted at 21:41:13 on May 25, 2016 ยท (Permalink)
I didn't get this far in your comment as I wanted to think about it first. Spent two hours thinking about it, graphing it, and I even wrote an algorithm to figure it out. I failed and felt really stupid. Then I went back to continue reading your comment to get to the line above...
robertbastian ยท 1 points ยท Posted at 22:12:26 on May 25, 2016 ยท (Permalink)
*Kรถnigsberg
elitelightning ยท 1 points ยท Posted at 02:33:49 on May 26, 2016 ยท (Permalink)
Dude what the fuck I didn't read the "it's impossible" part and spent an hour trying to do it. I understood why it wasn't working the whole time...
demonicpigg ยท 1 points ยท Posted at 14:23:45 on May 25, 2016 ยท (Permalink)
I stumbled across this while playing a game very much like this. When I then took graph theory I was so excited I had figured this out on my own lol.
CSMastermind ยท 1 points ยท Posted at 16:49:04 on May 25, 2016 ยท (Permalink)
Lol you know you're a nerd when you open a reddit thread about math trivia and you not only know the answer to the problem but also who first solved it.
Though to be fair if you had to guess which particular mathematician solved a given problem guessing Euler will be right more often than about anyone else.
BeardFace5 ยท 0 points ยท Posted at 14:26:07 on May 25, 2016 ยท (Permalink)
I think you are missing a part of the original question. Do you have to end up on the same land mass you started?
crh23 ยท 3 points ยท Posted at 14:41:50 on May 25, 2016 ยท (Permalink)
No, you just have to cross each bridge exactly once
BeardFace5 ยท 3 points ยท Posted at 14:48:25 on May 25, 2016 ยท (Permalink)
OK... I may have been swimming unintentionally. I wondered why I was so wet... please don't make a joke
Halo_Gentleman ยท 1 points ยท Posted at 15:39:29 on May 25, 2016 ยท (Permalink)
I don't know why you're being down voted. That is part of the original problem. Although, the other people are right in which it is impossible to walk on every bridge without using a bridge twice.
Source: Just finished a semester of graph theory in college
Additional proof: http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html
BeardFace5 ยท 2 points ยท Posted at 16:34:14 on May 25, 2016 ยท (Permalink)
No I think I'm getting dv'ed because I'm an idiot and broke the rules of only one crossing per bridge and too stupid to realize it.
ubergeek0 ยท -8 points ยท Posted at 14:43:30 on May 25, 2016 ยท (Permalink)
I hope that's a missing part, cause I saw a solution right away and had a moment where I thought I was a math genius.
metalshadow ยท 8 points ยท Posted at 14:44:42 on May 25, 2016 ยท (Permalink)
Do you wanna maybe rethink those solutions?
imeanithinkso ยท 2 points ยท Posted at 14:46:49 on May 25, 2016 ยท (Permalink)
They didn't say no swimming
ubergeek0 ยท 1 points ยท Posted at 14:53:00 on May 25, 2016 ยท (Permalink)
With the missing part of the question- yes, yes I do.
metalshadow ยท 3 points ยท Posted at 14:54:35 on May 25, 2016 ยท (Permalink)
On both solutions you crossed the river without crossing a bridge
ubergeek0 ยท 5 points ยท Posted at 15:07:04 on May 25, 2016 ยท (Permalink)
So we have proved that I am not a math genius and I also suck at reading comprehension and basic drawing skills....
drsatan1 ยท 3 points ยท Posted at 15:09:21 on May 25, 2016 ยท (Permalink)
Seems you're dumb. Sorry man.
ubergeek0 ยท 6 points ยท Posted at 15:09:41 on May 25, 2016 ยท (Permalink)
It is the prevailing opinion.
kungfu_stagerat ยท 6 points ยท Posted at 14:47:09 on May 25, 2016 ยท (Permalink)*
Uhhhh. I think you missed something about how bridges work. Or about the need for a bridge to cross water.
Why your solutions don't work.
dluminous ยท 1 points ยท Posted at 15:08:18 on May 25, 2016 ยท (Permalink)
To answer the question in your link, he's either Jesus or Moses, duh!
josh8010 ยท 1 points ยท Posted at 14:46:10 on May 25, 2016 ยท (Permalink)
Um, you're just crossing the lines, you have a place in each where you double back and don't cross a bridge, you are doing it incorrectly.
jywn4679 ยท 1 points ยท Posted at 14:53:00 on May 25, 2016 ยท (Permalink)
You cross the bottom left bridge twice.
BeardFace5 ยท 0 points ยท Posted at 14:49:09 on May 25, 2016 ยท (Permalink)
I may or may not have been in the same boat.
Posseon1stAve ยท 3 points ยท Posted at 15:06:46 on May 25, 2016 ยท (Permalink)
I think using a boat is implied as cheating.
BeardFace5 ยท -1 points ยท Posted at 15:08:29 on May 25, 2016 ยท (Permalink)
Yah. Thank you. Do you want me to explain the joke?
Posseon1stAve ยท 1 points ยท Posted at 15:21:49 on May 25, 2016 ยท (Permalink)
Only if it's a good joke.
BeardFace5 ยท 0 points ยท Posted at 16:35:44 on May 25, 2016 ยท (Permalink)
It's not.
purple_pixie ยท 295 points ยท Posted at 13:45:35 on May 25, 2016 ยท (Permalink)*
If you took 1 cent and invested it at 5% interest, compounded annually, back in
0AD1BC, it would now be worth 200 billion times the weight of the earth in gold.It's not maths in the sense of a pure maths fact, but it's a fun fact and it's maths-related.
And for our calculations:
Earth weight: 5.972 ร 1024 kg
Price of gold: $39223.59 kg-1
=>Cost of a golden earth: $2.34 x 1029
Annual compound interest formula:
return = investment x (interest)years invested for
plug in the numbers: return = $0.01 x 1.05 ^ 2016 = $5.22 x 1040
($5.22 x 1040 )/($2.34 x1029 ) = 222,822,878,846
Or about 200 billion.
The numbers were trimmed a bit for presentation so you might get some rounding error if you use those numbers exactly as presented
Gravitas81 ยท 218 points ยท Posted at 15:43:52 on May 25, 2016 ยท (Permalink)
I perfer Terry Pratchett's (possibly Douglas Adam's) take on it which was if you take 1 cent and invested it at 5% interest and came back in 200 years or so the 1 cent would have been eaten up entirely in bank charges.
purple_pixie ยท 29 points ยท Posted at 16:13:45 on May 25, 2016 ยท (Permalink)
It is often hard to distinguish between Pratchett's and Adams' humour / insight into the human condition, because they were both so refreshingly weird, smart and funny.
(I nearly corrected that "were" then realised they're both past tense. Sad times)
anatabolica ยท 7 points ยท Posted at 17:01:39 on May 25, 2016 ยท (Permalink)
:(
railz0 ยท 5 points ยท Posted at 19:28:01 on May 25, 2016 ยท (Permalink)
Happy towel day!
:(
Ozyman_Dias ยท 3 points ยท Posted at 09:38:08 on May 26, 2016 ยท (Permalink)
They were the 3 great British wits, each owning a comedy cross-genre:
Adams - SciFi/Comedy
Pratchett - Fantasy/Comedy
Gaiman - Horror/Comedy
purple_pixie ยท 2 points ยท Posted at 09:39:11 on May 26, 2016 ยท (Permalink)
My Gaiman knowledge is tragically limited, but it is something I'm planning to fix.
psiphre ยท 1 points ยท Posted at 22:17:05 on May 26, 2016 ยท (Permalink)
yes, improve your knowledge on gay men
RichtersMask ยท 1 points ยท Posted at 10:22:57 on May 26, 2016 ยท (Permalink)
Gaiman is alive... isn't he?
Ozyman_Dias ยท 1 points ยท Posted at 10:32:08 on May 26, 2016 ยท (Permalink)
Yes, haha absolutely.
I use were as an average.
RichtersMask ยท 1 points ยท Posted at 10:34:24 on May 26, 2016 ยท (Permalink)
Oh thank god.
columbus8myhw ยท 1 points ยท Posted at 12:28:35 on May 26, 2016 ยท (Permalink)
Wait for it
dusmeyedin ยท 1 points ยท Posted at 04:57:19 on May 26, 2016 ยท (Permalink)
Grant Naylor also did a bit in Red Dwarf where Lister left two pence in his account and after three million years in stasis he now owned most of the Earth.
But it was just an April Fools.
rusy ยท 15 points ยท Posted at 17:39:47 on May 25, 2016 ยท (Permalink)
To put this into more depressing terms, if you took 1 cent at birth, and invested it at 5%, by the time you retire at 65 you'd have 24 cents
Parey_ ยท 15 points ยท Posted at 15:05:59 on May 25, 2016 ยท (Permalink)
There is no 0AD.
purple_pixie ยท 8 points ยท Posted at 15:12:25 on May 25, 2016 ยท (Permalink)
Oh yeah, it went from 1 BC to 1 AD right?
BrowsOfSteel ยท 2 points ยท Posted at 23:36:59 on May 25, 2016 ยท (Permalink)
โADโ is a prefix.
2 BC
1 BC
AD 1
AD 2
purple_pixie ยท 1 points ยท Posted at 09:03:07 on May 26, 2016 ยท (Permalink)
I give up, man, they said maths fact.
If I knew I was gonna get grilled on my calendars I'd have stayed at home.
Oh wait, I am at home, typing this in my underwear. Rock on, the internet.
Parey_ ยท 2 points ยท Posted at 15:18:52 on May 25, 2016 ยท (Permalink)
It did, because the calendar was made using imprecise data (I believe). To be fair, there was no precise count of days and years like we have now. So itโs completely understandable that errors piled up.
thundergonian ยท 9 points ยท Posted at 15:39:28 on May 25, 2016 ยท (Permalink)*
Not because of imprecise data, but because of qualitative (not quantitative) semantics. AD 1 was the first year of the common century, hence AD 1 (lit. "The first year of our Lord"). It's the same reason why years 2001โ2100 are the 21st Century and years 1001โ2000 were the 2nd Millennium.
AsterJ ยท 3 points ยท Posted at 18:44:20 on May 25, 2016 ยท (Permalink)*
It's because Christians didn't have a concept of zero at the time.
zeekar ยท 3 points ยท Posted at 18:46:05 on May 25, 2016 ยท (Permalink)
There was no year zero because Europeans didn't know about zero when they came up with the numbering system.
That said, it's perfectly reasonable to talk about the year "0 AD" - or "0 CE", at least, if using 0 with AD makes you uncomfortable. Astronomers use 0 and negative years CE instead of BCE. You just have to remember that 0 AD/CE is the same year as 1 BC[E], not an extra year that comes between it and +1.
fyi1183 ยท 1 points ยท Posted at 17:40:22 on May 25, 2016 ยท (Permalink)
Yes there is.
Parey_ ยท 1 points ยท Posted at 23:11:10 on May 25, 2016 ยท (Permalink)
I expected this. Great game BTW
actual_factual_bear ยท 5 points ยท Posted at 16:41:04 on May 25, 2016 ยท (Permalink)
And this is the flaw in all economic forecasts which assume unending exponential growth instead of the logistics function.
marsten ยท 3 points ยท Posted at 17:30:04 on May 25, 2016 ยท (Permalink)
A corollary is that it is mathematically impossible for any company's growth rate (revenue, profit, stock market valuation) to exceed the GWP (gross world product) growth rate of 2-3% on an indefinite basis.
ableman ยท 1 points ยท Posted at 18:58:03 on May 25, 2016 ยท (Permalink)
Even at a 2% growth rate, you'd end up with $1.5 quadrillion. That's more than total world assets right now.
InSRCommentPostsYou ยท 3 points ยท Posted at 17:16:43 on May 25, 2016 ยท (Permalink)
TO THE TIME MACHINE!
cress560 ยท 3 points ยท Posted at 18:03:44 on May 25, 2016 ยท (Permalink)
How interesting
CatOfGrey ยท 3 points ยท Posted at 18:26:14 on May 25, 2016 ยท (Permalink)
This is actually a wonderful illustration that long-term growth on Planet Earth is definitely less than 5%.
If today's total world wealth is $250 trillion, and the total world wealth was $0.01 in 1 AD, that would identify a real interest rate of about 1.66%. Note that is also an overestimate, as the total world wealth in 1 AD was somewhat more than 1 cent, even in inflation-adjusted dollars.
FastFourierTerraform ยท 3 points ยท Posted at 00:40:28 on May 26, 2016 ยท (Permalink)
SashaTheBOLD ยท 2 points ยท Posted at 17:23:32 on May 25, 2016 ยท (Permalink)
This time traveler's weird trick can make you rich. Dr. Who hates him!
ableman ยท 1 points ยท Posted at 18:54:51 on May 25, 2016 ยท (Permalink)
It's more of a proof that no investment can possibly average 5% return for 2000 years.
[deleted] ยท 2 points ยท Posted at 23:42:44 on May 25, 2016 ยท (Permalink)
Similarly, I read something once like if we actually maintained exponential growth (2%) in food production from Roman times, the amount of bread we would produce fills the entire solar system.
barbecue_invader ยท 2 points ยท Posted at 00:29:58 on May 26, 2016 ยท (Permalink)
Isn't this how Fry got so wealthy that one time on Futurama?
darwin2500 ยท 2 points ยท Posted at 01:31:05 on May 26, 2016 ยท (Permalink)
No it wouldn't be, because you would singlehandedly cause the collapse of whatever currency you invested in, making it worthless.
MuseDrones ยท 2 points ยท Posted at 02:16:50 on May 26, 2016 ยท (Permalink)
Oh yes, my man neil peRT !
jdenniso ยท 1 points ยท Posted at 19:17:53 on May 25, 2016 ยท (Permalink)
Good luck getting a bank to give you 5% interest.
JackAceHole ยท 1 points ยท Posted at 19:44:54 on May 25, 2016 ยท (Permalink)
But there was no FDIC in 1 BC. The bank would just declare bankruptcy and default on your deposit.
_Eerie ยท 1 points ยท Posted at 15:54:27 on May 25, 2016 ยท (Permalink)
Did you think about things like inflation, devaluation etc.?
purple_pixie ยท 3 points ยท Posted at 16:10:53 on May 25, 2016 ยท (Permalink)
Not in the slightest, this is just plugging numbers into a calculator.
I don't think any currency has been around that long so I don't even know how you would begin to do that. But the number is just so staggeringly large that I can't imagine any considerations like inflation can have a meaningful impact on it.
mmmmmmBacon12345 ยท 3 points ยท Posted at 17:30:08 on May 25, 2016 ยท (Permalink)
You could probably do it by starting in Denari and converting to pound sterling when it starts. Rome was the world so everyone would have been able to tie their local currency to Roman currency
TheCodeSamurai ยท 22 points ยท Posted at 17:04:17 on May 25, 2016 ยท (Permalink)
If you take $1 and put it in a bank with 100% interest for a year, you get $2.
If you take $1, put it in a bank, take it out in six months, put it back in with the 100% interest (although because it's only six months you only put back $1.50), and then do that again, you get $2.25.
If you do that every four months for a year, you get $1.33 the first time, $1.79 the second, and $2.35 at the end.
What happens if you do that every millisecond of every day for a year? Every picosecond?
The answer is that as the number of times you compound approaches infinity, the total amount you get approaches e.
Idiotnextdoor_2 ยท 6 points ยท Posted at 17:10:06 on May 25, 2016 ยท (Permalink)
Brb going to the bank
QuintusVS ยท 2 points ยท Posted at 12:06:46 on May 27, 2016 ยท (Permalink)
Good luck with paying off the bank charges you'll rack up which instantly outgrow any profit you make.
Zarco19 ยท 2 points ยท Posted at 04:43:38 on May 26, 2016 ยท (Permalink)
Yep. This is the definition of e we used in my high school classes, the limit as n->infinity of (1+1/n)n. You can use this to see how the formula for compounding interest (i.e. you have money in the bank whose interest is calculated n times per year) - Return = Investment x (1+interest rate/n)nt - turns into the formula for continuous compounding - Return = Investment x ert - as you compound more and more times per year.
Screen_Watcher ยท 2 points ยท Posted at 17:59:10 on May 26, 2016 ยท (Permalink)
All I need now is $1.
zakky_b ยท 324 points ยท Posted at 14:11:28 on May 25, 2016 ยท (Permalink)
To find if a number is evenly divisible by 2: The last number is even.
To find if a number is evenly divisible by 3: add all the digits and if THAT number is divisible by 3, then the whole number is. (Ex. 744. 7+4+4=15. So 744 is evenly divisible by 3.)
To find if a number is evenly divisible by 4: As long as the last 2 digits in a number is divisible by 4, then the whole number will be. (Ex. 727483724 is divisible by 4 because the last 2 digits {24} is).
To find if a number is evenly divisible by 5: The last digit is 5 or 0 (that's an easy one).
To find if a number is evenly divisible by 6: If the number is divisible by both 2 AND 3, then it's evenly divisible by 6.
cheeseis ยท 230 points ยท Posted at 15:17:44 on May 25, 2016 ยท (Permalink)
Here's one for seven, in case you didn't know it. It's an old favorite math parlor trick of mine.
Double the last digit
Subtract that from the remaining digits
If the result is evenly divisible by 7, then the original number is as well.
Example: 182
2 doubled is 4
18-4=14, so 182 is evenly divisible by 7
zakky_b ยท 13 points ยท Posted at 15:23:34 on May 25, 2016 ยท (Permalink)
Ha! That's awesome! Never knew of any for 7, 8, or 9. Thanks so for the info.
cheeseis ยท 35 points ยท Posted at 15:29:40 on May 25, 2016 ยท (Permalink)
For eight, it's similar to 4. The last three digits must be a multiple of 8 (145373080, for example)
For nine, it's just like three except the digits should add to a multiple of nine.
jusjerm ยท 35 points ยท Posted at 16:59:15 on May 25, 2016 ยท (Permalink)
I like divisible by 11, if we want to keep going. Let's take a decently large number like 115973
Add up all the odd numbered digits (that is, the first, third, fifth... from the left in the string of numbers). 1+5+7 =13
Add up the even digits (second, fourth, etc). 1+9+3=13
Find the difference between both sums. 13-13= 0.
If the difference is 0 or a multiple of 11, then the original number is divisible by 11.
tommcdo ยท 17 points ยท Posted at 18:12:05 on May 25, 2016 ยท (Permalink)
0 is a multiple of 11 :)
jusjerm ยท 6 points ยท Posted at 18:25:11 on May 25, 2016 ยท (Permalink)
Yes, it is. However, some numbers (2841927, for instance) will leave you with a nonzero multiple of 11. I just meant to say that the difference between alternating digits won't always be zero to prove divisibility by eleven.
cheeseis ยท 3 points ยท Posted at 17:43:23 on May 25, 2016 ยท (Permalink)
I didn't know this one. Thanks!
sunz3000 ยท 11 points ยท Posted at 16:59:51 on May 25, 2016 ยท (Permalink)
I remember seeing someone post the rules up to 37 or something. But wikipedia has it for higher order: https://en.wikipedia.org/wiki/Divisibility_rule
Have fun!
tragicshark ยท 8 points ยท Posted at 19:15:19 on May 25, 2016 ยท (Permalink)
a little faster for 8:
****632-> 6 (even), 32 (4*8) = divisible by 8)****768-> 7 (odd), 68+4 -> 72 (9*8) = divisible by 8)NotCookingGrandma ยท 2 points ยท Posted at 23:02:31 on May 25, 2016 ยท (Permalink)
With 9, it's the same as 3, except when you add all the digits repeatedly until you get to one digit, and if it equals 9, then it is divisible by 9.
senatorskeletor ยท 8 points ยท Posted at 19:11:43 on May 25, 2016 ยท (Permalink)
Initial reaction: "this person doesn't know what they're talking about. if this were true, then any two-digit number where the first digit is twice the size of the second digit would be divisible by seven, and that's just not true. look at it: 21, 42, 63... wait a second... 84... holy shit."
thosethatwere ยท 4 points ยท Posted at 18:03:39 on May 25, 2016 ยท (Permalink)*
You can invent rules like this for any number*. For example:
Want to divide by 13?
Multiply the last digit by 9
Subtract that from the remaining digits
If the result is evenly divisible by 13, then the original number is as well.
Example:
13*455 = 5915
5 times 9 is 45.
591-45 = 546
Again:
6 times 9 is 54
54 - 54 = 0.
The reason this works is because 91 is a multiple of 13, just like 21 is a multiple of 7. In the algorithm you're subtracting large multiples of 7 or 13 and dividing by 10.
Want to invent your own? Take a number (preferably a prime), say 17, and find a multiple of that number that ends in a 1. For example 51 is 3 times 17, so we're going to use 5 and 1. The algorithm now is:
Multiply the last digit by 5
Subtract that from the remaining digits
If the result is evenly divisible by 17, then the original number is as well.
*: I should mention that the algorithm changes if for example you pick an even number and therefore can't find a multiple of it that ends in 1, but it's at most a cosmetic change, which is left for the reader ;)
scufferQPD ยท 4 points ยท Posted at 18:34:13 on May 25, 2016 ยท (Permalink)*
26...
...In case anyone wanted to know...
SlipperySherpa ยท 2 points ยท Posted at 20:59:22 on May 25, 2016 ยท (Permalink)
/r/theydidthemath
loptthetreacherous ยท 3 points ยท Posted at 17:59:26 on May 25, 2016 ยท (Permalink)
Proof of this:
Let's say the number is x and we break it up into the two parts we need, the first digit and all the other digits: 10b+a=x (a between 0 and 9, b any number, the multiply by 10 being there because we want b to be tens and greater)
rwv ยท 3 points ยท Posted at 19:11:16 on May 25, 2016 ยท (Permalink)
105 => 10 - 10 = 0
This one makes my head hurt since 0 is indeed divisible by 7.
112 => 11 - 4
98 => 9 - 16 = -7
Yeah, okay this is neat.
wiseIdiot ยท 2 points ยท Posted at 10:44:50 on May 30, 2016 ยท (Permalink)
Thank you! This trick was in my 7th grade maths textbook but I had completely forgotten about it.
jaredjeya ยท 1 points ยท Posted at 20:04:19 on May 25, 2016 ยท (Permalink)
That's going to save me so much time
RasmusSW ยท 1 points ยท Posted at 20:19:40 on May 25, 2016 ยท (Permalink)
If I remember correctly:
For 8 the last three digits has to be dividable by 8, like XXXXXXXX808
And for 9 the sum of all the digits in the number has to be dividable by 9, like 56727
orcscorper ยท 1 points ยท Posted at 23:53:37 on May 25, 2016 ยท (Permalink)
I wonder, when does a trick get so complicated that it becomes faster to just divide by seven (or whatever). Like 182/7=26 & 207+67=140+42.That's not really slower than 18-(2*2)=14 & 14/7=2.
cheeseis ยท 1 points ยท Posted at 00:20:06 on May 26, 2016 ยท (Permalink)
I just think it's fun, and for me it's easier to do mentally than long division. It mostly comes in handy when I need to quickly rule out 7 as a factor without actually needing to know the quotient.
columbus8myhw ยท 1 points ยท Posted at 12:35:16 on May 26, 2016 ยท (Permalink)
Explanation: If 10a+b is a multiple of 7, then so is 50a+5b (just five times it). Now, 50a+5b-(49a+7b)=a-2b, and subtracting multiples of 7 doesn't change divisibility by 7, so if 50a+5b is a multiple of 7 then so is a-2b.
Thus, if 10a+b is a multiple of 7, then so is a-2b. That's what this trick does.
KarlKastor ยท 5 points ยท Posted at 18:58:24 on May 25, 2016 ยท (Permalink)
(My homework which is due to tomorrow, is to build a deterministic finite automaton to detect multiples of four digit-by-digit.) It's simply because 100 is divisible by four so also every multiple of 100 is aswell. And to make it even easier to check if something is evenly divisible by 4:
The very last digit must be even.
If the last digit is 2 or 6 the digit before it (the second-to-last digit) must be odd.
If the last digit it is 0, 4 or 8 the before it (the second-to-last digit) must be even.
[deleted] ยท 2 points ยท Posted at 02:19:12 on May 26, 2016 ยท (Permalink)
Ah, automata theory... surprisingly intuitive for the most part. It was a fun class (:
canopus12 ยท 3 points ยท Posted at 18:55:35 on May 25, 2016 ยท (Permalink)
If the sum of the digits of a number is divisible by 9, the number is divisible by 9.
If the alternating sum of digits of a number is divisible by 11 the number is divisible by 11. 47817 => 4-7+8-1+7 = 11 so it's divisible by 11.
[deleted] ยท 2 points ยท Posted at 19:14:51 on May 25, 2016 ยท (Permalink)*
For funsies here's a breakdown of the 3's trick:
Evenly divisible by 3 (or 9)
Consider a number "x" where each digit is represented by a letter, with the one's place represented by "a", the ten's as "b", and so on. It can be represented like this (I'm gonna use a 4-digit number for example, but this can be extended to any number of digits):
x = a + b * 10 + c * 100 + d * 1000
Which you can also represent as:
x = (a * (0 + 1)) + (b * (9 + 1)) + (c * (99 + 1)) + (d * (999 + 1))
Multiply out and rearrange:
x = a + b + c + d + 9b + 99c + 999d
Now subtract on both sides:
x - (9b + 99c + 999d) = a + b + c + d
Ta-daaa. I grouped the stuff that we know is divisible by 3 into the parens, so all that's left is the x (our original number). It follows that if our original number is divisible by 3, the whole left side of the equation is.
From there, it follows that if left side of the equation is divisible by 3, the right side (which is the sum of the digits of x) is also divisible by 3.
The left and right sides are equal so this logic also works going the other direction (if the sum of digits of x is divisible by 3, then x must be divisible by 3).
This also works for 9, of course.
sokkawatertribe ยท 1 points ยท Posted at 18:16:02 on May 25, 2016 ยท (Permalink)
Although some other math facts IIT are more interesting, this is by far the most useful math fact posted thus far for the layman! If anyone is studying for SAT or even GRE these little math tips save you a lot of time.
Broken-Jinxie ยท 1 points ยท Posted at 18:34:01 on May 25, 2016 ยท (Permalink)
I have been looking for this list to help my grade school kid!! Thanks Man, You're the best!
jacob_ewing ยท 1 points ยท Posted at 19:12:24 on May 25, 2016 ยท (Permalink)
Or in more generic terms:
(edit: typo)
vikinick ยท 1 points ยท Posted at 19:41:18 on May 25, 2016 ยท (Permalink)
8 is last 3 digits as well.
muuus ยท 1 points ยท Posted at 19:41:42 on May 25, 2016 ยท (Permalink)
Elementary school math facts, nice.
DigNitty ยท 1 points ยท Posted at 19:43:44 on May 25, 2016 ยท (Permalink)*
Not as cool, but I've always found it interesting that in multiples of nine the second digits decrease and the first digit increases. Like this:
0 9
1 8 ......the first column increases 0,1,2,3,4...
2 7
3 6 .....the second column decreases 9,8,7,6...
4 5
5 4
6 3
7 2
8 1
9 0
9 9
108
117
126
Mrfish31 ยท 1 points ยท Posted at 20:32:28 on May 25, 2016 ยท (Permalink)
For 11:
A number is divisible by 11 if the sum of the digits in the odd columns (ones, hundreds, ten thousands, etc) is equal to the sum of the digits in the even columns (tens, thousands, hundred thousands, etc)
coffeeaddict_ ยท 1 points ยท Posted at 20:33:25 on May 25, 2016 ยท (Permalink)
where was this when i was in elementary school?!
manygoats ยท 1 points ยท Posted at 21:41:36 on May 25, 2016 ยท (Permalink)
Expanding on 3:
You can continue to add the digits together until you get to a single digit divisible by 3. (e.g. 843795 -> 8 + 4 + 3 + 7 + 9 + 5 = 36 -> 3 + 6 = 9 -> 9 is divisible by 3)
And using same method, if your final number is 9, then the original number is divisible by 9.
BlazingFox ยท 1 points ยท Posted at 23:19:02 on May 25, 2016 ยท (Permalink)
How about seven?
knightofwhocares ยท 1 points ยท Posted at 01:26:28 on May 26, 2016 ยท (Permalink)
I'm pretty sure that for 2x , for any number y where the last x digits are divisible by 2x , y is itself divisible by 2x .
At least, its true for any example I can think of.
awe778 ยท 1 points ยท Posted at 04:23:49 on May 26, 2016 ยท (Permalink)
And if that number is still too big, add the digits of that number and it will still retain its remainder if divided by 3.
SeraphimNoted ยท 1 points ยท Posted at 07:55:10 on May 26, 2016 ยท (Permalink)
What about 7?
yeahbitchphysics ยท 1 points ยท Posted at 11:32:40 on May 26, 2016 ยท (Permalink)
They don't teach that in the US? I learned that in 6th grade.
zakky_b ยท 1 points ยท Posted at 11:35:40 on May 26, 2016 ยท (Permalink)
I believe I learned this in 7th or 8th grade, also in US.
eldred2 ยท 1 points ยท Posted at 17:23:01 on May 26, 2016 ยท (Permalink)
The 'is divisible by three' algorithm can be made even easier, by:
Example: 1234567890987654321 => 1+2
3+4+56+7+89 0 9+8+76+5+43+2+1=54 => 5+4=9.Killa-Byte ยท 1 points ยท Posted at 06:47:17 on May 30, 2016 ยท (Permalink)
4th grade teacher taught me all but 4 and 6.
[deleted] ยท 117 points ยท Posted at 17:05:17 on May 25, 2016 ยท (Permalink)
When you are 27 that will be the most memorable xx age you will be.
11 = 1 you won't remember
22 = 4 most likely wont' remember any of it outside of pictures
33 = 27 Wooo
44 = 256 doubtful that any of us will live that long
Med_Tosby ยท 75 points ยท Posted at 19:03:13 on May 25, 2016 ยท (Permalink)
Speak for yourself. Given that I've lived 26 years and have died 0 times, at this rate I will still have 0 deaths by the time I'm 256 years old.
h0ax2 ยท 11 points ยท Posted at 20:42:24 on May 25, 2016 ยท (Permalink)
Hate to break it to you but you've died 0.4 times already (rough estimation)
Med_Tosby ยท 18 points ยท Posted at 20:46:40 on May 25, 2016 ยท (Permalink)
YOU DON'T KNOW ME!
Also 0.4 rounds down to 0 ipso facto I am still immortal
kurashu89 ยท 5 points ยท Posted at 01:06:32 on May 26, 2016 ยท (Permalink)
Is this Python 2 math?
[deleted] ยท 3 points ยท Posted at 20:46:32 on May 25, 2016 ยท (Permalink)
I hate to break it to you but you have actually died 26/85ths since you were born.
Supersting ยท 1 points ยท Posted at 22:54:27 on May 25, 2016 ยท (Permalink)
A classic proof by induction.
columbus8myhw ยท 1 points ยท Posted at 12:38:19 on May 26, 2016 ยท (Permalink)
Technically we only start dying at the age of 25
[deleted] ยท 5 points ยท Posted at 20:45:43 on May 25, 2016 ยท (Permalink)
I remember being pretty excited on my 33 birthday. Next one I'm celebrating will be 25. After that its a short leap to 62, then a LONG wait to 72 and 43 (also known as 26).
I like math but have very few people show up to my birthday parties.
xereeto ยท 1 points ยท Posted at 02:31:19 on May 27, 2016 ยท (Permalink)
I remember thinking when I turned 16 that my birthday was a power of two, and then being slightly upset when I realized I only had two more of those left.
SamPike512 ยท 3 points ยท Posted at 21:45:31 on May 25, 2016 ยท (Permalink)
2.92.9 = 21.925... More memorable than 27 I'd say
slickricflair ยท 3 points ยท Posted at 21:59:03 on May 25, 2016 ยท (Permalink)
27 must be a magical year because sometime during your 27th year, you would reach 10,000 days old. That's a transition from 4 digits to 5 digits. You don't remember all the other ones.
1= 1 day old
10= 10 days old
100= 100 days old
1000 = almost 3 years old
10000 = 27 and a few months
100000 = long dead
If you are younger than 27, you can find out when your 10000th day birthday is by going into excel and typing in your birthday (day month year). Simply add 10000 to that number will give you the upcoming date.
xereeto ยท 1 points ยท Posted at 02:36:10 on May 27, 2016 ยท (Permalink)
This reminds me of Ryan McHenry, the "Ryan Gosling won't eat his cereal" guy. He was a friend of my cousin's, and he posted on Twitter about reaching his 10,000th day. Then he died of bone cancer shortly after :(
theDocX2 ยท 2 points ยท Posted at 21:13:24 on May 25, 2016 ยท (Permalink)
Damn...it still true if you convert to months.
CrimsonCowboy ยท 2 points ยท Posted at 21:32:11 on May 25, 2016 ยท (Permalink)
Reminds me of how I get excited when my birthday is at a prime time of my life. Pun intended.
But there's always something fun bout any of those ages. Like,
6=2x3
30=2x3x5
105=3x5x7
Sets of consecutive primes. You only get a few.
[deleted] ยท 2 points ยท Posted at 07:50:08 on May 26, 2016 ยท (Permalink)
Cool! I'm my most memorable xx age right now.
TribeWars ยท 2 points ยท Posted at 15:41:54 on May 26, 2016 ยท (Permalink)
The http://www.oeis.org makes sure that every birthday your age number has an interesting property
latotokyo123 ยท 396 points ยท Posted at 11:43:50 on May 25, 2016 ยท (Permalink)
123 - 45 - 67 + 89 = 100.
123 + 4 - 5 + 67 - 89 = 100.
123 - 4 - 5 - 6 - 7 + 8 - 9 = 100.
1 + 23 - 4 + 5 + 6 + 78 - 9 = 100
Meaningless, but nonetheless pretty sick.
CatOnYourTinRoof ยท 45 points ยท Posted at 16:20:34 on May 25, 2016 ยท (Permalink)
I wrote some code that does this (it's a little more generalized than the problem you're looking for, but be careful -- add too many input options and the runtime goes up an extraordinary amount); here's what the output looks like:
Here's the code:
terminalvelocit3 ยท 11 points ยท Posted at 21:46:05 on May 25, 2016 ยท (Permalink)
Upvote for Python.
n0rs ยท 1 points ยท Posted at 03:53:57 on May 26, 2016 ยท (Permalink)
Now do it again, without eval!
CatOnYourTinRoof ยท 1 points ยท Posted at 16:28:44 on May 26, 2016 ยท (Permalink)
I could, but would rather not -- that would take a lot of effort. That code was something I put together from one of those "you should be able to complete these five problems in less than an hour" interview tests, and eval was the obvious route.
What I would be more interested in would be optimizing the algorithm more to identify cases that don't need to be tested. Like in the default example, if it starts with 123456 as a single number then clearly there's no operation with 789 that could end up reaching 100, so I could prune off a lot of the chains involving concatenation of digits. Generalizing the cases that can be ignored is far from trivial, though.
n0rs ยท 1 points ยท Posted at 01:01:41 on May 27, 2016 ยท (Permalink)
Eval is the obvious route, yes. But writing either your own parser or evaluating the result based on a tree of your three operations (concatenation, addition, subtraction) is also an interesting problem.
Pruning would be interesting too, but yes, not trivial.
CatOnYourTinRoof ยท 1 points ยท Posted at 15:37:03 on May 27, 2016 ยท (Permalink)
With three operations and little to worry about from order of operations, that it very doable. However, you may notice I have those as keyword params, so you can call it with other operations and other input lists. I've tested a few allowing for parentheses, multiplication, division, decimal points, mod arithmetic, and exponents, and writing that parser would be harder. Maybe I'll get to it eventually, but as noted, the pruning seems more interesting to me.
[deleted] ยท 6 points ยท Posted at 14:58:54 on May 25, 2016 ยท (Permalink)*
Now why do you do subtraction first instead of addition? Doesn't addition take a higher order of precedence than subtraction?
I.E PEMDAS?
I'm mainly referring to the first expression.
EDIT Huge apologies for my misinformation. I've always been taught PEMDAS(Well at least since I entered public school).
Ericcrash ยท 17 points ยท Posted at 15:05:16 on May 25, 2016 ยท (Permalink)
No, iirc addition and subtraction have the same precedence, same as how multiplication and division have the same precedence.
graaahh ยท 3 points ยท Posted at 17:26:14 on May 25, 2016 ยท (Permalink)
Yep, addition and subtraction have the same precedence if you treat subtraction like "adding a negative number", which is the correct way to do it. Otherwise, it can get a little messy. For example, I've seen beginner math students make the following mistake more than once: 9-8+2 = 9-10 = -1. But subtraction isn't really its own thing, it's just the opposite of adding a positive number. So in actuality, 9-8+2 = 9+(-8)+2 = 1+2 = 3.
phisho873 ยท 16 points ยท Posted at 15:29:20 on May 25, 2016 ยท (Permalink)*
This is a too common misconception. The order of operations should be thought of as PE(M/D)(A/S).
EDIT: Guys, don't downvote him (his comment is currently at -3). He didn't know something. He asked. What more can we ask for? While it may not be entirely true that "there's no such thing as a stupid question," this one wasn't stupid and if we suppress people questioning, that just leads to more widespread ignorance.
ananori ยท 3 points ยท Posted at 17:10:57 on May 25, 2016 ยท (Permalink)
All I wanna know is how such people have passed math exams up until high school graduation.
Suppose you encounter an equation saying 1 - 1 + 1=?. You would literally fail if you didn't know the correct order of operations.
phisho873 ยท 2 points ยท Posted at 17:28:34 on May 25, 2016 ยท (Permalink)
Yeah, I don't get it either, but it's a failure of specific teachers, specific school systems, and specific institutes of higher ed. Some people are clearly being taught incorrectly. Ain't their fault!
christianpowell416 ยท 1 points ยท Posted at 22:12:29 on May 25, 2016 ยท (Permalink)
Well we don't know enough to blame the teachers. You can have a great teacher and not learn anything if you don't want to.
christianpowell416 ยท 1 points ยท Posted at 22:13:22 on May 25, 2016 ยท (Permalink)
Wait... Is that not the same no matter how you do it?
ananori ยท 0 points ยท Posted at 22:31:06 on May 25, 2016 ยท (Permalink)
If addition preceded subtraction then it would be -1
christianpowell416 ยท 1 points ยท Posted at 23:40:26 on May 25, 2016 ยท (Permalink)
So 1+1=2, and 2-1=1...
Maybe I just have a mental roadblock and can't figure out how to do it incorrectly?
ananori ยท 1 points ยท Posted at 08:55:22 on May 26, 2016 ยท (Permalink)
1 - (1+1)
But I guess people misinterpreted the purpose of PEMDAS then. Changing the chronological order of performing operations without affecting the hierarchical is not wrong, although it's useless.
christianpowell416 ยท 1 points ยท Posted at 16:28:48 on May 26, 2016 ยท (Permalink)
Well you added parentheses that were not in the equation
ananori ยท 1 points ยท Posted at 16:43:55 on May 26, 2016 ยท (Permalink)
Yes, illustrating the assumption that addition precedes subtraction... that's what order of operations means. It means you can put parentheses around expressions by the given order of operations without changing the outcome.
christianpowell416 ยท 1 points ยท Posted at 19:38:52 on May 26, 2016 ยท (Permalink)
Omg I'm retarded
DennethMayhem ยท 4 points ยท Posted at 16:26:39 on May 25, 2016 ยท (Permalink)*
What country uses PEMDAS? I'm from Britain and we use BIDMAS. I have never heard of your method? What country are you from?
[deleted] ยท 2 points ยท Posted at 16:29:45 on May 25, 2016 ยท (Permalink)
What's the B and I?
SkyKiwi ยท 3 points ยท Posted at 16:31:46 on May 25, 2016 ยท (Permalink)
I don't know what I is. Where I'm from (New Zealand) we used BEDMAS.
Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
[deleted] ยท 2 points ยท Posted at 18:47:23 on May 25, 2016 ยท (Permalink)
Same in Canada, so far away and yet I always see so many similarities between our countries
DennethMayhem ยท 3 points ยท Posted at 16:32:51 on May 25, 2016 ยท (Permalink)
Bracket and Indeces (I think that's how it's spelt)
[deleted] ยท 2 points ยท Posted at 16:41:45 on May 25, 2016 ยท (Permalink)
Just looked it up. It's indices. I never realized that exponents had another name out there. Would you still use terms like "exponential growth" even though you don't say exponent?
AuroraHalsey ยท 2 points ยท Posted at 16:44:13 on May 25, 2016 ยท (Permalink)
Yeah, we do.
Woffus ยท 1 points ยท Posted at 16:48:18 on May 25, 2016 ยท (Permalink)
In the UK we also use BODMAS, the O is for orders.
DennethMayhem ยท 1 points ยท Posted at 20:24:35 on May 25, 2016 ยท (Permalink)
Yeah I was taught that in Primary school but my teacher last year told us that indices was a better word than order
DennethMayhem ยท 1 points ยท Posted at 19:27:52 on May 25, 2016 ยท (Permalink)
Yeah we do get taught exponential growth. We just use indices as the term for a number that is to the power of something. (I think that makes sense)
Malcolm_TurnbullPM ยท 1 points ยท Posted at 19:37:52 on May 25, 2016 ยท (Permalink)
australian here, my teacher taught bodmas (Brckets, Of, division multiplication addition subtraction)
KingDarkBlaze ยท 1 points ยท Posted at 19:39:30 on May 25, 2016 ยท (Permalink)
It's an American thing?
Freddy216b ยท 3 points ยท Posted at 16:00:53 on May 25, 2016 ยท (Permalink)
Addition and subtraction have the same precedence so are completed in order from left to right. As much as i hate seeing them the Facebook "only 1 in 65.8 people will get this right" are good thought experiments for order of operations. Just don't look at the comments on them, 64.8 people are usually, actually wrong.
DennethMayhem ยท 1 points ยท Posted at 16:26:41 on May 25, 2016 ยท (Permalink)
What country uses PEDMAS? I'm from Britain and we use BIDMAS. I have never heard of your method? What country are you from?
[deleted] ยท 2 points ยท Posted at 16:36:04 on May 25, 2016 ยท (Permalink)
US where I got taught it 6th-12th grade.
DennethMayhem ยท 1 points ยท Posted at 19:28:41 on May 25, 2016 ยท (Permalink)
Huh, never heard of that before. Do you realise that parenthesis is the incorrect term and the definition of parenthesis makes PEMDAS incorrect?
[deleted] ยท 1 points ยท Posted at 19:34:51 on May 25, 2016 ยท (Permalink)
Honestly no. I've never questioned it as I thought it was right (now I know I was wrong).
DennethMayhem ยท 1 points ยท Posted at 20:22:54 on May 25, 2016 ยท (Permalink)
Yeah, I actually thought that it just meant bracket, obviously I was wrong as well. My mum told me that today.
[deleted] ยท 1 points ยท Posted at 20:32:49 on May 25, 2016 ยท (Permalink)
So am I at fault for my education's screw-up?
DennethMayhem ยท 1 points ยท Posted at 20:39:59 on May 25, 2016 ยท (Permalink)
Of course not, I'm pretty sure Pearson Education are at fault
[deleted] ยท 1 points ยท Posted at 20:46:14 on May 25, 2016 ยท (Permalink)
Because there's a crud ton of things my school taught me that are wrong. I prefer homeschool 1000 fold.
DennethMayhem ยท 1 points ยท Posted at 21:17:32 on May 25, 2016 ยท (Permalink)
There's a lot wrong with countries education systems, just happened to be lots in America
[deleted] ยท -2 points ยท Posted at 16:29:14 on May 25, 2016 ยท (Permalink)
GET OUT OF THIS MATH THREAD, PLEBIAN!
LegendaryGinger ยท 1 points ยท Posted at 20:24:03 on May 25, 2016 ยท (Permalink)
This is my favorite mildly interesting one
BoogsterSU2 ยท 1 points ยท Posted at 01:51:24 on May 26, 2016 ยท (Permalink)
Keepin' it ๐ฏ
Kr1tya3 ยท 840 points ยท Posted at 11:46:15 on May 25, 2016 ยท (Permalink)
73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001
Mirrorboy17 ยท 580 points ยท Posted at 13:05:00 on May 25, 2016 ยท (Permalink)
Just don't tell reddit that was on Big Bang Theory
Wait, shit
CJ_Jones ยท 85 points ยท Posted at 14:44:42 on May 25, 2016 ยท (Permalink)*
I preferred Raj's opinion of the best number ever being 5,318,008 because when typed into a calculator and turned upside down it spells BOOBIES.
I watch TBBT, come at me.
bsievers ยท 26 points ยท Posted at 16:15:22 on May 25, 2016 ยท (Permalink)
A lot of people love to hate that show because it's 'not true to geek culture', but it's probably way closer to geek culture than it is to waitress-at-a-cheesecake-factory culture.
source: have physics degree, work as engineer at a tech company, say shit like they do all the time.
Pm_me_any_dragon ยท 12 points ยท Posted at 17:05:56 on May 25, 2016 ยท (Permalink)
My problem isnt that it contains too little geek culture.
Its that they use it as a punchline.
Eg. Simply mentioning d&d is used as a punchline.
CJ_Jones ยท 6 points ยท Posted at 17:06:18 on May 25, 2016 ยท (Permalink)
People hate it because it makes fun of nerd culture as well as having humour that is not noteworthy. But I like it regardless.
Source: Have Maths degree, work as Implementation Analyst
karijay ยท 1 points ยท Posted at 18:20:02 on May 25, 2016 ยท (Permalink)
The humour is below the standard of acceptable (so slightly higher than 2 Broke Girls), but the relationships bewteen the characters are very well written.
[deleted] ยท 2 points ยท Posted at 21:48:49 on May 25, 2016 ยท (Permalink)
I hate the show because, like every other Chuck Lorre comedy, is devoid of humor.
Sketches_Stuff_Maybe ยท 5 points ยท Posted at 17:04:25 on May 25, 2016 ยท (Permalink)
Have you tried Silicon Valley? It's a much better show in my opinion for that kind of humor.
bsievers ยท 9 points ยท Posted at 17:12:24 on May 25, 2016 ยท (Permalink)
I'm a cheap bastard and won't pay for HBO. But I have considered putting on the ol eye patch and peg leg for that one.
Sketches_Stuff_Maybe ยท 1 points ยท Posted at 17:18:00 on May 25, 2016 ยท (Permalink)
It's on TV pretty often, without an HBO subscription in my area, but you do you man :)
[deleted] ยท 1 points ยท Posted at 17:40:49 on May 25, 2016 ยท (Permalink)
ARRR
bl1y ยท 0 points ยท Posted at 18:38:29 on May 25, 2016 ยท (Permalink)
FTFY
dh363 ยท 1 points ยท Posted at 20:11:09 on May 25, 2016 ยท (Permalink)
But they're in academia, which is culturally FAR different from any other geeky job (for example, exactly 0 of my fellow PhD students were big gamers like the guys on the show). Their behavior is really not seen at all in academia.
bl1y ยท 1 points ยท Posted at 18:39:46 on May 25, 2016 ยท (Permalink)
I hate Big Bang Theory because it's lazy writing. Boobies upside down on a calculator bit? Every single 3rd grade boy has done that.
Haragorn ยท 34 points ยท Posted at 14:58:42 on May 25, 2016 ยท (Permalink)
You're already suffering enough.
CJ_Jones ยท 6 points ยท Posted at 14:59:58 on May 25, 2016 ยท (Permalink)
I'll suffer more at the weekend when I have a photo with Raj (Kunal Nayyar)
[deleted] ยท 4 points ยท Posted at 15:40:11 on May 25, 2016 ยท (Permalink)
If I was using RES or whatever I'd tag you, but I'm mobile so
RemindMe! 5 Days
imyy4u ยท 3 points ยท Posted at 15:31:49 on May 25, 2016 ยท (Permalink)
Uhh...don't you mean 5,318,008?
Lord_Surskit ยท 5 points ยท Posted at 15:26:57 on May 25, 2016 ยท (Permalink)
BOOBEIS?
CJ_Jones ยท 12 points ยท Posted at 15:28:05 on May 25, 2016 ยท (Permalink)
They're the only thing a dyslexic person can get off to.
Morfee ยท 1 points ยท Posted at 15:25:19 on May 25, 2016 ยท (Permalink)
Haven't you got the 1 and 3 the wrong way round?
CJ_Jones ยท 2 points ยท Posted at 15:26:21 on May 25, 2016 ยท (Permalink)
FUUUUCKKK
Jurph ยท 0 points ยท Posted at 16:17:34 on May 25, 2016 ยท (Permalink)
BAZINGA!
Wiinamex ยท 4 points ยท Posted at 19:00:54 on May 25, 2016 ยท (Permalink)
Reddit: "Wow, neat fact! Oh, it's from Big Bang Theory...I hate that fact."
TheElectrozoid ยท 4 points ยท Posted at 14:46:13 on May 25, 2016 ยท (Permalink)
THIS WAS ON BIG BANG THEORY
CatalystEXE ยท 1 points ยท Posted at 17:59:24 on May 25, 2016 ยท (Permalink)
what
TheElectrozoid ยท 1 points ยท Posted at 18:11:06 on May 25, 2016 ยท (Permalink)
this was on big bang theory
UCanJustBuyLabCoats ยท 1 points ยท Posted at 08:23:24 on May 26, 2016 ยท (Permalink)
Guess that means the writers of that show discovered it.
NolanOnTheRiver ยท -5 points ยท Posted at 15:25:25 on May 25, 2016 ยท (Permalink)
Welp, now i have to pretend i never read that stupid fact
Alexanderdaawesome ยท -2 points ยท Posted at 15:59:10 on May 25, 2016 ยท (Permalink)
why? they stole it from actual nerds. we're taking it back!
jetblackcrow ยท 51 points ยท Posted at 13:07:35 on May 25, 2016 ยท (Permalink)
I can't believe you've done this
mayofmay ยท 4 points ยท Posted at 16:20:09 on May 25, 2016 ยท (Permalink)
Not the only reason that 73 is the best number.
Itself and its mirror and 100 plus both numbers are all primes (73, 37, 137, 173)
If you take 73 and 100 more than its mirror, 37 (137) and multiply them together you get 10,001. Which leads to a calculator trick I learned when I was young: Take any four-digit number and multiply it by 73, then multiply the result by 137, your result is the four-digit number repeated twice.
RickHalkyon ยท 2 points ยท Posted at 17:20:36 on May 25, 2016 ยท (Permalink)
73 was already my favorite number, now what?
Spacetchi ยท 2 points ยท Posted at 04:30:24 on May 26, 2016 ยท (Permalink)
There's more to this! They're both sexy primes, which means that they differ from another prime by 6. Even more, they're sexy prime triplets! For 73, that's (67, 73, 79), and for 37, that's (31, 37, 43).
derrman ยท 1 points ยท Posted at 15:31:37 on May 25, 2016 ยท (Permalink)
This reminds me of the way to remember how many books are in the Bible. There are 66 books, 39 of which are in the Old Testament. What is 3*9? The number of books in the New Testament, 27.
karlw1 ยท 1 points ยท Posted at 16:06:26 on May 25, 2016 ยท (Permalink)
I've gone cross-eyed
GoldenWizard ยท 1 points ยท Posted at 16:47:36 on May 25, 2016 ยท (Permalink)
Always thought the last part of that was retarded. Obviously if it's a palindrome it's the same backwards, it doesn't need to be stated...
CatalystEXE ยท 1 points ยท Posted at 17:59:06 on May 25, 2016 ยท (Permalink)
Half Life 3 confirmed
spicyhippos ยท 1 points ยท Posted at 20:24:28 on May 25, 2016 ยท (Permalink)
...but being a palindrome means it reads the same backwards...
christina4409 ยท 1 points ยท Posted at 23:14:51 on May 25, 2016 ยท (Permalink)
Stating it's a palindrome and what it is backwards is redundant.
Peregrine_x ยท 1 points ยท Posted at 14:47:43 on May 25, 2016 ยท (Permalink)
have you read cryptonomicon?
Googleboots ยท 0 points ยท Posted at 15:31:24 on May 25, 2016 ยท (Permalink)
21 is not the mirror of 37
Targens ยท 1 points ยท Posted at 16:08:52 on May 25, 2016 ยท (Permalink)
Yeah because 37 is mirror of 73.
Hogwarts9876 ยท 0 points ยท Posted at 10:37:48 on May 26, 2016 ยท (Permalink)
No, but 21 is the mirror of 12. It is written a little confusingly!
TheLonelyPillow ยท -1 points ยท Posted at 16:27:26 on May 25, 2016 ยท (Permalink)
But why is this cool or anything? Especially the last bit?
I don't understand it completely, so I think that's why I am having a hard time trying to see its coolness.
prometheusg ยท 1 points ยท Posted at 21:16:53 on May 25, 2016 ยท (Permalink)
It's a quote from Sheldon on the show The Big Bang Theory.
BiffManly ยท 67 points ยท Posted at 14:47:03 on May 25, 2016 ยท (Permalink)
To find the next square of a sequence of counting numbers, simply add the current number and the next one to the square of the current one.
For example, start with 5*5=25
Now you add 5 and the next number, 6 ~ 25+5+6=36
And this number will be the next number (6) squared.
This trick works for all integers
jusjerm ยท 4 points ยท Posted at 17:04:59 on May 25, 2016 ยท (Permalink)
Ok, this one is breaking me.
anatabolica ยท 53 points ยท Posted at 17:14:18 on May 25, 2016 ยท (Permalink)*
If you think about it geometrically it's easy.
To make that a 5x5 square, what do you need to add?
EDIT: Also, algebraically: (n+1)2 = n2 + 2n + 1 = n2 + n + (n+1)
jusjerm ยท 8 points ยท Posted at 17:18:09 on May 25, 2016 ยท (Permalink)
Great explanation.
[deleted] ยท 10 points ยท Posted at 17:51:07 on May 25, 2016 ยท (Permalink)
Fuck you man that was awesome.
jacob_ewing ยท 3 points ยท Posted at 19:26:08 on May 25, 2016 ยท (Permalink)
It also goes well with the fact that if you add a series of odd numbers starting with one, the sum will be the square of the length of your series.
e.g. 1 + 3 + 5 + 7 + 9 = 25
The reason for this becomes quite apparent with a little bit of introductory calculus.
anatabolica ยท 1 points ยท Posted at 20:08:34 on May 25, 2016 ยท (Permalink)
That's another good one geometrically actually.
It's fun how many different ways these can be proved.
kurashu89 ยท 1 points ยท Posted at 01:08:37 on May 26, 2016 ยท (Permalink)*
Hey, I recognize that from high school. Wish it had been explained this way.
Edit: Just whiteboarded an explanation to my girlfriend and she was not impressed. Also, fuck high school.
JPK314 ยท 1 points ยท Posted at 03:06:58 on May 26, 2016 ยท (Permalink)
There's a word for the row and column of dots you add to get from one square number to the next, but I forget it and it's now bothering me :(
mr_ewe ยท 5 points ยท Posted at 17:15:54 on May 25, 2016 ยท (Permalink)*
Why does this work?
Because multiplication is repeated addition. 5*5=5+5+5+5+5
If we add another 5 we get (5+5+5+5+5)+5=5*6
Which can be written as 6+6+6+6+6. We add another 6 and get (6+6+6+6+6)+6=6*6
I hope this doesn't need formatting.
But generalize, n2+(n)+(n+1)=n2+2n+1=(n+1)2
Edit: formatting...
[deleted] ยท 1 points ยท Posted at 20:15:47 on May 25, 2016 ยท (Permalink)
Yea, I got to this proof too.
(n+1)2 - n2 = 2n + 1 = n + (n+1)
So to find 62 - 52, it's 5 + 6.
[deleted] ยท 5 points ยท Posted at 17:49:01 on May 25, 2016 ยท (Permalink)
Another one that I don't remember specifically where I read it is that the difference between perfect squares is simply a series of odd numbers.
So if you look at
1, 4, 9, 16, 25, 36, 49
The difference between each of those numbers is
3, 5, 7, 9, 11, 13
I couldn't tell you why intuitively though.
[deleted] ยท 2 points ยท Posted at 20:18:37 on May 25, 2016 ยท (Permalink)
f(x) = x2 yields 1,4,9,16,...
The difference between two sequential numbers, x and x+1, is given by:
f(x+1) - f(x) = (x+1)2 - x2 = 2x+1
Which gives us 3,5,7,9,11,...
pacoheadley ยท 1 points ยท Posted at 17:25:36 on May 26, 2016 ยท (Permalink)
I randomly figured this one out when I was younger. I'm glad to see it posted.
ZackVixACD ยท 1 points ยท Posted at 19:26:45 on May 25, 2016 ยท (Permalink)
This trick works for all real number. That's because
a2 = (a-1)2 + (a-1)+a
BiffManly ยท 1 points ยท Posted at 19:39:58 on May 25, 2016 ยท (Permalink)
Though it's less obvious/applicable once you get into decimals.
DrossSA ยท 1 points ยท Posted at 20:14:28 on May 25, 2016 ยท (Permalink)
You can also add each consecutive odd number starting at 1.
1 = 1 (12)
1 + 3 = 4 (22)
1 + 3 + 5 = 9 (32)
1 + 3 + 5 + 7 = 16 (42)
FIERY_URETHRA ยท 1 points ยท Posted at 20:45:56 on May 25, 2016 ยท (Permalink)
(x+1)2 = x2 + 2x + 1 = x2 + x + (x+1)
etienne_valejo ยท 1 points ยท Posted at 22:25:27 on May 25, 2016 ยท (Permalink)
You have just discovered that (n+1)2 = n2 + 2n + 1
Or, the way you have described it, (n+1)2 = n2 + n + (n + 1)
BiffManly ยท 1 points ยท Posted at 22:59:48 on May 25, 2016 ยท (Permalink)
Thinking in common numbers rather than formulas is (surprisingly) often much easier for somebody.
Cosmonaut1356 ยท 327 points ยท Posted at 11:50:12 on May 25, 2016 ยท (Permalink)
That you can use your hands to do your nines times tables without doing any multiplication!
You just hold up 10 fingers Counting from the left, fold down the finger with the number you want to multiply by 9. The fingers on the left of the folded finger represent the number in the tens slot and the fingers on the right of the folded finger represent the number in the ones slot!
e.g. 9 * 6 You fold down your 6th finger. there are 5 fingers on the left and 4 on the right. 9 * 6 = 54
MakeltStop ยท 24 points ยท Posted at 15:15:38 on May 25, 2016 ยท (Permalink)
Related to this, if you add up the digits in any multiple of nine, and repeat the process until you have a single digit, you will always end up at nine.
Example:
CoffeeJedi ยท 4 points ยท Posted at 17:24:19 on May 25, 2016 ยท (Permalink)
I learned that from Square One TV!
https://youtu.be/Q53GmMCqmAM
(yeesh, that's some sub-potato quality there)
peterdragon ยท 2 points ยท Posted at 18:39:13 on May 25, 2016 ยท (Permalink)
That's where I learned it. Still my favorite easy fact.
yosarian77 ยท 2 points ยท Posted at 01:49:46 on May 26, 2016 ยท (Permalink)
It's the finger man!
https://www.youtube.com/watch?v=-WOgLltWhgg
Bagfaceman2014 ยท 1 points ยท Posted at 01:15:52 on May 31, 2016 ยท (Permalink)
I learned it from 9 hours 9 persons 9 doors
jacob_ewing ยท 3 points ยท Posted at 18:09:56 on May 25, 2016 ยท (Permalink)
The relationship in the numbers with this is beautiful. It's the same relationship that makes this rule work for multiples of three (if the sum of the digits is a multiple of three, then the number itself is). That all has to do with the fact that the number has a multiple that is one less than the base in which it's expressed. That of course means that if you express the number in hexadecimal, it won't work for multiples of nine, but ~will~ work for multiples of 3, 5 and 15. Similarly in base twelve, it will only work for multiples of 11.
When I realized how this worked, I was so thrilled that I had to write about it. Blogged it here if you're interested.
cartmancakes ยท 1 points ยท Posted at 18:31:05 on May 25, 2016 ยท (Permalink)
it works with 3 as well.
peterdragon ยท 3 points ยท Posted at 18:50:19 on May 25, 2016 ยท (Permalink)
You always end in multiples of 3 but not 3. 3x7=21 2+1=3 3x5=15 1+5=6 3x9=27 2+7=9
cartmancakes ยท 2 points ยท Posted at 19:09:31 on May 25, 2016 ยท (Permalink)
Oh yeah. My mistake.
[deleted] ยท 1 points ยท Posted at 04:01:59 on May 26, 2016 ยท (Permalink)
In fact this is how you know whether a number is divisible by 9 or not. From the top of my head, try 162. 1+6+2=9.
From the calculator, 162 / 9 = 18.
Try doing the same with 3.
Aalchemist ยท 6 points ยท Posted at 15:25:18 on May 25, 2016 ยท (Permalink)
Or you multiply by 10 and then subtract the number. 96= 106 - 6 = 54.
Moobs_like_Jagger ยท 6 points ยท Posted at 15:59:58 on May 25, 2016 ยท (Permalink)
I think you used asterisks and Reddit formatted your comment as if you were trying to make italics.
Aalchemist ยท 4 points ยท Posted at 17:48:45 on May 25, 2016 ยท (Permalink)
At least now I know how to make *italics. Bam! Thanks, I corrected the comment.
_Artos_ ยท 2 points ยท Posted at 20:10:39 on May 25, 2016 ยท (Permalink)
It still looks wonky
[deleted] ยท 0 points ยท Posted at 17:22:04 on May 25, 2016 ยท (Permalink)*
[deleted]
Aalchemist ยท 1 points ยท Posted at 17:47:39 on May 25, 2016 ยท (Permalink)
LOL. 9x6=10x6 - 6. Thanks!
2seven7seven ยท 10 points ยท Posted at 15:21:34 on May 25, 2016 ยท (Permalink)*
Or just remember that x * 9=x * 10 - x so 6 * 9=60 - 6=54
christianpowell416 ยท 4 points ยท Posted at 22:16:48 on May 25, 2016 ยท (Permalink)
And that x * 8 = x * 10 - 2x and so on and so forth...
orcscorper ยท 2 points ยท Posted at 23:57:57 on May 25, 2016 ยท (Permalink)
Your way works even if you have no fingers. That's definitely better.
Ioseb ยท 6 points ยท Posted at 15:58:09 on May 25, 2016 ยท (Permalink)
I just count 9, 18, 27, 36, 45, etc, as you add one number to the tenth, and withdraw one number from the other. It's quite simple.
Finger skills are always appreciated though.
hoxem ยท 4 points ยท Posted at 15:31:17 on May 25, 2016 ยท (Permalink)
This trick helped me get through third grade
darthchris4 ยท 7 points ยท Posted at 14:32:32 on May 25, 2016 ยท (Permalink)
Learned that from T-Bag on Prison Break
SamwiseTheOppressed ยท 1 points ยท Posted at 17:46:48 on May 25, 2016 ยท (Permalink)
Except that he did it completely incorrectly on the show. Surely someone in the room knew the trick!
darthchris4 ยท 1 points ยท Posted at 20:31:42 on May 25, 2016 ยท (Permalink)
That was the first time I'd seen it.
PianoMastR64 ยท 3 points ยท Posted at 17:41:37 on May 25, 2016 ยท (Permalink)
09
18
27
36
45
54
63
72
81
90
Ranger207 ยท 2 points ยท Posted at 17:12:54 on May 25, 2016 ยท (Permalink)
Also, up to 9 * 9, the numbers in the tens and ones add up to 9. Ex: 9 * 8 = 72, 7 + 2 = 9.
Abble ยท 1 points ยท Posted at 19:05:43 on May 25, 2016 ยท (Permalink)
Same would work with 9x10=90, as 9+0=9.
BelongingsintheYard ยท 2 points ยท Posted at 17:33:08 on May 25, 2016 ยท (Permalink)
This is the first thing on this thread that I've understood
nicxcin ยท 3 points ยท Posted at 14:27:33 on May 25, 2016 ยท (Permalink)
I've been doing this in maths for years! So so helpful
JordanCardwell ยท 3 points ยท Posted at 14:44:43 on May 25, 2016 ยท (Permalink)
Wow, I had forgotten that for probably 20 years. Thanks for bringing that fact back from the dusty section of my brain's library.
UristMasterRace ยท 2 points ยท Posted at 14:38:23 on May 25, 2016 ยท (Permalink)
Jaime Escalante taught me that
https://www.youtube.com/watch?v=-WOgLltWhgg
Machtung7 ยท 2 points ยท Posted at 17:08:40 on May 25, 2016 ยท (Permalink)
How do I reach these keeds?
notquitejaidi ยท 1 points ยท Posted at 15:50:59 on May 25, 2016 ยท (Permalink)
but I only have 8 fingers :(
Solinvictusbc ยท 1 points ยท Posted at 21:05:47 on May 25, 2016 ยท (Permalink)
Plot twist for any number of fingers (x) you can do multiples of (x-1) so in your case multiples of 7.
With a small catch though, fingers to the right are still ones, but fingers to the left are no longer 10s place but (x) place, worth x. So 8 in your case.
For example
1 x 7, put down your finger to the left you have 0 - 7 or 7
2 x 7, 1-6 or 8+6 or 14
3 x 7, 2-5 or 16+5 or 21
Your welcome
realog173 ยท 1 points ยท Posted at 15:53:02 on May 25, 2016 ยท (Permalink)
Or you just memorize them because they are easy. Bonus: you never look like an idiot doing mental math.
chrissycapstick ยท 1 points ยท Posted at 17:17:08 on May 25, 2016 ยท (Permalink)
I graduated high school 16 years ago. I started substitute teaching last year, i had to learn that from an elementary school student.
hardonchairs ยท 1 points ยท Posted at 17:59:03 on May 25, 2016 ยท (Permalink)
I've been doing this since 3rd grade. 9*x = 10*x - x.
JeBalon ยท 1 points ยท Posted at 18:31:47 on May 25, 2016 ยท (Permalink)
Finger math In action:
https://youtu.be/-WOgLltWhgg
Curly_Fried_Mushroom ยท 1 points ยท Posted at 19:33:55 on May 25, 2016 ยท (Permalink)
I just realised you can do this with numbers higher than 10, for example 17:
There would be 16 numbers to the left of it, so you start with 160. Then you do 10-17, for -7.
-7 + 160 = 153 = 9 x 17
edgykitty ยท 1 points ยท Posted at 20:56:18 on May 25, 2016 ยท (Permalink)
You're a hero. You got people talking about Monty Hall, and Graham's number, and all sorts of other things, and you're keeping it real with finger counting tricks.
kingsnoss ยท 15 points ยท Posted at 14:36:13 on May 25, 2016 ยท (Permalink)*
I'm a fan of the idea that there are different levels of infinity. For example, the set of integers and the set of real numbers are both infinite size; however, the set of real numbers is way more infinite than the set of integers. In fact the set of real numbers between 0 and 1 is way more infinite than the set of integers. Much of the theory around infinite sets was developed by a guy named Cantor. He was the perfect combination of insane and brilliant.
[deleted] ยท 3 points ยท Posted at 23:48:41 on May 25, 2016 ยท (Permalink)
There are actually infinite sizes of infinity, you can continually take power sets of an aleph-naught sized set and they're provably more infinite, because no isomorphism can exist between a set and its power set.
However it's unprovable if sets exist between these levels of infinity.
dozza ยท 1 points ยท Posted at 12:54:01 on May 26, 2016 ยท (Permalink)
Unprovable or unproved? If unprovable, that's really interesting, how come?
[deleted] ยท 1 points ยท Posted at 19:36:30 on May 26, 2016 ยท (Permalink)
I'm actually not sophisticated enough in math to say why, but it's proved that you cannot prove the existence of infinities between these sets.
dasignint ยท 2 points ยท Posted at 03:25:58 on May 26, 2016 ยท (Permalink)
I'd like to point out that there is a minority of mathematicians, called finitists, who hold that all of this is incoherent, idiotic bullshit, Cantor was a gigantic hack, and the rest of us merely fell for his seductive but superficial cleverness.
kingsnoss ยท 1 points ยท Posted at 11:56:01 on May 26, 2016 ยท (Permalink)
No offense but, I think finitism is incoherent, idiotic bullshit.
wasdo ยท 802 points ยท Posted at 11:53:05 on May 25, 2016 ยท (Permalink)*
If you put 23 people in a room, there's over 50% chance that at least two of them have gotten a stuffed animal as a birthday present on the same day.
Sitk042 ยท 14 points ยท Posted at 16:46:38 on May 25, 2016 ยท (Permalink)
In 7th grade, my teacher did this, we happened to have 23 people in the class, but three of us (including me) had the same birthday...
aj_thenoob ยท 4 points ยท Posted at 17:35:05 on May 25, 2016 ยท (Permalink)
We did the same in 5th grade. Didn't work, and we had 28 people.
tehosiris ยท 1 points ยท Posted at 08:09:38 on May 26, 2016 ยท (Permalink)
it works every time 50% of the time
TheSemiTallest ยท 159 points ยท Posted at 13:03:51 on May 25, 2016 ยท (Permalink)
I see what you did there...
cool12y ยท 273 points ยท Posted at 13:17:21 on May 25, 2016 ยท (Permalink)
To those who didn't... Its actually a fact that if there are 23 people in the same room there's a 50percent chance that two of em have the same birthday
971365 ยท 114 points ยท Posted at 13:36:59 on May 25, 2016 ยท (Permalink)
Can you explain why a stuffed animal though?
edit: oh is it a joke? lol i thought it was some clever way to say they share a birthday
NolanOnTheRiver ยท 11 points ยท Posted at 15:26:40 on May 25, 2016 ยท (Permalink)
Still don't get it
971365 ยท 32 points ยท Posted at 15:47:10 on May 25, 2016 ยท (Permalink)
Sort of an anti joke. Most people already know the birthday paradox so he instead says something really obvious.
WhatsPotato ยท 1 points ยท Posted at 04:15:46 on May 26, 2016 ยท (Permalink)
What makes that a paradox?
Axleboy57 ยท 25 points ยท Posted at 14:44:00 on May 25, 2016 ยท (Permalink)
But why MALE models?
CrazyKirby97 ยท -10 points ยท Posted at 15:48:31 on May 25, 2016 ยท (Permalink)
TRIGGERED
Anne_Franks_Dildo ยท 2 points ยท Posted at 20:52:38 on May 25, 2016 ยท (Permalink)
whoosh
SucksAtFormatting ยท 5 points ยท Posted at 16:57:12 on May 25, 2016 ยท (Permalink)
It's just misdirection.
cutdownthere ยท 2 points ยท Posted at 17:53:47 on May 25, 2016 ยท (Permalink)
Maybe its a joke on the abundance of stuffed animals given as gifts for birthdays, especially to new borns.
JTswift ยท 8 points ยท Posted at 14:18:20 on May 25, 2016 ยท (Permalink)
How many people do you need in a room for a 50% of the same EXACT birthday? (Day, Month, and Year)
different_pathway ยท 8 points ยท Posted at 17:32:09 on May 25, 2016 ยท (Permalink)
Since I didn't see anyone attempt this, I did some very rough brute force calculations with a small program, using US age demographics, and it hovered around 50% when there were around 202 people.
I have no idea if I made any glaring errors, so if anyone else wants to take a shot at it, please do. :)
innni ยท 3 points ยท Posted at 14:45:53 on May 25, 2016 ยท (Permalink)*
To solve this, we would have to have a set range of years.
This is the equation for 1 year, where n is the number of people.
1 - (364/365)n! = 0.5
For 10 years (assuming 2 leap years), the equation would be:
1 - (3651/3652)n! = 0.5
That fraction there is ((total days - 1) / total days)
Of course I can solve this to
n! = log(total days - 1 /total days) (0.5)
Just correct this if I've done something wrong.
JTswift ยท 0 points ยท Posted at 14:55:40 on May 25, 2016 ยท (Permalink)
Find the oldest person alive and use that year.
Jackin_Jill ยท 6 points ยท Posted at 15:09:41 on May 25, 2016 ยท (Permalink)
But there are going to be more and more people the more recent the year becomes. You'd need some data about population demographics if you want to answer the question accurately
JTswift ยท -4 points ยท Posted at 15:11:42 on May 25, 2016 ยท (Permalink)
Sigh. I didn't mean to use ONLY the year of the oldest person. Find the oldest person alive. That's the far end of your years to include.
So, if the oldest person was born in 1910, then you need to include everything from 1910 to now.
BDTexas ยท 3 points ยท Posted at 15:13:33 on May 25, 2016 ยท (Permalink)
I don't think that's what he was saying. He's saying he doesn't know the distribution of ages, which you need to know to answer this question.
mattenthehat ยท 1 points ยท Posted at 23:02:10 on May 25, 2016 ยท (Permalink)
But that doesn't fit with the problem. Births probably aren't evenly distributed among days/months either, but the problem assumes that they are. By the same logic you can assume that there's an even distribution of birth years too.
[deleted] ยท 1 points ยท Posted at 07:24:44 on May 26, 2016 ยท (Permalink)
[deleted]
mattenthehat ยท 1 points ยท Posted at 08:51:24 on May 26, 2016 ยท (Permalink)
It just depends on the question you're answering. The original question asks how many people you'd need to have a certain percentage chance of having two individuals with the same birth date (month and day) given a even distribution of births. Real birth data by month (for 2014) has an average of 12.375 births per month per 1,000 people, with a standard deviation of 0.81968 (source). That is a not insignificant deviation, yet the question states that it is acceptable to ignore it.
If you ask the same question of shared birth dates (month, day, and year) given an even distribution of births per year between (for example) 1910 and 2009, you still have a valid, and mathematically interesting question. Perhaps it does not have as much bearing on real life due to the larger deviation (mean 18.56825 births per 1,000 people, standard deviation 4.455987 (source), but that does not mean its a completely invalid question (and it is a much easier one to solve in order to get a rough estimate).
Edit: Here is the very sloppy excel spreadsheet I used for calculations, in case anyone is really interested enough to dig that deep.
kingsnoss ยท 4 points ยท Posted at 14:48:09 on May 25, 2016 ยท (Permalink)*
I'm not sure about 50%, but for a 100% chance, the pigeon hole principle tells us that you need 367. That's the number of days in a year plus one and plus one again in case someone was born on Feb 29 of a leap year.
Edit: Just realized you said year too. I don't know how to do that.
JTswift ยท 4 points ยท Posted at 14:55:07 on May 25, 2016 ยท (Permalink)
I'm certainly no math expert, but I feel positive that the number is way higher than 367.
Two people might have August 8th as a birthday, but one may be born in 1990 and the other in 1972.
kingsnoss ยท 2 points ยท Posted at 14:55:47 on May 25, 2016 ยท (Permalink)
Yes I just realized he said year too.
RobotMaster1 ยท 1 points ยท Posted at 23:39:49 on May 25, 2016 ยท (Permalink)
Thanks for picking my birthday.
JTswift ยท 3 points ยท Posted at 06:11:38 on May 26, 2016 ยท (Permalink)
What's your mother's maiden name and the number on the back of your credit card? You know, just for fun.
RobotMaster1 ยท 1 points ยท Posted at 07:28:04 on May 26, 2016 ยท (Permalink)
Asking for a friend?
LiberalFirepower ยท 1 points ยท Posted at 04:24:32 on May 26, 2016 ยท (Permalink)
How many people do you need to put into a room until all of them have the same birthday?
Joe_Baker_bakealot ยท 3 points ยท Posted at 20:09:09 on May 25, 2016 ยท (Permalink)
Wait, how the heck does that work? There's 365 days in a year and only 23 people. How does that end up working up to a coin toss of two people having the same birthday?
GringoDeMaio ยท 3 points ยท Posted at 21:36:23 on May 25, 2016 ยท (Permalink)
Because it's not the odds of a particular person (say, you) finding another with the same birthday. It's the odds of any 2 people out of the 23 sharing it.
So you've got your 22 chances to match up, the next guy has 21 (because he already compared with you), the guy after him has 20 (he's already compared with you and second dude) and so on.
You end up with 22+21+20...2+1 (works out to 253) possible pairings.
rogue5hadow ยท 1 points ยท Posted at 17:05:32 on May 25, 2016 ยท (Permalink)
So if there's 46 there's a 100% chance 2 of then have the same birthday? Or does it not work like that?
TheSemiTallest ยท 2 points ยท Posted at 20:11:24 on May 25, 2016 ยท (Permalink)
At 70 people it becomes 99.9% likely.
RIF_IN_FECES ยท 1 points ยท Posted at 18:09:04 on May 25, 2016 ยท (Permalink)
Tbh I think it gets to 90 something percent? There's an interesting wiki article on it if you look. But obviously it wouldn't be certain
[deleted] ยท 1 points ยท Posted at 17:25:55 on May 25, 2016 ยท (Permalink)
*better than 50%
*at least two
[deleted] ยท -16 points ยท Posted at 14:06:00 on May 25, 2016 ยท (Permalink)*
Which is a misquoted fun fact based upon false assumptions
Edit: typical reddit down voting me when i state the truth
TwatsThat ยท 8 points ยท Posted at 14:25:46 on May 25, 2016 ยท (Permalink)
unless you're mean either February 29th is a day or birthdays aren't evenly distributed, would you care to elaborate?
[deleted] ยท 1 points ยท Posted at 20:00:11 on May 25, 2016 ยท (Permalink)*
The entire thing is modeled off of a n sample being truly randomly generated with conditions that are not naturally occurring.
People always cite this as a fun fact but ignores the actual implications of what it means. It is a model generated to test a variety of means in an idealistic scenario of statistical testing.
So we can use this fun fact in that context only. Can't just throw it out like it was here as that is untrue.
It was pointed out that without equal probability of each day of the year that the odds are probably higher. And that is very much likely. But that changes the claim, the mathematics, and the application is what is being cited.
Tldr: dont cite controlled assumption based statistical tests for real life application. Its simply wrong
[deleted] ยท -10 points ยท Posted at 14:28:15 on May 25, 2016 ยท (Permalink)
What you just said in itself is one such assumption
TwatsThat ยท 19 points ยท Posted at 14:34:54 on May 25, 2016 ยท (Permalink)
so, no, you wouldn't care to elaborate. Thanks.
-jFk- ยท 5 points ยท Posted at 14:34:36 on May 25, 2016 ยท (Permalink)
with an uneven distribution the chance would be even higher.
[deleted] ยท -5 points ยท Posted at 15:04:38 on May 25, 2016 ยท (Permalink)
That is highly likely. But it would disrupt the basic probability calculations being used in the paradox.
BDTexas ยท 6 points ยท Posted at 15:14:33 on May 25, 2016 ยท (Permalink)
It's not a paradox though.
[deleted] ยท 2 points ยท Posted at 19:42:44 on May 25, 2016 ยท (Permalink)
Its called the birthday paradox
Kayyam ยท 0 points ยท Posted at 15:28:30 on May 25, 2016 ยท (Permalink)
What assumptions ?
Lost4468 ยท 0 points ยท Posted at 16:07:26 on May 25, 2016 ยท (Permalink)
What are those?
cool12y ยท 5 points ยท Posted at 13:17:21 on May 25, 2016 ยท (Permalink)
To those who didn't... Its actually a fact that if there are 23 people in the same room there's a 50percent chance that two of em have the same birthday
Sheriff_K ยท 7 points ยท Posted at 19:00:05 on May 25, 2016 ยท (Permalink)
Oh, you..
GreatBabu ยท 1 points ยท Posted at 19:22:25 on May 25, 2016 ยท (Permalink)
*on the same day.
Selvey808 ยท 1 points ยท Posted at 20:35:53 on May 25, 2016 ยท (Permalink)
how is this math supposed to work out?
jsbennett86 ยท 2 points ยท Posted at 23:30:48 on May 25, 2016 ยท (Permalink)*
Since the probability of A is 1 - (the probability of not A), the probability of a birthday being shared in a group of 23 people = 100% - 49.3% = 50.7%.
relvant_usernam ยท 1 points ยท Posted at 21:16:10 on May 25, 2016 ยท (Permalink)
Same day as in same day and month? Even if not, how the hell is there a 50% chance with 23 people and 30 days in a month?
lumeno ยท 1 points ยท Posted at 22:43:25 on May 25, 2016 ยท (Permalink)
Sorry, I don't understand this. Let's say that the probability that two people in a room of 23 have a birthday on the same day is X. Doesn't the probability you are trying to calculate also depend on the prior probability of stuffed animals being given to anyone as a birthday present? And so this could be arbitrarily low and you can't really say there's over 50% chance?
jar-of-plasma ยท 1 points ยท Posted at 23:48:14 on May 25, 2016 ยท (Permalink)
The stuffed animal part is made up, but the paradox itself is true.
lumeno ยท 1 points ยท Posted at 03:35:34 on May 26, 2016 ยท (Permalink)
Right, but doesn't the stuffed animal part make his statement technically false even if the "paradox" part is true?
imbored04 ยท 1 points ยท Posted at 00:15:41 on May 26, 2016 ยท (Permalink)
ELI5?
barbecue_invader ยท 1 points ยท Posted at 00:28:30 on May 26, 2016 ยท (Permalink)
Stuffed animal? Really?
New_at_school ยท 1 points ยท Posted at 14:12:03 on May 26, 2016 ยท (Permalink)
I have 120 students in my class but none have same bday as mine
Killa-Byte ยท 1 points ยท Posted at 06:42:18 on May 30, 2016 ยท (Permalink)
Bullshit. Of all 6 my classes, of 30 people each, no 2 people in any one class share a birthday with any other peopl in that class.
vipros42 ยท 258 points ยท Posted at 14:34:57 on May 25, 2016 ยท (Permalink)
an average apple weighs one Newton
SmartassComment ยท 7 points ยท Posted at 18:25:36 on May 25, 2016 ยท (Permalink)
But how many figs in a Newton?
0vinq0 ยท 16 points ยท Posted at 18:14:45 on May 25, 2016 ยท (Permalink)
I like this one too, because after learning it, every time I had to consider an x Newton load, I imagined x apples stacked on top of each other on that point. Made problems a bit more entertaining.
Mettalink ยท 18 points ยท Posted at 16:51:45 on May 25, 2016 ยท (Permalink)
How is this a math fact?
vipros42 ยท 2 points ยท Posted at 17:43:25 on May 25, 2016 ยท (Permalink)
It appears to require simple maths that is beyond some...
theinfiniteidea ยท 5 points ยท Posted at 17:56:52 on May 25, 2016 ยท (Permalink)
simple physics
Denziloe ยท 1 points ยท Posted at 18:14:49 on May 25, 2016 ยท (Permalink)
Simple biology.
QuintusVS ยท 1 points ยท Posted at 12:14:59 on May 27, 2016 ยท (Permalink)
Not really anything to do with biology.
Denziloe ยท 0 points ยท Posted at 20:33:13 on May 27, 2016 ยท (Permalink)
The weight of an apple has nothing to do with biology?
Ok bro cool comment.
QuintusVS ยท 2 points ยท Posted at 20:49:20 on May 27, 2016 ยท (Permalink)
Not really, mass is just a property of an object, the fact that that object is an apple doesn't really mean it has anything to do with biology.
If you were calculating the gravitational force exerted on an archaeology textbook doesn't mean it has anything to do with archaeology.
Denziloe ยท 0 points ยท Posted at 21:13:39 on May 27, 2016 ยท (Permalink)
TIL biologists don't care about properties of biological objects.
Eonwe_of_Manwe ยท -3 points ยท Posted at 21:11:39 on May 25, 2016 ยท (Permalink)
WHY COULDN'T YOU HAVE POSTED THIS BEFORE MY OCR PHYSICS EXAM??????
vipros42 ยท 11 points ยท Posted at 21:45:31 on May 25, 2016 ยท (Permalink)
Sorry. Let me know your timetable and I'll provide useful information when appropriate
Eonwe_of_Manwe ยท -1 points ยท Posted at 07:14:30 on May 26, 2016 ยท (Permalink)
XD ty very much
Joe_Gunby ยท 3 points ยท Posted at 23:05:32 on May 25, 2016 ยท (Permalink)
Newton's second law and Archimedes principle can piss off, and Jesus Christ those multiple choice questions were boring
[deleted] ยท -28 points ยท Posted at 15:50:10 on May 25, 2016 ยท (Permalink)
[deleted]
vipros42 ยท 50 points ยท Posted at 15:56:09 on May 25, 2016 ยท (Permalink)
yes, Newton is a unit of weight, kilogram is a unit of mass
edit: because I'm an idiot
Santi871 ยท 40 points ยท Posted at 16:08:24 on May 25, 2016 ยท (Permalink)*
Weight is force, so it's measured in units of force
Pedantic correction: weight is a force
vipros42 ยท 17 points ยท Posted at 16:10:07 on May 25, 2016 ยท (Permalink)
Better explanation than mine.
Denziloe ยท 5 points ยท Posted at 18:15:35 on May 25, 2016 ยท (Permalink)
Yes. Pay more attention in class.
[deleted] ยท 0 points ยท Posted at 23:52:59 on May 25, 2016 ยท (Permalink)*
[deleted]
Denziloe ยท 4 points ยท Posted at 00:30:04 on May 26, 2016 ยท (Permalink)
He said "an apple weighs"... how did you translate that to "the apple's mass is" rather than "the apple's weight is"..?
Saying an apple weighs 100 grams is indeed technically incorrect because grams measure mass which is different from weight. But in common parlance you will normally hear grams referred to as a measure of weight, because most people don't understand the difference.
[deleted] ยท -7 points ยท Posted at 17:11:47 on May 25, 2016 ยท (Permalink)
[deleted]
vipros42 ยท 9 points ยท Posted at 17:36:34 on May 25, 2016 ยท (Permalink)
1 kg exerts just under 10 Newtons. At least look shit up before arguing
johnnymo1 ยท 52 points ยท Posted at 13:47:11 on May 25, 2016 ยท (Permalink)
At any point in time, somewhere on the Earth, there is a point such that the spot directly opposite it, on the other side of the planet, has precisely the same temperature and barometric pressure.
lordanubis79 ยท 7 points ยท Posted at 14:44:49 on May 25, 2016 ยท (Permalink)
Can you show me a mathematical proof of this?
johnnymo1 ยท 11 points ยท Posted at 14:51:55 on May 25, 2016 ยท (Permalink)
It's the Borsuk-Ulam theorem, which actually extends much further than the case I mentioned. The simpler case of maps from the circle to R is actually quite easy to see if you've seen the intermediate value theorem before.
Of course, my "physical example" is a bit simplified. It's assuming the earth is a sphere, and temperature and pressure are continuous. We can fix up that first part by considering a spherical shell in the atmosphere instead of necessarily the surface of the earth.
incathuga ยท 10 points ยท Posted at 16:09:35 on May 25, 2016 ยท (Permalink)*
You don't actually care that it's not quite a sphere, because the surface of the Earth is homeomorphic to a sphere. The proof only cares about topology, not the ambient metric space, so we can redefine opposite to mean whatever we want it to mean. In this case, the obvious thing is put a line through your point on the surface and the center of the Earth and see where it pops out, but we could just as easily define opposite to mean something different
two inches west (or any other arbitrary point relative to your initial point)(Edit: As pointed out by /u/rawling, this example isn't quite nice enough; see my reply to his comment for a better example), and the proof still works out.johnnymo1 ยท 1 points ยท Posted at 16:12:06 on May 25, 2016 ยท (Permalink)
I'd thought about that before and figured as much, but couldn't really make it precise so I was conservative about saying such things if I wasn't sure. :)
rawling ยท 1 points ยท Posted at 21:35:25 on May 25, 2016 ยท (Permalink)
Doesn't that get weird near the poles?
incathuga ยท 2 points ยท Posted at 22:22:39 on May 25, 2016 ยท (Permalink)
Okay, I lied very slightly. What you want is an open continuous bijection (basically, a nice function) from the surface of the Earth to the surface of the Earth; we'll call this function opp. Then for any continuous function f from the surface of the Earth to the real plane (we'll use the function evaluating temperature and air pressure), there exists a point x such that f(x) = f(opp(x)).
So in particular, two inches to the west isn't really as nice as we want; thanks for pointing that out. Two degrees west might be nicer, although that fixes the poles, so it's not really an interesting example. Maybe rotate two degrees west and then shift by rotating about an axis through the equator, and that's a better example, though complicated to explain.
vidango ยท 3 points ยท Posted at 15:00:37 on May 25, 2016 ยท (Permalink)
What? I call bluff
Philias ยท 17 points ยท Posted at 15:14:53 on May 25, 2016 ยท (Permalink)*
Nope.
Consider two points on opposite sides of the earth. Let t1 be the temperature of the first point and t2 be the temperature of the other. Now consider dt=t1-t2. If dt is ever zero it means the temperature is the same at both points.
Assume that dt starts out positive (it works out the same if it starts out negative), now begin rotating point 1 and point 2 around the sphere, always keeping them opposite each other.
Now think about what happens when point 1 and point 2 have traded their original places. dt=t1-t2 will now be negative (if it started out positive).
So, dt went from positive to negative, always changing continuously. That means that at some point in between dt must have been zero. At that point the temperatures on the opposite sides were the same.
(Of course, this all assumes that temperature changes continuously. Ie. that there are no sudden jumps from one temperature to another. For example the temperature isn't 100 degrees at one pointment and right next to it the temperature is 0 degrees.)
koopashell ยท 7 points ยท Posted at 18:46:40 on May 25, 2016 ยท (Permalink)*
I follow it up to this, but how can it account for two variables? I can see how there would be a point for barometric pressure and another, different point for temperature, but not a point where both match.
*Edit - I looked at the wiki and I think I grasp it mathematically, but not 100% intuitively.
*Edit2 - Holy balls I think I get it. Technically you could cut the earth into infinite circles. So start with the equator and find your two points, then rotate the equator an infinitely small amount and get your next points. Since temperature is continuous, the next point should be infinitely adjacent to the previous. Keep rotating and getting points until you've done a full 180, those points define a ring around the circle. Then do the same thing for pressure, sure enough those two rings have to cross and there are your points. Neat.
BlugyBlug ยท 2 points ยท Posted at 14:02:33 on May 26, 2016 ยท (Permalink)
You don't have to do the same thing for pressure. Imagine you have your dt =0 ring for temperature. Then, for pressure, place your two points on the dt = 0 ring. Rotate your two points along the dt = 0 ring and at some point on this ring dp will be 0. Now you've found your point, because by definition dt=0 on the ring.
koopashell ยท 2 points ยท Posted at 14:17:00 on May 26, 2016 ยท (Permalink)
damn you are right - same solution but more straightforward reasoning.
fantabularistical ยท 1 points ยท Posted at 03:34:03 on May 26, 2016 ยท (Permalink)
That... is brilliant. Did you come up with that yourself?
koopashell ยท 1 points ยท Posted at 05:55:56 on May 26, 2016 ยท (Permalink)
yeah but full disclosure: It's been a few years but I took a lot of math in college. calc 1-4, diff eq, linear algebra, algorithms, complex variables, intro to analysis (prob most relevant), discrete math, etc. I never took topology but this sort of proof seems like an extension of real analysis, and it's the same thinking that goes into a lot of proofs for theorems in complex variables.
Mito_Bluebird ยท 1 points ยท Posted at 21:54:43 on May 26, 2016 ยท (Permalink)
That is fascinating. Could you help me understand it better? Around which axis do you rotate the equator? Around which circle do the points define a ring(ring=region bounded by two cricles)? Is dt=0 on every point in the ring or on a path bounded by the ring.
Also what happens if one of the two initial points with dt=0 is a local temperature maximum and the other one is a local minimum? Even when temperature is continuous there wouldn't be a pair of adjacent points with dt=0.
samkostka ยท 1 points ยท Posted at 20:37:54 on May 25, 2016 ยท (Permalink)
So it's kind of like the Mean Value Theorem? That's how I understand it anyway
johnnymo1 ยท 1 points ยท Posted at 15:07:48 on May 25, 2016 ยท (Permalink)
See my response here.
It's not precisely true as I have stated it, but for a continuous function from the 2-sphere to R2 , which is essentially how we think of temperature and pressure on everyday scales at the surface of the earth, it is true.
Hobey-One ยท 1 points ยท Posted at 14:47:34 on May 25, 2016 ยท (Permalink)
Could you prove this? It sounds amazing but a bit unbelieveable to me...
johnnymo1 ยท 2 points ยท Posted at 14:58:31 on May 25, 2016 ยท (Permalink)
Yep. See my response to /u/lordanubis79
loptthetreacherous ยท 1 points ยท Posted at 17:29:40 on May 25, 2016 ยท (Permalink)
I was confused, thinking you meant every point had this quality.
jusjerm ยท 1 points ยท Posted at 17:02:26 on May 25, 2016 ยท (Permalink)
Those points are called antipodes
callyg30 ยท 0 points ยท Posted at 15:35:41 on May 25, 2016 ยท (Permalink)
Can you prove this
johnnymo1 ยท 3 points ยท Posted at 15:44:48 on May 25, 2016 ยท (Permalink)
It's a slightly fictionalized version of the Borsuk-Ulam theorem for the case n = 2.
SpartanLegend ยท 83 points ยท Posted at 14:19:44 on May 25, 2016 ยท (Permalink)
In AP Calc we learned about Gabriel's Horn, a geometric figure with finite volume but infinite surface area. So basically, you could fill it with paint but not paint the inside. Cool stuff
Ian666 ยท 19 points ยท Posted at 18:35:44 on May 25, 2016 ยท (Permalink)
If you can fill the inside with paint, isn't then the inside necessarily painted?
[deleted] ยท 5 points ยท Posted at 23:44:51 on May 25, 2016 ยท (Permalink)
Don't stress the physical analogy, it always embeds a contradiction. For one, you can't fill it with paint because then you would be sending paint an infinite distance in finite time.
theasianpianist ยท 2 points ยท Posted at 02:29:50 on May 26, 2016 ยท (Permalink)
He meant the outside. Can't paint the outside.
Zarco19 ยท 3 points ยท Posted at 04:34:55 on May 26, 2016 ยท (Permalink)
the inside has the same surface area.
fantabularistical ยท 1 points ยท Posted at 03:22:13 on May 26, 2016 ยท (Permalink)
It isn't painted to a consistent depth, though. It's painted to a depth that approaches 0.
FreddeCheese ยท 16 points ยท Posted at 18:12:12 on May 25, 2016 ยท (Permalink)
You can't paint the outside.
StatikDynamik ยท 5 points ยท Posted at 18:41:53 on May 25, 2016 ยท (Permalink)
Time for a relevant Vsauce.
vonflare ยท 1 points ยท Posted at 23:32:13 on May 25, 2016 ยท (Permalink)
that was great!
pete101011 ยท 2 points ยท Posted at 17:58:48 on May 25, 2016 ยท (Permalink)
Funny thing is this can be found in electrical signals. In an ideal sense, it's an impulse.
bobbysilk ยท 5 points ยท Posted at 19:08:31 on May 25, 2016 ยท (Permalink)
Took me a few days to accept that you can have a spike that is infinitely tall but with an area of 1.
pete101011 ยท 5 points ยท Posted at 19:22:11 on May 25, 2016 ยท (Permalink)
It's crazy interesting. One of the uses is for stadiums and concert halls. You generate a close impulse sound and measure it at different locations. What you get is a signal convolved with the acoustics of the large room and then you can change how the speakers work so it nullifies any weird artifacts generated by the shape of the room.
bobbysilk ยท 5 points ยท Posted at 19:47:05 on May 25, 2016 ยท (Permalink)
Yep. Or you can do the opposite and make it sound like you're in any other room. I had to do this for a lab, where we were given a clap (impulse response) from concert halls or cathedrals and convolved it with someone speaking to make it sound like they were speaking in that concert hall / cathedral.
daPistachio ยท 1 points ยท Posted at 21:58:38 on May 25, 2016 ยท (Permalink)
this is very interesting to me. where can i go to to learn more about this
bobbysilk ยท 2 points ยท Posted at 14:42:29 on May 26, 2016 ยท (Permalink)
I wouldn't know where to start. I learned it in a signal theory class but it's not something I would recommend picking up as a hobby. Maybe Google/YouTube around for convolution, impulse response, inverse convolution and it'll get the ball rolling.
[deleted] ยท 1 points ยท Posted at 20:16:40 on May 25, 2016 ยท (Permalink)
What if you place it in a pool ful with paint?
z3ktorm ยท 5 points ยท Posted at 20:46:15 on May 25, 2016 ยท (Permalink)
It wont fit. It's infinitely long
[deleted] ยท 0 points ยท Posted at 21:01:08 on May 25, 2016 ยท (Permalink)
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z3ktorm ยท 1 points ยท Posted at 21:05:04 on May 25, 2016 ยท (Permalink)
Well okey then. Then you would need an infinitely long pool
itmustbemitch ยท 1 points ยท Posted at 23:03:42 on May 25, 2016 ยท (Permalink)
yo though there's no such thing as an "infinity number" (just an infinity, because infinity is never a number) and the different sizes of infinity apply to cardinalities of infinite sets, not limits like the the biggest size a pool could have
[deleted] ยท 1 points ยท Posted at 20:27:50 on May 25, 2016 ยท (Permalink)*
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YoyoEyes ยท 1 points ยท Posted at 20:46:53 on May 25, 2016 ยท (Permalink)
Not necessarily true. A sequence can increase by a number that approaches 0 and still diverge. For example, a Harmonic series which is the sum of 1/n starting from n=1 and going on to infinity. Even though 1/n approaches 0, the sum of the sequence still approaches infinity.
[deleted] ยท -2 points ยท Posted at 20:59:29 on May 25, 2016 ยท (Permalink)*
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PM_ME_YOUR_PAULDRONS ยท 5 points ยท Posted at 21:08:25 on May 25, 2016 ยท (Permalink)*
This is not correct. Note that 1 + 1/2 + 1/3 + 1/4 is bigger than 2.
1 + 1/2 + 1/3 + 1/4 = 12/12 + 6/12 + 4/12 + 3/12 = 25/12 = 2 + 1/12.
You can actually show that for any real number r there is some integer n such that if you add up the first n terms in the harmonic series you end up with a number bigger than r. This is what we mean by the series diverging.
The growth of the sum of the first n terms is logarithmic, the sum is greater than log(n+1) but less than log(n) + 1. Logarithmic growth is ridiculously slow, the example which is usually given is that the sum of the first 1043 terms is less than 100. Nevertheless there is some number of terms which will take you over a million, trillion etc.
YoyoEyes ยท 2 points ยท Posted at 21:12:31 on May 25, 2016 ยท (Permalink)
No. What you're thinking of is the sum of 1/n2 which equals 2.
musicotic ยท 2 points ยท Posted at 23:30:14 on May 25, 2016 ยท (Permalink)
no that's pi2 /6
YoyoEyes ยท 1 points ยท Posted at 23:46:15 on May 25, 2016 ยท (Permalink)
God damn it you're right. I was thinking of 1/2n
Mocha2007 ยท 63 points ยท Posted at 17:19:52 on May 25, 2016 ยท (Permalink)
How the hell has nobody mentioned the four color theorem?
You only need at most four colors to color any map without the same colors touching.
Unless the map is in the shape of a torus or something. Then it's seven.
beleaguered_penguin ยท 7 points ยท Posted at 21:28:13 on May 25, 2016 ยท (Permalink)
It's really easy to prove it for six colours, and just a tiny bit harder to prove it for five.
Four though... fuck that.
rawling ยท 1 points ยท Posted at 21:34:15 on May 25, 2016 ยท (Permalink)
Can you share a link? I failed to prove the four-colour one a lot as a kid, I'd like to see what a proof with 6 colours actually looks like.
---lll--- ยท 1 points ยท Posted at 21:49:41 on May 25, 2016 ยท (Permalink)
No link cause om mobile. But the proof for 4 colors is huge, so good luck!
rawling ยท 5 points ยท Posted at 21:53:06 on May 25, 2016 ยท (Permalink)
Managed to find one: https://natureofmathematics.wordpress.com/lecture-notes/four-and-five-color-theorems/
I don't think younger-me knew Euler's formula...
Furoan ยท 2 points ยท Posted at 03:28:44 on May 26, 2016 ยท (Permalink)
Younger you was a scrub. We should team up and take his lunch money, and use it to buy some crayons from crayola.
Porridgeandpeas ยท 1 points ยท Posted at 23:53:07 on May 25, 2016 ยท (Permalink)
All this math stuff on Reddit is making me excited to graduate and I can learn math in my spare time for fun. This will be the first, thanks!
TheOnlyMeta ยท 4 points ยท Posted at 00:12:02 on May 26, 2016 ยท (Permalink)
The 4 colour theorem is a result of graph theory... and it's such a strange topic. The statement is easy enough for a 5 year old to understand but the proof required deep mathematical insight alongside heavy computational power. It's a subject where there doesn't seem to be any rhyme or reason to the results, no elegance. The 4 colour theorem is almost just a beautiful coincidence.
[deleted] ยท 3 points ยท Posted at 19:39:37 on May 25, 2016 ยท (Permalink)*
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ChiefPockets ยท 4 points ยท Posted at 19:49:33 on May 25, 2016 ยท (Permalink)
I believe "they" say that corners touching doesn't count, but I think you raise a good point.
ArcticReloaded ยท 4 points ยท Posted at 20:52:54 on May 25, 2016 ยท (Permalink)
To be precisely, you can paint any planar graph with 4 colors (3 if there are no triangles). If you "translate" your map into a graph with vertices and edges you see that the pizza example is not planar. ;-)
christina4409 ยท 1 points ยท Posted at 23:53:28 on May 25, 2016 ยท (Permalink)
I don't believe you. Why would you need 4?
Mocha2007 ยท 1 points ยท Posted at 23:57:45 on May 25, 2016 ยท (Permalink)
...If you have four countries which all border each other...? E.g. Belgium-Luxembourg-Germany-France.
christina4409 ยท -1 points ยท Posted at 00:26:14 on May 26, 2016 ยท (Permalink)
I don't see why just two wouldn't suffice. Say, white for the country, black for the border, also black for the name.
Mocha2007 ยท 2 points ยท Posted at 00:43:07 on May 26, 2016 ยท (Permalink)
Because you're coloring the countries not the border.
christina4409 ยท 0 points ยท Posted at 00:46:18 on May 26, 2016 ยท (Permalink)
So then you only need one color for the countries.
Mocha2007 ยท 1 points ยท Posted at 00:59:33 on May 26, 2016 ยท (Permalink)
The countries are next to each other. They can't be the same color.
christina4409 ยท -3 points ยท Posted at 01:07:14 on May 26, 2016 ยท (Permalink)
What's the point of that?
And what if you have 5 that touch at one point? Or 20?
Mocha2007 ยท 2 points ยท Posted at 01:26:27 on May 26, 2016 ยท (Permalink)
Sometimes countries form next to each other...? There's not really a point to this it's just a thing that kinda happens...
Points are not borders. Borders are edges.
christina4409 ยท -2 points ยท Posted at 02:03:28 on May 26, 2016 ยท (Permalink)
No I mean the point of not having the countries be the same color.
fullmoondeathclassic ยท 2 points ยท Posted at 16:28:40 on May 26, 2016 ยท (Permalink)
The problem isn't really about coloring a world map, that's just an easy example of how it can be used.
Lemerney2 ยท 1 points ยท Posted at 09:47:42 on May 26, 2016 ยท (Permalink)
There is no point! But not everything has to have one to be interesting.
[deleted] ยท 1 points ยท Posted at 10:45:18 on May 26, 2016 ยท (Permalink)
Because if every country is the same colour it's all indistinguishable (assuming no borders.)
christina4409 ยท 1 points ยท Posted at 11:22:11 on May 26, 2016 ยท (Permalink)
Why not just use borders and cut colors in half?
And that 4 colors fails pretty quickly with enclaves and exclaves.
[deleted] ยท 1 points ยท Posted at 11:25:38 on May 26, 2016 ยท (Permalink)
It's not supposed to be literally a world map. It's how many colours, maximum, do you need to colour a plane of contiguous areas.
christian-mann ยท 1 points ยท Posted at 10:51:20 on May 26, 2016 ยท (Permalink)
That is the definition of the problem.
Wisteso ยท -2 points ยท Posted at 21:34:45 on May 25, 2016 ยท (Permalink)
I think you mean that you need at least four colors. You could certainly do it with 5 or more colors.
Mocha2007 ยท 2 points ยท Posted at 21:54:23 on May 25, 2016 ยท (Permalink)
Nope. I meant what I said.
liquidpig ยท 2 points ยท Posted at 22:50:13 on May 25, 2016 ยท (Permalink)
Imagine I give you a map that is just a rectangle and it's divided into "countries" that are just vertical stripes. You could color the map black-white-black-white... so that each black stripe only ever touches white stripes. Sure, you COULD use 27 different colors, but you can make it so that no two countries of the same color touch by just using two colors.
But I could then draw another map where you'd have to have two countries of the same color touch if I only let you use 2 colors. Maybe this map requires you to use 3. Sure, you COULD use 27 colors, but this map requires you to use 3.
I could then come up with a harder map and require you to use 4 colors.
I cannot come up with a map that requires you to use 5. Sure, you could use 5, but you will never be required to use 5.
Supersting ยท 2 points ยท Posted at 22:57:08 on May 25, 2016 ยท (Permalink)
You could, but did you need them?
JoeHook ยท 1 points ยท Posted at 23:07:37 on May 25, 2016 ยท (Permalink)
Does one need 28 pairs of shoes?
The answer is yes. Trust me, I know what you're thinking, but trust me, it's yes.
99shadow25 ยท 1 points ยท Posted at 21:56:29 on May 25, 2016 ยท (Permalink)
Nope, most. You could have a map with 5.73ร1010000 countries and that you can do it with 4 would still hold true every time.
[deleted] ยท -2 points ยท Posted at 23:00:36 on May 25, 2016 ยท (Permalink)*
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Aterion ยท 3 points ยท Posted at 23:19:06 on May 25, 2016 ยท (Permalink)
green could be orange, cause touching with a corner doesn't count.
Porridgeandpeas ยท 1 points ยท Posted at 23:55:22 on May 25, 2016 ยท (Permalink)
And what about white?
dragonfyre173 ยท 1 points ยท Posted at 23:57:08 on May 25, 2016 ยท (Permalink)
If green is turned orange, white is effectively your fourth color.
Porridgeandpeas ยท 1 points ยท Posted at 00:01:29 on May 26, 2016 ยท (Permalink)
True! Thanks
Mocha2007 ยท 2 points ยท Posted at 00:00:38 on May 26, 2016 ยท (Permalink)
Nope.
Solution: https://i.imgur.com/S3dhegU.png
88gavinm ยท 0 points ยท Posted at 23:26:24 on May 25, 2016 ยท (Permalink)
Interesting.
kimera-houjuu ยท 349 points ยท Posted at 14:16:15 on May 25, 2016 ยท (Permalink)
.999... = 1
Here:
x = .999...
10x = 9.999...
10x = 9 + .999...
10x = 9 + x (since x = .999... )
9x = 9
x = 1
Snytbaggen ยท 50 points ยท Posted at 15:13:12 on May 25, 2016 ยท (Permalink)
Also:
1/3 = 0.333...
3*1/3 = 3*0.333...
3*1/3 = 3/3
3*0.333... = 0.999...
3/3 = 1
0.999... = 1
thegraaayghost ยท 19 points ยท Posted at 15:55:36 on May 25, 2016 ยท (Permalink)
The first one works better, because many people's intuition will tell them that 3*.333... is 1, but not .999...
I usually follow up with something like yours after I've shown them the first one, just to help it sink in.
The first one is pretty much impossible to argue with, and tends to blow people's minds.
[deleted] ยท 2 points ยท Posted at 23:21:24 on May 25, 2016 ยท (Permalink)
I'm the opposite. I think you have to already intuit 0.999... = 1 to intuit that 0.999...*10 = 9.999... I always just use addition.
1/3 = 0.333...
1/3 + 1/3 = 0.333... + 0.333... = 2/3 = 0.666...
2/3 + 1/3 = 0.666... + 0.333... = 3/3 = 0.999... = 1
thegraaayghost ยท 2 points ยท Posted at 03:14:56 on May 26, 2016 ยท (Permalink)
How do you figure? You just need to know that multiplying by 10 moves the decimal point to follow that step.
[deleted] ยท 1 points ยท Posted at 03:51:50 on May 26, 2016 ยท (Permalink)
Good point, I hadn't thought of it like that. I think I was taught this using the notation with a single digit of the repeating decimal and a line over it so addition made more sense like that.
thegraaayghost ยท 2 points ยท Posted at 03:55:13 on May 26, 2016 ยท (Permalink)
Oh, I was taught that way too, and that's the notation I use (I'm a teacher). But of course, I don't know of any good ways to represent that on Reddit. I probably only recognized the proof immediately because I show it to people frequently.
Machtung7 ยท 1 points ยท Posted at 17:19:38 on May 25, 2016 ยท (Permalink)
or
1/9 = .111...
2/9 = .222...
3/9 = .333...
...
8/9 = .888...
9/9 = .999...
but 9/9 is also = 1.
therefore 1 = .999...
maz-o ยท 1 points ยท Posted at 19:15:16 on May 25, 2016 ยท (Permalink)
or even simpler:
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...
3/3 = 1
0.999... = 1
Ddyer11 ยท 1 points ยท Posted at 00:55:30 on May 26, 2016 ยท (Permalink)
I've actually been thinking about this a good bit lately. The best way I've come to accept (dumb it down) it is to essentially look at it as 1.0000 repeating with a 1 at the end of the zeroes. If you accept that the zeroes are infinite, it's much easier to understand.
Phil0042 ยท 20 points ยท Posted at 15:16:52 on May 25, 2016 ยท (Permalink)
Alternatively, if you're willing to accept 1/3 = 0.333..., then just multiply both sides by 3!
rantforupdate ยท 61 points ยท Posted at 15:51:20 on May 25, 2016 ยท (Permalink)
That gave me 2=1.999...
ManBearPig1865 ยท 13 points ยท Posted at 16:09:44 on May 25, 2016 ยท (Permalink)
Congrats, you are now Terrance Howard.
bsievers ยท 19 points ยท Posted at 16:23:13 on May 25, 2016 ยท (Permalink)
/u/rantforupdate was pointing out that 3! is 3 factorial, 3*2*1 so multiplying both sides by 3! actually ends up with you multiplying both sides by 6 and complicating the proof.
ManBearPig1865 ยท 2 points ยท Posted at 16:25:37 on May 25, 2016 ยท (Permalink)
I really wasn't going through the math, but if you're unfamiliar with Terryology(actor Terrance Howard's math system) it very much worth a Google. The joke might make a bit more sense then.
bsievers ยท 3 points ยท Posted at 16:38:15 on May 25, 2016 ยท (Permalink)
Yeah, I've read it, and cried afterwards.
I just meant that the original comment wasn't using any mistaken math and didn't want anyone misled. Though introducing people in this thread to terryology may be interesting...
ManBearPig1865 ยท 2 points ยท Posted at 16:44:43 on May 25, 2016 ยท (Permalink)
I may or may not have created a new account called RealTerranceHoward and left that root 2 = 1. I was a little late to respond but I figure it would be worth it to those in on Terryology.
-100-Broken-Windows- ยท 3 points ยท Posted at 17:34:31 on May 25, 2016 ยท (Permalink)
/r/UnexpectedFactorial
thestickystickman ยท 1 points ยท Posted at 10:50:39 on May 26, 2016 ยท (Permalink)
So 6?
Phil0042 ยท 1 points ยท Posted at 11:17:01 on May 26, 2016 ยท (Permalink)
It's not a factorial, I'm just really excited about this topic.
Lord_Charlemagne ยท 6 points ยท Posted at 16:33:46 on May 25, 2016 ยท (Permalink)
I forget the proof exactly but I think the most legitimate proof is the one using geometric series. Something along the lines of this: .99999 repeating is the same as .9 +.09 +.009 +.0009 ... which is a geometric series where first term a=.9 and ratio r = .1. using the geometric series sum, the series sum is equal to a/(1-r) = .9 / (1-.1) = .9 / .9 = 1. Correct me if anything is wrong but I think this is what it is
SpiderOnTheInterwebs ยท 2 points ยท Posted at 16:53:28 on May 25, 2016 ยท (Permalink)
Yeah this is right. I like this proof better than all the rest. Feels more legitimate for some reason.
RobinLSL ยท 4 points ยท Posted at 21:41:19 on May 25, 2016 ยท (Permalink)
The problem with the "usual" proof is that there is a slight leap of faith when you start with x=0.9... and move to 10x=9.99... You indirectly use some kind of distributive property of multiplication over infinite sums, which does need to be justified properly.
LDVINJCMNT ยท 2 points ยท Posted at 18:10:49 on May 25, 2016 ยท (Permalink)
I always understood the 'sum' of a mathematical series was the limit, as in the lowest number that would never be reached by that series, rather than the actual sum of all the values?
johnnymo1 ยท 2 points ยท Posted at 19:02:01 on May 25, 2016 ยท (Permalink)
It is a limit, yes. But it's not quite right to think of it as something which can't be reached by the series. If that were true, what's 0 + 0 + 0 + 0 + ...?
[deleted] ยท 1 points ยท Posted at 19:06:15 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 1 points ยท Posted at 19:14:33 on May 25, 2016 ยท (Permalink)
1 + 0 + 0 + 0 + ...
There's an infinite series that doesn't start at the limit, reaches its limit, and never exceeds it.
[deleted] ยท 1 points ยท Posted at 19:17:36 on May 25, 2016 ยท (Permalink)*
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johnnymo1 ยท 0 points ยท Posted at 19:18:30 on May 25, 2016 ยท (Permalink)
Why does it need to?
[deleted] ยท 1 points ยท Posted at 19:24:18 on May 25, 2016 ยท (Permalink)*
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johnnymo1 ยท 2 points ยท Posted at 19:29:29 on May 25, 2016 ยท (Permalink)
What does being a geometric series have to do with it? Your qualm doesn't seem to be specific to geometric series. In fact, you never even mentioned geometric series. You said:
etc.
[deleted] ยท 1 points ยท Posted at 19:32:29 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 19:36:16 on May 25, 2016 ยท (Permalink)
You've raised no issue specific to geometric series. What does it matter what the original proof was? Your statement applies to infinite series in general. The fact that the initial proof was a geometric series is irrelevant.
But even if we were talking about geometric series specifically, what about this example:
Which you don't seem to have said anything about. Except the post immediately after it, which I honestly can't make heads or tails of.
[deleted] ยท 1 points ยท Posted at 19:38:33 on May 25, 2016 ยท (Permalink)
[deleted]
johnnymo1 ยท 2 points ยท Posted at 19:41:41 on May 25, 2016 ยท (Permalink)
I think the primary issue is seeing a limit, and hence a series, as a "process." A series is not "reaching" anything. 0.9 + 0.09 + 0.009 + ... is equal to its sum as an infinite series, which is 1.
[deleted] ยท 1 points ยท Posted at 19:43:54 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 19:46:16 on May 25, 2016 ยท (Permalink)
The series is not reaching anything. 0.9 + 0.09 + ... is not going anywhere, it's just a number.
[deleted] ยท 1 points ยท Posted at 19:50:17 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 19:53:35 on May 25, 2016 ยท (Permalink)
It is absolutely equal to 1. By definition it is equal to 1. It is equal to the limit of its sequence of partial sums, {0.9, 0.99, 0.999, ... }, whose limit is unequivocally 1, again by definition.
[deleted] ยท 0 points ยท Posted at 19:56:33 on May 25, 2016 ยท (Permalink)
[deleted]
johnnymo1 ยท 2 points ยท Posted at 20:11:21 on May 25, 2016 ยท (Permalink)*
This is what I was talking about, thinking of the limit as a process. I think it confuses a lot of people. It would be best to stop imagining an infinite sum as a process, or thinking of a man adding up terms for the rest of forever. It's very confusing to think of that way. An infinite series is a limit of a sequence of partial sums. A limit is a number that satisfies the definition of a limit for the sequence.
[deleted] ยท 1 points ยท Posted at 20:14:19 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 20:16:49 on May 25, 2016 ยท (Permalink)
This is directly at odds with:
The series never reaches anything. The sum of the series is one number.
Once again, how about this series: 0 + 0 + 0 + ...? That's an infinite geometric series. You can use the formula to find its sum.
[deleted] ยท 1 points ยท Posted at 20:19:11 on May 25, 2016 ยท (Permalink)
[deleted]
johnnymo1 ยท 2 points ยท Posted at 20:23:14 on May 25, 2016 ยท (Permalink)
Because it's untrue. I'm not the one arguing with literally all mathematicians. There are numerous proofs that 0.999... = 1 that don't rely on series, how do you reconcile them with your belief that 0.9 + 0.99 + 0.999 + ... apparently does not equal 1?
That series is not a process. It is a representative for a number, and that number is 1.
That sounds like you've just thrown out a case as not proper because you don't like it. But fair enough, defining the common ratio for it is a little problematic.
[deleted] ยท 1 points ยท Posted at 20:26:03 on May 25, 2016 ยท (Permalink)*
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johnnymo1 ยท 2 points ยท Posted at 20:27:37 on May 25, 2016 ยท (Permalink)
Equality alone should tell you that. 1 + 3 = 4 is not representative of me putting two things together to get something different, the equals sign literally means "these two things are the same."
As for your not being convinced, what number falls between 0.999... and 1?
[deleted] ยท 1 points ยท Posted at 20:32:06 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 20:37:18 on May 25, 2016 ยท (Permalink)
"Adding up" is how we calculate things, and that is a process, but I think any algebraist would disagree with you that that's how we should interpret the mathematics itself, and I think empirically your rejection of well-proven mathematics is good reason to believe that that's not a helpful way to think of it.
No it's not, because the integers don't have the property that between any two distinct numbers there exists another number. The reals do have that property. It's easy to see, for instance, that (9 + 10)/2 is not an integer, but for any two distinct rational numbers, (9 + 10)/2 is a rational number which lies strictly between them. Not sure why you'd think you can just change number systems and expect all properties to carry over, but the fact that the reals have that property comes straight from the axioms for the construction of the real numbers. See Principles of Mathematical Analysis by Rudin if you don't believe me.
[deleted] ยท 1 points ยท Posted at 20:49:21 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 2 points ยท Posted at 21:00:00 on May 25, 2016 ยท (Permalink)
That's is patently not what I am saying. In fact, what I just said is that 1 + 3 = 4 means that 1 + 3 and 4 are different representations of precisely the same object, which is quite the opposite of what you just said I implied.
If they were mathematicians I'd say that's frankly embarrassing for their respective universities, but what is "math-based?" I have spoken with many an electrical engineer, for example, who has had deep-seated misunderstandings of the structure of the real numbers. A math-based degree does not a mathematician make.
Also, I will admit that "all mathematicians" was a bit of hyperbole to begin with. There are some wacky mathematicians (see: N.J. Wildberger). But the vast, vast majority understand this. It's taught in introductory analysis classes.
I don't see how that's the case. In fact, that doesn't follow from the axioms at all, but specifically I don't see your reasoning for it. All distinct real numbers have finite distances from each other. Arbitrarily small, yes, but finite.
[deleted] ยท 1 points ยท Posted at 21:17:01 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 1 points ยท Posted at 21:31:27 on May 25, 2016 ยท (Permalink)
I understand this. It's definitely not intuitive. In fact, I still find it a bit strange. This sort of thing causes some problems in places. For instance, proving that a line and a plane have the same cardinality. There is a common way to do this that involves taking points in the plane and interleaving the digits of their x and y coordinates together to get a single number that represents a point on the line (I was actually shown this in my general relativity class, and have found it other places since). The problem is, this isn't actually well-defined! The issue is that if you have a number like (0.500...,0.400...), trying to "interleave digits" to map it to a number like (0.540000...) can also be written as (0.4999...,0.3999...), which maps to (0.4399...) which is different from 0.54 no matter how you slice it. Luckily, there's a way to fix up this method into something that works, I just wanted to point out that even though the issue is settled, that doesn't mean it's not thorny. My general relativity professor was not ignorant of these sorts of issues, his research is closer to pure mathematics than physics despite being a physics professor, but even he didn't seem to notice the problem.
I feel a little bad that our discussion got somewhat heated, but hopefully it wasn't too bad. You definitely shouldn't take my word for it just because a lot of people believe it, but that should at least make you think. :)
If you want an introduction to this stuff that's gentler than Rudin (which is famously tough) take a look at something like Understanding Analysis by Abbott. I found it to be very gentle and clear. Rudin is far from gentle.
Good talking to you.
[deleted] ยท 2 points ยท Posted at 21:46:23 on May 25, 2016 ยท (Permalink)
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johnnymo1 ยท 1 points ยท Posted at 21:55:42 on May 25, 2016 ยท (Permalink)*
I have to take responsibility for part of it, but only because I have had so many discussions about this before. It starts feeling like arguing with one incredibly hard-headed person over the course of years...
It may also interest you to know that I am a convert! I didn't believe this either when I first saw it, but then I hadn't really taken a strong interest in math, and had taken no calculus at that point. That's my excuse and I'm sticking to it. :)
The later chapters are calculus based, which it seems you might have had some exposure to if you know what a geometric series is, but the first few chapters can be read by pretty much anyone (given a certain amount of mathematical maturity). Good luck!
Lord_Charlemagne ยท 1 points ยท Posted at 23:39:57 on May 25, 2016 ยท (Permalink)
I think it depends on the type of series because different series have different behaviors. Geometric is very different from an alternate series for example
jusjerm ยท 8 points ยท Posted at 16:41:39 on May 25, 2016 ยท (Permalink)
I can only imagine how many "you can also explain it with 1/3.." comments this will force upon you by the end of the day"
Nibiria ยท 5 points ยท Posted at 17:32:10 on May 25, 2016 ยท (Permalink)
Is this only true because numerals are an imperfect representation for...well, numbers, I guess?
jgthespy ยท 2 points ยท Posted at 18:48:42 on May 25, 2016 ยท (Permalink)*
Kinda. It's a side effect of how decimal notation is defined. Any number whose decimal representation ends in a000... has a second decimal representation that ends in (a-1)999...
http://picklenerd.com/math/decimal-expansion/
http://picklenerd.com/math/decimal-expansion-interactive/
_HyDrAg_ ยท 1 points ยท Posted at 07:10:48 on September 6, 2016 ยท (Permalink)*
You can describe it a sum of an infinite series and it's still true. (.9 + .09 + .009 ...)
http://www.wolframalpha.com/input/?i=Sum+9+*+(1%2F10)%5Ex+x%3D1+to+infinity
dny6 ยท 10 points ยท Posted at 15:22:57 on May 25, 2016 ยท (Permalink)*
is this a real proof of this or a fallacy?
edit: thanks everyone! I am but a humble biologist with enough math background to be skeptical! Very cool :)
panascope ยท 28 points ยท Posted at 16:16:52 on May 25, 2016 ยท (Permalink)
If you'd like to think of it another way, try and find a number between .999... and 1.
KING_CH1M4IRA ยท -4 points ยท Posted at 18:39:24 on May 25, 2016 ยท (Permalink)
You don't need to. I like to think of .999... like an asymptotic curve, a
linenumber that continually approachesa given curve1 but does notmeetequal it at any finite distance.Saytahri ยท 9 points ยท Posted at 19:11:50 on May 25, 2016 ยท (Permalink)
It's an infinite sum, and stopping it early at any point it will be less than 1, but the value of the infinite sum is 1.
DiceboyT ยท 9 points ยท Posted at 20:17:11 on May 25, 2016 ยท (Permalink)
That's like trying to argue that pi is rational because you like to think of it as 22/7.
KING_CH1M4IRA ยท -1 points ยท Posted at 22:16:34 on May 25, 2016 ยท (Permalink)
That sounds like the opposite of what I'm saying. You can continue counting off 9s until the end of time, but it isn't 1. You keep getting closer, but you never get there.
panascope ยท 4 points ยท Posted at 00:02:31 on May 26, 2016 ยท (Permalink)
Counting 9s for a quadrillion years isn't equal to .999... of course.
Right, but we're not talking about limits here, we're talking about the number .999..., a number which is exactly equal to 1.
SaveTheSpycrabs ยท 3 points ยท Posted at 01:11:00 on May 26, 2016 ยท (Permalink)
You don't continue counting until the end of time. If you stop counting at the end of time, you've left to count an infinite number of nines still. They are the same value. There is no counting, but in order for something to never quite reach another number, there has to be another step to counting it.
For example, if you stop for a moment during this "counting" and you realize that you aren't quite there, you can add another 9 and you have a number that is between your stopped number and one. The idea of .999.... Is that it represents the entirety of the infinity. You have an infinite number of nines. Think about as if you're taking a bite of a muffin, but each bite is half as small as the last. If your initial bite was only half of the muffin, will you ever complete your muffin? Get back to me with an answer.
inconspicuous_male ยท 3 points ยท Posted at 01:10:51 on May 26, 2016 ยท (Permalink)
You're correct. At ant finite distance, .999... will not reach 1.
Think about why you put the word finite there
[deleted] ยท -3 points ยท Posted at 17:27:00 on May 25, 2016 ยท (Permalink)
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stripesonfire ยท 2 points ยท Posted at 18:17:31 on May 25, 2016 ยท (Permalink)
that is less than .999...
[deleted] ยท -4 points ยท Posted at 20:52:26 on May 25, 2016 ยท (Permalink)
.99910..
redstonerodent ยท 9 points ยท Posted at 17:35:16 on May 25, 2016 ยท (Permalink)
It's not quite legitimate, but it's easy to make it rigorous using the definition of convergence of series.
To see you need to be more careful, consider:
x=1+2+4+8+16+...
2x=2+4+8+16+...
x-2x=(1+2+4+...)-(2+4+...)
-x=1
x=-1
Il_Gigante_Buono ยท 7 points ยท Posted at 15:52:47 on May 25, 2016 ยท (Permalink)
It's real.
Dr-K-G ยท 5 points ยท Posted at 17:27:37 on May 25, 2016 ยท (Permalink)
It's real but it cheats a bit because you'd technically need to prove that multiplying by 10 moves the decimal point one to the right.
Nyth ยท 1 points ยท Posted at 23:38:49 on May 25, 2016 ยท (Permalink)
It's a bit of both in a way.
It's real, but only because infinity and our numbering system don't really quite work well together.
Similarly you could say that 1 - 0.999... = 0, but you can also say that 1 - 0.999... = 1/infinity.
Infinity and our number scale just don't really work well.
ThatEconGuy ยท 1 points ยท Posted at 01:58:23 on May 26, 2016 ยท (Permalink)
It's not a proof, but the result is real. This is just a way to help people who aren't strong in calculus intuitively understand what's going on.
[deleted] ยท -8 points ยท Posted at 17:26:07 on May 25, 2016 ยท (Permalink)*
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willywag ยท 7 points ยท Posted at 17:58:15 on May 25, 2016 ยท (Permalink)
Yes, it is. 1/3 is precisely equal to 0.333...
It's not precisely equal to 0.3 or 0.33 or 0.33333333333 or any other representation with a finite number of 3s. But the notation "0.333..." means that the 3s go on forever. And that is precisely equal to 1/3.
[deleted] ยท -4 points ยท Posted at 18:01:52 on May 25, 2016 ยท (Permalink)
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Filobel ยท 4 points ยท Posted at 18:15:07 on May 25, 2016 ยท (Permalink)
I think your definition of precision is wrong.
jgthespy ยท 1 points ยท Posted at 18:42:05 on May 25, 2016 ยท (Permalink)
That's because yours is based in the real world and has nothing whatsoever to do with math.
[deleted] ยท 0 points ยท Posted at 19:37:06 on May 25, 2016 ยท (Permalink)
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jgthespy ยท 1 points ยท Posted at 19:47:43 on May 25, 2016 ยท (Permalink)
No it's a side effect of how the notation is defined. The nice thing about math is that 0.333... is perfectly precise because we know exactly what it means even though it's technically missing information. We know that it refers to 1/3 which is not missing information. Likewise, we know that 1.000... refers to 1 and 0.999... also refers to 1. It doesn't matter which way we choose to write it because our ultimate goal is to know which single object we're talking about, so it can't be a flaw in the number system or the notation because both representations do exactly what they're supposed to. They tell us that we're talking about 1.
And 0.999... = 1.000... in all numbers systems because that's how the notation is defined. You'll have to redefine your notation if you want 0.999... to be infinitesimally close to 1 in other number systems.
http://picklenerd.com/math/decimal-expansion-interactive/
willywag ยท 1 points ยท Posted at 19:29:19 on May 25, 2016 ยท (Permalink)
What is your definition of precision?
"1/3" and "0.333..." are two different representations of the same exact number. There is no number that is between them.
KSFT__ ยท 3 points ยท Posted at 17:46:45 on May 25, 2016 ยท (Permalink)
No, it's completely correct. The numbers are equal.
[deleted] ยท -6 points ยท Posted at 17:58:33 on May 25, 2016 ยท (Permalink)
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Rsaesha ยท 3 points ยท Posted at 18:14:15 on May 25, 2016 ยท (Permalink)
Saying 0.999... can't equal 1 because 0.999... is not 1 is a bit like saying 1/2 can't equal 0.5 because 1/2 is not 0.5. That is to say, just because two numbers look different doesn't mean their value is different.
0.999... and 1 are two different numerical representations of the value "1". 3/3 is another numerical representation of the value "1".
This is true for all bases. In base 3 (like your example), 0.222... is equal to 1.
[deleted] ยท -3 points ยท Posted at 18:32:30 on May 25, 2016 ยท (Permalink)
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jgthespy ยท 2 points ยท Posted at 18:43:48 on May 25, 2016 ยท (Permalink)*
No it isn't. Decimal notation is the name in every number system. There are other number systems with infinitesimals but 0.999... is not how you would write 1-infinitesimal.
Filobel ยท 1 points ยท Posted at 18:14:47 on May 25, 2016 ยท (Permalink)
0.9999 is not 1. 0.99 repeating is 1, that's the whole point of the proof. If you think it is false, then please prove that they are different numbers.
Another way to show that they are the same number is that any two numbers that are different has at least 1 number in between them. In fact, they have an infinite number of numbers between them. For instance. Between 1 and 2, there is 1.5. There is also 1.1, 1.123, 1.59178279345983474520897352, etc.
Now, please show me a number that is found between 0.9999 repeating and 1.
mintsponge ยท 17 points ยท Posted at 16:53:18 on May 25, 2016 ยท (Permalink)
This is probably my least favourite mathematical fact. I get why it is true, I understand how it works mathematically with a ton of different proofs, but I still refuse to accept that, from a philosophical standpoint, .99 recurring is ever truly equal to 1
ninjalink84 ยท 18 points ยท Posted at 17:46:32 on May 25, 2016 ยท (Permalink)
In one sense, that's probably because you have an almost correct intuition of what .999... is. We define infinitely recurring numbers as the limit of rational numbers. So .9999... is the number you get by finishing the sequence {.9,.99,.999,.9999,...}. The limit of this sequence is exactly 1. But in our real world, we don't have infinity, an at each step of this sequence, it's distinct from 1.
That said, let me state one somewhat philosophical problem with considering them as distinct numbers. There is a number between any two numbers, right? Well, what's the number between 1 and .9999999999.... ? It's impossible to write such a number down. In other words, these two numbers are infinitely close to each other (no space between them) but are different from each other. How can this be the case? It doesn't fit our understanding of the universe and how its order works.
inherendo ยท 5 points ยท Posted at 22:33:35 on May 25, 2016 ยท (Permalink)
I think a better way is to use the fact that the reals are dense. No matter how small your epsilon, you cannot find a find an interval that contains .999... and not 1. Thus they are the same.
Kahzgul ยท -1 points ยท Posted at 20:17:18 on May 25, 2016 ยท (Permalink)
This proof also disproves the "infinite points" problem. Namely the theory that nothing can actually move because in order to move from point A to point B you have to pass through an infinite number of points that lie between them, and it would take forever to traverse an infinite distance. Common sense shows this to obviously be false, but it takes the proof of 0.999...=1 to prove the claim is false. Namely, there are distances so small as to be literally indistinct from one another, and thus any two points, close enough together, are effectively the same point. Therefore stating that an infinite number of points exist between any two points A and B is a meaningless statement - in order to truly define distinct points, they must be far enough apart from one another to measure, and thus there cannot be an infinite number of them. It is therefore possible to traverse both a finite number of distinct points and an infinite number of indistinct ones.
VincentPepper ยท 2 points ยท Posted at 21:35:50 on May 25, 2016 ยท (Permalink)
Is that about point's in the real world or in a Mathematical sense? The number of points is only an issue to begin with if you assume there is a lower limit in time/energy required to move from one point to the one next to it.
This is only true if you cannot measure arbitrary small distances. Which probably holds in the real world since there are plank lengths and other Quantum stuff I'm not familiar with.
But in Math that is not true since the distance between points can be infinitely small. So we can measure any distance, no matter how small.
Between every two distinct points there ARE infinite many Points in Math. For one example:
Just imagine the distance between the points on a number line. No matter how big or small the distance between them if it's a real value we can measure it. (Actually also for complex ones but that gets complicated.)
So if we can measure it we know what half of it is. So we can also tell that and where the point exactly between the two is. Start again using the first point and the resulting middle point of that calculation and you can repeat the process getting another point. Then you can take that point to get another one and you can do this forever. And at each step you will have an exact number for where the Point lies. Resulting in a infinite series of points.
Kahzgul ยท -3 points ยท Posted at 22:42:40 on May 25, 2016 ยท (Permalink)*
Right, that's exactly the problem. And the proof that 0.999... = 1 solves it, because there exists some limit for the measurable distance between points such that 0.000...1 = 0. Evidencing that there is actually a limit to the number of distinct points between any two points.
edit to show the proof of that statement:
0.999... = 1
0.999...+0.000...1 = 1 + 0.000...1
1 = 1 + 0.000...1
0 = 0.000...1
ninjalink84 ยท 1 points ยท Posted at 00:37:12 on May 26, 2016 ยท (Permalink)
... what?
Kahzgul ยท 0 points ยท Posted at 00:42:33 on May 26, 2016 ยท (Permalink)
which part was confusing?
ninjalink84 ยท 4 points ยท Posted at 01:25:10 on May 26, 2016 ยท (Permalink)
Why does .9999999....+.000000...1=1? It's not like there can be infinitely many zeroes there.
Kahzgul ยท 1 points ยท Posted at 16:28:25 on May 26, 2016 ยท (Permalink)
Why can't there be?
ninjalink84 ยท 2 points ยท Posted at 18:52:59 on May 26, 2016 ยท (Permalink)
To be short, it's because the notation doesn't really mean anything. There are multiple ways it can be interpreted so that it does make sense, such as what /u/VincentPepper did, or interpreting it as an infinitesimal, but the claim seemed to be that .0000...1 was a number that made sense in some self evident way, which isn't really the case.
VincentPepper ยท 0 points ยท Posted at 08:48:40 on May 26, 2016 ยท (Permalink)
Why not? Assuming he wants infinit zeros we can replace it with the series 1/10n where n converges to infinity.
Of course the value of the series is also zero so his proof is not actually one.
It's wrong because 1 + 0.00...1 is the same as 1 and so his result is 1 = 1 which means he doesn't proof there is a contradiction.
VincentPepper ยท 1 points ยท Posted at 08:37:01 on May 26, 2016 ยท (Permalink)
That step is wrong unless you follow it with 1= 1. 0.99... is the same as 1. If you write 1 instead of 0.99.. which we can because we know the same it would be:
1+0.0..1 = 1 + 0.00..1
1 = 1 + 0.00...1
Which doesn't make sense. Because either 0.00..1 is distinct from zero in which case the transformation on the left side is wrong. Or it is zero in which case the one on the right side is while not wrong irritating because it's the same value as 1.
As it stands you treat it different on each side of the equation resulting in a wrong proof.
It helps to try and think about what 0.00...1 should actually be, as a value. I could think of two ways here.
Which would mean it's zero proving the above pointless.
Ok so let's define it as a infinite number of zeros followed by a one! Let's try this.
You can get an arbitrary number of zeros by rewriting it as 1/10n where n is the number of zeros. So let's just put infinity as n and be done.
So now we get 1/infinity. But what is 1/infinity? Short answer: It's once again zero.
For a long explaination of 1/infinity you could look here: http://math.stackexchange.com/questions/44746/one-divided-by-infinity
VincentPepper ยท 1 points ยท Posted at 09:04:49 on May 26, 2016 ยท (Permalink)
For another approach: If you say there is a smallest mathematical defined length l that is different from zero you have to be able to define it.
So l = some formula.
But if you come to me and say "Hey l is the smallest thing!" I can always say: "But l/2 is smaller and also defined" Which is true and why there is no smallest number.
The infinite points "problem" is not wrong because there are not infinite many points. (There are). But because the absolute distance doesn't change no matter in how many parts you break it.
As the number of points increases the length between them decreases.
Break it in two parts each is half of it. Four parts each a quarter.
Until at infinit many distances the length becomes infinite small.
At which point the math becomes tricky, but you can show that even these infinite many distances which are infinitly small sum up to the same total distance that was between your two starting points.
epwnym ยท -4 points ยท Posted at 18:28:38 on May 25, 2016 ยท (Permalink)
No it isn't. It's no more impossible than "writing down" an infinitely recurring set using an ellipsis. Just because the Real Number system doesn't have denotation for infinitesimal differences (I don't think) doesn't mean we couldn't invent one.
0.0โฆ1
or
0.
01 (imagine that strikethrough is an overline)jgthespy ยท 6 points ยท Posted at 18:40:55 on May 25, 2016 ยท (Permalink)
You can't just invent new real numbers by giving them notation. Whatever you invent is part of a different number system that extends the reals. It is not a real number.
And while we're at it, why don't you go ahead and define that notation? What exactly does it represent and how can you use it for other numbers?
Bob_Droll ยท 6 points ยท Posted at 19:08:27 on May 25, 2016 ยท (Permalink)
I feel as though we're about to witness the birth of an entirely new branch of mathematics.
ninjalink84 ยท 5 points ยท Posted at 22:31:41 on May 25, 2016 ยท (Permalink)
Not really, since mathematicians have already considered a math along these lines. A number bigger than 0 but smaller than any other number is called infinitessimal and are used extensively when looking at the hyperreal numbers.
jgthespy ยท 5 points ยท Posted at 18:27:11 on May 25, 2016 ยท (Permalink)
1.000... = 0.999...
It's just decimal notation. They're both different ways of writing the same thing, but one of them is less annoying to write because we can just dump the zeroes and write 1.
This is actually true for every number that has a terminating decimal expansion. They all can be written as x.abcd000... or as x.abc(d-1)999...
http://picklenerd.com/math/decimal-expansion-interactive/
jgthespy ยท 1 points ยท Posted at 18:38:09 on May 25, 2016 ยท (Permalink)*
Aww that other guy deleted his comment. I'm just going to reply to myself then.
It's a side effect of the notation that you're going to run into regardless of which base you pick. Changing the base just changes which numbers have two representations. If the denominator of a number is equal to a product of powers of its prime factors, then it has two representations in the base-n equivalent of decimal notation. So anything in base 10 with a denominator equal to 2a * 5b has two different decimal representations.
Seraphaestus ยท 2 points ยท Posted at 20:29:44 on May 25, 2016 ยท (Permalink)
If it isn't equal to 1 then there must be a number in between 0.9 recurring and 1, as the set of real numbers is not discrete. Which means there must be some number 0.9...1. But there are infinite 9s, so this hypothetical 1 is never reached; the number is simply 0.9 recurring.
chromeless ยท 1 points ยท Posted at 07:08:22 on May 26, 2016 ยท (Permalink)
I completely agree with you in this instance. 0.999... = 1 is simply a result of a combination of the properties of the real number system and the notation we use for it. None of the 'proofs' (most of them make unstated assumptions in round about ways) do anything to show that infinitesimal numbers are impossible, which is what most people are really asking when they pose the question, as they are not and there are number system extensions where numbers less than any finite real number but greater than zero are possible.
scooley01 ยท -2 points ยท Posted at 23:29:32 on May 25, 2016 ยท (Permalink)
The way I rationalize it in my head is that .999~ and 1 are not exactly the same number, as our intuition tells us. But they're so infinitely close together that there can be no meaningful or useful distinction between them. Our mathematics cannot differentiate between them, as shown in the proofs that you can find, but by definition they are not exactly the same number.
[deleted] ยท 2 points ยท Posted at 04:14:41 on May 26, 2016 ยท (Permalink)
No, they are exactly the same number.
scooley01 ยท -2 points ยท Posted at 04:17:37 on May 26, 2016 ยท (Permalink)
They're both being represented in decimal numbers. It's not possible for two values to be represented by different numerals in the same format...that's by definition not how numbers work.
[deleted] ยท 3 points ยท Posted at 04:31:28 on May 26, 2016 ยท (Permalink)
It's okay for numbers to have different fraction representations. You think 4/2=6/3 right? It's the same thing with decimals. There's no reason why a number can't have two different decimal expansions.
[deleted] ยท 1 points ยท Posted at 04:21:19 on May 26, 2016 ยท (Permalink)
Proof?
Can you define the real numbers? Hint: if you don't know what Cauchy sequences or Dedekind cuts are, no you can't.
jgthespy ยท 1 points ยท Posted at 00:31:20 on May 27, 2016 ยท (Permalink)
By the definition of decimal notation, that's exactly how numbers work. All numbers with terminating decimal expansions have a second representation. e.g. 0.5 = 0.4999...
This is a fact, and it's much more interesting to think about why it's true than to argue incorrectly that it isn't just because it doesn't match up with what you learned when you were 8 years old.
Liquid_Fire_ ยท -4 points ยท Posted at 22:01:35 on May 25, 2016 ยท (Permalink)
Well you're in luck because its not true. The issue with the proof is that he replaces .999... with x. You can't do that because x is fundamentally a different number than the .999... that was replaced with.
Mr_Facepalm ยท 3 points ยท Posted at 23:07:59 on May 25, 2016 ยท (Permalink)
You don't do much math, do you?
Liquid_Fire_ ยท -2 points ยท Posted at 23:54:53 on May 25, 2016 ยท (Permalink)
What issue do you have with my math? Are you saying x *10 = x? Cause I'm sorry to tell you that you would be wrong.
Mr_Facepalm ยท 2 points ยท Posted at 17:50:29 on May 26, 2016 ยท (Permalink)
Apparently you don't know what variables are.
MichaelOChE ยท 7 points ยท Posted at 15:02:17 on May 25, 2016 ยท (Permalink)
I was going to say there's a proof of this using an infinite series, but this works, too.
Dr-K-G ยท 5 points ยท Posted at 17:26:38 on May 25, 2016 ยท (Permalink)
If you'd really want to use the above proof rigourously you first need to prove that multiplying by 10 is the same thing as moving the decimal point one to the right which again requires using infinite series. Infinite series are unavoidable because that's how decimal representation is defined.
Zarco19 ยท 1 points ยท Posted at 04:54:39 on May 26, 2016 ยท (Permalink)
True, but for people who are really struggling with this, it's probably because they don't know a whole lot of math. These simple and loose arguments will probably work better than trying to talk about infinite series. At best, they probably don't get it and miss out on understanding it, and at worst they think you belong on r/iamverysmart.
TheDeathanimator ยท 10 points ยท Posted at 15:32:11 on May 25, 2016 ยท (Permalink)
There's also 1/3 + 1/3 + 1/3 = 1 and .3333... + .3333... + .3333... = .9999...
.3333... = 1/3
[deleted] ยท 7 points ยท Posted at 14:41:38 on May 25, 2016 ยท (Permalink)
always liked this one
[deleted] ยท 8 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
Same. Mainly because it is so hard for most people to accept, and watching their internal struggle to accept a fact that has been logically proven is amazing and insightful.
chromeless ยท 2 points ยท Posted at 07:30:05 on May 26, 2016 ยท (Permalink)
The reason it's "difficult to accept" is because I suspect that a lot of people who are curious about the answer aren't so much interested in say, what the limit of a sequence defined by lim[n from 1 to infinity] (sum of, for k from 1 to n: ( 9*10-k)) is. What they are interested in is whether or not infinitesimal numbers 'exist', and this why the solution to this other problem baffles them so much, it does nothing to show that they can't exist in itself or in what context this can be said to be true.
PresidentWeevil ยท 3 points ยท Posted at 16:12:58 on May 25, 2016 ยท (Permalink)
Can also be explained (a little bit easier) like this:
1/3 = 0.3333...
3 x 1/3 = 3/3 = 1
But if 1/3 = 0.3333...
3 x 1/3 = 0.999...
Therefore
0.999... = 1
DynaBeast ยท 1 points ยท Posted at 16:53:51 on May 25, 2016 ยท (Permalink)
You could also say 10/3 = 3.3333... , x = 10/3 = 3.3333... , 3x = 9.999999.... = 10.
Milky_Andromeda ยท 1 points ยท Posted at 16:58:53 on May 25, 2016 ยท (Permalink)
Another proof:
1/3 = 0.33333..... Multiplying both sides of the equation by 3 yields: 1/3 X 3 = 0.33333..... X 3 3/3 = 0.99999..... 1 = 0.99999.....
chrissycapstick ยท 1 points ยท Posted at 17:30:29 on May 25, 2016 ยท (Permalink)
I am looking at this, but you got rid of x on one side but didn't get rid of it on the other. I am really confused by the work, but I am not really good at math either, so I can't dispute it.
Edit: and I found it.
SureLockHomes_sc ยท 1 points ยท Posted at 17:34:09 on May 25, 2016 ยท (Permalink)
This looks interesting, could something similar be done with other numbers?
jgthespy ยท 2 points ยท Posted at 18:53:19 on May 25, 2016 ยท (Permalink)*
Yes. Any number with a terminating decimal expansion (i.e. ends in 000...) has two different decimal representations. For example:
0.5 = 0.4999...
0.2483 = 0.2482999...
Remember that 0.5 = 0.5000... and we just chop off the 0's because it's clear what the number 0.5 represents. If we chop off the 9's from 0.4999..., we get 0.4 which is not the number we're trying to represent. That's why you only ever learn about one representation and why it seems to weird to find out that there's a second way to write the same number. It's just annoying to write it that way so we don't.
[deleted] ยท 1 points ยท Posted at 17:48:53 on May 25, 2016 ยท (Permalink)
I lost you here. I was expecting to see:
10x = (10)0.999...
If you are trying to prove to me that 0.999... = 1, then you cannot say 10x = 9.999... in the same proof!
By the way I DO accept that 0.999... = 1, but I am not satisfied with the above proof.
jgthespy ยท 1 points ยท Posted at 18:28:19 on May 25, 2016 ยท (Permalink)
http://picklenerd.com/math/decimal-expansion-interactive/
This is a visual explanation.
KarlKastor ยท 1 points ยท Posted at 18:49:38 on May 25, 2016 ยท (Permalink)
if someone still doesn't believe this, ask them what the difference between 1 and 0.999...(reoccurring) is. Some will answer 0.000...(reoccurring)1 then point out that you will never reach the 1 because there are infinitly many zeroes before it.
meh100 ยท 1 points ยท Posted at 18:53:36 on May 25, 2016 ยท (Permalink)
That's not a proof. The step from x = .999... to 10x = 9.999... assumes that what 9.999... is is known. The same assumption is in that step as in the claim that .999... = 1.
nicksayswatzup ยท 1 points ยท Posted at 18:55:12 on May 25, 2016 ยท (Permalink)
Also: 1/3 = .333โฆ 1/3 * 3 = 3/3 = .999โฆ =1
lickwidforse2 ยท 1 points ยท Posted at 19:03:30 on May 25, 2016 ยท (Permalink)
Wouldn't .999... + .0...1 = 1
jgthespy ยท 1 points ยท Posted at 19:12:42 on May 25, 2016 ยท (Permalink)
.0...1 isn't a real number.
lickwidforse2 ยท 1 points ยท Posted at 19:15:06 on May 25, 2016 ยท (Permalink)
.999... Is not either is it?
jgthespy ยท 1 points ยท Posted at 19:25:40 on May 25, 2016 ยท (Permalink)*
0.999... is a real number because it's equal to 1. A number that's infinitesimally close to 1 is not a real number, and you wouldn't write it as 0.999... because that notation already means something, and that something just happens to be the same thing that 1.000... means.
lickwidforse2 ยท 1 points ยท Posted at 19:29:10 on May 25, 2016 ยท (Permalink)
I thought .999... Meant ".9 repeating infinitely" my mistake.
jgthespy ยท 1 points ยท Posted at 19:30:26 on May 25, 2016 ยท (Permalink)
It does. And 1.000... means 1.0 repeating infinitely. Neither one of them refers to things being infinitely small.
lickwidforse2 ยท 1 points ยท Posted at 19:42:57 on May 25, 2016 ยท (Permalink)
I'm not convinced that .999... = 1.000... If you imagine each decimal place as a step 90% of the remaining "distance" to 1, and you repeat that 90% step infinitely, you will never reach 1. Rounding to one makes a ton of sense for realistic applications of course, but I'm saying the actual value is more accurately ( 1 - an infinitely small number)
jgthespy ยท 1 points ยท Posted at 19:48:07 on May 25, 2016 ยท (Permalink)
http://picklenerd.com/math/decimal-expansion-interactive/
lickwidforse2 ยท 1 points ยท Posted at 20:00:22 on May 25, 2016 ยท (Permalink)
That's a really cool app. Not applicable as far as I could see on my phone, but still really cool.
jgthespy ยท 1 points ยท Posted at 22:19:02 on May 25, 2016 ยท (Permalink)
Thanks! It doesn't do 0.999...=1 (on purpose) but 0.999...=1 for the exact same reason that 0.4999...=0.5. There are actually two representations for every number that has a terminating decimal expansion.
This is just how things are defined. Real numbers and decimal notation both have rigorous definitions and you can't really disagree with a definition. You can only provide a different definition that you think is better, and that's a lot more difficult than you might think.
The cool thing about math is that a lot of the stuff you use is built on top of a lot of abstraction. The real numbers are a metric space which means that they're also a topological space, and we know a lot of things about both of those structures in general. That means that everything that we know about topological spaces and everything that we know about metric spaces automatically applies to the real numbers. Real numbers are also a field which means that we can apply all of the things that we know about fields in general to real numbers. Since they're a field, they can be used to build a vector space which means that we can USE real numbers to do all kinds of awesome stuff in linear algebra.
If you change the definition of the reals, then it's very possible that you will lose a lot of the properties that these other structures require. So it's totally okay to say that you can imagine a number that gets infinitely close to 1 but never touches it. It's just not a real number. It is a hyperreal number and a surreal number, but it still wouldn't be written as 0.999... You can write it as 1-ฮต where ฮต is your infinitesimal, just like you suggested at the end of your post.
And so based on what I've said, this just isn't how decimal notation works. You're totally free to come up with your own notation, but when we say that 0.999...=1 we're using a very specific set of numbers and very specific notation, and people get really tripped up on it because they've been using those numbers and that notation forever without truly understanding what they mean. So my little app is just to show you how we construct a decimal. It's not my opinion, that's just how it works. And we don't have to round because we're doing math, not science. It is perfectly valid to talk about the end of an infinitely repeating process because we're not limited by reality and we can irrefutably prove that our result follows from our hypotheses.
conanap ยท 1 points ยท Posted at 19:47:55 on May 25, 2016 ยท (Permalink)
other than the 1/3 proof and this proof, also from geometric series:
0.99999999999.... = 0.9 + 0.09 + 0.009.... = 9/10 + 9/100 + 9/1000....
note ratio between each term is 1/10. 9/10 * 1/10 = 9/100, 9/100 * 1/10 = 9/1000....
then we have r = ratio, |r| = 1/10 < 1, so it converges to 9/10 / (1 - r) = 9/10 / (9/10) = 1
from_dust ยท 1 points ยท Posted at 22:27:50 on May 25, 2016 ยท (Permalink)
Is there any broader implications here? I mean... It breaks my brain a little but does this suggest that there is a finite quantity of numbers since there is a point where .999... = 1? Or that 1!=1 because 1=.999.... ?
AndrewBot88 ยท 1 points ยท Posted at 20:13:25 on May 28, 2016 ยท (Permalink)
Bit late here, but no. There are still infinitely many numbers between 0 and 1. For any given number .9...9 you can add another digit to the end and it won't be equal to 1. It's only at an infinite number of 9's that it becomes 1.
solos90 ยท 1 points ยท Posted at 23:55:44 on May 25, 2016 ยท (Permalink)
Similarly, 1/3=.333.....
3x0.3333...=0.9999.....
But 3x1/3=1
Therefore, 0.999.....=1
nerdhappy ยท 1 points ยท Posted at 01:45:45 on May 26, 2016 ยท (Permalink)
I never liked the 10x = 9.999... part.
I know that 10 x .9999 = 9.999, but is there a proof that the "shift the decimal point to the right" is allowed to be used on infinitely repeating decimals?
Thisismyaccount0 ยท 1 points ยท Posted at 01:46:59 on May 26, 2016 ยท (Permalink)
The 10x = 9.999 is wrong If x = .999 , 10x = 9.99 You can't trick me
kimera-houjuu ยท 1 points ยท Posted at 04:11:22 on May 26, 2016 ยท (Permalink)
It's .999... not .999
Yes they're different
ManPumpkin ยท 1 points ยท Posted at 05:16:30 on May 26, 2016 ยท (Permalink)
x=.555...
10x =9.555...
10x = 9 + .555...
10x = 9 + x
9x = 9
x = 1
1 = 0.555...
kimera-houjuu ยท 2 points ยท Posted at 05:46:13 on May 26, 2016 ยท (Permalink)
10x =9.555... is wrong.
ManPumpkin ยท 1 points ยท Posted at 05:55:41 on May 26, 2016 ยท (Permalink)
God damn it, I knew it didn't look right.
Sullivanm01 ยท 1 points ยท Posted at 06:25:36 on May 26, 2016 ยท (Permalink)
I'm so dumbfounded right now
I don't know how that works...but it does
Can anyone help me understand this? I thought .999 DIDN'T equal one...
Drnorman91 ยท 1 points ยท Posted at 07:14:10 on May 26, 2016 ยท (Permalink)
That's completely wrong, because 9x=8.991 10x=9.99 9.99-1x=9x=8.991
ShiningRaven ยท 1 points ยท Posted at 08:48:35 on May 26, 2016 ยท (Permalink)
This also works:
Most people agree that: 1/3 = .333...
Therefore:
3 * 1/3 = 3 * .333... 3/3 = .999... 1 = .999...
MrFisterrr ยท 1 points ยท Posted at 08:57:04 on May 26, 2016 ยท (Permalink)
I never understood this. I've never done a math question where you defined the exact value of X beforehand and then find the exact value after.
Anthro_Fascist ยท 8 points ยท Posted at 17:03:55 on May 25, 2016 ยท (Permalink)*
Ooh, I have so many. Let me list them:
I will add more as I find. Most of the facts are from the book Things to Make and Do in the Fourth Dimension by Matt Parker.
[deleted] ยท 2 points ยท Posted at 01:22:43 on May 26, 2016 ยท (Permalink)
[deleted]
Anthro_Fascist ยท 1 points ยท Posted at 01:52:01 on May 26, 2016 ยท (Permalink)
Whoops! I meant one-twist.
JonJonFTW ยท 1 points ยท Posted at 21:21:53 on May 25, 2016 ยท (Permalink)
To add, phi squared is phi plus one.
gronkspike25 ยท 3113 points ยท Posted at 11:09:41 on May 25, 2016 ยท (Permalink)*
If a pizza has radius z and depth a, its volume is pi *z *z *a.
ktkps ยท 863 points ยท Posted at 11:50:04 on May 25, 2016 ยท (Permalink)
takes out the measuring tape
dukbcaaj ยท 363 points ยท Posted at 13:00:50 on May 25, 2016 ยท (Permalink)
measures the radius of the pizza
jetblackcrow ยท 653 points ยท Posted at 13:05:13 on May 25, 2016 ยท (Permalink)
2 penis lengths
thefrenchdentiste ยท 2171 points ยท Posted at 13:07:52 on May 25, 2016 ยท (Permalink)*
I'm a big fan of bite-size pizzas too!
lobotomize ยท 465 points ยท Posted at 13:13:48 on May 25, 2016 ยท (Permalink)
rekt
J0K3R2 ยท 229 points ยท Posted at 13:54:56 on May 25, 2016 ยท (Permalink)
Press F to pay respects
Godzuki17 ยท 5 points ยท Posted at 15:34:02 on May 25, 2016 ยท (Permalink)
One upvote = one penis enlargement surgery
KitchitiKipi ยท 5 points ยท Posted at 14:54:21 on May 25, 2016 ยท (Permalink)
Put some respeck on it
bigvow ยท 1 points ยท Posted at 16:41:02 on May 25, 2016 ยท (Permalink)
All tree ya'll
serendipitousevent ยท 1 points ยท Posted at 16:03:45 on May 25, 2016 ยท (Permalink)
Please: deep pan with double respeck.
daguil68367 ยท 2 points ยท Posted at 14:02:38 on May 25, 2016 ยท (Permalink)
F
daguil68367 ยท 1 points ยท Posted at 14:02:43 on May 25, 2016 ยท (Permalink)
U
DoWhile ยท 0 points ยท Posted at 14:30:23 on May 25, 2016 ยท (Permalink)
N
JohnnyHendo ยท 4 points ยท Posted at 14:32:38 on May 25, 2016 ยท (Permalink)
K
Squid0110 ยท 2 points ยท Posted at 14:33:34 on May 25, 2016 ยท (Permalink)
Y
ZheVulture ยท 2 points ยท Posted at 14:36:11 on May 25, 2016 ยท (Permalink)
T
FrareBear ยท 2 points ยท Posted at 14:38:47 on May 25, 2016 ยท (Permalink)
R
lobotomize ยท 1 points ยท Posted at 14:49:29 on May 25, 2016 ยท (Permalink)
A
CharlesDickensABox ยท 0 points ยท Posted at 14:52:37 on May 25, 2016 ยท (Permalink)
M
joemass ยท 2 points ยท Posted at 15:04:53 on May 25, 2016 ยท (Permalink)
A for effort.
CharlesDickensABox ยท 2 points ยท Posted at 15:06:15 on May 25, 2016 ยท (Permalink)
FUNKYTRAMA! WE DID IT, EVERYONE!
pokemonpasta ยท 1 points ยท Posted at 15:18:25 on May 25, 2016 ยท (Permalink)
Is that a Futurama spin-off?
JohnnyHendo ยท 1 points ยท Posted at 16:04:08 on May 25, 2016 ยท (Permalink)
Yeah it takes place in the 1970s.
mister11th ยท 2 points ยท Posted at 22:17:12 on May 25, 2016 ยท (Permalink)
P
daguil68367 ยท 0 points ยท Posted at 14:33:37 on May 25, 2016 ยท (Permalink)
Y
Projectdefy ยท 1 points ยท Posted at 21:08:55 on May 25, 2016 ยท (Permalink)
P
tree_jayy ยท 1 points ยท Posted at 03:08:26 on May 26, 2016 ยท (Permalink)
F
[deleted] ยท 1 points ยท Posted at 04:27:52 on May 26, 2016 ยท (Permalink)
F
mitchtv33 ยท 1 points ยท Posted at 15:39:13 on May 25, 2016 ยท (Permalink)
F
WubWubDing ยท 1 points ยท Posted at 16:19:30 on May 25, 2016 ยท (Permalink)
F
Tobias_durden ยท 1 points ยท Posted at 18:21:20 on May 25, 2016 ยท (Permalink)
F
donutdog12 ยท 0 points ยท Posted at 16:57:26 on May 25, 2016 ยท (Permalink)
Fffffffffffffffffffff
tarmon21 ยท 0 points ยท Posted at 17:08:50 on May 25, 2016 ยท (Permalink)
F :( rip man
[deleted] ยท 0 points ยท Posted at 18:21:51 on May 25, 2016 ยท (Permalink)
Press B to apply Burn cream
[deleted] ยท -1 points ยท Posted at 15:29:45 on May 25, 2016 ยท (Permalink)
ffffffffffffff
mbleslie ยท 0 points ยท Posted at 15:07:02 on May 25, 2016 ยท (Permalink)
what if it was stephen tyler responding though?
[deleted] ยท 8 points ยท Posted at 14:18:29 on May 25, 2016 ยท (Permalink)
Fun fact: "bite" actually means"cock" in French
TheRiverOtter ยท 7 points ยท Posted at 14:29:11 on May 25, 2016 ยท (Permalink)
But isn't it pronounced like the English word 'beet'?
tamatoaCoco ยท 4 points ยท Posted at 17:31:38 on May 25, 2016 ยท (Permalink)
Oui.
TheRiverOtter ยท 2 points ยท Posted at 17:49:59 on May 25, 2016 ยท (Permalink)
But isn't this pronounced like the English word 'we'?
PVT_TT ยท 2 points ยท Posted at 21:45:43 on May 25, 2016 ยท (Permalink)
aye
TheRiverOtter ยท 2 points ยท Posted at 21:59:41 on May 25, 2016 ยท (Permalink)
But isn't this pronounced like the English letter 'I'?
Also, I'm warning you. Once more and you'll be held in contempt of court!
Mattoww ยท 4 points ยท Posted at 15:09:28 on May 25, 2016 ยท (Permalink)
At first I thought that was the joke but then I remember redditors can only say "omelette du fromage" in french.
[deleted] ยท 1 points ยท Posted at 17:18:14 on May 25, 2016 ยท (Permalink)
that's so infortunรฉ
Habtra ยท 3 points ยท Posted at 14:50:10 on May 25, 2016 ยท (Permalink)
It's funny cause in French, bite means penis.
BastouXII ยท 3 points ยท Posted at 15:41:45 on May 25, 2016 ยท (Permalink)
Wich is doubly funny to French speakers since bite (pronounced "bit") is French slang for "dick".
timmaeus ยท 3 points ยท Posted at 13:23:10 on May 25, 2016 ยท (Permalink)
Hold the sausage
TheRiverOtter ยท 2 points ยท Posted at 14:28:36 on May 25, 2016 ยท (Permalink)
Let me get my tweezers.
Swigity_swooty ยท 1 points ยท Posted at 15:22:19 on May 25, 2016 ยท (Permalink)
Mmmm bagel bites
GO-DUCKS ยท 1 points ยท Posted at 15:26:33 on May 25, 2016 ยท (Permalink)
You must have a mouth like a horse.
Phase714 ยท 1 points ยท Posted at 17:34:24 on May 25, 2016 ยท (Permalink)
Bagel Bites are da bomb
miked4o7 ยท 1 points ยท Posted at 17:48:07 on May 25, 2016 ยท (Permalink)
In all seriousness though... I fucking love bagel bites.
[deleted] ยท 1 points ยท Posted at 18:13:05 on May 25, 2016 ยท (Permalink)
Who doesn't love bagel bites
KitSuneSvensson ยท 0 points ยท Posted at 13:40:54 on May 25, 2016 ยท (Permalink)
I got some bad news for you, bro..
stewy97 ยท 1 points ยท Posted at 15:01:59 on May 25, 2016 ยท (Permalink)
0.5 bananas
DocJawbone ยท 1 points ยท Posted at 15:58:27 on May 25, 2016 ยท (Permalink)
swaffles pizza
sgol ยท 1 points ยท Posted at 16:42:17 on May 25, 2016 ยท (Permalink)
Instructions unclear - pizza stuck in fan
I_Am_Slightly_Evil ยท 1 points ยท Posted at 17:04:45 on May 25, 2016 ยท (Permalink)
I'm sorry about your tiny pizza, next time order a small so you can have a bigger one.
MeOfAllTrades ยท 1 points ยท Posted at 17:21:11 on May 25, 2016 ยท (Permalink)
1/2 lorde
lordtuts ยท 1 points ยท Posted at 18:17:13 on May 25, 2016 ยท (Permalink)
He said pizza, not totino's pizza rolls
MonkeyNin ยท 1 points ยท Posted at 18:23:20 on May 25, 2016 ยท (Permalink)
Do you have to put your penis in every pizza?
therock21 ยท 2 points ยท Posted at 13:04:30 on May 25, 2016 ยท (Permalink)
fails
Peregrine7 ยท 1 points ยท Posted at 14:45:38 on May 25, 2016 ยท (Permalink)
FWIW a standard medium/small pizza is 11", a large/regular is 13"
Project2r ยท 1 points ยท Posted at 15:21:04 on May 25, 2016 ยท (Permalink)
I'm gonna have order pizzas everyday till i check this out. recommendations?
ademnus ยท 1 points ยท Posted at 16:07:56 on May 25, 2016 ยท (Permalink)
I ate the results, sorry.
khan_the_terrible ยท 1 points ยท Posted at 14:38:44 on May 25, 2016 ยท (Permalink)
says forget it and eats pizza
easyas8910 ยท 0 points ยท Posted at 15:48:24 on May 25, 2016 ยท (Permalink)
Puts on robe and wizard hat
TheBestBigAl ยท 3 points ยท Posted at 14:11:23 on May 25, 2016 ยท (Permalink)
My measuring tape only goes up to m :-(
somenamestaken ยท 3 points ยท Posted at 15:09:37 on May 25, 2016 ยท (Permalink)
You can't eat a pizza with that
headmustard ยท 2 points ยท Posted at 14:39:56 on May 25, 2016 ยท (Permalink)
it measures the pizza with the tape it does this whenever it's told
mrboombastic123 ยท 2 points ยท Posted at 15:22:34 on May 25, 2016 ยท (Permalink)
Puts dick back in pants
Places tape directly against pizza without wiping it down first or something
bio180 ยท 2 points ยท Posted at 15:26:41 on May 25, 2016 ยท (Permalink)
takes out spork
d07c0m ยท 1 points ยท Posted at 23:50:07 on May 25, 2016 ยท (Permalink)
takes out big sausage
ktkps ยท 1 points ยท Posted at 02:17:54 on May 26, 2016 ยท (Permalink)
found the kinky pizza delivery guy
Spartan2470 ยท 417 points ยท Posted at 12:59:48 on May 25, 2016 ยท (Permalink)
For those that may not know, /u/gronkspike25 appears to be a spambot that copies and pastes previous comments. Here it copied and pasted /u/crazyei8hts's comment from this thread.
Kunstfr ยท 48 points ยท Posted at 13:03:51 on May 25, 2016 ยท (Permalink)
I mean, I've seen this answer so many times here on /r/AskReddit, and checking his comment history, he seems to answer people
Spartan2470 ยท 94 points ยท Posted at 14:35:42 on May 25, 2016 ยท (Permalink)
He's not a bot, but is very angry. He just sent me this:
ijizz ยท 29 points ยท Posted at 15:44:10 on May 25, 2016 ยท (Permalink)
Well, at least his argument was relatively well substantiated as opposed to just blatant swearing.
gronkspike25 ยท 10 points ยท Posted at 15:54:06 on May 25, 2016 ยท (Permalink)
Like I said.....I'm on reddit a lot. I have nothing better to do.
[deleted] ยท -2 points ยท Posted at 16:18:00 on May 25, 2016 ยท (Permalink)
[deleted]
lordtuts ยท 3 points ยท Posted at 18:19:09 on May 25, 2016 ยท (Permalink)
You mean kinda like what you're doing?
glider97 ยท 19 points ยท Posted at 15:15:54 on May 25, 2016 ยท (Permalink)
wow you fucked up.
Capn_Barboza ยท 9 points ยท Posted at 15:24:02 on May 25, 2016 ยท (Permalink)
Everyone on reddit is a bot except you!
zmemetime ยท 1 points ยท Posted at 03:25:45 on May 26, 2016 ยท (Permalink)
HAHAHA, I RECONGIZE THE HUMOUR IN THIS POST, AND AS A HUMAN I AGREE!
mokabrown97 ยท 2 points ยท Posted at 20:23:43 on May 25, 2016 ยท (Permalink)
Your username used to be my password for a lot of my online accounts.
glider97 ยท 1 points ยท Posted at 00:35:48 on May 26, 2016 ยท (Permalink)
Cool. Any particular reason?
mokabrown97 ยท 2 points ยท Posted at 00:36:57 on May 26, 2016 ยท (Permalink)
I'm a glider pilot, born in 97
glider97 ยท 1 points ยท Posted at 00:41:10 on May 26, 2016 ยท (Permalink)
Wow, that's really cool, though! How long have you been a glider pilot?
Must've scared you a bit, seeing my username. :D
mokabrown97 ยท 1 points ยท Posted at 00:43:37 on May 26, 2016 ยท (Permalink)
Dude the Canadian cadet program does wonders for kids. Got it in 2013, I was 16 at the time. Haha I was just like "whoa that's cool" I actually had that password until this past year.
[deleted] ยท 49 points ยท Posted at 15:18:44 on May 25, 2016 ยท (Permalink)
The fact that he sent you this is really sad.
JamEngulfer221 ยท 7 points ยท Posted at 18:57:00 on May 25, 2016 ยท (Permalink)
I don't really think it is. Some made a false accusation to him and he responded in private to the person that did it.
He's just defending himself, jeez
akjax ยท 3 points ยท Posted at 23:28:45 on May 25, 2016 ยท (Permalink)
I love that about Reddit. It's like it's perfectly OK to accuse people you've never met of lying about their personal life or even not being real, but the second you try to defend yourself you're "sad", "over reacting" and "care too much about karma".
akjax ยท 1 points ยท Posted at 23:30:00 on May 25, 2016 ยท (Permalink)
Yeah, because calling out someone as not a real person isn't sad, but trying to defend yourself when someone says you aren't even real? Soooo pathetic. /s
kjhwkejhkhdsfkjhsdkf ยท 10 points ยท Posted at 15:27:43 on May 25, 2016 ยท (Permalink)
Did you ask him how he feels about a tortoise lying on its back?
[deleted] ยท 7 points ยท Posted at 16:20:35 on May 25, 2016 ยท (Permalink)
[deleted]
gronkspike25 ยท 2 points ยท Posted at 16:30:03 on May 25, 2016 ยท (Permalink)
Is this a Blade Runner reference?
kjhwkejhkhdsfkjhsdkf ยท 4 points ยท Posted at 16:32:48 on May 25, 2016 ยท (Permalink)
yes
dude_pirate_roberts ยท 3 points ยท Posted at 17:34:24 on May 25, 2016 ยท (Permalink)*
Keep on posting (and reposting) as you feel the need, /u/gronkspike25, and please ignore complaints about reposting. When you (re)post good stuff, the reddit experience is improved for the vast majority of people who are mature enough to simply move on to the next comment, when they see something familiar.
I've been attacked really viciously a couple times for offerings of original material. One was a joke of my own invention, that I think is pretty funny, which I posted to /r/jokes with the hope and expectation that some redditors would enjoy it. One of the first three responses was someone's sarcastic "Oh you are so funny!" with a truly ghastly image -- like I was humorless but had a huge and distorted grandiouse self-image. I shuddered -- and deleted my joke. The memory is still painful.
I've allowed myself to be intimidated by that.
Don't let that happen to you.
In a spirit of kinship, I repost the relevant XKCD about the 10,000 who learn about well-known things for the first time every day in the US.
Today I'm one of the 10,000: that's a new one for me, and I am looking forward to sharing it with my son when it matches his math skills.
I'm a jokey guy. Sometimes my jokes kill. Often they don't. I'm OK with any response -- except for the asshole who feels obliged to share his opinion that "That's not funny.".
It requires no wit or intelligence to remark that something is not funny -- or that something has been posted before.
akjax ยท 1 points ยท Posted at 23:32:58 on May 25, 2016 ยท (Permalink)
Yep, it's like there's a select group of people who literally spend all their time on Reddit and they see literally every post and get seriously offended by any content that isn't 100% original.
I mean that post spartan accused gronk of copying is over a year old. There's plenty of people that didn't see that post and never will, so why make a big deal over it?
[deleted] ยท 2 points ยท Posted at 17:52:46 on May 25, 2016 ยท (Permalink)
He's so lifelike! Where can I get one?
SmartSoda ยท 8 points ยท Posted at 15:43:29 on May 25, 2016 ยท (Permalink)
He could've told you the last two words and I think he wouldn't be wrong to do so.
KaiserVonScheise ยท 2 points ยท Posted at 16:03:27 on May 25, 2016 ยท (Permalink)
lol u dick
[deleted] ยท -2 points ยท Posted at 16:19:46 on May 25, 2016 ยท (Permalink)
/u/gronkspike25 needs to get a fucking life, this is pathetic and 10x worse.
ActionScripter9109 ยท 3 points ยท Posted at 17:52:12 on May 25, 2016 ยท (Permalink)
Alright, I guess it's a real person this time...
*closes /r/spambotwatch tab*
gronkspike25 ยท 11 points ยท Posted at 13:59:07 on May 25, 2016 ยท (Permalink)
Everyone on reddit is a bot, except you.
Spartan2470 ยท 1 points ยท Posted at 13:06:22 on May 25, 2016 ยท (Permalink)*
He also just did it here too. But after taking a second look, I think you're right. Although the account does a lot coping and pasting of previous comments, there does seem to be human intervention too.
TheRehabKid ยท 293 points ยท Posted at 13:49:00 on May 25, 2016 ยท (Permalink)
I'm not trying to be a jerk here, but...
Do people actually care if it's a bot giving an answer that actually answers the question? Like...karma means absolutely nothing. I just don't get why people care about this.
Spartan2470 ยท 263 points ยท Posted at 13:51:18 on May 25, 2016 ยท (Permalink)
That's a good question because many people don't even know that there are bots. This type of activity is indicative of a spambot. And spambots really do hurt reddit. They often copy top comments and are gilded for it. Most people prefer to guild (and connect with) people and not bots. If you're not familiar with them, the "What's the Point?" section on this page may help to explain. Also, there was a very good write up here.
ccfreak2k ยท 14 points ยท Posted at 15:39:59 on May 25, 2016 ยท (Permalink)
How do we know you aren't a bot?
QuintusVS ยท 1 points ยท Posted at 12:23:12 on May 27, 2016 ยท (Permalink)
Everyone on reddit is a bot except you.
TheRehabKid ยท 29 points ยท Posted at 14:00:23 on May 25, 2016 ยท (Permalink)
Thanks!
I never thought about people gilding bots.
Gravitasnotincluded ยท 14 points ยท Posted at 14:50:10 on May 25, 2016 ยท (Permalink)
even still. why would you care? Gold doesn't do anything except help reddit
TheRehabKid ยท 7 points ยท Posted at 16:04:01 on May 25, 2016 ยท (Permalink)*
I mean, it's not a huge deal...but when you spend your money to gild someone, you're trying to give them certain perks of the site that only gilded users get...so I can see why someone would feel defrauded out of their five bucks in that situation.
RuneKatashima ยท 1 points ยท Posted at 22:21:49 on May 25, 2016 ยท (Permalink)
Been gilded before. What perks? /s
Seriously the "perks" are useless.
Gold the fucking bots. Keep Reddit running.
imfatal ยท 0 points ยท Posted at 23:54:42 on May 25, 2016 ยท (Permalink)
RES already gives you pretty much every perk and more that you get from gold. Who cares honestly? The whole point is to fund Reddit.
speedisavirus ยท 8 points ยท Posted at 16:05:51 on May 25, 2016 ยท (Permalink)
Or guilding bots endorses the idea reddit can monetize via bots
asphaltdragon ยท 1 points ยท Posted at 16:18:47 on May 25, 2016 ยท (Permalink)
That's exactly why I care!
Help Reddit! Make more spambots!
josephdevon ยท 0 points ยท Posted at 15:47:52 on May 25, 2016 ยท (Permalink)
Really? Man this is all I masturbate to nowadays.
TheSilversky64 ยท 3 points ยท Posted at 15:22:34 on May 25, 2016 ยท (Permalink)
Genuine question here: Does Reddit gold not support Reddit, regardless of whether or not it's given to a bot or a human?
everyday847 ยท 7 points ยท Posted at 14:53:53 on May 25, 2016 ยท (Permalink)
If you don't know you're gilding a bot, not a person, then your illusory connection is just as "real" as a connection to a "person," right, insofar as it's something that makes you feel good?
On the other hand maybe gilders often send followup PMs to the gildee asking how good gold feels, and maybe that's awkward when the replies are all "I don't know. Maybe your social security number would help me figure it all out."
[deleted] ยท 0 points ยท Posted at 15:09:18 on May 25, 2016 ยท (Permalink)
[deleted]
lordtuts ยท -2 points ยท Posted at 18:21:05 on May 25, 2016 ยท (Permalink)
So either way, reddit gets paid. I don't think thats what I'd define as "hurting" reddit
[deleted] ยท 15 points ยท Posted at 14:34:14 on May 25, 2016 ยท (Permalink)
[deleted]
TheRehabKid ยท 4 points ยท Posted at 16:02:28 on May 25, 2016 ยท (Permalink)
Do people actually look at karma when analyzing a post?
ASongOnceKnown ยท 3 points ยท Posted at 21:11:34 on May 25, 2016 ยท (Permalink)
No, but reddit uses your karma and the age of your account to determine how much to "trust" a user, meaning the site would ignore more red flags from an established, high-karma account than from a brand new account.
Luwi00 ยท 7 points ยท Posted at 15:11:43 on May 25, 2016 ยท (Permalink)
I acutally dont care about the Karma, but I do care about bots reposting, because I want to talk to a human and not a piece of code.
TheRehabKid ยท 2 points ยท Posted at 16:04:15 on May 25, 2016 ยท (Permalink)
I can understand that.
[deleted] ยท 3 points ยท Posted at 16:56:34 on May 25, 2016 ยท (Permalink)
If it means actually new and interesting answers get less attention, yes? No one likes having to scroll past reposts to see the actual answers. Having reposts show up on occasion so people who missed them the first time can see them is one thing, but you don't need the same set of answers repeated every single time a question is asked.
lakerswiz ยท 3 points ยท Posted at 18:48:07 on May 25, 2016 ยท (Permalink)
They build up an account with history and then sell them so companies can shill.
SithLord13 ยท 2 points ยท Posted at 23:05:14 on May 25, 2016 ยท (Permalink)
Aside from the obvious (without OC there's no content so we need to encourage OC over reposts), there's also the fact that spambots are often later sold for astroturfing. Lots of subs involve talking about your experience with a business. Someone with no history is often scrutinized/less trusted than someone who's posted often/has high karma/has been gilded.
This is also done for political causes too like pro/anti Russia/Israel/Hillary.
[deleted] ยท 2 points ยท Posted at 16:55:26 on May 25, 2016 ยท (Permalink)
Karma does mean something, and post quality really means something. A good, recognized and under-the-radar spambot can be invaluable to a PR team trying to promote a product.
conditionalcognition ยท 2 points ยท Posted at 18:33:15 on May 25, 2016 ยท (Permalink)
I'm relatively new to reddit and was oblivious to this until now. I guess I imagined that the reddit community wouldn't stand for such behavior. Then again, if one doesn't even realize the inauthentic nature, whose to blame. I hate feeling ignorant, but appreciate learning something to counter my lack of info.
TIL: metaspammers copy and paste comments all over reddit and sometimes get gilded for this regurgitation.
akjax ยท 2 points ยท Posted at 23:35:59 on May 25, 2016 ยท (Permalink)*
Also, sometimes, such as in this case, people accuse real people of being bots or whatever when they're actually totally wrong.
Since you're new to Reddit, know this. You will see comments you naturally believe, such as someone trying to get the word around that an account isn't real, or giving a seemingly through explanation of recent or political events. They seem like they know what they're talking about and they have so much evidence, when coupled with a clear and conscience (and often slightly humorous) writing style, it's easy to assume they're an expert.
Except so often it's total BS, or at least not as true as the person writing it thinks it is. Take literally everything you read on here with a grain of salt. Reddit loves to point fingers, but that doesn't mean it gets it right.
[deleted] ยท 1 points ยท Posted at 15:05:16 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท -3 points ยท Posted at 15:13:25 on May 25, 2016 ยท (Permalink)
[deleted]
swaldron ยท 0 points ยท Posted at 20:18:21 on May 25, 2016 ยท (Permalink)
He may or may not be a bot but he is a Patriots fan, the worst of all sins
gronkspike25 ยท 1 points ยท Posted at 20:42:29 on May 25, 2016 ยท (Permalink)
Hey now!
BlinkDaggerOP ยท 8 points ยท Posted at 14:46:31 on May 25, 2016 ยท (Permalink)
gimma pi-zzaaaaaaa
stewmberto ยท 5 points ยท Posted at 16:09:53 on May 25, 2016 ยท (Permalink)
Whipped cream poured like waterfallllllls
asphaltdragon ยท 2 points ยท Posted at 16:28:04 on May 25, 2016 ยท (Permalink)
Ah, deep dish.
wasdo ยท 40 points ยท Posted at 12:09:51 on May 25, 2016 ยท (Permalink)
You seem like a cool guy, I've always liked typing 80085 into my calculator.
thisisdjjjjjjjjjj ยท 4 points ยท Posted at 14:35:07 on May 25, 2016 ยท (Permalink)
You mean 58008
(You gotta turn it around)
ktkps ยท -2 points ยท Posted at 12:18:16 on May 25, 2016 ยท (Permalink)
I liked to see 305007 upside down in a calculator
russmbiz ยท 37 points ยท Posted at 12:51:47 on May 25, 2016 ยท (Permalink)
LOOSOE?
ComaToys ยท 0 points ยท Posted at 14:59:48 on May 25, 2016 ยท (Permalink)
Sadly, after my mastectomy I was 55378008
PM__ME__LOLI ยท 3 points ยท Posted at 15:49:51 on May 25, 2016 ยท (Permalink)
I've said it last time and I'll say it again, how the fuck is this a maths fact at all, let alone an interesting one? I'm not trying to be a jerk here, but this is literally if i define an equation with letters in a word, the equation will spell that word. I mean, ok? If I define three variables u,c,k, I can define a function f(u,c,k). Is anyone impressed? Maybe it's a useful mneonic for some people to remember how to calculate a cylinder's volume, but that about it.
[deleted] ยท 1 points ยท Posted at 18:03:17 on May 25, 2016 ยท (Permalink)
Yeah. You right.
RedAnonym ยท 6 points ยท Posted at 11:48:31 on May 25, 2016 ยท (Permalink)
A dimension 2 pizza area: Pizz
Gtobes ยท 1 points ยท Posted at 19:28:23 on May 25, 2016 ยท (Permalink)
What if this 2 dimension pizza had radi of "s" would it be Piss?
ktkps ยท 1 points ยท Posted at 12:27:49 on May 25, 2016 ยท (Permalink)
z = r eit+c
Latifire ยท 12 points ยท Posted at 12:35:08 on May 25, 2016 ยท (Permalink)
I'm innocent Please explain
IanMalkaviac ยท 1 points ยท Posted at 17:11:04 on May 25, 2016 ยท (Permalink)
I think he was trying to say rehkt in a funny way which is slang for wrecked meaning to watch someone win an argument so thoroughly that it appears to be painful to the other person.
Latifire ยท 1 points ยท Posted at 17:15:25 on May 25, 2016 ยท (Permalink)
Oh okay I got it now
iamzombus ยท 2 points ยท Posted at 15:25:47 on May 25, 2016 ยท (Permalink)
y = r3/3
TheSemiTallest ยท 2 points ยท Posted at 12:51:04 on May 25, 2016 ยท (Permalink)
Here's a shirt that has a diagram
ThisChangesNothing ยท 1 points ยท Posted at 14:43:59 on May 25, 2016 ยท (Permalink)
This changes everything.
tylerlawhon ยท 1 points ยท Posted at 14:50:39 on May 25, 2016 ยท (Permalink)
Wouldn't that actually be pi * (z*z) *a since the radius would be squared?
[deleted] ยท 1 points ยท Posted at 17:18:40 on May 25, 2016 ยท (Permalink)
Same thing
tylerlawhon ยท 1 points ยท Posted at 17:21:05 on May 25, 2016 ยท (Permalink)
Ehh.. not completely. They way he wrote it it'd be
((pi *z) *z) *a which wouldn't be correct.
[deleted] ยท 1 points ยท Posted at 18:08:49 on May 25, 2016 ยท (Permalink)
Yes it would. Associative Property of multiplication: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)
Dear_Watson ยท 1 points ยท Posted at 15:28:08 on May 25, 2016 ยท (Permalink)
Seems pretty straight forward
dieagoodman ยท 1 points ยท Posted at 16:00:24 on May 25, 2016 ยท (Permalink)
All i see is pointer dereferencing
The_Nipple_Tickler ยท 1 points ยท Posted at 16:06:26 on May 25, 2016 ยท (Permalink)
If a rectangular prism with a square base has a width of s and a height of a, then its volume is ass.
bassinastor ยท 1 points ยท Posted at 16:20:20 on May 25, 2016 ยท (Permalink)
I've always thought this one was stupid because they're variables, you can call them anyway. All you're saying is that if you take pi, add two z's and then an a, you get pizza. Like no shit, that what spelling is.
dummy_roxx ยท 1 points ยท Posted at 17:58:01 on May 25, 2016 ยท (Permalink)
Those who are amazed , you need not be.Pizza is just a cylinder albeit the one with small height. As volume of cylinder is Pi *radius2 *height. So it's just a bit clever presentation of same fact to make it sound cool.
DaanishS ยท 1 points ยท Posted at 20:30:07 on May 25, 2016 ยท (Permalink)
Pretty simple stuff tbh and can be applied on other objects. Volume = area of face * length
TommySonNJT ยท 1 points ยท Posted at 02:07:03 on May 26, 2016 ยท (Permalink)
And if you add 6.3m to its circumference, it's radius will increase 1m.
Chucklesinator ยท 1 points ยท Posted at 05:05:00 on May 26, 2016 ยท (Permalink)
Assuming the pizza has constant depth
NocturnalEmissary ยท 1 points ยท Posted at 12:01:02 on May 25, 2016 ยท (Permalink)
Also pie is eight something
amytee252 ยท 1 points ยท Posted at 16:30:13 on May 25, 2016 ยท (Permalink)
This is my favourite in this thread.
gronkspike25 ยท 1 points ยท Posted at 16:30:31 on May 25, 2016 ยท (Permalink)
Happy cake day!
amytee252 ยท 1 points ยท Posted at 16:56:28 on May 25, 2016 ยท (Permalink)
Thank you :-).
Titus_Bramble ยท -1 points ยท Posted at 11:59:37 on May 25, 2016 ยท (Permalink)
It is a good one.
It is unfortunate, though, that the convention would be to swap the letters for radius and depth, since the depth is along the z-axis in cylindrical coordinates, and because... radius has an 'a' in it? (I'm aware that radii are often labelled 'r' in physics, but for some reason 'a' seems to be the second choice when 'r' is taken)
Firth_of_Fifth ยท -1 points ยท Posted at 12:38:21 on May 25, 2016 ยท (Permalink)
Or z *a *z *pi.
dafuzzbudd ยท 0 points ยท Posted at 13:45:11 on May 25, 2016 ยท (Permalink)
ALGEBRAIC!
[deleted] ยท 19 points ยท Posted at 14:49:15 on May 25, 2016 ยท (Permalink)
There's a one-to-one correspondence between Mersenne Primes and Even Perfect Numbers.
dixego ยท 1 points ยท Posted at 17:21:40 on May 25, 2016 ยท (Permalink)
Wait, what? How does one prove this?
[deleted] ยท 4 points ยท Posted at 17:25:24 on May 25, 2016 ยท (Permalink)
https://primes.utm.edu/notes/proofs/EvenPerfect.html
dixego ยท 1 points ยท Posted at 17:46:51 on May 25, 2016 ยท (Permalink)
That's actually amazing.
iamnotsven ยท 1 points ยท Posted at 18:26:27 on May 25, 2016 ยท (Permalink)
Dr. Caldwell is a bad ass professor. Did you go to UTM as well?
[deleted] ยท 1 points ยท Posted at 18:27:49 on May 25, 2016 ยท (Permalink)
Nope. I found that link at the top of the Google.
iamnotsven ยท 1 points ยท Posted at 18:28:48 on May 25, 2016 ยท (Permalink)
Ah okay. :(
[deleted] ยท 120 points ยท Posted at 11:31:40 on May 25, 2016 ยท (Permalink)
Math works every time.
galacticdick ยท 12 points ยท Posted at 14:11:02 on May 25, 2016 ยท (Permalink)
You know what phrase I hate? "The exception that proves the rule". Same reason I love maths. It always works.
Xenomech ยท 8 points ยท Posted at 15:33:56 on May 25, 2016 ยท (Permalink)
The word "proves" in that saying means "tests", not "verifies".
So, it's not "The exception verifies the rule", it's "The exception tests the rule". The saying makes a lot more sense that way.
We don't use the word "proof" to mean "test" much anymore (except maybe in the phrase "proving grounds"), so the correct meaning of the sentence is lost.
Similarly, the phrase "The proof is in the pudding" is actually supposed to be "The proof of the pudding is in the tasting" (or eating). "Proof" in that sense also means "to test".
Kayyam ยท 4 points ยท Posted at 15:40:29 on May 25, 2016 ยท (Permalink)*
That's not what the expression means. The expression means the exact same thing as"the smoke proves the fire".
You can't have an exception without a rule. Therefore, if you're pointing to an exception, that means there is a rule.
The expression though was never meant to be accurate.
Xenomech ยท 4 points ยท Posted at 15:43:28 on May 25, 2016 ยท (Permalink)
I stand somewhat corrected.
galacticdick ยท 1 points ยท Posted at 16:15:14 on May 25, 2016 ยท (Permalink)
Interesting, thanks :)
dalr3th1n ยท 3 points ยท Posted at 15:26:03 on May 25, 2016 ยท (Permalink)
Can you construct a mathematical proof of this statement?
Dr-K-G ยท 2 points ยท Posted at 17:30:42 on May 25, 2016 ยท (Permalink)
It's by definition
Ahdilable ยท 3 points ยท Posted at 15:13:44 on May 25, 2016 ยท (Permalink)
Is this true? I'd like to hear a story where math hasn't worked.
[deleted] ยท 6 points ยท Posted at 16:33:15 on May 25, 2016 ยท (Permalink)
Check out Russel's Paradox. Basically for a long time mathematicians weren't very careful when talking about sets and just used their intuition to assert basic facts. Then Russel comes along and gives something that sounds fairly innocent but turns out to be paradoxical. So math panics and cobbles together ZF, the set of axioms most math is based on now. (and then the axiom of choice comes along giving ZFC. Choice is really cool, look it up!).
Also there's Godel's completeness and incompleteness theorems, which basically tells us that as soon as a set of axioms is complex enough to be interesting, it is impossible to prove with the axioms that the axioms are consistent. That is, it's impossible to prove that the theory generated by the axioms is contradiction free.
Ahdilable ยท 2 points ยท Posted at 16:47:43 on May 25, 2016 ยท (Permalink)
This seems really interesting but the Wikipedia page looks incredibly uninviting. Can you give me a ELI5 of what the essence of this is and does that mean the axioms we hold today can be considered truth?
Also this "sets" math, completely goes over my head...what exactly do they mean by set? Perhaps once I gain an understanding of it, I can teach myself from there.
[deleted] ยท 4 points ยท Posted at 17:39:48 on May 25, 2016 ยท (Permalink)*
I think maybe I shouldn't have mentioned the completeness theorem, it's less related to the point I was trying to make than I thought, and honestly I don't know enough logic (the field of math that it concerns) to properly give an intuition for what it means.
One thing it definitely doesn't do is tell us that the axioms we use today can be considered absolutely true. Godel's incompleteness theorem means that we have no way of knowing that there isn't a contradiction hidden deep in ZF. Though something that's kindof fun is that if we assume ZF is consistent, then each of ZF plus the axiom of choice and ZF plus the negation of the axiom of choice are self consistent. We can't even know that Peano arithmetic is contradiction free. Peano arithmetic is defined by our axioms for the natural numbers. It says things like 0 is a natural number, each natural number has a next natural number (adding 1), a=a, if a=b then b=a, if a=b and b=c then a=c, etc. Basically it is possible, although extraordinarily unlikely, that our very concept of a number is contradictory
Sets, on the other hand, I can help with. A set is essentially a collection of objects. If something is contained in a set, we call it a member or element of that set. You can talk about the set of even numbers, the set of numbers divisible by 98, or the set of all giraffes if you want. You can even talk about sets of sets, eg the set of all sets of integers, which has as elements the set of all primes, the set of all integers greater than 9, the set of my favorite integers, and all the other literally uncountable (which has formal meaning) sets of integers. So at first glance it seems like the set of all sets that don't contain themselves is a valid set (that's Russel's paradox). Maybe you're concerned that the statement seems self referential, and that's exactly what you should be worried about. The problem with that set is determining whether or not it should be considered a member of itself. If it's not a member of itself, then it does not contain itself and is thus by definition a member of itself. That's clearly contradictory, so we consider the other option. If it's a member of itself, then by definition it's not a member of itself, another contradiction. The only conclusion is that this set is neither a member of itself nor is not a member of itself, which is problematic. The set thus must not exist in the first place. Mathematicians came up with ZF so that we can say precisely what sets are allowed and what we're allowed to do with them.
A while ago I wrote up a talk about the axiom of choice. It's pretty hastily put together, so it's by no means well written, but it starts off with a basic set theory intro and then talks about some really cool axiom of choice stuff, so maybe you'll find it interesting.
https://docs.google.com/document/d/1DOlk2KTQukWSc0-9VQBxxz5JxKGGPxvvsWINVfR7QLU/edit?usp=sharing
kogasapls ยท 2 points ยท Posted at 17:20:33 on May 25, 2016 ยท (Permalink)
Axioms are like assumptions. We look for consequences of these assumptions rather than some inherent truth to the assumptions themselves (generally). For example, we know that 1+1=2 as a consequence of our definitions of 1, 2, addition, and equality (or a set of other concepts which leads to the same result), but it makes no sense to ask if our definitions of 1, 2, addition and equality are "true." Instead, we can ask if they are valid/consistent (yielding no contradictions) or strong enough (yielding meaningful results), etc.
Dr-K-G ยท 2 points ยท Posted at 17:34:25 on May 25, 2016 ยท (Permalink)
Sets are basically just collection of objects.
Godel's completeness theorem is a bit difficult to explain if you have no background in higher math at all. But "does that mean the axioms we hold today can be considered truth" is not what it means. The completeness theorem means that every statement that is true in every model of an axiomatic system is also provable with the axiomatic system. A model is just a thing in which all axioms are true.
[deleted] ยท 2 points ยท Posted at 17:59:10 on May 25, 2016 ยท (Permalink)
If I have a logical system that is complicated enough to be able to encode basic arithmetic then I have a way of creating meta statements for which it's not possible to decide whether the statement is true or not in the logical system that I started with. So if my system is contradiction free it will necessarily have statements that it cannot answer by itself. Repeat ad infinitum, giving the impossibility of any logical system that will be able to answer every possible question.
qazadex ยท 3 points ยท Posted at 15:18:20 on May 25, 2016 ยท (Permalink)
Well, we kind of hope it does. We don't know if ZFC (our basic axioms of mathematics) are consistent or not.
Dr-K-G ยท 1 points ยท Posted at 17:30:24 on May 25, 2016 ยท (Permalink)
Even if they aren't we can always find a new axiom system to work with.
CoolLordL21 ยท 2 points ยท Posted at 15:59:23 on May 25, 2016 ยท (Permalink)
Tell that to my broken calculator.
[deleted] ยท 1 points ยท Posted at 16:14:06 on May 25, 2016 ยท (Permalink)
I'm still banking on peano arithmetic being inconsistent
Dr-K-G ยท 2 points ยท Posted at 17:37:14 on May 25, 2016 ยท (Permalink)
If Peano arithmetic is inconsistent then so is ZFC because you can prove that PA is consistent within ZFC.
[deleted] ยท 0 points ยท Posted at 19:42:57 on May 25, 2016 ยท (Permalink)
If Peano arithmetic is inconsistent, much more than ZFC goes down the drain. It'll be awesome. My mathematician friends all say they would cry.
dh363 ยท 1 points ยท Posted at 20:16:11 on May 25, 2016 ยท (Permalink)
It wouldn't be as bad as people think. There would suddenly be a lot more people working on getting foundations right but a lot of maths built on it would still be fine, and most likely easily reconstructive from whatever new axioms we come up with
Dr-K-G ยท 0 points ยท Posted at 20:05:35 on May 25, 2016 ยท (Permalink)
Well if PA is inconsistent then the natural numbers as we know them can't exist. That's also why realistically it is impossible that PA is inconsistent. We actually have a few consistency proves for PA in other axiomatic systems which we too expect to be consistent.
drewblank ยท 1 points ยท Posted at 17:14:42 on May 25, 2016 ยท (Permalink)
No when I do it.
[deleted] ยท 1 points ยท Posted at 15:27:19 on May 25, 2016 ยท (Permalink)
[deleted]
Dr-K-G ยท 3 points ยท Posted at 17:35:20 on May 25, 2016 ยท (Permalink)
Not really.
Salbee ยท -13 points ยท Posted at 14:22:40 on May 25, 2016 ยท (Permalink)
Thank you for spelling it correctly. "Maths" makes me cringe.
secretredditer ยท 19 points ยท Posted at 14:44:23 on May 25, 2016 ยท (Permalink)
Fun fact! Outside of America people say maths!
pleaseimbeggingyou ยท 3 points ยท Posted at 15:23:07 on May 25, 2016 ยท (Permalink)
It's mathematics not mathematic, you're wrong.
[deleted] ยท 6 points ยท Posted at 15:26:53 on May 25, 2016 ยท (Permalink)
Mathsematics
Salbee ยท 0 points ยท Posted at 20:16:49 on May 25, 2016 ยท (Permalink)
Mathematics is singular, which is why Americans use the word math. I don't know a good reason for why everyone else says maths, which is why it makes me cringe.
pleaseimbeggingyou ยท 1 points ยท Posted at 20:25:20 on May 25, 2016 ยท (Permalink)
"Mathematics"
โ-----------------โ
"Math" + "s"
Salbee ยท 0 points ยท Posted at 03:44:55 on May 26, 2016 ยท (Permalink)
Ugh.
ValiantSerpant ยท 0 points ยท Posted at 15:34:14 on May 25, 2016 ยท (Permalink)
Math. Lego. Stop adding s to the end of words that don't have an s
[deleted] ยท 19 points ยท Posted at 15:06:44 on May 25, 2016 ยท (Permalink)
[deleted]
Slacker5001 ยท 3 points ยท Posted at 18:22:32 on May 25, 2016 ยท (Permalink)
Don't be afraid to ask for an explanation. There are a lot of math brained people like myself floating around in here that I'm sure would gladly attempt to explain in some way.
anorex ยท 9 points ยท Posted at 18:43:44 on May 25, 2016 ยท (Permalink)
According to Flonase, 6 > 1
88gavinm ยท 2 points ยท Posted at 23:44:51 on May 25, 2016 ยท (Permalink)
Incredible!
Impossibru!
ithoughtyousaidgoat ยท 102 points ยท Posted at 13:52:43 on May 25, 2016 ยท (Permalink)
5318008
Addie_Goodvibes ยท 7 points ยท Posted at 14:01:31 on May 25, 2016 ยท (Permalink)
yes everyone loves 8008135
Machtung7 ยท 3 points ยท Posted at 17:26:55 on May 25, 2016 ยท (Permalink)
I thought it was 55318008
Bob_Droll ยท 9 points ยท Posted at 19:30:34 on May 25, 2016 ยท (Permalink)
There once was a lady with boobs that weight 69 pounds, (enter '69' in the calculator)
which was too, too, too much! (enter '222' in the calculator)
So she went to 51st street (enter '51' in the calculator)
to see Dr. X. (hit the multiply button)
She had eight operations (enter '8' in the calculator)
which left her... (press equals button and turn calculator upside down)
8008ใฅฦฯฯ
ithoughtyousaidgoat ยท 1 points ยท Posted at 07:49:29 on May 26, 2016 ยท (Permalink)
It is, but I thought that might be just a UK thing? Is it not?
Machtung7 ยท 1 points ยท Posted at 12:39:31 on May 26, 2016 ยท (Permalink)
Not sure. Though, on further delving through this page, it looks like they're both correct, depending on what you are referring. Where I'm from (US), it was 55318008 for Boobless, but I see that 5318008 is for Boobies. Interesting.
d0ntblink ยท 2 points ยท Posted at 00:04:54 on May 26, 2016 ยท (Permalink)
NSFW!
Imadoctah ยท 1 points ยท Posted at 16:02:40 on May 25, 2016 ยท (Permalink)
This needs more attention
mattenthehat ยท 1 points ยท Posted at 23:20:38 on May 25, 2016 ยท (Permalink)
I'm sure there's plenty of people who'd be happy to give your 5318008 some attention
BigWaveSmallOcean ยท 1 points ยท Posted at 16:20:05 on May 25, 2016 ยท (Permalink)
Show me you're working out
ThalanirIII ยท 1 points ยท Posted at 17:45:19 on May 25, 2016 ยท (Permalink)
do you want to see my muscles? I can show you I'm working out?
YOU'RE=/=YOUR
BigWaveSmallOcean ยท 1 points ยท Posted at 17:53:10 on May 25, 2016 ยท (Permalink)
Yeah that was the joke...cause he put a number that looked like boobies so I said he should show his working out but as if it was talking about going to the gym. Puns...puns everywhere
RWBYSanctum ยท 15 points ยท Posted at 14:26:22 on May 25, 2016 ยท (Permalink)
0! somehow equals 1
dragonfyre173 ยท 12 points ยท Posted at 14:56:56 on May 25, 2016 ยท (Permalink)
Isn't that just an accepted rule to make recursive calculations easier?
hepeee ยท 36 points ยท Posted at 16:02:50 on May 25, 2016 ยท (Permalink)
A factorial of n is the number of ways to arrange n things. 0 things, one way.
dragonfyre173 ยท 10 points ยท Posted at 16:11:18 on May 25, 2016 ยท (Permalink)
Oh damn, it just clicked. Never thought of it that way!
ZizekIsMyDad ยท 4 points ยท Posted at 19:18:06 on May 25, 2016 ยท (Permalink)
That isn't the reason though. You were basically right with your first comment, 0! = 1 because by convention, the result of multiplying 0 numbers is 1. It's the same reason that x0 = 1. It could have easily been 0, but I think that like you said, it makes recursive calculations easier.
See https://en.wikipedia.org/wiki/Empty_product
Best_Towel_EU ยท 3 points ยท Posted at 21:17:26 on May 25, 2016 ยท (Permalink)
x0 = 1 because xn / xn = xn-n = x0 = 1
Also, if you wanted to derive for example f(x) = 2x you'd derive it to f'(x) = 2x0 = 2*1 = 2. If x0 = 0, then f'(x) = 2x0 = 0, which is a strange derivative.
[deleted] ยท 2 points ยท Posted at 02:53:18 on May 26, 2016 ยท (Permalink)
Not entirely. Going from n! to (n-1)! is effectively the same as dividing n! by n. If n = 1 then (n-1)! = (1-1)! = 0! = 1!/1 = 1/1 = 1
Zarco19 ยท 1 points ยท Posted at 05:02:33 on May 26, 2016 ยท (Permalink)
It connects very well with algebra/group theory for the empty product to be 1, because 1 is the multiplicative identity, i.e. a x 1 = 1 x a = a for all a.
In algebra, I like to think of numbers more as something you "do" to another number by combining them within the group operation, rather than a "thing." The identity is the number that doesn't do anything. So, you can imagine doing as many identities as you want and not changing what you started with. As such, any number can really be thought of as some sort of process being done to the identity.
The identity is the baseline you get before you start multiplying by anything, so it's what you end with if you multiply by nothing at all.
inconspicuous_male ยท 5 points ยท Posted at 19:08:26 on May 25, 2016 ยท (Permalink)
Also 5! =54321
5!/5 = 4! = 4321
4!/4 =3! = 321
3!/3 = 2! = 21
2!/2 = 1! = 1
1!/1 = 0!. What is 1!/1?
ninja edit: I'm not fixing the formatting
christina4409 ยท 2 points ยท Posted at 23:58:45 on May 25, 2016 ยท (Permalink)
There is one way to arrange nothing.
thestickystickman ยท 1 points ยท Posted at 11:20:35 on May 26, 2016 ยท (Permalink)
That's because it's 00. x0 = 1 for all values of x, because you're multiplying 1 by x zero times.
kevlarisforevlar ยท 15 points ยท Posted at 18:48:34 on May 25, 2016 ยท (Permalink)
There is an illegal number.
robertbastian ยท 3 points ยท Posted at 22:27:32 on May 25, 2016 ยท (Permalink)
Someone call 911
Bentheflame ยท 3 points ยท Posted at 01:01:17 on May 26, 2016 ยท (Permalink)
Most sources change a few numbers so they don't get sued or fined, this number won't get anyone killed.
d0ntblink ยท 1 points ยท Posted at 00:09:54 on May 26, 2016 ยท (Permalink)
I NEED AN ADULT!
[deleted] ยท 1 points ยท Posted at 01:47:15 on May 26, 2016 ยท (Permalink)
reported
Tunderbar1 ยท 30 points ยท Posted at 14:54:33 on May 25, 2016 ยท (Permalink)*
The nine-times table.
1 * 9 = 9 -----> 9 = 9
2 * 9 = 18 -----> 1 + 8 = 9
3 * 9 = 27 -----> 2 + 7 = 9
4 * 9 = 36 -----> 3 + 6 = 9
5 * 9 = 45 -----> 4 + 5 = 9
6 * 9 = 54 -----> 5 + 4 = 9
7 * 9 = 63 -----> 6 + 3 = 9
8 * 9 = 72 -----> 7 + 2 = 9
9 * 9 = 81 -----> 8 + 1 = 9
So when multiplying 9 times any single digit, the digit minus 1 gives you the tens digit, 9 minus the tens digit give you the ones digit.
And reverse it for division.
I killed it with this grand knowledge in grade 1. Been going downhill ever since.
reassemblethesocial ยท 5 points ยท Posted at 16:24:59 on May 25, 2016 ยท (Permalink)
The discrete numbers comprising any product of 9 will add up to 9 in a similar way. This rule applies to any number multiplied by 9:
Or, going bigger:
This works for every number. Doesn't matter how large.
Tunderbar1 ยท 2 points ยท Posted at 16:28:22 on May 25, 2016 ยท (Permalink)
Yup.
An0therB ยท 2 points ยท Posted at 18:25:00 on May 25, 2016 ยท (Permalink)
Most times that you add 9 to a number, 1 is added to the tens digit and 1 is subtracted from the ones digit. Other times, one is added to the hundreds, nine is subtracted from the tens digit, and one is subtracted from the ones digit.
9 + 9 = 18
36 + 9 = 45
92 + 9 = 101
Of course, for numbers with more digits the process is more complex, but the idea is the same.
This is a consequence of our base-10 number system. In any number system, this trait is exhibited by multiples of the number 1 less than the base.
In base 4:
12 x 3 = 102, 1 + 2 = 3
Base 8:
6 x 7 = 52, 5 + 2 = 7
Base 16:
7 x F = 69, 6 + 9 = F
Binary:
1101 x 1 = 1101, 1 + 1 + 1 = 11, 1 + 1 = 10, 1 = 1.
It's pretty cool.
Phoenixness ยท 2 points ยท Posted at 00:04:36 on May 26, 2016 ยท (Permalink)
Just something to add:
9 *10 = 90 -----> 9 + 0 = 9
9 * 11 = 99 -----> 9 + 9 = 18 -----> 1 + 8 = 9
9 * 12 = 108 -----> 1 + 0 + 8 = 9
9 * 13 = 117 -----> 1 + 1 + 7 = 9
...
9 * 487 = 4383 -----> 4 + 3 + 8 + 3 = 18 -----> 1 + 8 = 9
EDIT: I realize /u/reassemblethesocial said the same thing
[deleted] ยท 1 points ยท Posted at 21:50:39 on May 25, 2016 ยท (Permalink)
[deleted]
Tunderbar1 ยท 1 points ยท Posted at 22:58:40 on May 25, 2016 ยท (Permalink)
Nice.
Noremac812 ยท 1 points ยท Posted at 02:30:43 on May 26, 2016 ยท (Permalink)
also interestingly...
91=09 <--> 90
92=18 <--> 81
93=27 <--> 72
94=36 <--> 63
95=45 <--> 54
96=54 <--> 45
97=63 <--> 36
98=72 <--> 27
99=81 <--> 18
910=90 <--> 09
edit: the fuck is wrong with my nines?
[deleted] ยท 196 points ยท Posted at 14:01:22 on May 25, 2016 ยท (Permalink)
Did you know the Americans call maths math?
atoms12123 ยท 71 points ยท Posted at 16:02:32 on May 25, 2016 ยท (Permalink)
Did you know mathematics is a singular word, and that Americans started referring to it as math before the English referred to it as maths?
inconspicuous_male ยท 18 points ยท Posted at 18:52:06 on May 25, 2016 ยท (Permalink)
Very unrelated but accent historians believe the modern American accent is closer to the British accents of 300 years ago than the modern British accent
awildpoliticalnerd ยท 2 points ยท Posted at 23:28:46 on May 25, 2016 ยท (Permalink)
Out of curiosity, which American accent did they focus on?
inconspicuous_male ยท 1 points ยท Posted at 01:17:25 on May 26, 2016 ยท (Permalink)
No clue. Probably typical New England accents
givememyrapturetoday ยท 3 points ยท Posted at 23:44:16 on May 25, 2016 ยท (Permalink)
You mean linguists?
This factoid is attributed in large to the loss of rhoticity in most accents of England; to say the modern American accent is 'closer' is disingenuous and ill-informed.
hextree ยท 15 points ยท Posted at 15:12:28 on May 25, 2016 ยท (Permalink)
That's crazy
Icaninternetplease ยท 3 points ยท Posted at 17:52:30 on May 25, 2016 ยท (Permalink)
Aluminium. Math.
[deleted] ยท 3 points ยท Posted at 18:01:17 on May 25, 2016 ยท (Permalink)
I'll stick with the gold.
relvant_usernam ยท 1 points ยท Posted at 21:23:10 on May 25, 2016 ยท (Permalink)
Someone give this man gold!
Brawndo91 ยท 11 points ยท Posted at 16:21:46 on May 25, 2016 ยท (Permalink)
Is maths a British thing? I just thought it was people trying to be cute. Now I can be less annoyed when I see that.
[deleted] ยท 18 points ยท Posted at 16:28:14 on May 25, 2016 ยท (Permalink)
Yeah they do maths and play a lot of sport. Go figure.
qwerto14 ยท 5 points ยท Posted at 19:06:16 on May 25, 2016 ยท (Permalink)
No. I won't go figure.
[deleted] ยท 10 points ยท Posted at 19:07:53 on May 25, 2016 ยท (Permalink)
Sorry go figures
Underbelly ยท 3 points ยท Posted at 00:20:42 on May 26, 2016 ยท (Permalink)
In Australia and NZ we also say maths.
jmarcandre ยท 5 points ยท Posted at 16:03:36 on May 25, 2016 ยท (Permalink)
Canadians, too, for the most part. Older generation sometimes says maths to much confusion and delight.
[deleted] ยท 23 points ยท Posted at 15:35:08 on May 25, 2016 ยท (Permalink)
Because it's correct.
SEX_LIES_AUDIOTAPE ยท 11 points ยท Posted at 16:23:53 on May 25, 2016 ยท (Permalink)
I, too, enjoy mathematic.
AsterJ ยท 28 points ยท Posted at 18:51:16 on May 25, 2016 ยท (Permalink)
If you take an Introductory Economics class do you call it "econ 101" or "econs 101"?
givememyrapturetoday ยท 2 points ยท Posted at 23:48:53 on May 25, 2016 ยท (Permalink)
"stats 101" has more hits than "stat 101". Your argument says zilch, aside from the fact that you're obviously not a linguist.
PregnantApple ยท 2 points ยท Posted at 00:35:48 on May 26, 2016 ยท (Permalink)
The entire debate is stupid, with elitists from both sides. English has many stupid rules, so it would be unreasonable to try to justify one way over the other. Math has been around for nearly a century longer, while Maths makes sense in the sense that mathematics is plural, though many other words such as the aforementioned economics contradict that, while some others support it. You people need to get over yourselves.
givememyrapturetoday ยท 2 points ยท Posted at 01:37:25 on May 26, 2016 ยท (Permalink)
You wrote the most of anyone!
Edit: relevant XKCD
PregnantApple ยท 2 points ยท Posted at 20:10:37 on May 26, 2016 ยท (Permalink)
So far, all you have been doing is trying to argue an arbitrary linguistic point. Not even. All you have been doing is just attacking those without the same view as you. Sad, really.
givememyrapturetoday ยท -1 points ยท Posted at 20:16:13 on May 26, 2016 ยท (Permalink)
Well gee don't get your knickers in a knot, it's just a bit of fun.
DrSandbags ยท 32 points ยท Posted at 16:44:14 on May 25, 2016 ยท (Permalink)
I use a lot of maths in my econs courses.
ThatSprintingGuy ยท 3 points ยท Posted at 07:44:18 on May 26, 2016 ยท (Permalink)
Statistics = stat or stats? Mathematics = math or maths?
I'm going to do some economics I'm going to do an economic (doesn't make sense)
I'm going to do some mathematics I'm going to do a mathematic (doesn't make sense)
I'm going to do some statistics I'm going to do a statistic
There's a classic debate in the UK about how to pronounce the word scone You can either pronounce it like cone as in s'cone' or like gone as in sc'one'
My point being there is more than one way at looking at things. Just food for thought
[deleted] ยท 7 points ยท Posted at 19:23:00 on May 25, 2016 ยท (Permalink)
Mathematics is singular
DCdictator ยท 10 points ยท Posted at 19:19:55 on May 25, 2016 ยท (Permalink)
Mathematics is a singular noun that ends in an s. You don't abbreviate something and then randomly make it plural, that's absurd.
givememyrapturetoday ยท 2 points ยท Posted at 23:50:04 on May 25, 2016 ยท (Permalink)
As is maths.
the_dirtiest ยท 1 points ยท Posted at 02:19:19 on May 26, 2016 ยท (Permalink)
why would you randomly cut out "ematic" when shortening a word? Why keep the "s"?
givememyrapturetoday ยท 2 points ยท Posted at 05:25:34 on May 26, 2016 ยท (Permalink)*
The evolution of language is indeed a very interesting subject! I'm afraid I can't answer your question, however there's a very interesting series on the history of the English language called The Adventure of English which you may find fascinating!
Edit: etymology of mathematic curious indeed!
VsAcesoVer ยท 17 points ยท Posted at 16:35:55 on May 25, 2016 ยท (Permalink)
math stands for mathematics. Otherwise it'd be math's, where the apostrophe stands for 'ematic'
Gl33m ยท 7 points ยท Posted at 19:40:41 on May 25, 2016 ยท (Permalink)
You shorten mathematics by stopping the word.
You don't say math
ematics you say mathematics.100percent_right_now ยท 0 points ยท Posted at 23:12:45 on May 25, 2016 ยท (Permalink)
Sure beats that damn mathsematics.
fnord_happy ยท 0 points ยท Posted at 16:46:09 on May 25, 2016 ยท (Permalink)
Lol k. If you say so. That's settled then
sourc3original ยท -2 points ยท Posted at 20:54:22 on May 25, 2016 ยท (Permalink)
lol
RossBossTM ยท 2 points ยท Posted at 16:17:09 on May 25, 2016 ยท (Permalink)
As a young Canadian I was completely unaware that the rest of the world called it maths
w675 ยท 6 points ยท Posted at 18:38:51 on May 25, 2016 ยท (Permalink)
Don't worry about it, the rest of the world is wrong.
[deleted] ยท 1 points ยท Posted at 19:22:14 on May 25, 2016 ยท (Permalink)
As you can see in this comment thread, math is the correct way to say it.
[deleted] ยท 6 points ยท Posted at 16:45:14 on May 25, 2016 ยท (Permalink)
[deleted]
KirbyElder ยท -4 points ยท Posted at 16:56:17 on May 25, 2016 ยท (Permalink)
Car is short for carriage. This does not change the fact that if you shorten "carriages" you end up with "cars", not "car".
TrapperM ยท 9 points ยท Posted at 18:08:37 on May 25, 2016 ยท (Permalink)
Except that mathematics is a singular word, not plural. You don't have one mathematic and several mathematics. Its just a word that ends with an s. So your analogy doesn't really hold.
w675 ยท 6 points ยท Posted at 18:37:17 on May 25, 2016 ยท (Permalink)
Yeah, nice try.
Calling mathematics maths is implying that mathematics is plural, which is false. Mathematics is defined as the study of topics such as quantity, structure, space, and change.
The study. The singular study of those topics. Argument over.
BigWaveSmallOcean ยท 4 points ยท Posted at 16:18:39 on May 25, 2016 ยท (Permalink)
Is that because they don't know how to do multiples WAAAAAAAAAAAY!
Denroll ยท -1 points ยท Posted at 17:28:57 on May 25, 2016 ยท (Permalink)
WWI, WWII... want us to keep going?
BigWaveSmallOcean ยท 0 points ยท Posted at 17:54:12 on May 25, 2016 ยท (Permalink)
If you want, anything else we've won?
stoirtap ยท 1 points ยท Posted at 18:42:38 on May 25, 2016 ยท (Permalink)
WWC? (Women's World Cup)
LedditHiveMind ยท 1 points ยท Posted at 18:50:06 on May 25, 2016 ยท (Permalink)
It's not the most logical way but it's my way
snapcracklesplat ยท 1 points ยท Posted at 19:22:22 on May 25, 2016 ยท (Permalink)
wait I thought the person who made his post was just an idiot
JackAceHole ยท 1 points ยท Posted at 19:45:36 on May 25, 2016 ยท (Permalink)
Americans took the "s" from "maths" and put it on "sport" to make "sports" (as in "the sports page")
bakugandrago18 ยท 1 points ยท Posted at 22:35:05 on May 25, 2016 ยท (Permalink)
FTFY /s
Miknarf ยท 1 points ยท Posted at 22:47:04 on May 25, 2016 ยท (Permalink)
Only when there's one of them. Like history class. You wouldn't call it histories class.
WillyMacBatman ยท 1 points ยท Posted at 23:21:23 on May 25, 2016 ยท (Permalink)
Thats because "maths" has 5 letters and we can't count that high.
Tsukaisute1 ยท 1 points ยท Posted at 23:42:52 on May 25, 2016 ยท (Permalink)
http://separatedbyacommonlanguage.blogspot.jp/2007/03/maths.html
OdysseusX ยท 0 points ยท Posted at 15:54:34 on May 25, 2016 ยท (Permalink)
I was trying to find this comment. This short question is so obviously not written by an American. Between favourite/favorite and maths/math. It stood out to me.
Maths makes sense because mathematics. But. Growing up hearing it only as let's study math. Here are some math problems. Etc. it just feels weird saying and hearing maths.
And forget about that crazy as U showing up everywhere.
mr_ewe ยท 3 points ยท Posted at 16:37:11 on May 25, 2016 ยท (Permalink)
What's your favorite colour?
Stuart_P ยท 6 points ยท Posted at 16:42:13 on May 25, 2016 ยท (Permalink)
Centre.
Did I did it good?
PWNY_EVEREADY3 ยท 1 points ยท Posted at 17:02:19 on May 25, 2016 ยท (Permalink)
You did
OdysseusX ยท 3 points ยท Posted at 16:52:14 on May 25, 2016 ยท (Permalink)
Grey
Mmbopbopbopbop ยท 3 points ยท Posted at 17:09:30 on May 25, 2016 ยท (Permalink)
Aluminium
tregorman ยท 1 points ยท Posted at 19:51:35 on May 25, 2016 ยท (Permalink)
Lift
qwerto14 ยท 0 points ยท Posted at 19:07:44 on May 25, 2016 ยท (Permalink)
Math makes more sense. Mathematics is a singular term, you just take the ematics off.
skizfrenik_syco ยท 0 points ยท Posted at 15:57:42 on May 25, 2016 ยท (Permalink)
Or "What the hell are those things"
actual_factual_bear ยท 0 points ยท Posted at 16:49:41 on May 25, 2016 ยท (Permalink)
We just haven't gotten our head around the fact that there is more than one.
Kitbixby ยท 0 points ยท Posted at 21:16:04 on May 25, 2016 ยท (Permalink)
Did you know know Americans correctly call the subject with calculations math--and not maths?
Huomenna ยท 128 points ยท Posted at 13:35:24 on May 25, 2016 ยท (Permalink)
Pi day was celebrated on 3/14/15, even though 3.1415 is less accurate than 3.1416
MrXian ยท 194 points ยท Posted at 15:09:15 on May 25, 2016 ยท (Permalink)
That's because we celebrated pi second. 3/14/15 9:26:54
sex_panther96 ยท 5 points ยท Posted at 17:58:27 on May 25, 2016 ยท (Permalink)
I am proud to say I witnessed my watch strike 9:26:54am on march 14th 2015. I had been waiting for that single moment since I had learned about pi day six years earlier.
MrXian ยท 4 points ยท Posted at 18:14:36 on May 25, 2016 ยท (Permalink)
I had an alarm set on my watch and I got to explain it to my running mates.
[deleted] ยท 1 points ยท Posted at 22:04:06 on May 25, 2016 ยท (Permalink)
Well it's all arbitrarily based on some Roman jurors decree so...
In TouchMyDuck calendar (which is the world's first variable calendar) every day is Pi day.
popedarren ยท 5 points ยท Posted at 16:16:33 on May 25, 2016 ยท (Permalink)
Wait a minute... I only know pi out to a few digits, but I think the last one is wrong there in your comment...
3.141592653589 = 3/14/15 9:26:53.589
Oh... you rounded up the milliseconds into a second. I see! Never mind. Carry on... well, I guess I could just not submit this comment... nah.
Edit: missed the next to last digit on left side of my pi to date
random_runner ยท 22 points ยท Posted at 16:24:18 on May 25, 2016 ยท (Permalink)
No, if you wait a minute you're too late and it'll be 3/14/15 9:27:54
ThreeHourRiverMan ยท 35 points ยท Posted at 14:11:48 on May 25, 2016 ยท (Permalink)
Not on Price is Right!
(Rounding isn't always preferable to truncation.)
IndigoMontigo ยท 9 points ยท Posted at 15:12:27 on May 25, 2016 ยท (Permalink)
It was also celebrated on 3/14/16.
And it will be celebrated next year on 3/14/17.
skizfrenik_syco ยท 9 points ยท Posted at 15:54:11 on May 25, 2016 ยท (Permalink)
It's celebrated every year on 3/14 though.
galacticdick ยท 6 points ยท Posted at 14:09:47 on May 25, 2016 ยท (Permalink)
I knew the next digit was 9, but for some reason this never occurred to me
EElectricGirl ยท 2 points ยท Posted at 16:02:41 on May 25, 2016 ยท (Permalink)
That's why we celebrate at 9:26
Yurika_BLADE ยท 2 points ยท Posted at 16:12:04 on May 25, 2016 ยท (Permalink)
That's why we celebrated it at 9:26:53 AM
CourierOfTheWastes ยท 1 points ยท Posted at 17:08:48 on May 25, 2016 ยท (Permalink)
I'm a dork and had shepherds pie, pie flavoured vodka in Coca Cola, and an Oreo pie for desert.
I had it at 9:26 pm.
kogasapls ยท 1 points ยท Posted at 17:25:40 on May 25, 2016 ยท (Permalink)
It was also celebrated on 3/14/16.
whatthefuckulookinat ยท 1 points ยท Posted at 18:47:11 on May 25, 2016 ยท (Permalink)
I celebrate pi day every 3/14, not just in 2015
PoisonousPlatypus ยท 1 points ยท Posted at 19:06:09 on May 25, 2016 ยท (Permalink)
Except exactly pi occurred to infinite precision during pi day.
Kitbixby ยท 1 points ยท Posted at 21:15:02 on May 25, 2016 ยท (Permalink)
Pi day is celebrated as March 14
astrojg ยท 1 points ยท Posted at 17:59:07 on May 25, 2016 ยท (Permalink)
Didn't know there was 14 months in the year
_Lady_Deadpool_ ยท 7 points ยท Posted at 16:15:23 on May 25, 2016 ยท (Permalink)*
You can estimate the number of zeros in front of a large factorial easily. For example, 100! has 24 zeros.
The number of zeros in front of a multiplicative expansion is equal to the number of 10's inside it. For example, say you have 3*5*10*10 = 1500, two zeros,
Now, 10 = 2*5 and when you fully expand q factorial there are a lot more 2's than 5's, so the number of 10's equals the number of 5's.
10! = 10*9*8*7*6*5*4*3*2*1
10! = 5*2*3*3*2*2*2*7*3*2*5*2*2*3*2*1
For 100! there are 20 fives (100/5 = 20), plus an additional five for each multiple of 25 (25, 50, 75, 100) so there are 20+4 = 24 zeros at the front of 100!
Another example: 52! has 10 fives plus one for 25 and one for 50 = 12 zeros
kevin_with_rice ยท 1 points ยท Posted at 03:02:40 on May 26, 2016 ยท (Permalink)
My dad was telling me about a programming competition he was in (back in the 80s) where this was the problem. His team ending up winning because they figured it out before anyone else. Really cool fact!
MrMeow251 ยท 6 points ยท Posted at 17:16:10 on May 25, 2016 ยท (Permalink)
0!=1
anguksung ยท 4 points ยท Posted at 23:51:25 on May 25, 2016 ยท (Permalink)
As a programmer, I see what you did there.
InSkyLimitEra ยท 42 points ยท Posted at 12:25:45 on May 25, 2016 ยท (Permalink)*
I have always enjoyed the birthday paradox. How many people does it take in a room to boost the probability over 50% that two people share a birthday in that room? Most people tend to guess much higher numbers, but the answer is just 23 people.
It's a great demonstration of how intuitively bad most people are at probability, which is relevant to so many areas of life. Lottery ticket, anyone?
Edit: in response to some comments, I agree it's probably better called "birthday problem," not "birthday paradox." But it is referred to by both names.
TheSemiTallest ยท 20 points ยท Posted at 13:24:30 on May 25, 2016 ยท (Permalink)
I've always loved this fact, and find it similarly interesting that at 70 people there is a 99.9% chance of birthday-sharing.
Unambiguous ยท 2 points ยท Posted at 04:42:06 on May 26, 2016 ยท (Permalink)
And with 367 people there is a 100% chance!!! Wow!!!
ExeusV ยท 1 points ยท Posted at 20:13:29 on May 25, 2016 ยท (Permalink)
There's difference between lottery with e.g 49 numbers (6=win) and "ridiculous" fact like this bday problem.
JTswift ยท 1 points ยท Posted at 14:22:17 on May 25, 2016 ยท (Permalink)
I asked this to another person, but...
How many people do you need for that birthday to also include the same Year?
Multai ยท 2 points ยท Posted at 15:42:10 on May 25, 2016 ยท (Permalink)
Depends on what chance there is of having a certain birthyear. Are kids included? Are old people included? What 'limit' is there? We know the limit of birthdays is 365, but for age there is no real limit. (We all die, but at what point?)
The chance of n people sharing NO birthdays is (366-1)/365 * (366-2)/365 * (366-3)/365 * .... * (366-n)/365 * 100
Just subtract this from 100 to get the chance of at least 2 people sharing their birthday.
Note: Feel free to point it out if I'm wrong
Instead of days you could do years, assuming people can be anywhere from 0 to 80 years old (and assuming the odds are even for all ages) you could change 366 in the formula to 81 and 365 to 80. After you've calculated the chance of the year being the same just multiply that by the chance given by my other formula. Then it's just a case of finding what n gives you a chance of more than 50 percent.
I personally wouldn't know of a way to find this number without making a MASSIVE excel file that would do it for me, but there are probably ways.
CaptainSasquatch ยท 3 points ยท Posted at 16:43:14 on May 25, 2016 ยท (Permalink)
633
Assuming there are 29,200 possible birthdays (most people born on actual February 29 are legally born on March 1). If we assume that the population pyramid is flat i.e a uniform distribution of all birthdays from 1936-05-26 to 2016-05-25. Then the chance of noone in a group of N people share a birthday and birthyear is 29,200!/((29,200-N)!*29,200N).
Since you specified Excel I decided to do it in Excel. Excel freaks out if you try and calculate 29,200! or PERMUT(29200, 70) so we'll do it the roundabout way.
log(a*b) = log(a) + log(b)
log(x!) = log(x)+log(x-1)+log(x-2)...log(1)
log(29,200!/(29,200-N)!) = log(29,200)+log(29,199)+log(29,198)...+log(29,200-N)
log(29,200N) = N*log(29,200)
So 29,200!/((29,200-N)!*29,200N) = EXP(sum(log(29,200-i),i=0,N-1)-Nlog(29,200))
In Excel formulas
First column is N, 3rd column is sum(log(29,200-i),i=0,N-1) 4th column is Nlog(29,200)), 5th column is probability of no match.
Multai ยท 2 points ยท Posted at 16:46:59 on May 25, 2016 ยท (Permalink)
Hmm interesting, /r/theydidthemath I guess?
Just tagging /u/JTswift so he can see this too.
CaptainSasquatch ยท 2 points ยท Posted at 16:53:15 on May 25, 2016 ยท (Permalink)
In real life, groups are not uniformly random wrt birth year so you'll probably need less people. A school class is normally used in the example of the original birthday paradox so the chances are very high that you'll have overlap in birth year also.
CaptainSasquatch ยท 1 points ยท Posted at 16:43:40 on May 25, 2016 ยท (Permalink)
633
I explain how I got it in my comment below
loptthetreacherous ยท 1 points ยท Posted at 16:51:42 on May 25, 2016 ยท (Permalink)
The birthday paradox assumes a perfectly even distribution of birthdays throughout the year, which is probably near enough true as far as I know.
Birthyears is a lot harder because (unlike birthdays) they won't be evenly distributed and we don't know how old the oldest people are.
kogasapls ยท 1 points ยท Posted at 17:40:06 on May 25, 2016 ยท (Permalink)
You can still establish an upper bound. The less evenly distributed the birthdays, the fewer people you need on average. So assuming perfectly even distribution gives you the maximum average number of people.
ltouroumov ยท 1 points ยท Posted at 20:12:10 on May 25, 2016 ยท (Permalink)
Here is the distribution of birthdays through the year. If I remember right that's taken from the US bureau of statistics so it should be reasonably accurate.
DeprestedDevelopment ยท 1 points ยท Posted at 15:24:34 on May 25, 2016 ยท (Permalink)
In no way is that a paradox.
crossedstaves ยท 3 points ยท Posted at 16:05:40 on May 25, 2016 ยท (Permalink)
Its not a paradox to math, but its a paradox to man. If you're being rigid, then the existence of a paradox invalidates the logic of the math, and therefore we resolve the paradox by changing the assumptions so that math can work and be logical. The abstract concepts of logic and math, do no permit paradox to exist within them. And so nothing which remains in math or logic may be a paradox.
The point is going around and telling people that things aren't really a paradox is completely goddamn pointless. By being pedantic about paradox you reach a point where paradox isn't actually a thing, and if its not a thing its not worth defending the use of the word. In defending you destroyed it, and thus you fall into a paradox.
DeprestedDevelopment ยท 1 points ยท Posted at 00:39:46 on May 26, 2016 ยท (Permalink)
It isn't a paradox lmao.
TDenverFan ยท 0 points ยท Posted at 16:23:29 on May 25, 2016 ยท (Permalink)
That's not a paradox
tahitiisnotineurope ยท -19 points ยท Posted at 14:04:37 on May 25, 2016 ยท (Permalink)
funny its total bullshit.
demonicpigg ยท 9 points ยท Posted at 14:29:12 on May 25, 2016 ยท (Permalink)
It's not, it's mathematically air tight. Also, a couple of days ago the fact came up, and another person and myself both tested databases which included random people. You can see what we found here.
tahitiisnotineurope ยท -2 points ยท Posted at 16:08:54 on May 25, 2016 ยท (Permalink)
"random"
demonicpigg ยท 3 points ยท Posted at 18:26:36 on May 25, 2016 ยท (Permalink)
So, to prove this, lets work backwards a bit. Imagine, you have a whole bunch of people (lets say 100, but it doesn't matter as you can do this with any number of people).
You ask the first one what their birthday is. What's the chance it doesn't share a date with someone who's already been asked? 365/365, as no dates have been used. The second person is asked, and the chance of them not sharing a birthdate with someone already asked is 364/365. This is because 364 days of the year haven't been said yet. The third had 363/365, the fourth 362/365.
If you continue this out to n you get 365-(n-1)/365. You then multiply them all out to get the actual chance of no one sharing a birthday. This turns into (1/365)n * 365! / (365-n)!
The exclamation points are factorials which basically means 365 * 364 * 363 * ... * 2 * 1. By dividing by (365-n)! you end up with 365 * 364 * 363 * ... * (365 - n).
When you plug in 23 for n you end up with (1/365)23 * 365!/342! โ 0.492703. This means the chance, with 23 people, you have a 49.27% chance of two people in the group not sharing a birthday. Simply subtract from 100% to find the chance that two people will have a shared birthday (~50.73%).
tahitiisnotineurope ยท 2 points ยท Posted at 07:57:28 on May 26, 2016 ยท (Permalink)
I love this now.
demonicpigg ยท 1 points ยท Posted at 13:16:34 on May 26, 2016 ยท (Permalink)
Glad I could share something awesome with you!
Lost4468 ยท 2 points ยท Posted at 16:11:07 on May 25, 2016 ยท (Permalink)
How?
tahitiisnotineurope ยท -2 points ยท Posted at 16:13:15 on May 25, 2016 ยท (Permalink)
how white man.
loptthetreacherous ยท 1 points ยท Posted at 17:08:58 on May 25, 2016 ยท (Permalink)
Care to explain how it's total bullshit? The only problem there can be is birthdays aren't perfectly evenly distributed, but as far as I know they're even enough not to make a massive difference.
kogasapls ยท 1 points ยท Posted at 17:40:33 on May 25, 2016 ยท (Permalink)
Less even distribution would actually bring the number down.
tahitiisnotineurope ยท -1 points ยท Posted at 17:52:56 on May 25, 2016 ยท (Permalink)
all i'm saying is its not math. its society. people fuck when power goes out.. spring is storm season. storms affect wide areas. people are born around 9 months later so on and so on. math is used to calculate the facts. the facts are not a math vs human "quirk" like (oh thats so counter intuitive)
methyboy ยท 3 points ยท Posted at 18:02:19 on May 25, 2016 ยท (Permalink)
All of those things have the effect of making it more likely for people to share birthdays.
The birthday paradox says that in a room of 23 randomly-selected people, there is a greater than 50% chance that at least two of them share a birthday. That is true regardless of how birthdays are distributed. The fact that birthdays aren't uniformly distributed just raises the probability even higher above 50%.
tahitiisnotineurope ยท 0 points ยท Posted at 18:04:28 on May 25, 2016 ยท (Permalink)
i wish i could understand the math well enough to explain it simply. so bullshitty.
methyboy ยท 2 points ยท Posted at 18:06:32 on May 25, 2016 ยท (Permalink)
You seem to be saying that it's bullshit because birthdays come in "clumps" (e.g., people are more likely to have sex in the spring, etc). Is that what you were trying to get at?
If so, you're wrong. That makes the birthday paradox more true, not less.
tahitiisnotineurope ยท -1 points ยท Posted at 18:07:00 on May 25, 2016 ยท (Permalink)
when i first began computing this all out i was trying to say that people won't share a birthday. i'm always doing this. i put a decimal in the wrong place. always some mundane detail. (this is not a mundane detail... michael!
loptthetreacherous ยท 2 points ยท Posted at 18:03:18 on May 25, 2016 ยท (Permalink)
Are you aware that statistics is a branch of mathematics? Also, the "9 months after a power shortage has an influx of births" is bullshit.
ktkps ยท 113 points ยท Posted at 11:44:37 on May 25, 2016 ยท (Permalink)
Principia Mathematica has several hundred pages dedicated to prove the validity of the expression 1+1=2.
Karl_von_Moor ยท 202 points ยท Posted at 13:29:37 on May 25, 2016 ยท (Permalink)
There is a difference between "several hundred pages dedicated to prove the validity of the expression 1+1=2" and "After several hundred pages it is proven that 1+1=2".
thosethatwere ยท 1 points ยท Posted at 16:24:17 on May 25, 2016 ยท (Permalink)
Only if there's stuff that comes before the proof of 1+1=2 that isn't used in the proof of 1+1=2.
marcelluspye ยท 14 points ยท Posted at 17:25:50 on May 25, 2016 ยท (Permalink)
There is
Denziloe ยท 3 points ยท Posted at 18:17:48 on May 25, 2016 ยท (Permalink)
No, that's still not what the word 'dedicated' means. If the stuff before is used to establish stuff other than 1 + 1 = 2 (which it definitely is), then that stuff wasn't "dedicated" to the proof of 1 + 1 = 2 because that wasn't its sole purpose.
thosethatwere ยท 3 points ยท Posted at 18:21:29 on May 25, 2016 ยท (Permalink)*
Ah, I didn't see the word dedicated in there. It's not usually in such claims, only that several hundred pages are required to prove the validity of the expression 1+1=2, which is in fact a true statement - there are several hundred pages of proofs used in building up the argument that culminates in the proof of 1+1=2.
Being even more pedantic (as one is wont to in this field) I should correct myself and say that my previous statement isn't correct in another way: even if there are some pages that do not present useful in the proof of 1+1=2, there still could be several hundred, albeit not consecutive, pages of mathematics leading up to the proof. As I'm already on this high horse of pedantry I should perhaps point out that my statement was a necessary condition, not a sufficient one, and therefore in such a pedantic view (as I have taken only in this paragraph) you objection to my (incorrect) claim is also false.
Mirrorboy17 ยท 117 points ยท Posted at 13:14:39 on May 25, 2016 ยท (Permalink)
In my first year at university a lecturer spent 50 minutes trying to show what a number was. At the end she said "oh hang on that was wrong" - and never returned to it... now I've no idea what a number is
[deleted] ยท 23 points ยท Posted at 14:15:37 on May 25, 2016 ยท (Permalink)
If you're still wondering, I recommend Frege's "Foundations of Arithmetic". It's dated, but well-written and heavily influenced Russell (who wrote the aforementioned Principia Mathematica).
PlayfulPhilosopher ยท 2 points ยท Posted at 16:08:25 on May 25, 2016 ยท (Permalink)
Frege and Russell independently came up with what is now known as the Frege-Russell definition of number, which can also be found in Russell's "The Principles of Mathematics" (1903). Russell did not read Frege in detail until he went looking for Frege's solution to what we now call Russell's Paradox (Russell simply called it "the Contradiction").
I do also recommend reading Frege's "Foundations". Russell's "Introduction to Mathematical Philosophy" (1919) is a good introduction as well, for those who do not wish to read Principia Mathematica itself.
SidusObscurus ยท 5 points ยท Posted at 15:49:40 on May 25, 2016 ยท (Permalink)
It's really not as bad as some teachers can make it seem. Especially if leaving out the Irrational numbers is good enough for you.
The Natural numbers are sets containing some number of elements. Addition of two natural numbers is taking the disjoint union of the sets that those two numbers are. Throw in a bunch of extra rigor and some words on congruence classes to formalize it all, and you're ready for arithmetic.
For example, 2 is really the set containing two elements { 0, 1 }. And so 1+1 = {0} U* {0} = {(0,0)} U {(0,1)} = {(0,0), (0,1)} = 2 as it contains two elements and so.
From here you build everything else:
Subtraction is the inverse of addition. You now have negative numbers (the Integers).
Multiplication is repeated addition.
Define fractions as the number pair (p,q) and expand the your earlier operations to have the rules you'd expect. We now have the Rational numbers.
Division is then just multiplication by a fraction.
So far, it's been easy, but now comes the most difficult part, the one big trick that actually gives you all the numbers:
Consider putting fractions on a number line and notice that there's always "space" between any two fractions you pick. Is that "space" a number? Not yet. You have to fill in the "spaces", by completing the the Rational numbers. You make every sequence of numbers that converges into a new number and give it a name. Lots of these sequences were already Rational numbers, but we just created some new numbers too.
For example:
2 = (2,2,2,2,2,2 ...) but also = (19/10, 199/100, 1999/1000 ... ) since the distance between elements of these sequences goes to 0.
0 = (0,0,0 ... ) but also = (1, 1/2, 1/4, 1/8 ... ) for the same reason
And a new number Pi = (3, 31/10, 314/100 ...) which, from its definition, can be shown not to be a Rational number. It's a newly created number, an Irrational number
Most people like to understand this with decimals, which is really the same thing, just with a different notation.
2 = 2.000... but also = 1.999...
Pi = 3.14159...
Once you have these sequences, you expand your operations to work with the sequences, show that this completion makes the number line "full" (there are no more numbers hiding somewhere), and BAM you have the Real numbers. From absolutely nothing other than logic, disjoint unions, and definitions (and taking the power set is hiding somewhere in there too).
You now have "numbers", the most fundamental tool in math, and are ready to build everything else in math.
stormblooper ยท 1 points ยท Posted at 18:55:49 on May 25, 2016 ยท (Permalink)
Logic and sets are more fundamental tools.
CosineTau ยท 8 points ยท Posted at 15:01:04 on May 25, 2016 ยท (Permalink)
They're arbitrary structures that we build up from sets of elements, and govern them by algebraic axioms and at least one operator (+, *).
In order for them to "be" algebraic (rings, groups, etc) they need to satisfy at least some of those axioms.
If they don't, that's ok. They can still be something else. That's the arbitrary part
ThePopeShitsInHisHat ยท 3 points ยท Posted at 16:58:59 on May 25, 2016 ยท (Permalink)
What's a set? What's an element? What are axioms and operators? What does it mean to satisfy those axioms, or for a proposition to be true?
That's why Russell takes hundreds of pages to prove "1+1=2": because he needs to lay all the proper foundations beforehand.
I like your concise definition of number, but maybe that lecturer was going through all the "let's define sets and axioms" process?
shmameron ยท 0 points ยท Posted at 16:07:11 on May 25, 2016 ยท (Permalink)
Username checks out.
Retbull ยท 1 points ยท Posted at 15:26:27 on May 25, 2016 ยท (Permalink)
A number is the thing between two different sets that is the same. So if I have 6 apples and 6 pears 6 is what is the same between them. This isn't really a proof so much as a fun way of thinking of it though.
LBJSmellsNice ยท 1 points ยท Posted at 17:07:15 on May 25, 2016 ยท (Permalink)
It's just a unit of counting is all
Slacker5001 ยท 1 points ยท Posted at 18:06:54 on May 25, 2016 ยท (Permalink)
Although I've never had "number" defined, I've been exposed to a few ways of building number systems.
Natural numbers can be built using Peano axoims and successor functions. Adding basic arithmetic properties can give you all other systems all the way up to rational numbers. This isn't too mind blowing to understand so I encourage anyone to go look at it if they are interested.
To build the real number system you can use Cantor sets or Dedekind cuts to define your numbers. This is a little more complex of a notion. Say you want to define the number "2". The idea of both methods is pretty much make two groups of numbers, one group being all the numbers smaller than 2 and the other being all the numbers greater than 2. Then you pretty much just say in fancy math terms that 2 is what is squished between those two groups. In a way we are defining 2 by what it isn't.
I'm not sure how you build the set of complex numbers from there, other than they are an extension of the reals in some form or way.
That's about all I know about building number systems personally. And there is the philosophical side of it as explained by a cool Numberphile video.
Denziloe ยท 1 points ยท Posted at 18:18:34 on May 25, 2016 ยท (Permalink)
What the hell kind of lecture is this? What course was it?
ZenosAss ยท 1 points ยท Posted at 18:50:49 on May 25, 2016 ยท (Permalink)
Reminds me of a story my math prof used to tell us, from back when he was a math student.
Apparently the lecturer is in the middle of a long-ish proof of something and says, "...and from this, it is obvious that-" and just stops and frowns for a bit. He walks out of the hall and the students awkwardly wait around for like 5 minutes. Then the lecturers strides back in and immediately starts up again, "Yes, it is obvious that..."
[deleted] ยท 1 points ยท Posted at 14:19:34 on May 25, 2016 ยท (Permalink)
If I remember my first year college maths right, numbers are sets. Yeah, I know...
thosethatwere ยท 1 points ยท Posted at 16:30:32 on May 25, 2016 ยท (Permalink)
Define a set.
Define the empty set as a set with no elements.
Define 0:= the empty set = {}
Define 1:= the set of the empty set = { {} }
Define 2:= the set of (the set of the empty set) and (the empty set) = { { {} } , {} } = { 0, 1} = {1} union with 1
Define (n+1):= n union with { n }
[deleted] ยท 6 points ยท Posted at 16:23:28 on May 25, 2016 ยท (Permalink)
Very misleading to say that.
They were developing set theory, which is "fundamental math" in the sense that all questions can be phrased in set theory language and all proofs can be derived from set theory's axioms.
What they showed was that set theory is capable of reproducing the integers, defining addition, and reproducing all of our familiar facts and intuitions about it. This is a boon because set theory makes use of fewer primitive notions than Peano arithmetic does.
ktkps ยท 2 points ยท Posted at 04:52:25 on May 26, 2016 ยท (Permalink)
I read this like batman - it was apt.
jywn4679 ยท 3 points ยท Posted at 14:54:41 on May 25, 2016 ยท (Permalink)
That was far more about trying to create a good grounding for math, rather than actually proving that 1+1=2. Nobody even doubted that 1+1=2, and a rigorous proof is not needed other than to ensure the grounding is correct.
[deleted] ยท 1 points ยท Posted at 14:06:53 on May 25, 2016 ยท (Permalink)
try putting up '10' fingers (01010), I dare you
Ronny070 ยท 1 points ยท Posted at 14:49:02 on May 25, 2016 ยท (Permalink)
Good thing we have Terrence Howard to disprove those lies and enlighten us with proof.
_Pornosonic_ ยท 1 points ยท Posted at 16:05:23 on May 25, 2016 ยท (Permalink)
Tldr? I have always wondered why 1+1=2. I am serious.
dotThink ยท 3 points ยท Posted at 18:31:41 on May 25, 2016 ยท (Permalink)*
This is not the Principia proof, but it's something.
First, the axioms:
Now, let's define the first couple of natural numbers after 0:
1 = S(0)
2 = S(1) = S(S(0))
We now define addition recursively:
a + 0 = a
a + S(b) = S(a + b)
Let's use our definition:
1 + 1 = S(0) + S(0) = S(S(0) + 0)) = S(S(0)) = 2
Look up "Peano axioms" or "Peano arithmetic" is you want the full version of what I have talked about.
sprankton ยท 1 points ยท Posted at 16:57:01 on May 25, 2016 ยท (Permalink)
Principia set out to prove all major mathematical theorems in something called symbolic logic. The idea was that this system would be better for mathematical proofs than English or any other verbal language because it had less ambiguity. It didn't really take hundreds of pages to prove that 1+1=2 so much as it took that long to establish the concept of numbers and arithmetic in order to prove that 1+1=2.
loptthetreacherous ยท 1 points ยท Posted at 16:33:59 on May 25, 2016 ยท (Permalink)
Not as extreme, but along the same line: The first book of Euclid's Elements is a 48 page proof of pythagoras's theorem.
DCdictator ยท 1 points ยท Posted at 19:22:12 on May 25, 2016 ยท (Permalink)
The interesting thing about the 1+1=2 proof is that they keep getting longer because we keep using weaker and weaker definitions of 1, thereby strengthening our entire system of mathematics by only needing to rely on weaker assumptions.
Mac_Lilypad ยท 1 points ยท Posted at 13:25:40 on May 25, 2016 ยท (Permalink)
wasn't their final conclusion that you can't prove that 1+1=2 ?
idontlikethisname ยท 3 points ยท Posted at 15:58:57 on May 25, 2016 ยท (Permalink)
I'm not a mathematician, but my understanding is that the conclusion was that you can't fully prove a system like mathematics, you have to make some base assumptions. The proof for 1+1=2 is completely valid if you already have a definition for what "+" is. Bertrand wanted to provide proofs and definitions for everything in math, but found that such task was impossible.
speedisavirus ยท 1 points ยท Posted at 16:10:12 on May 25, 2016 ยท (Permalink)
You can probe it via the definition of addition. The only way you can't is if you prove the additive properties and numerical properties of addition are wrong. Which you can't.
bunker_man ยท 0 points ยท Posted at 13:40:26 on May 25, 2016 ยท (Permalink)
It was also written by the guy who started the best religion of all time!
jakefromstatefarm10 ยท -2 points ยท Posted at 14:08:23 on May 25, 2016 ยท (Permalink)
It's not proving the validity its proving the concepts that go into math using 1+1=2. You could do this in one step. Subtract 1 from both sides and then u get 1=1 and by the reflexive ppty this is true.
visor841 ยท 5 points ยท Posted at 15:24:46 on May 25, 2016 ยท (Permalink)
"Subtract 1 from both sides" would require first proving that 2-1=1. Which is basically the same problem.
jakefromstatefarm10 ยท 1 points ยท Posted at 15:27:54 on May 25, 2016 ยท (Permalink)
Read the first part of my comment.
visor841 ยท 4 points ยท Posted at 16:23:34 on May 25, 2016 ยท (Permalink)
I did. To use your proof, you need to already know that subtracting 1 from the 2 on the right side of the equation gives you 1, i.e. 2-1=1. This is unrelated to proving the concepts.
jakefromstatefarm10 ยท 0 points ยท Posted at 16:30:37 on May 25, 2016 ยท (Permalink)
And we do know that subtracting 1 from 2 gives you 1. Do you even know what you're arguing?
visor841 ยท 2 points ยท Posted at 16:34:24 on May 25, 2016 ยท (Permalink)
How do we know that subtracting 1 from 2 gives you 1?
jakefromstatefarm10 ยท 1 points ยท Posted at 16:39:49 on May 25, 2016 ยท (Permalink)
Because of proofs like the one in the original comment.
visor841 ยท 1 points ยท Posted at 16:41:39 on May 25, 2016 ยท (Permalink)
That's my point. If that was yours, I'm sorry I was misunderstanding you.
jakefromstatefarm10 ยท 2 points ยท Posted at 16:43:14 on May 25, 2016 ยท (Permalink)
It was. I said he wasn't proving 1+1=2, he was proving the mathematical techniques we use everyday that make such equations easy.
jywn4679 ยท 2 points ยท Posted at 15:26:30 on May 25, 2016 ยท (Permalink)
If you want a rigorous proof that 1+1=2 you need to do a lot more than that. For a start, it is much easier to prove 1+1=2 than it is to define subtraction.
Also, you started with 1+1=2 and deduced that 1=1, this is not valid. You could similarly say 1=0, multiple both sides by 0 to get 0=0, which is true, and so 1=0.
jakefromstatefarm10 ยท 2 points ยท Posted at 15:30:00 on May 25, 2016 ยท (Permalink)
I said this in my comment that they weren't proving 1+1=2 they were just using it as a filler equation to prove the mathematical theorems we use everyday.
speedisavirus ยท 0 points ยท Posted at 16:12:00 on May 25, 2016 ยท (Permalink)
No you can't. You can prove a single property of the definition of multiplication.
jywn4679 ยท 0 points ยท Posted at 16:14:07 on May 25, 2016 ยท (Permalink)
I can't what?
speedisavirus ยท 0 points ยท Posted at 16:18:28 on May 25, 2016 ยท (Permalink)
Your entire second sentence.
Source: I can actually write proofs and know axioms of basic operators.
jywn4679 ยท 0 points ยท Posted at 16:20:32 on May 25, 2016 ยท (Permalink)
I was showing why his method of proof was flawed, because by the same method I can prove that 1=0.
Source: I get paid to do math.
CubesphereSSB ยท 17 points ยท Posted at 13:48:12 on May 25, 2016 ยท (Permalink)
The numbers of the Binomial coefficients correspond with 11x:
First row: (1 0) and (1 1) (dunno how to do the math writing thing) 1 1 = 111
Second row: (2 0), (2 1), (2 2): 1 2 1 = 112
Third row: (3 0), (3 1), (3 2), (3 3): 1 3 3 1 = 113
and so on...
ClareDeLoon ยท 6 points ยท Posted at 15:39:20 on May 25, 2016 ยท (Permalink)
Because they're the coefficients of (a+b)n for a=10, b=1 :)
You get 1x103 + 3x102 x1 + 3x10x12 + 1x13 etc
I never noticed that...
LlanowarElf ยท 4 points ยท Posted at 15:38:07 on May 25, 2016 ยท (Permalink)
AKA Pascal's Triangle
[deleted] ยท 1 points ยท Posted at 18:00:46 on May 25, 2016 ยท (Permalink)
Now find the fibonacci sequence hidden in pascal's triangle...
musicotic ยท 1 points ยท Posted at 23:36:27 on May 25, 2016 ยท (Permalink)
Look here
Link
PaulsRedditUsername ยท 18 points ยท Posted at 17:01:34 on May 25, 2016 ยท (Permalink)
My favorite number is 142,857.
142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
142857 x 7 = 999999 ?!?
mandyrooba ยท 7 points ยท Posted at 18:44:36 on May 25, 2016 ยท (Permalink)
There's an explanation for this higher up in the thread, and its talked about in a numberphile video about cyclics.
Phoenixness ยท 5 points ยท Posted at 00:09:12 on May 26, 2016 ยท (Permalink)
1/7 =0.142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857 recurring
GokuMoto ยท 2 points ยท Posted at 03:47:08 on May 26, 2016 ยท (Permalink)
it is also the set of repeating digits for the right side of a decimal in any interger divided by 7 that doesn't produce another interger
prmcd16 ยท 1 points ยท Posted at 01:37:58 on May 26, 2016 ยท (Permalink)
142,857 = (1/7)*100000
The 9's come up because 1/7 is 0.142857 repeated.
thestickystickman ยท 1 points ยท Posted at 11:17:59 on May 26, 2016 ยท (Permalink)
That's because 1/7 is 0.142857 recurring.
howtofall ยท 30 points ยท Posted at 13:00:49 on May 25, 2016 ยท (Permalink)
The pythagorean theorem and the equation of a circle are the exact same! A lot of people might see the two and notice they look almost exactly the same but at most it's just a small notice usually. Think about it like this a circle is all of the points that are the same distance from a central point and the pythagorean theorem gives you the length of the long line of a right triangle. Therefore if you find all possible lengths of the two other legs of the triangle for any given length of the long leg you've found all of the (x, y) coordinates of the circle! Also interestingly enough the absolute value function is also the exact same as the pythagorean theorem.
I'm about to get on a plane and literally copied and pasted this from my comment history but I'm sure if people wanna know someone will tell you about absolute value.
JaeD08 ยท 4 points ยท Posted at 17:24:56 on May 25, 2016 ยท (Permalink)
aka Trigonometry
Distance between two points on a plane also can be found from the Pythagorean theorem but that one's pretty obvious.
[deleted] ยท 2 points ยท Posted at 22:09:05 on May 25, 2016 ยท (Permalink)*
And this is how sinx and cosx are defined, a circle of radius 1, in which a triangle with its hypotenuse as the circle radius and it's horizontal base (centre circle to right-most edge) is cosx and while hypotenuse swings around the circle the changing vertical side of the triangle is sinx.
From Pythagoras we get the circle equation horizontal2 + vertical2 = 1 which in our case is sin2(x) + cos2(x) = 1 so that equation isn't some nice derived relation to make college easier, it's actually the first contact. All the other stuff you might think as more basic actually came by this or much later, like sinx = O/H.
[deleted] ยท 1 points ยท Posted at 17:26:12 on May 25, 2016 ยท (Permalink)
equation of a circle
care to elaborate OP, something doesn't add up here
pemboo ยท 2 points ยท Posted at 17:32:52 on May 25, 2016 ยท (Permalink)*
So in the cartesian plane (normal x-y graph) you can define a circle with the equation (x-a)2 + (y-b)2 = r2
Where (a,b) are the coordinates for the centre of the circle and r is the radius.
Take a circle around the origin and you get the equation x2 + y2 = r2
Edit: pressed save half way through, will continue this post
Pythagoras theorem says that for any right angled triangle, with the sides labelled a, b and c, c being the hypotenuse, then the sides satisfy the equation a2 + b2 = c2 which should look familiar.
Now this could be mere coincidence, but it's not.
It turns out that if you take any diameter of a circle and draw straight lines from the end points to the edge of the circle so that both these lines meet, it will form a right angled triangle with the diameter as the hypotenuse.
[deleted] ยท 1 points ยท Posted at 17:43:59 on May 25, 2016 ยท (Permalink)
i see. thank you
[deleted] ยท 1 points ยท Posted at 18:00:35 on May 25, 2016 ยท (Permalink)
Lost you here :/ my visual imagination skills are shot right now
pemboo ยท 1 points ยท Posted at 18:11:29 on May 25, 2016 ยท (Permalink)*
Let me draw something with my phone since I'm sat in the pub, gimme 10
Edit: okay here is the picture http://m.imgur.com/58z8Yok
So the red line is an arbitrary diameter of the circle and the blue dot is an arbitrary point on the circle.
The two green straight lines going from the ends of the diameter to the blue point form a right angle labelled A.
This is true for ANY diameter you choose and ANY point on the circle.
Obviously, choosing your blue dot as the end of the diameter doesn't make a triangle so don't start!
[deleted] ยท 1 points ยท Posted at 18:33:07 on May 25, 2016 ยท (Permalink)
ooooooooooooooooooooooooh i get it!
pemboo ยท 1 points ยท Posted at 18:51:13 on May 25, 2016 ยท (Permalink)
It's pretty cool. If you leave c (the hypotenuse) constant and then draw EVERY right angled triangle that fits. (There's a lot, like infinity lots, uncountable infinity lots) you get a perfect circle with radius c/2.
GokuMoto ยท 1 points ยท Posted at 03:24:58 on May 26, 2016 ยท (Permalink)
well if you add in a z axis you could choose your bleu dot on the end of the diameter but further down the z axis. that would still make a right triangle just on a different plane
graaahh ยท 1 points ยท Posted at 17:45:01 on May 25, 2016 ยท (Permalink)
Absolute value's where you make stuff that's negative positive, because you don't care if it's negative or positive, you care about its distance from zero.
thestickystickman ยท 1 points ยท Posted at 11:13:19 on May 26, 2016 ยท (Permalink)
Woah.
raging_asshole ยท 16 points ยท Posted at 15:05:40 on May 25, 2016 ยท (Permalink)
Take a dollar amount. Move your decimal one place to the left. You have just calculated 10%. Add half as much, and you have 15%. Double it instead, and you have 20%.
I know that seems painfully obvious and simple, but I'm always shocked by the number of adults that need a calculator to figure out their tip on a restaurant bill. It's not hard.
SillyFlyGuy ยท 0 points ยท Posted at 20:01:54 on May 25, 2016 ยท (Permalink)
I can do the fractional multiplication in my head; 10%, 15%, 20%, 25% and then even integrate 12.5%, 17.5% and 22.5%. But I need my fingers and some scratch paper to add the tip and bill together.
caleb1021 ยท 3 points ยท Posted at 20:27:50 on May 25, 2016 ยท (Permalink)
I don't think you meant integrate.
SillyFlyGuy ยท 2 points ยท Posted at 21:55:28 on May 25, 2016 ยท (Permalink)
Probably not. My math isn't very strong.
caleb1021 ยท 2 points ยท Posted at 22:23:39 on May 25, 2016 ยท (Permalink)
Integrating means finding the area under a curve. The most basic integration is power rule where you add one to the power and divide by the new power. So ax becomes (ax+1)/x+1. There are others ways like u-sub, integration by parts, tabular method, partial fractions, improper integrals, and others. It's calculus.
AlbastruDiavol ยท 0 points ยท Posted at 00:21:06 on May 26, 2016 ยท (Permalink)
Just saying, if you're using "a" as a constant and "x" as your dependent variable, your formula is wrong. Sounds like you kinda wanted to just run down the list of loosely related concepts from an intro calc class.
caleb1021 ยท 1 points ยท Posted at 10:41:55 on May 26, 2016 ยท (Permalink)
A is not the constant obviously. You are right that it should be bโขax but I didn't find that necessary
wkndgolfer ยท 13 points ยท Posted at 15:59:41 on May 25, 2016 ยท (Permalink)*
There is a really easy way to multiply by 11. You take the number you are multiplying, add its digits together, then insert that number between the two original numbers. It can get confusing when you have to carry numbers or you have more than two numbers.
Example 11*23 = take 23, comprised of 2 and 3 , add them together, you get 5 so the answer is 253.
11*34 = take 34, comprised of 3 and 4, add them to get 7, insert seven between original two digits, answer is 374.
Take a three digit number, 123 * 11. In this case you add the first two number to get the second, 1+2 = 3, then you add the last two numbers to get the third place, so 2+3 = 5, the first and last numbers remain the same. So 123*11 = 1353
This works for any number multiplied by 11 but gets complex when you have to carry a value forward because your addition resulted in a number 10 or over. Another three digit example, take 11 * 235. Add the first and second digit, 2+3 = 5, add the second and third digit, 3+5=8, insert the values you calculated between the original first and last digit. 11 * 235 = 2585
Edit, some spacing to make things read better.
not_gern_blanston ยท 2 points ยท Posted at 16:02:39 on May 25, 2016 ยท (Permalink)
that is pretty cool!
thestickystickman ยท 1 points ยท Posted at 11:22:24 on May 26, 2016 ยท (Permalink)
That only works between 10 and 90 though.
wkndgolfer ยท 1 points ยท Posted at 15:54:51 on May 27, 2016 ยท (Permalink)
My last two examples contradict your statement.
Take a three digit number, 123 * 11. In this case you add the first two number to get the second, 1+2 = 3, then you add the last two numbers to get the third place, so 2+3 = 5, the first and last numbers remain the same. So 123*11 = 1353
This works for any number multiplied by 11 but gets complex when you have to carry a value forward because your addition resulted in a number 10 or over. Another three digit example, take 11 * 235. Add the first and second digit, 2+3 = 5, add the second and third digit, 3+5=8, insert the values you calculated between the original first and last digit. 11 * 235 = 2585
jfree02 ยท 6 points ยท Posted at 18:04:57 on May 25, 2016 ยท (Permalink)
English: Voting theory fails.
Say we want to put an airport somewhere on the surface of the earth. We'll let some large number of people (at least 2) vote on its location. There is no voting scheme that has the following 3 properties:
1) If everyone wants the airport in place a, it gets put in place a
2) Everyone's vote has the same weight
3) Minor changes in a voter's preference for placement will not result in major changes in the outcome of the vote.
Math: For n > 1, there is no continuous map f: (S2)n \to Sn that a) Is invariant under the action of S_n on (S2)n which permutes the factors
b) Satisfies f(x,x,...,x) = x.
CannonLongshot ยท 130 points ยท Posted at 13:08:49 on May 25, 2016 ยท (Permalink)*
"Forty" is the only
wordnumber in the English language with all of its letter in alphabetical order.Karl_von_Moor ยท 250 points ยท Posted at 13:32:55 on May 25, 2016 ยท (Permalink)
No.
SEX_LIES_AUDIOTAPE ยท 11 points ยท Posted at 16:20:07 on May 25, 2016 ยท (Permalink)
"No it is not"
ThreeHourRiverMan ยท 133 points ยท Posted at 14:04:41 on May 25, 2016 ยท (Permalink)*
Abs
is
alloy
ally
am
ad
an
be
beer
by
cent
dim
din
dot
...
Maybe he meant only number?
CannonLongshot ยท 15 points ยท Posted at 14:18:08 on May 25, 2016 ยท (Permalink)
I did, have an internet cookie for noticing my incompetence.
Project2r ยท 2 points ยท Posted at 15:25:27 on May 25, 2016 ยท (Permalink)
you bounced back. it's all good.
doofinator ยท 2 points ยท Posted at 18:44:31 on May 25, 2016 ยท (Permalink)
Can you think of a word that contains all of the vowels, in alphabetical order?
That is , A E I O U Y. I know there's at least one, but there may be more.
One of them is facetiously.
lepetrus ยท 1 points ยท Posted at 21:59:34 on May 25, 2016 ยท (Permalink)
Almost
romkyns ยท 1 points ยท Posted at 15:46:34 on May 25, 2016 ยท (Permalink)
Can you find another one that has 5 letters without duplication? Just wondering if one can add enough restrictions to make "forty" the only match...
mandyrooba ยท 2 points ยท Posted at 18:40:56 on May 25, 2016 ยท (Permalink)
Abort, adept, first, glory, ghost, lots more probably. I couldn't find an exhaustive list but even with six letters there's quite a few. Aegilops, eight letters long, is the longest word whose letters are arranged in alphabetical order. Seven letter words with this property include beefily and billowy. Six letter words include abhors, accent, access, almost, biopsy, bijoux, billow, chintz, effort, and ghosty.
romkyns ยท 1 points ยท Posted at 19:24:53 on May 25, 2016 ยท (Permalink)
Nice!
OutOfStamina ยท 4 points ยท Posted at 14:55:54 on May 25, 2016 ยท (Permalink)
People who are coming in after /u/CannonLongshot edited his post and wondering why /u/kari_von_moor has upvotes, "no" is a counter example to the original phrasing of this post.
Apparently OP accidentally said it was the only word, and not that it was the only number, when written out, and "no" is a counter example, and not a refutation of the new claim.
As it stands, no one has a counter example to the new claim, that "forty" is a the only number written out whose letters are all in ascending alphabetical order.
CannonLongshot ยท 3 points ยท Posted at 14:59:24 on May 25, 2016 ยท (Permalink)
Thank you for clarifying! I've now left the original phrasing struck-through, so as to not confuse anyone else.
I totally didn't get the "no" comments. Too elegant for my brain, I feel.
Zywakem ยท 42 points ยท Posted at 14:04:52 on May 25, 2016 ยท (Permalink)*
FTFY
Edit: turns out I missed /u/cannonlongshot 's other typo.
CannonLongshot ยท 5 points ยท Posted at 14:13:51 on May 25, 2016 ยท (Permalink)
Have edited it already, but thanks!
davvblack ยท 0 points ยท Posted at 15:24:51 on May 25, 2016 ยท (Permalink)
123 is in alphabetical order.
ratmfreak ยท -1 points ยท Posted at 14:30:57 on May 25, 2016 ยท (Permalink)
FIFTY?
Drazz00 ยท 2 points ยท Posted at 15:22:46 on May 25, 2016 ยท (Permalink)
Fity.
[deleted] ยท 1 points ยท Posted at 16:49:38 on May 25, 2016 ยท (Permalink)
Tree fiddy?
r00t1 ยท 1 points ยท Posted at 14:53:17 on May 25, 2016 ยท (Permalink)
FTFY
pokemonpasta ยท 2 points ยท Posted at 15:27:00 on May 25, 2016 ยท (Permalink)
FTFY
TLDM ยท 9 points ยท Posted at 14:43:37 on May 25, 2016 ยท (Permalink)
And "One" is the only number with its letters in reverse alphabetical order.
CannonLongshot ยท 2 points ยท Posted at 14:47:44 on May 25, 2016 ยท (Permalink)
BOOM this is what I signed up for
5DSpence ยท 1 points ยท Posted at 14:50:46 on May 27, 2016 ยท (Permalink)
Unless you count "pi" :P
TLDM ยท 2 points ยท Posted at 15:21:41 on May 27, 2016 ยท (Permalink)
Could you count e and i too?
iiaddr ยท 2 points ยท Posted at 14:23:54 on May 25, 2016 ยท (Permalink)
What about e and i?
CannonLongshot ยท 2 points ยท Posted at 14:30:33 on May 25, 2016 ยท (Permalink)
I could edit once more to phrase the question in as unambiguous a way as possible, but I approve too much of this lateral thinking to do so.
Trumps_the_main_man ยท 2 points ยท Posted at 15:41:24 on May 25, 2016 ยท (Permalink)
That's Numberwang!!
[deleted] ยท 3 points ยท Posted at 14:14:19 on May 25, 2016 ยท (Permalink)
Not so good in English, m8.
CannonLongshot ยท 1 points ยท Posted at 15:01:25 on May 25, 2016 ยท (Permalink)
You can't pay attention in every lesson.
Bossmanjr_MAGA ยท 5 points ยท Posted at 13:24:39 on May 25, 2016 ยท (Permalink)
Yeah I dont think this is true.
CannonLongshot ยท 5 points ยท Posted at 13:44:27 on May 25, 2016 ยท (Permalink)
If you can give a counter-example feel free.
[deleted] ยท 18 points ยท Posted at 14:01:08 on May 25, 2016 ยท (Permalink)
no
JesterOfSpades ยท 2 points ยท Posted at 13:49:19 on May 25, 2016 ยท (Permalink)
And not a math fact.
fnord_happy ยท 1 points ยท Posted at 16:42:09 on May 25, 2016 ยท (Permalink)
Well maths ish. Come on jester
CannonLongshot ยท 1 points ยท Posted at 17:50:44 on May 25, 2016 ยท (Permalink)
Originally it wasn't. Now it's been fixed to be a maths fact :)
NeverBeenStung ยท 1 points ยท Posted at 15:22:46 on May 25, 2016 ยท (Permalink)
What other number is spelled in alphabetic order?
tjml1331 ยท 1 points ยท Posted at 14:09:33 on May 25, 2016 ยท (Permalink)
Think he's saying number written out, not every word ever.
CannonLongshot ยท -1 points ยท Posted at 14:18:33 on May 25, 2016 ยท (Permalink)
Ding-ding-ding!
JanEric1 ยท 0 points ยท Posted at 13:45:14 on May 25, 2016 ยท (Permalink)*
no
Edit: abcdefghijklmnop
he had "word" instead of "number" in his comment before the edit.
CannonLongshot ยท 1 points ยท Posted at 14:45:57 on May 25, 2016 ยท (Permalink)
I did indeed, I'm going through these and replying to make it clear.
Also, didn't even notice that was what you were going for, so your joke worked on way too many levels for me.
sand_eater ยท 1 points ยท Posted at 14:40:19 on May 25, 2016 ยท (Permalink)
Forty is a word
CannonLongshot ยท 1 points ยท Posted at 14:43:51 on May 25, 2016 ยท (Permalink)
The post originally said "word", now it says "number".
You are technically correct (the best kind).
[deleted] ยท 1 points ยท Posted at 16:29:54 on May 25, 2016 ยท (Permalink)
[deleted]
Kliiq ยท 1 points ยท Posted at 21:07:09 on May 25, 2016 ยท (Permalink)
Yeah I'm not sure about that one
[deleted] ยท 1 points ยท Posted at 17:02:40 on May 25, 2016 ยท (Permalink)
Uh... what about e?
weird_guy152 ยท 1 points ยท Posted at 18:31:04 on May 25, 2016 ยท (Permalink)
One is the only number with letters in reverse alphabetical order.
ProfessorButtercup ยท 0 points ยท Posted at 13:37:16 on May 25, 2016 ยท (Permalink)
Fix? Fox?
CannonLongshot ยท 2 points ยท Posted at 13:45:14 on May 25, 2016 ยท (Permalink)
slaps head How stupid of me!
Edit: But seriously, guys, couldn't any of you tell I was talking about numbers on a maths thread? I'm bad with words, I'm a mathematician, not a writer!
chesterjosiah ยท 0 points ยท Posted at 14:00:38 on May 25, 2016 ยท (Permalink)*
Just off the top of my head: abs, ail, ant, any, big, boy, coy
Edit: OP changed his comment to say "Only
wordnumber with its letters in alphabetical order".CannonLongshot ยท 0 points ยท Posted at 14:15:58 on May 25, 2016 ยท (Permalink)
Funny number system you have there, what base is that?
chesterjosiah ยท 1 points ยท Posted at 14:30:07 on May 25, 2016 ยท (Permalink)
You're the worst kind of redditor. You made a mistake in your post, and when people correct you, you edit your post and then make fun of the people who corrected you. Shame on you.
CannonLongshot ยท 0 points ยท Posted at 14:42:27 on May 25, 2016 ยท (Permalink)*
I was planning on going through to all the posts I made replying to those people to make it clear that I messed up, I'm just at work and have random stretches of free time.
I'd be more inclined to agree with you if the "making fun of" wasn't possibly the most light-hearted banter I've seen on Reddit for a long while.
Also, I totally forgot that the score formatting existed on Reddit, I shall use it now! :)
[deleted] ยท -1 points ยท Posted at 14:07:37 on May 25, 2016 ยท (Permalink)*
eightCannonLongshot ยท 1 points ยท Posted at 14:14:55 on May 25, 2016 ยท (Permalink)
"i" comes after "g" and "h"
[deleted] ยท 0 points ยท Posted at 14:31:08 on May 25, 2016 ยท (Permalink)
awoops
[deleted] ยท 0 points ยท Posted at 14:41:22 on May 25, 2016 ยท (Permalink)
[deleted]
CannonLongshot ยท 2 points ยท Posted at 14:44:19 on May 25, 2016 ยท (Permalink)
Urgh. Not in any dialect I've heard of.
itsfoine ยท 49 points ยท Posted at 13:47:29 on May 25, 2016 ยท (Permalink)
And you know what? We're going to win.
Yeah, we're gonna win even if I have to go into the auditorium and personally jerk off every guy in the audience.
That's a lot of jerking.
And we only have ten minutes to present.
So So, we're fucked, aren't we? Yeah, even if he's jerking two at a time, there are, what, 800 guys in that room? So that's 400 times whatever the mean jerk-time is.
The what?
Mean jerk-time. I mean, it doesn't matter, but, hypothetically, time is equal to 400 total jerks at a two-dick rate.
Unless Erlich jerks off four guys at a time, and then we can cut that in half.
How would he do four guys? He's got two hands, so that's two dicks at a time, right?
Look, you have two guys on either side with their dicks, tip to tip, so you're going full-length. Four, see?
Oh - From the middle out. That does make sense.
Like two Shake Weights?
Yeah, so what we're trying to do, hypothetically, is minimize time, which is 800 dudes, multiplied by mean-jerk time, divided by four dicks at a time. Of course, Erlich would have to pre-sort guys by height, so that their dicks lined up.
Not by height, technically. The measurement that we're looking for, really, is dick to floor. Call that D2F.
Huh.
You know, if a guy's dick was long enough, it would be able to reach up or down to another guy with a different D2F. The longer the dick, the greater the D2F bridge, but I would still be able to jerk it off in one smooth motion I'd just have to jerk it on an angle.
So D2F sub-1 needs to equal D2F sub-2, and D2F sub-3 needs to equal D2F sub-4, where length L creates a complimentary shaft angle call that theta d. Now the orgasm threshold is a function of lambda sub from the time from the time he created the orgasm
Guys, does girth-similarity affect Erlich's ability to jerk different dicks simultaneously? Shit.Yeah, I think it would.Of course, it does.Time to orgasm, or T2O, has to be the same for each matching pair of dicks otherwise I'm wasting a lot of great strokes on a guy that's already busted.
Unless you can hotswap dicks in and out. So on a downstroke, you get a new one in. So when you stroke up you're not wasting any energy. Even so I think this is the most reliable metric for stamina.
kilkil ยท 15 points ยท Posted at 14:39:58 on May 25, 2016 ยท (Permalink)
/r/evenwithcontext
Zarco19 ยท 3 points ยท Posted at 05:21:29 on May 26, 2016 ยท (Permalink)
Fun fact, there's a mathematical paper they wrote to go with it:
https://www.scribd.com/doc/228831637/Optimal-Tip-to-Tip-Efficiency
UltimateInferno ยท 2 points ยท Posted at 17:31:45 on May 25, 2016 ยท (Permalink)
Me and my friends had a similar conversation.
thisisnotdan ยท 3 points ยท Posted at 15:16:39 on May 25, 2016 ยท (Permalink)
I, um...I think you meant to post this somewhere else. It looks like you put a lot of...effort into it, so I figured I'd do you the courtesy of letting you know so you could post it where you intended.
Delta-Sniper ยท 25 points ยท Posted at 16:24:32 on May 25, 2016 ยท (Permalink)
This is a quote from Silicon Valley.
AstariiFilms ยท 1 points ยท Posted at 08:36:42 on June 3, 2016 ยท (Permalink)
The entire thing?
trollinn ยท 10 points ยท Posted at 14:23:52 on May 25, 2016 ยท (Permalink)
I'm probably going to get the details wrong, but you can mathematically define the real numbers. The basic idea is that you define certain properties of a set, then you prove the real numbers have these properties, then you prove that all sets with these properties are identical up to isomorphism, then you artificially construct such a set (we used Dedekind cuts in the class I took), then viola you've defined the real numbers. Also I should note the first line in the Analysis textbook we used was "we will not attempt to define the word set" so...
pemboo ยท 4 points ยท Posted at 17:44:19 on May 25, 2016 ยท (Permalink)*
If you couldn't mathematically define the reals then we wouldn't use them, seems like a tautological statement.
Importantly, you must first construct the set of rationals before you get the reals, which in turn require the integers, which in turn require you define the wholes...
[deleted] ยท 4 points ยท Posted at 18:27:04 on May 25, 2016 ยท (Permalink)
Newton, Leibniz, Euler and I think even Gauss did not have a definition of real numbers as we do today.
dh363 ยท 1 points ยท Posted at 20:23:55 on May 25, 2016 ยท (Permalink)
I mean, today's real numbers are on firmer ground than even times after dedekind cuts were done, because our foundations for set theory are far stronger, and the natural numbers can be constructed from set theory. And the foundations of logic are far stronger, too. So in a way the foundations of all these number systems in general are actually much more solid than when the individual axiomatizations and contractions were first conceived.
Slacker5001 ยท 3 points ยท Posted at 18:17:49 on May 25, 2016 ยท (Permalink)
You can define the sets before the reals using Peanio axioms and properties of arithmetic (i.e. groups and fields stuff). Once you have that that is when you can move to Dedekind cuts or Cantour sets to define your reals.
I think the mind blowing nature of this is more, before you learn it yourself, who the fuck thinks about defining a "number". Up to when you start learning about sets and such, your just using numbers and your understanding of them is not proved in any way, only built in a superficial way up to that point in school.
pemboo ยท 1 points ยท Posted at 18:20:34 on May 25, 2016 ยท (Permalink)*
Doesn't every class have that one prick who thinks he is smart by asking the teacher "but what is a number, they're not even real?"
I don't think it's mind blowing at all that we have rigorous definitions of our number systems.
Slacker5001 ยท 1 points ยท Posted at 20:26:55 on May 25, 2016 ยท (Permalink)
I have never run into that personally. And at least for me it was mind blowing when we rigorously defined it for the first time. You can definitely disagree, there are plenty of valid feelings and perspectives on it. But it is mind blowing to some people at least.
Zarco19 ยท 1 points ยท Posted at 05:19:20 on May 26, 2016 ยท (Permalink)
I mean, there's the dick who is like "this is all made up, fuck this shit" and there's the dick who is like "how do we know this all works?" looks deeper into it, and then revolutionizes math or some shit
trollinn ยท 1 points ยท Posted at 17:55:24 on May 25, 2016 ยท (Permalink)
That's true, but to someone not familiar with analysis I think it would be pretty interesting that that is something you can do, and that it is necessary.
Slacker5001 ยท 2 points ยท Posted at 18:21:39 on May 25, 2016 ยท (Permalink)
If your interested in that sort of stuff I would definitely suggest taking a class on Modern/Abstract Algebra or a similar topic. It covers groups and fields and the properties that go with them. Pretty much it helps show why those certain defined properties that seem to come out of nowhere work the way they do.
Helps explain the "real numbers work like this, now don't ask questions" thing that seems to happen early in higher math education.
trollinn ยท 1 points ยท Posted at 18:34:33 on May 25, 2016 ยท (Permalink)
You're completely right. I actually took Abstract Algebra before Analysis (although I took and then dropped Analysis I the semester before) and it made the beginning third much easier.
Slacker5001 ยท 2 points ยท Posted at 20:25:16 on May 25, 2016 ยท (Permalink)
I made the mistake of taking Analysis first. It was horridly difficult. Abstract Algebra would have been a nice background if I had taken it first.
BritishEnglishPolice ยท 1 points ยท Posted at 23:42:21 on May 25, 2016 ยท (Permalink)
*voilร
TheOnlyMeta ยท 1 points ยท Posted at 00:31:43 on May 26, 2016 ยท (Permalink)
Is it shocking that we can define the real numbers mathematically? Why would we study the object in such detail if we couldn't define it? I don't mean to rain on your parade, but as a matter of fact it's fairly easy to define the real numbers by just assuming the least upper bound property or some other completeness property. We don't need to worry about any isomorphisms or some overly technical machinery.
Logic and set theory is an entirely different realm of study to real analysis, which is probably why your lecturer didn't dwell on the logical basis of the subject. Rest assured that with the right axioms the real numbers pop out very naturally.
trollinn ยท 1 points ยท Posted at 03:40:13 on May 26, 2016 ยท (Permalink)
But it is still something the average person wouldn't even think needs to be done, despite how natural or easy it may be.
GBDickinson ยท 5 points ยท Posted at 17:27:24 on May 25, 2016 ยท (Permalink)
Multiply 9 by any number, and add the digits of the product until you get a single digit, and that single digit will always be 9.
Example: 9 x 278 = 2,502 2+5+2 = 9
[deleted] ยท 5 points ยท Posted at 19:06:04 on May 25, 2016 ยท (Permalink)
0!= 1
De-Vox ยท 3 points ยท Posted at 21:22:55 on May 25, 2016 ยท (Permalink)
Also true in computer science!
Pixel_Veteran ยท 2 points ยท Posted at 23:02:40 on May 25, 2016 ยท (Permalink)
I love how they just decided this just so that factorial could be a recusrsive funtion.
Porridgeandpeas ยท 1 points ยท Posted at 23:55:49 on May 25, 2016 ยท (Permalink)
Recursive?
dragonfyre173 ยท 4 points ยท Posted at 00:01:21 on May 26, 2016 ยท (Permalink)
A recursive function is one that repeatedly calls itself. i.e., the definition of recursion is the definition of recursion.
Therefore, factorial(3) is 3 * factorial(2) = 3 * 2 * factorial(1) = 3 * 2 * 1.
Note that factorials act VASTLY differently with anything other than positive or zero integers, and are much more difficult to figure out.
WorkIsOverrated ยท 1 points ยท Posted at 01:09:30 on May 26, 2016 ยท (Permalink)
Almost fucked myself over on a test because I said 0!=0 without actually checking. But I cross checked it by computer and hand and corrected it.
TyrelSanders331 ยท 4 points ยท Posted at 21:27:52 on May 25, 2016 ยท (Permalink)
7 ate 9
Doitforlolz ยท 5 points ยท Posted at 22:16:34 on May 25, 2016 ยท (Permalink)
Square root of 69 is 8 something.
Zalzagor ยท 1 points ยท Posted at 23:19:18 on May 25, 2016 ยท (Permalink)
I've been tryin to work it out.
Toph_er ยท 13 points ยท Posted at 16:58:51 on May 25, 2016 ยท (Permalink)
My favourite fact is that any number to the power of 0 is 1.
How can that be? Well, 162 * 162 = 164 right? Well with division you just subtract the powers. 162 / 162 = 160. When you look at any number like a fraction, e.g. 2/2, then 2/2 = 1 right? So that means 162 / 162 = 1, therefore 160 = 1 as well.
DutchmanDavid ยท 4 points ยท Posted at 20:41:44 on May 25, 2016 ยท (Permalink)
I always thought of it in this way:
163 = 1 * 16 * 16 * 16
162 = 1 * 16 * 16
161 = 1 * 16
160 = 1
This makes negative exponents also make sense:
16-3 = 1 / 16 / 16 / 16
16-2 = 1 / 16 / 16
16-1 = 1 / 16
16-0 = 1
How about fractional exponents?
163/2 = sqrt(1 * 16 * 16 * 16)
162/2 = sqrt(1 * 16 * 16)
161/2 = sqrt(1 * 16)
160/2 = sqrt(1)
163/3 = cbrt(1 * 16 * 16 * 16)
162/3 = cbrt(1 * 16 * 16)
161/3 = cbrt(1 * 16)
160/3 = cbrt(1)
Now combine negative and fractional exponents!
16-3/2 = sqrt(1 / 16 / 16 / 16)
16-2/2 = sqrt(1 / 16 / 16)
16-1/2 = sqrt(1 / 16)
16-0/2 = sqrt(1)
16-3/3 = cbrt(1 / 16 / 16 / 16)
16-2/3 = cbrt(1 / 16 / 16)
16-1/3 = cbrt(1 / 16)
16-0/3 = cbrt(1)
I think I finally got this whole abstraction thing that exists in math.
[deleted] ยท 1 points ยท Posted at 22:00:36 on May 25, 2016 ยท (Permalink)
Thanks for the work you put in to that. How would it include or adapt to meet 00, I never understood it
Lehona ยท 3 points ยท Posted at 23:32:52 on May 25, 2016 ยท (Permalink)
Well, you can't do 0n/0n, because that would obviously be dividing by zero, so it's usually undefined. Sometimes it gets defined as 1 because it makes calculation easier and doesn't mess with the results anyway.
[deleted] ยท 1 points ยท Posted at 21:58:51 on May 25, 2016 ยท (Permalink)
Except 00 which is undefined.
TheOnlyMeta ยท 1 points ยท Posted at 00:19:25 on May 26, 2016 ยท (Permalink)
What about 00 ? ;)
fireatx ยท 2 points ยท Posted at 09:58:08 on May 26, 2016 ยท (Permalink)
By his example...
02 / 02 = 00
we know 02 = 0, and division by 0 is undefined. therefore
02 / 02 is undefined
Toph_er ยท 1 points ยท Posted at 18:26:38 on May 27, 2016 ยท (Permalink)
Google Calculator also says its 1 for some reason XD, but I am pretty sure there is a lot of arguing over the fact of if it should be 1, 0 or undefined.
BonScoppinger ยท 32 points ยท Posted at 13:41:33 on May 25, 2016 ยท (Permalink)
8 = 23 and 9=32 are the only powers of natural numbers whose difference is exactly 1
askjgdbnionio ยท 46 points ยท Posted at 15:34:39 on May 25, 2016 ยท (Permalink)
False.
1=12 and 2=21.
actual_factual_bear ยท 6 points ยท Posted at 16:48:46 on May 25, 2016 ยท (Permalink)
Or 0n and and 1m for any n,m in the natural numbers.
green_meklar ยท 6 points ยท Posted at 18:49:04 on May 25, 2016 ยท (Permalink)
OP specified 'powers of natural numbers'. 0 isn't a natural number, so 0n isn't a power of a natural number.
K4mp3n ยท 4 points ยท Posted at 20:35:43 on May 25, 2016 ยท (Permalink)
In some cases 0 is defined as a natural number, in others not
green_meklar ยท 1 points ยท Posted at 22:08:36 on May 25, 2016 ยท (Permalink)
My understanding is that 'natural number' specifically refers to {1,2,3,...} while 'whole number' specifically refers to {0,1,2,3,...}.
Lehona ยท 1 points ยท Posted at 23:36:49 on May 25, 2016 ยท (Permalink)
Whole numbers means the same as integers and includes the natural numbers, their negative counterparts and 0.
[deleted] ยท 1 points ยท Posted at 22:36:31 on May 25, 2016 ยท (Permalink)
No. 0 is never specified as a natural number. It is a whole number.
[deleted] ยท 2 points ยท Posted at 00:01:09 on May 26, 2016 ยท (Permalink)
Really? My numerical semigroups text right here has zero as a natural number. Many places include 0 in the naturals.
[deleted] ยท 1 points ยท Posted at 05:28:23 on May 29, 2016 ยท (Permalink)
I might be wrong then. But if 0 is a natural number, whats the difference between Natural and Whole numbers?
[deleted] ยท 1 points ยท Posted at 05:30:09 on May 29, 2016 ยท (Permalink)
Nobody uses whole numbers. Never seen it used in any recent literature. People specify N union {0} usually if they don't believe the naturals contains zero.
K4mp3n ยท 1 points ยท Posted at 11:42:02 on May 29, 2016 ยท (Permalink)
At least in germany it would be all negative, 0 and all postive numbers {...;-2;-1;0;1;2;...}
[deleted] ยท 1 points ยท Posted at 16:36:52 on May 29, 2016 ยท (Permalink)
Those are integers.
K4mp3n ยท 2 points ยท Posted at 19:38:34 on May 29, 2016 ยท (Permalink)
A thank you, them it is the names that Digger in German that I got wrong.
[deleted] ยท 1 points ยท Posted at 00:00:28 on May 26, 2016 ยท (Permalink)
That's well-debated, many people include 0 in the naturals.
graaahh ยท 1 points ยท Posted at 17:39:53 on May 25, 2016 ยท (Permalink)
Good job, Dwight.
galacticdick ยท 11 points ยท Posted at 14:08:05 on May 25, 2016 ยท (Permalink)*
26 is the only integer number to lie between a square and a cube.
Edit: only known number (don't think it's been solidly proven) and by "lie between" I mean directly next to in terms of integers (25 is square, 27 is cube)
Edit 2: has been proven, I'm an idiot
TLDM ยท 5 points ยท Posted at 14:53:44 on May 25, 2016 ยท (Permalink)
I can think of lots of integers which lie between a square and a cube :P
HighRelevancy ยท 2 points ยท Posted at 15:32:34 on May 25, 2016 ยท (Permalink)
But not consecutively between them
galacticdick ยท 2 points ยท Posted at 16:14:47 on May 25, 2016 ยท (Permalink)
Yes but not directly next to ie. 25 is a square number and 27 is a cube number
BurningLed ยท 3 points ยท Posted at 14:55:24 on May 25, 2016 ยท (Permalink)
(of natural numbers)
heap42 ยท 1 points ยท Posted at 15:39:42 on May 25, 2016 ยท (Permalink)
How do you proof that
UniformCompletion ยท 1 points ยท Posted at 17:59:10 on May 25, 2016 ยท (Permalink)
It is not easy to approach a problem like this with elementary methods. In fact, Fermat probably had an incorrect proof of this fact.
The simplest proof I know of that y2 = x3 - 2 has only the solution (3,5) involves using unique factorization in the ring of numbers of the form a + bโ(-2), where a and b are integers.
I am not sure of the best method to approach y2 = x3 + 2, but a similar method may work, and in any case there are algorithms that have been used to identify all solutions.
Here is a good survey of the techniques used in solving these and similar equations.
jusjerm ยท 1 points ยท Posted at 16:42:57 on May 25, 2016 ยท (Permalink)
*Adjacent to a square and a cube
galacticdick ยท 1 points ยท Posted at 21:26:19 on May 25, 2016 ยท (Permalink)
Thanks I couldn't think of the word :)
ben1996123 ยท 1 points ยท Posted at 17:46:47 on May 25, 2016 ยท (Permalink)*
it can be proven by factoring y2=x3-2 over the ring Z[โ-2] to get (y+โ-2)(y-โ-2) = x3, then since Z[โ-2] is a unique factorization domain and a gcd domain, you can show (with a bit of work) that y+โ-2 must be a perfect cube in Z[โ-2], so y+โ-2 = (a+bโ-2)3 for some integers a,b. expanding shows that 3a2b-2b3 = 1, which has b=1 and a=ยฑ1 as the only integer solutions. this gives y=(ยฑ1+โ-2)3-โ-2=ยฑ5, which gives x=3, and so x3-1=y2+1=26 is the only solution
UniformCompletion ยท 1 points ยท Posted at 17:56:13 on May 25, 2016 ยท (Permalink)
It has been solidly proven. Equations of the form y2 = x3 + k (which are a type of elliptic curve) are called Mordell equations, and there are algorithmic methods for solving them, which have been applied at least for all k in [-10000,10000].
In fact, there are exactly two integers lying between a square and a cube: they are 26 and 0.
A reasonably accessible treatment of the methods used to solved these equations is found in these notes by Keith Conrad.
2nd_law_is_empirical ยท 3 points ยท Posted at 15:09:54 on May 25, 2016 ยท (Permalink)
Raised to 1 is still a power.
heap42 ยท 1 points ยท Posted at 15:39:20 on May 25, 2016 ยท (Permalink)
How do you proof that ?
BonScoppinger ยท 1 points ยท Posted at 16:11:46 on May 25, 2016 ยท (Permalink)
This theoreme is called Catalan's conjecture. You can read about it on wikipedia. The proof is actually quite complicated and it took people more than 150 years to come up with one.
skizfrenik_syco ยท 1 points ยท Posted at 15:56:01 on May 25, 2016 ยท (Permalink)
What about 12 and 21 ?
BonScoppinger ยท 1 points ยท Posted at 16:10:37 on May 25, 2016 ยท (Permalink)
well, if you're leaving out that trivial case
itsfoine ยท 35 points ยท Posted at 11:49:24 on May 25, 2016 ยท (Permalink)*
When you are multiplying by 9, if you hold your two hands up and lower the digit you want to multiply by, it makes the number. For example, if you want to do 9 * 4. You face the palm of your hands, lower your ring finger. You have three to the left of the finger you put down and six to the right to make 36. 9 * 4 = 36. This works all the way from 9 * 1 to 9 * 10 Neat math fact / trick
redditsoaddicting ยท 5 points ยท Posted at 12:44:22 on May 25, 2016 ยท (Permalink)
I think you meant 9*1 to 9*10. You dropped a couple \s.
bsievers ยท 1 points ยท Posted at 16:27:41 on May 25, 2016 ยท (Permalink)
I was trying to figure out how he was being sarcastic, til I realized you meant he forgot the backslashes and was pluralizing it.
redditsoaddicting ยท 1 points ยท Posted at 16:41:05 on May 25, 2016 ยท (Permalink)
Before the edit, Markdown turned it into italics. The backslashes were to escape the asterisks.
bsievers ยท 1 points ยท Posted at 16:42:31 on May 25, 2016 ยท (Permalink)
Yeah I figured it out, just took a min.
MentallyPsycho ยท 5 points ยท Posted at 13:09:00 on May 25, 2016 ยท (Permalink)
This trick saved my ass in school.
WikiWantsYourPics ยท 4 points ยท Posted at 14:18:45 on May 25, 2016 ยท (Permalink)
I mean, it's cute, but how much easier do you find it than doing 10x-x? So 9*8 is 80-8 = 72 for example.
rakuanu ยท 5 points ยท Posted at 15:06:28 on May 25, 2016 ยท (Permalink)
Oh that's neat. The method I used growing up was (x-1)+y=9 where x is the number of times to multiply by 9 and y is the remainder that gives you 9. So 9*7 is 6+3 so 63!
Galactius ยท 3 points ยท Posted at 15:13:11 on May 25, 2016 ยท (Permalink)
I guess I'm one of the few who just learned this stuff the hard way...
WikiWantsYourPics ยท 1 points ยท Posted at 15:42:34 on May 25, 2016 ยท (Permalink)
OK, that's basically equivalent.
Guack007 ยท 1 points ยท Posted at 16:53:25 on May 25, 2016 ยท (Permalink)
My method as well
MentallyPsycho ยท 0 points ยท Posted at 17:39:43 on May 25, 2016 ยท (Permalink)
A lot easier, actually. No extra math is needed, the answer's right there on your hands.
[deleted] ยท 2 points ยท Posted at 15:26:46 on May 25, 2016 ยท (Permalink)
Or the fact that the products of 9 *1 through 10 is counting upwards in the 10s place and counting downwatrds in the ones place.
luckyinkykyky ยท 1 points ยท Posted at 15:03:08 on May 25, 2016 ยท (Permalink)
My fifth grade maths teacher who taught us this was missing a finger...
[deleted] ยท 1 points ยท Posted at 20:38:18 on May 25, 2016 ยท (Permalink)
4 *9 =40 - 4
5 *9 = 50 -5
7 *9 = 70- 7
This is faster for me than looking at my fingers.
parumph ยท 10 points ยท Posted at 14:58:21 on May 25, 2016 ยท (Permalink)
Casting out nines to check your math.
https://en.m.wikipedia.org/wiki/Casting_out_nines
mandyrooba ยท 4 points ยท Posted at 18:51:42 on May 25, 2016 ยท (Permalink)
what
[deleted] ยท 13 points ยท Posted at 15:17:25 on May 25, 2016 ยท (Permalink)
That you can keep halving a positive value forever and it will always be more then 0.
ncnotebook ยท 3 points ยท Posted at 21:51:25 on May 25, 2016 ยท (Permalink)
looks at the body
fuck
[deleted] ยท 1 points ยท Posted at 23:57:32 on May 25, 2016 ยท (Permalink)
Depends because your phrasing is bad. Forever makes me think of a limit, in which case halving a value forever would get you zero. However, if you have the sequence An = 1/n, then while the limit of the sequence approaches 0, no term is equal to zero. It's also why infinity is not a number.
TheOnlyMeta ยท 1 points ยท Posted at 00:22:08 on May 26, 2016 ยท (Permalink)
You can keep halving it for any amount of time, but not forever. 'Unbounded but finite time' is different to 'infinite time/forever', and it's a fairly important distinction to make.
panoramicjazz ยท 89 points ยท Posted at 11:23:48 on May 25, 2016 ยท (Permalink)
10 / 8.1 = 1.23456789012
I seriously stumbled upon this on my calculator last month. I know a lot about math, but this interbreasts me the most. Please... no one spoil why this works.
[deleted] ยท 216 points ยท Posted at 11:39:06 on May 25, 2016 ยท (Permalink)
[deleted]
Kildragoth ยท 37 points ยท Posted at 11:52:18 on May 25, 2016 ยท (Permalink)
There is a video on this type of equation and they all seem to be missing an 8.
PM_Sinister ยท 47 points ยท Posted at 12:15:21 on May 25, 2016 ยท (Permalink)
They're missing the "number" two spaces before the 0 (8 for one digit, 98 for two digits, 998 for three digits, etc). This is caused by the 0 is actually 10 (or 100 or 1000, depending on how many digits are in each "number"), so it carries. The 9 becomes a 0, carrying 1 over to the 8, which becomes a 9. Since it doesn't carry over again after that point, the 7 is left unchanged, making it look like the 8 is skipped.
pcyr9999 ยท 3 points ยท Posted at 18:39:17 on May 25, 2016 ยท (Permalink)
Ok so OP was correct in that 10/8.1=1.(2)(3)(4)(5)(6)(7)(8)(9)(10)...
Parenthesis for visibility only
bluesam3 ยท 5 points ยท Posted at 12:46:59 on May 25, 2016 ยท (Permalink)
137174210/1111111111 has the 8 in.
[deleted] ยท 1 points ยท Posted at 04:37:19 on May 26, 2016 ยท (Permalink)
[deleted]
bluesam3 ยท 1 points ยท Posted at 13:11:01 on May 26, 2016 ยท (Permalink)
Yeah, but that doesn't recurr.
DonkeyTeeth2013 ยท 2 points ยท Posted at 16:21:16 on May 25, 2016 ยท (Permalink)
Also, if you multiply 12345679 by any multiple of 9 less than 100 (some number X), the result will be (X/9) repeating 9 times; e.g. 12345679 * 63 = 777,777,777
SassyMcPants ยท 1 points ยท Posted at 15:00:18 on May 25, 2016 ยท (Permalink)
You can use 137174210/111111111 if you want to include the eight.
panoramicjazz ยท 1 points ยท Posted at 19:57:10 on May 25, 2016 ยท (Permalink)
No!!! I thought I stumbled upon something golden.
panoramicjazz ยท 1 points ยท Posted at 19:57:44 on May 25, 2016 ยท (Permalink)
Why is 6 afraid of 7? Because 7 is a registered 6-offender.
__Shrek ยท 32 points ยท Posted at 11:41:26 on May 25, 2016 ยท (Permalink)
Immediately thought about 10 and 8.1 with regards to the Windows operating systems... MICROSOFT IS BEHIND THIS! IT'S A CONSPIRACY MAN!
obsoletelearner ยท 1 points ยท Posted at 16:15:18 on May 25, 2016 ยท (Permalink)
illuminate confurmed!
anoobitch ยท 21 points ยท Posted at 13:10:52 on May 25, 2016 ยท (Permalink)
oh, so thats why windows 10 came after windows 8.1
InappropriateTA ยท 6 points ยท Posted at 14:52:10 on May 25, 2016 ยท (Permalink)
If that is an autocorrect, I would be very interbreasted in seeing your message history.
NeverBeenStung ยท 4 points ยท Posted at 15:08:17 on May 25, 2016 ยท (Permalink)
I'm coming up with 1.23456790
I don't see an 8 in there.
panoramicjazz ยท 1 points ยท Posted at 19:55:46 on May 25, 2016 ยท (Permalink)
You could be right... I may have missed it
obsoletelearner ยท 2 points ยท Posted at 16:14:43 on May 25, 2016 ยท (Permalink)
whats an interbreast?
panoramicjazz ยท 1 points ยท Posted at 19:55:21 on May 25, 2016 ยท (Permalink)
Was a typo I thought sounded funny.
pemboo ยท 1 points ยท Posted at 17:30:40 on May 25, 2016 ยท (Permalink)
You can easily make what ever decimal you want as a fraction, even repeating ones.
Let's do .01234567890123456789.....
Call it x
100000000000x = 123456789.01234567890.....
100000000000x - x = 123456789
Therefore x = 123456789/9999999999
graaahh ยท 1 points ยท Posted at 17:39:05 on May 25, 2016 ยท (Permalink)
Try dividing by 8.10000007.
thosethatwere ยท 1 points ยท Posted at 17:42:32 on May 25, 2016 ยท (Permalink)
10 / 8.1 = 1.23456790123...
I fixed it for you:
13,717,421 / 1,111,111,111,000,000,000
Don't worry, I won't spoil it for you.
bobotheking ยท 1 points ยท Posted at 22:01:25 on May 25, 2016 ยท (Permalink)
If you're interested in this type of thing, look up the Champernowne constant. My favorite approximation is 60499999499/490050000000. Both the numerator and denominator look innocuous, even a little "structured", but they approximate the constant out to almost 200 digits.
[deleted] ยท -2 points ยท Posted at 14:26:08 on May 25, 2016 ยท (Permalink)
10 / 8.1 = 1.2345679
1.2345679 x 8.1 = 9.9999
????
icywindflashed ยท 4 points ยท Posted at 14:30:00 on May 25, 2016 ยท (Permalink)
It's because calculators can't memorize infinite decimals. They will round them up at a certain points and when you do the inverse product the last digits are missing
HimDaemon ยท 1 points ยท Posted at 15:26:32 on May 25, 2016 ยท (Permalink)
Btw, 9.999... = 10
kogasapls ยท 1 points ยท Posted at 17:13:03 on May 25, 2016 ยท (Permalink)
1.2345679 * 8.1 doesn't give 9.999..., just 9.99999999.
CrystalNiner ยท 0 points ยท Posted at 18:05:04 on May 25, 2016 ยท (Permalink)
That's just a weakness with our base 10 system. Nothing exactly new.
MonkeyNin ยท 1 points ยท Posted at 18:37:58 on May 25, 2016 ยท (Permalink)
What does that have to do with base-10? The problem occurs because floating point does not have an infinite number of bits to represent the number.
liarandathief ยท 18 points ยท Posted at 11:59:54 on May 25, 2016 ยท (Permalink)
If you tie a string around a basket ball. And similarly you tie a string around the earth (assume both are perfect spheres). If you raise the string 1 foot off the surface of each. The amount of additional string you will need is the same.
chesterjosiah ยท 9 points ยท Posted at 14:19:01 on May 25, 2016 ยท (Permalink)
The length of string needed to go around a sphere with radius r:
The length of string needed to go around the same sphere but 1 foot off the surface:
The difference is:
So you need 2ฯ feet of string, regardless of the radius of the sphere!
jab416171 ยท 1 points ยท Posted at 22:14:47 on May 25, 2016 ยท (Permalink)
Is it 2ฯ feet or meters? Or does it not matter, as long as you're using the same units the whole time?
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3ixpfm
chesterjosiah ยท 1 points ยท Posted at 22:39:24 on May 25, 2016 ยท (Permalink)
Yep! It's whatever unit you used for the distance between the earth and the string.
Tafkah ยท 11 points ยท Posted at 13:03:29 on May 25, 2016 ยท (Permalink)
There's a mathematical proof that every whole number is interesting. You can find an interesting fact about each whole number one by one. For example, 0 is the only number that can be multiplied by any other number without changing; 1 is the only number that is its own inverse; 2 is the only even prime number; 3 is the smallest odd prime number; 4 is the smallest square of a different number; etc. If you ever come to a number for which you can't find an interesting fact, that number is now the smallest whole number for which you couldn't find an interesting fact, which makes it interesting. Therefore all whole numbers are interesting.
WikiWantsYourPics ยท 3 points ยท Posted at 14:26:08 on May 25, 2016 ยท (Permalink)*
Related: what's the smallest number that can't* be described in eleven words or less? https://en.wikipedia.org/wiki/Berry_paradox
ObviousPenguin ยท 2 points ยท Posted at 17:45:55 on May 25, 2016 ยท (Permalink)
Can't*
The smallest (natural) number that can is 1.
Slacker5001 ยท 2 points ยท Posted at 18:48:45 on May 25, 2016 ยท (Permalink)
It amusing me that this even exists. Thank you for the knowledge today!
ZizekIsMyDad ยท 3 points ยท Posted at 19:40:09 on May 25, 2016 ยท (Permalink)
But if the next whole number is defined as the smallest uninteresting number, the previous whole number is no longer the smallest uninteresting number, making it uninteresting again
Th3NXTGEN ยท 1 points ยท Posted at 20:41:32 on May 25, 2016 ยท (Permalink)
Art Benjamin?
Tafkah ยท 2 points ยท Posted at 12:44:34 on May 26, 2016 ยท (Permalink)
I may have learned that from Art Benjamin. He was a professor at my college, and he taught a couple of my classes. But I probably heard it from Francis Su (professor at the same college, who may have heard it from prof. Benjamin). He started every class with a math fun fact, and this was the first one that popped into my head.
10sPlaya ยท 4 points ยท Posted at 17:13:50 on May 25, 2016 ยท (Permalink)
as a former accountant... - when summing two sets of presumed identical values - if the results are different - take the difference - sum the digits of the difference - if the value is evenly divisible by 9 - then there is a transposition error somewhere in the number sets
avematthew ยท 2 points ยท Posted at 23:07:12 on May 25, 2016 ยท (Permalink)
This is the best fact in here so far; it's cool, and useful!
10sPlaya ยท 2 points ยท Posted at 14:32:53 on May 26, 2016 ยท (Permalink)
it's old school, and really from my past life, how it really applies, if you are using a 10 key, with a tape, and you get a different value while confirming, if you compare the tapes, you will find a transpose error
NoOne0507 ยท 3 points ยท Posted at 17:41:21 on May 25, 2016 ยท (Permalink)
How useless the definition of a tensor is.
A tensor is something that follows the tensor transformation law
Beo1 ยท 4 points ยท Posted at 18:01:32 on May 25, 2016 ยท (Permalink)
The average number of average numbers between 0 and 1 that you must add together to reach 1 is e.
[deleted] ยท 4 points ยท Posted at 18:06:45 on May 25, 2016 ยท (Permalink)*
[deleted]
IAmDanimal ยท 2 points ยท Posted at 18:16:17 on May 25, 2016 ยท (Permalink)
This limerick, it followed the path,
It was clean like Fermat in a bath.
And if true then it's crazy,
But alas I'm too lazy,
'Cause to be honest, I didn't do the math.
andy10889 ยท 4 points ยท Posted at 18:16:48 on May 25, 2016 ยท (Permalink)
My favorite fact is typical math is true despite if you believe it or not.
Quihatzin ยท 4 points ยท Posted at 18:18:54 on May 25, 2016 ยท (Permalink)
Any 2 digit number subtracted by its mirror is nine times the difference if the two numbers. Like 51-15 is 5-1 * 9
DM_Me_YourThot ยท 5 points ยท Posted at 19:30:01 on May 25, 2016 ยท (Permalink)
What's the integral of 1/cabin? log(cabin).......
[deleted] ยท 2 points ยท Posted at 22:53:07 on May 25, 2016 ยท (Permalink)
*log(cabin) +c
musicotic ยท 1 points ยท Posted at 23:45:05 on May 25, 2016 ยท (Permalink)
only if integral of 1/cabin dcabin
KarmaAdjuster ยท 4 points ยท Posted at 22:06:30 on May 25, 2016 ยท (Permalink)
It's not the most useful thing, but I was pretty proud of myself for figuring this one out (including why it works) while I was in the 5th grade.
For the numbers 17, 18, and 19, you can quickly figure out their square by multiplying the last digit by 4 to get the first to digits of the number, and then you can get the last digit by remembering what the last digit would be if you just took the square of the last digit.
So for 172:
4 x 7 = 28
7 x 7 = 49
Thus giving you 172 = 289
There is a more complicated formula that lets you apply this pattern to any number, but it looses it's beautiful simplicity.
MrUnderdawg ยท 2 points ยท Posted at 22:45:14 on May 25, 2016 ยท (Permalink)
In grade 9, I figured out the formula x2 + y2 +2xy =(x+y)2 and thought I was a genius. I got pretty pissed when I learned it the next year in Algebra 2.
KarmaAdjuster ยท 2 points ยท Posted at 22:53:06 on May 25, 2016 ยท (Permalink)
Just because someone else figured it out before you learned about doesn't mean you weren't a genius. :) I just means you weren't the first genius.
DankWarMouse ยท 3 points ยท Posted at 23:17:26 on May 25, 2016 ยท (Permalink)
Every prime number above 3 is 6n +/- 1.
Swiggety666 ยท 5 points ยท Posted at 23:55:10 on May 25, 2016 ยท (Permalink)
I like this because it is easy for young people to understand and gets the them interested in maths
If we take the odd numbers and add them together:
1=1=12
1+3=4=22
1+3+5=9=32
1+3+5+7=16=42
And on it goes. It is very easy to prove which helps.
xanthalasajache ยท 3 points ยท Posted at 03:17:03 on May 26, 2016 ยท (Permalink)
Belphegor's Prime 1000000000000066600000000000001
* 13 zeroes
* sandwiched by 1
* devil's number at the middle
* obvs a prime number
EuniceGutierrez ยท 4 points ยท Posted at 11:43:31 on May 26, 2016 ยท (Permalink)
You can consummately change over miles and kilometers utilizing the Fibonnaci arrangement.
1 2 3 5 8 13 21 34....
Every number, after a couple, is miles and the number after it is practically the relating number of kilometers and the other way around.
iSquanch ยท 1 points ยท Posted at 13:56:54 on May 26, 2016 ยท (Permalink)
That's actually super useful
unlimitedanna ยท 13 points ยท Posted at 12:14:16 on May 25, 2016 ยท (Permalink)
111,111*111,111= 12345654321
Kertelen ยท 6 points ยท Posted at 15:09:27 on May 25, 2016 ยท (Permalink)
1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321
1111 * 1111 = 1234321
11111 * 11111 = 123454321
And so on.
13467 ยท 3 points ยท Posted at 17:38:02 on May 25, 2016 ยท (Permalink)
Itโs easy to see why this works using schoolbook multiplication:
EKomadori ยท 1 points ยท Posted at 15:15:40 on May 25, 2016 ยท (Permalink)
Up to 111,111,111, the result will count up to the length and then back down to 1:
1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321
1,111 * 1,111 = 1234321
...
111,111,111 * 111,111,111 = 12345678987654321
UristMasterRace ยท -2 points ยท Posted at 14:38:47 on May 25, 2016 ยท (Permalink)
I, too, had a graphing calculator in high school.
Yajirobe404 ยท 6 points ยท Posted at 15:00:37 on May 25, 2016 ยท (Permalink)
There are truths in Math that cannot be proven.
vikinick ยท 1 points ยท Posted at 19:47:50 on May 25, 2016 ยท (Permalink)
There are untruths in math that can also be proven.
Slacker5001 ยท 1 points ยท Posted at 18:52:57 on May 25, 2016 ยท (Permalink)*
In what sense? As a math major I spend 99% of my time proving various things from the most "obvious" like why does 1+1=2 work, to really complex shit for my level.
If your implying that math has to be built on at least some assumptions, then I argue that so does the universe and our existence. It's a huge more philosophical question at that point of what is a "truth" and how do we know it's true.
Edit: I realized that the original comment said there are some unsolvable problems and not that math itself is unprovable. Oppsy, my bad.
[deleted] ยท 2 points ยท Posted at 19:43:47 on May 25, 2016 ยท (Permalink)
I believe he is refering to gรถdels incompleteness theorem
Slacker5001 ยท 1 points ยท Posted at 19:58:46 on May 25, 2016 ยท (Permalink)
Would make more sense. I always interpreted it as saying that there are inherent underlying assumptions in mathematics that are necessary for the proof of all things that follow. Everything from there is provable but it is proof based off a fundamental assumption.
[deleted] ยท 2 points ยท Posted at 20:03:02 on May 25, 2016 ยท (Permalink)
[deleted]
Slacker5001 ยท 1 points ยท Posted at 20:49:35 on May 25, 2016 ยท (Permalink)
That kind of comment gives the wrong idea in a world where people already say that math has no point and comes out of people's asses. The fact that people need to make some assumptions is irrelevant. On a philosophical level everything makes assumptions and by that logic everything is unprovable or provable on potentially false terms. Which is not how we look at the world or science/math. Math is built on assumptions, but assumptions that are well thought out, necessary, and fit out intuitive understanding of numbers as human beings. So no one is making random unproven assumptions to prove whatever they want.
maz-o ยท 1 points ยท Posted at 19:26:09 on May 25, 2016 ยท (Permalink)
why does 1+1=2 work?
Slacker5001 ยท 1 points ยท Posted at 20:23:36 on May 25, 2016 ยท (Permalink)
If I remember correctly there is a fancy ass proof in Principia Mathematica about it. I've never read it myself though so I'm just going to talk about what I know that makes it true.
There are two ways to look at it I think. One is a more formal proof way, the other is more to help understanding at a slightly more in depth level but really isn't a proof.
Basic arithmetic works because of the properties of groups. They are pretty simple rules that you can probably read and understand yourself, regardless of what level of math your at. They pretty much say, take a group of something (in our case a specific group of numbers) and define and operation on it (in our case addition) and a list of certain properties hold.
You can then use and play with those properties to show that 1+1=2 "works" in various situations. What people seem to not realize is that it doesn't always "work". Because of the way groups are defined, you could technically make your group to be anything you wanted, it doesn't even have to be made up of numbers. And you can define your new "addition" to work however you want. You can make 1 + 1 = fish if you want. The important thing is though, using the definition of groups you can show that it works for the numbers and operations as we are used to them (aka how you learn them normally in school).
This though really relies on the fact that you know the definition of this "addition" thing and "numbers". If you want to break it down into it's fundamental level you need to use successor functions and the peano axioms. These are just formal ways to define how we think about numbers, like "2 comes after 1".
With how it is defined (which you can see in more detail on the wiki if you like) we can just simply say:
2 = S(1) = S(1+0) = 1 + S(0) = 1 + 1
This right here is a more formal proof of why it works in the case of natural numbers. And you can prove it works with other groups of numbers (i.e. reals, integers, rationals, complex, etc).
TL:DR - We have a formal definition for the idea "2 comes after 1" that we can use to prove it along with this thing called "groups"
[deleted] ยท 1 points ยท Posted at 00:16:28 on May 26, 2016 ยท (Permalink)
You cannot prove there exist infinities of sizes between the repeated powersets of aleph-naught.
Prefocus ยท 18 points ยท Posted at 12:28:59 on May 25, 2016 ยท (Permalink)
.333 repeating + .666 repeating = 1
TheSemiTallest ยท 55 points ยท Posted at 13:25:32 on May 25, 2016 ยท (Permalink)
related to this: .999 repeating is the exact same number as 1, not just very very close.
pazur13 ยท 2 points ยท Posted at 14:04:03 on May 25, 2016 ยท (Permalink)
What's the reasoning behidn this? I always believed that if it's an infinite amount of nines, it's an infinitely little number (however little sense this description makes) away from 1.
[deleted] ยท 6 points ยท Posted at 14:16:44 on May 25, 2016 ยท (Permalink)
It behaves exactly the same way as 1 in every way. Therefore it is the same number as 1, just a different representation.
Proof:
0.333... = 1/3
Take both sides times 3.
0.999... = 3/3
3/3 = 1
Therefore
0.999... = 1
Elim_Tain ยท 0 points ยท Posted at 14:53:27 on May 25, 2016 ยท (Permalink)
Holy shit. You just did a MUCH better job of explaining this than my HS math teacher. He just went on and on. This is so simple.
joshthewaster ยท 7 points ยท Posted at 15:18:43 on May 25, 2016 ยท (Permalink)
This is simple because you believe that .333 repeating equals 1/3 but it equals 1/3 for the same reason .999 =1. This proof just hides the real reasons because you already believe the part about 1/3. That said I have used this to convince people of this fact and think it works well enough for that purpose.
brwbck ยท 8 points ยท Posted at 16:42:54 on May 25, 2016 ยท (Permalink)*
Yes. Better way of doing it:
x = 0.999...
10*x = 9.999...
10*x - x = 9.999... - 0.999... = 9
9*x = 9
x = 1
EDIT: Also, if 0.999... is not equal to 1, then we should be able to construct a number that's halfway between them. Try finding me a number halfway between 0.999... and 1. How would you even write it?
Stickyballs96 ยท 2 points ยท Posted at 17:32:01 on May 25, 2016 ยท (Permalink)
This is what made me understand. The 1/3 = 0.333... was helpful but still didn't convince me.
[deleted] ยท 2 points ยท Posted at 19:56:20 on May 25, 2016 ยท (Permalink)*
The reason I didn't use this version was because people often argue that 10*0.999... /= 9.999..., which doesn't make any sense, because multiplication by the base (10 in this case) is just shifting all digits to the left by 1 place. But getting into number bases is another topic that might be confusing.
I like your argument regarding finding a number inbetween 0.999... and 1, as there exists, by definition, a real number between any two real numbers that aren't equal.
[deleted] ยท 2 points ยท Posted at 19:54:26 on May 25, 2016 ยท (Permalink)
I agree that it has its flaws, but I think it demonstrates the concept very well - especially for people who aren't very mathematically inclined.
joshthewaster ยท 1 points ยท Posted at 19:57:01 on May 25, 2016 ยท (Permalink)
I agree.
DrFegelein ยท 2 points ยท Posted at 14:20:33 on May 25, 2016 ยท (Permalink)
1/3 is 0.3 recurring. 3*(1/3) is 1, or in decimal notation, 3*0.3 recurring is 0.9 recurring.
[deleted] ยท 1 points ยท Posted at 00:13:18 on May 26, 2016 ยท (Permalink)
There are quite a few reasons why.
For instance, I could say that, (.999...)x(.999...)=(.999...), and (.999...)x1=(.999...), which means (.999...) is acting as an identity and 1 is as well. There are trivial proofs that groups under a binary operation have a unique identity, thus 1=(.999...).
You could also note, that (.999...) and 1 are both rational numbers, 1/1 and 1/1. Assuming you don't buy the mapping between the rationals and the reals, you can cite the theorem about the density of the irrationals in the reals, which would show that there exist irrational numbers between any two rational numbers, as well, there exists rational numbers between any two irrational numbers. I'll assert as a claim that there exists no rational or irrational numbers between (.999...) and 1. Think on that for a while.
As well, if (.999...) did not equal 1 then [(.999...),1] would be a compact space. This would mean it's isomorphic to any other compact space. However, no mapping exists between [(.999...),1] and [0,1].
Really, what's going on is, you're saying there's an infinitely little number, but there isn't. Infinitely little means zero. If I give you (.999...), you have to be able to produce a number that I can add to it to get 1. If you give me any positive value 0.00...001, you've added past 1. Since no positive real number can be added to (.999...) to get 1, we can be sure (.999...)=1.
[deleted] ยท 1 points ยท Posted at 04:19:11 on May 26, 2016 ยท (Permalink)
That's the point. There is no such thing as "infinitely small" in the real numbers.
[deleted] ยท 1 points ยท Posted at 14:19:09 on May 25, 2016 ยท (Permalink)
[deleted]
The_Batmen ยท 13 points ยท Posted at 14:50:19 on May 25, 2016 ยท (Permalink)
Easy way
0.333... = 3/9 = 1/3
0.666... = 6/9 = 2/3
0.333... + 0.666... = 1/3 + 2/3 = 1
The way with an actual explanation
Between every two numbers there is an infinite number of other numbers. Between 0.1 and 0.2 are 0.11, 0.12, 0.111, 0,198 and so on.
Between 0.888... and 0.9 is an infinite number of numbers. You can just add a 9 at the end of 0.888...: 0.89, 0.889, 0.8889 and so on.
Now we have 0.999... and 1. You can't add 9 at the end because the end is always a 9. Therefore there isn't a number between 0.999... and 1 which means it is the same number.
[deleted] ยท 4 points ยท Posted at 14:52:19 on May 25, 2016 ยท (Permalink)
[deleted]
The_Batmen ยท 1 points ยท Posted at 14:55:40 on May 25, 2016 ยท (Permalink)
What do you not understand about my explanation?
[deleted] ยท 1 points ยท Posted at 15:02:12 on May 25, 2016 ยท (Permalink)
[deleted]
MrTheSpork ยท 3 points ยท Posted at 15:12:05 on May 25, 2016 ยท (Permalink)
They're not different numbers, just different representations of the same number. It's like saying that three thirds is the same as 1 - it's a different representation, but exactly the same. The 0.999...=1 is a less intuitive version of the same.
The_Batmen ยท 5 points ยท Posted at 15:12:22 on May 25, 2016 ยท (Permalink)
Just imagine it likewalls. The first number is a red wall, the second number is a blue wall. The numbers between it are free space.
1 = blue wall (---)
2 = red wall (---)
Between 1 and 2 are other numbers. The wall is something like --- --- It has free space between them. They are two walls.
1 = blue wall (---)
0.999... = red wall (---)
This looks more like ------ Both parts of the wall look different but they aren't seperated by free space. It's the same wall that looks different depending on where you look.
Does this make sense?
pemboo ยท 3 points ยท Posted at 17:47:46 on May 25, 2016 ยท (Permalink)
You're convoluting this beyond belief.
You can have two different ways of symbolically representing the same number
Multai ยท 2 points ยท Posted at 15:09:00 on May 25, 2016 ยท (Permalink)
0.99999 = x
9.99999 = 10x
9 = 9x
1 = x
1 = 0.999999
mailboxrumor ยท 1 points ยท Posted at 15:19:43 on May 25, 2016 ยท (Permalink)
I show this to my algebra students and they freak out.
D-Shap ยท 1 points ยท Posted at 23:39:17 on May 25, 2016 ยท (Permalink)
Except when dealing with hyperreal numbers friend
Supersnazz ยท -1 points ยท Posted at 15:39:58 on May 25, 2016 ยท (Permalink)
Until you start working with hyperreal numbers, then they become different again.
kogasapls ยท 3 points ยท Posted at 17:43:32 on May 25, 2016 ยท (Permalink)
They don't. 0.999... is defined as the sum (x from 1 to inf.) of 9 * 10-x , which is 1 even in the hyperreals.
chesterjosiah ยท 16 points ยท Posted at 13:56:05 on May 25, 2016 ยท (Permalink)
1/3 + 2/3 = 1
jacko2178 ยท 1 points ยท Posted at 15:57:20 on May 25, 2016 ยท (Permalink)
No way, this math fact is blowing my mind!
oberynMelonLord ยท 3 points ยท Posted at 13:23:57 on May 25, 2016 ยท (Permalink)
that's because
and
because
Put in
and you get
ashep24 ยท 2 points ยท Posted at 15:36:52 on May 25, 2016 ยท (Permalink)
I had the hardest time believing this until I realized "why can't there be more than one decimal representation of the same number?" The answer is there is no reason. 0.999... and 1 are written ways of describing the same number.
cob59 ยท -3 points ยท Posted at 14:54:46 on May 25, 2016 ยท (Permalink)
Let's say x = 0.999, then 10x = 9.990
Therefore 9.990 - 0.999 = 8.991
Adding more nines to x:
9.999... - 0.999... = 8.99(...)991 โ 9
oberynMelonLord ยท 0 points ยท Posted at 15:11:20 on May 25, 2016 ยท (Permalink)
that 1 never shows up, because there will always be another 9 in both numbers. that's the point of periodic numbers.
the thing is, 0.999... is not exactly 1. for every 9 you hang at the end of the end the number tends to get closer and closer to 1. This is the correct way of saying it, I think.
cob59 ยท -1 points ยท Posted at 15:32:59 on May 25, 2016 ยท (Permalink)
Even if the 1 "doesn't show up" (I don't know what this means mathematically), 9x value will still be 8.999..., not 9.
The formula you're giving is a limit. Calculating a limit towards +โ is not the same thing as solving for x=+โ, which is not allowed if the function/series is not defined for such a value.
kogasapls ยท 4 points ยท Posted at 17:45:02 on May 25, 2016 ยท (Permalink)
Taking the limit is exactly what you're doing with the ellipsis. 0.999... is the limit of the partial sums of 9 * 10-x , which is 1.
cob59 ยท 1 points ยท Posted at 19:23:28 on May 25, 2016 ยท (Permalink)
Then the whole arithmetical hocus-pocus I was answering to was just a tautology, since 0.999... is equal to 1 by definition.
kogasapls ยท 2 points ยท Posted at 19:36:32 on May 25, 2016 ยท (Permalink)
You're right, it's a tautology. Tautologies have a purpose in math and logic. All tautological statements are necessarily true. If you can show that a statement is tautological, you then show that it is true. The thing you were responding to is just a way to help people see that 1 = 0.999...
cob59 ยท 1 points ยท Posted at 19:57:42 on May 25, 2016 ยท (Permalink)*
I explained here why the 2nd part of his demonstration is flawed (or at least why it didn't convince me)
kogasapls ยท 2 points ยท Posted at 20:12:00 on May 25, 2016 ยท (Permalink)
You can't add a digit after an infinite number of 9s. There is no "after" the infinite number of 9s. 0.999...91 isn't a well-defined number. Also, 10 * 0.999... is not 9.999...0, it's just 9.999..., with the same (infinite) amount of 9s. See Hilbert's hotel.
cob59 ยท 0 points ยท Posted at 20:42:10 on May 25, 2016 ยท (Permalink)
Where did you get that 0.999...91 from? The result was 8.999...91.
If you think something from the Hilbert's Paradox disproves something I said, please tell me which part. Just don't throw some wikipedia article at my face.
kogasapls ยท 1 points ยท Posted at 20:57:34 on May 25, 2016 ยท (Permalink)
... it doesn't actually matter. Neither 0.999...91 nor 8.999...91 is a well defined number. 0.999... * 10 = 9.999..., not 9.999...0. Shifting an infinite series of 9s does not leave a gap at the end. This is related to the example of Hilbert's hotel.
VerbableNouns ยท 16 points ยท Posted at 12:28:32 on May 25, 2016 ยท (Permalink)
In Duodecimal, the tenth eleventh and twelth numbers are pronounced "dek", "el", and "doh".
2nd_law_is_empirical ยท 4 points ยท Posted at 15:10:54 on May 25, 2016 ยท (Permalink)
Fus Roh Duh?
rzezzy1 ยท 2 points ยท Posted at 15:15:56 on May 25, 2016 ยท (Permalink)
I've never heard it addressed as duodecimal; only dozenal. It seems, though, that my phone's dictionary has duodecimal and not dozenal. TIL.
VerbableNouns ยท 2 points ยท Posted at 15:23:00 on May 25, 2016 ยท (Permalink)
StDoodle ยท 1 points ยท Posted at 16:44:49 on May 25, 2016 ยท (Permalink)
Duodecimal, the beautiful system that brings in the simplicity of conversion inherent in the metric system but still allows for your units places to represent the artistically valued relationships of halves, thirds, quarters and sixths without needing infinite-repeating decimal places.
SepulchreOfAzrael ยท 13 points ยท Posted at 12:41:44 on May 25, 2016 ยท (Permalink)
1/7 is an interesting decimal
Multiples of 1/7 produce cyclic permutations of 1/7:
More interestingly, when you break any of those 6-digit sequences in the middle and add, you get 999.
Also, when the decimal is multiplied by 7, it again generates a sequence of 9s: 0.999999...
ragout ยท 5 points ยท Posted at 14:37:56 on May 25, 2016 ยท (Permalink)
Isn't it just an error caused by rounding?
6/7 * 7 would just be 6 no?
[deleted] ยท 6 points ยท Posted at 15:06:44 on May 25, 2016 ยท (Permalink)
.9 repeating is 1.
IAmA_Catgirl_AMA ยท 1 points ยท Posted at 15:03:42 on May 25, 2016 ยท (Permalink)
If you turn that upside down you get 666. 666 has three digits. In your example, you have shown three repetitions for each number. The third number begins with the digit 4, and the fourth number is shifted by three digits.
All these numbers arise from dividing by the magical number seven.
Coincidence?
I think not!
Greatgrowler ยท 9 points ยท Posted at 13:32:31 on May 25, 2016 ยท (Permalink)
Take any whole number, add the digits up, and if the answer is divisible by 3, then so is the original number.
[deleted] ยท 6 points ยท Posted at 14:24:16 on May 25, 2016 ยท (Permalink)
It works for 9 as well. I.e. if the sum of the digits of a number is divisible by 9 then the original number is also divisible by 9.
Actually, I found that the trick works in any base system. So, in a base N system, you can find whether a number is divisible by N-1 by checking if the sum of its digits are divisible by N-1. The trick also works on any of N-1's divisors. In base 10's case, 3 is a divisor of 9.
E.g. 61 (base 8) has the sum of its digits 7 which means is divisible by 7. And it's true, 61(base 8) = 49(base 10).
rocketguy2 ยท 1 points ยท Posted at 17:07:50 on May 25, 2016 ยท (Permalink)
You can also do this for 19, if you take of the last two digits, multiply them by four then add it to the other digits, if this divides by 19, then so does the number
wfaulk ยท 1 points ยท Posted at 14:49:26 on May 25, 2016 ยท (Permalink)
Which means that if that sum is still too big to easily determine its divisible-by-three-ness, you can just add the sum's digits.
L-ot-O-MO ยท 1 points ยท Posted at 18:00:34 on May 25, 2016 ยท (Permalink)
And if the original number is even, it is also divisible by 6.
iredditalready5 ยท 6 points ยท Posted at 16:29:57 on May 25, 2016 ยท (Permalink)
-40 degrees Celsius = -40 degrees Fahrenheit
comox ยท 9 points ยท Posted at 17:25:39 on May 25, 2016 ยท (Permalink)
That 6 is afraid of 7 because 7 ate 9.
SillyFlyGuy ยท 6 points ยท Posted at 20:09:50 on May 25, 2016 ยท (Permalink)
6 is afraid of 7 because 7 is a registered six offender.
ncnotebook ยท 2 points ยท Posted at 22:10:39 on May 25, 2016 ยท (Permalink)
Well, it is true that six was afraid of seven because seven is a registered six offender. What you didn't hear was what happened afterwards. Five had six with seven, who also eight nine.
Don't forget the other numbers: zero went to three, for five, but two also had three for five (2 + 3 = 5). Yet zero won. Still, two three's for five.
Numbers are cannibalistically perverted bastards, especially 5 and 7.
vladikostek ยท 71 points ยท Posted at 15:10:02 on May 25, 2016 ยท (Permalink)
First we state that girls require time and money
Girls = Time X Money
And as we all know "time is money"
Time = Money
Therefore if we substitute
Girls = Money X Money = (Money)2
And because "money is the root of all evil":
Money = โEvil
Therefore:
Girls = (โEvil)2
And we are forced to conclude that:
Girls = Evil
Donkey__Xote ยท 51 points ยท Posted at 15:44:07 on May 25, 2016 ยท (Permalink)
There's a scholarly paper about this. "Mathematical Proof that Girls are Evil".
Even more importantly though, squared square-root is an absolute value.
Therefore, girls are absolutely evil, QED.
[deleted] ยท 1 points ยท Posted at 20:49:36 on May 25, 2016 ยท (Permalink)*
[deleted]
ThereAreOnlyTwo ยท 1 points ยท Posted at 08:50:14 on May 26, 2016 ยท (Permalink)
i can Help you with that!
indian_nerd_for_life ยท 16 points ยท Posted at 15:45:00 on May 25, 2016 ยท (Permalink)
I don't think so. If girls are worth time AND money then it's
girls = time + money
So the final answer you get is
girls = 2(evil)1/2
Or in other words, 2 times the root of evil. I'm on mobile so I don't have the root symbol.
ViridianKumquat ยท 11 points ยท Posted at 18:21:01 on May 25, 2016 ยท (Permalink)
Or you could go the bitwise arithmetic route.
Let's say you make ยฃ30,000 a year. There are 31,557,600 seconds in a year.
Convert that back to decimal and the number of girls is 1312.
I don't know where I'm going with this.
indian_nerd_for_life ยท 2 points ยท Posted at 18:45:05 on May 25, 2016 ยท (Permalink)
If you can get that many women with that kind of salary, I can only imagine the life with a 6 figure salary.
ViridianKumquat ยท 2 points ยท Posted at 19:46:26 on May 25, 2016 ยท (Permalink)
Things would get pretty awesome at ยฃ131,071. But as soon as you start earning a pound more than that, it's a different story.
Edit: accidentally a word.
DrSandbags ยท 3 points ยท Posted at 17:00:00 on May 25, 2016 ยท (Permalink)
If you assume the impacts of time and money are not separable, then it makes sense to model them as an interaction term. The marginal impact of time on girls is affected by the amount of money you're spending. The marginal value of one extra day holding spending fixed at $100 is worth more in value to a girl than one extra day holding spending fixed at $10. Similarly the marginal impact of an extra dollar is greater the higher the time commitment. Formally:
pd=partial derviative
(pd)girls/(pd)time = 1*money
(pd)girls/(pd)money = 1*time
The original inspiration for the Cobb-Douglas production function was to solve this very issue where the original formula was:
Girls = P*Talpha*M1-alpha
where P is a penis size parameter and alpha is a preference parameter.
vladikostek ยท 1 points ยท Posted at 17:24:08 on May 25, 2016 ยท (Permalink)
^ So much this ^
indian_nerd_for_life ยท 1 points ยท Posted at 17:49:05 on May 25, 2016 ยท (Permalink)
Sure but I think then the value of money would decrease exponentially in value.
For example,
If you were to find the limit of the value of money, then the difference in the happiness of the girl would not increase much between 10 million and 50 million since the difference in what you could do would not be that much different. Thus, even if the difference between 50 and 500 may be large it doesn't work for all values of n, where n is the increase in happiness achieved by spending certain amounts of money.
DrSandbags ยท 1 points ยท Posted at 17:59:16 on May 25, 2016 ยท (Permalink)*
The answer to diminishing marginal returns is to make girls a concave function of money (and/or time), but you can still make money and time nonseperable while modelling either or both with diminishing returns.
Edit: it may not even matter much because 99% of the time a linear approximation of the marginal impact will work well enough. It also has the great benefit of supporting the original conclusion (that girls are evil) ๐
indian_nerd_for_life ยท 2 points ยท Posted at 18:06:57 on May 25, 2016 ยท (Permalink)
True, you are right about considering them together. Thanks for clearing that up
mr_ewe ยท 2 points ยท Posted at 16:51:30 on May 25, 2016 ยท (Permalink)
Just square both sides. Then one quarter of square girls are evil.
Doesn't tell me anything about cool girls, but at least I know 3 out of 4 nerdy ones can be trusted!
Hashtag feminism.
indian_nerd_for_life ยท 1 points ยท Posted at 17:50:31 on May 25, 2016 ยท (Permalink)
Smart.
ZizekIsMyDad ยท 7 points ยท Posted at 18:23:15 on May 25, 2016 ยท (Permalink)
That doesn't follow. The statement
is not equivalent to the equation
actual_factual_bear ยท 5 points ยท Posted at 16:55:12 on May 25, 2016 ยท (Permalink)
I think I have found a small mistake in your derivation. When you reach the statement "money is the root of all evil" it doesn't say which root, but you have assume the square (second) root. There are actually three possibilities, two of which you have not considered. Either money is the square root of evil, another nth root of evil, or multiple/all roots of evil. If it was a specific root they would have just said, "Money is the square root of all evil" or "Money is the tenth root of all evil" so the most likely case is "Money is the nth root of all evil for n in the natural numbers". Therefore, at step 4 you should have something like:
Girls = nโEvil
Where n is any natural number. From which it follows that:
Girls = (nโEvil)2
And we are forced to conclude that
Girls = (n/2)โEvil
Porridgeandpeas ยท 1 points ยท Posted at 23:57:24 on May 25, 2016 ยท (Permalink)
If you have 2 girls on the go, n=2. Then man is evil.
maz-o ยท 4 points ยท Posted at 19:19:28 on May 25, 2016 ยท (Permalink)
"time and money" is not the same as "time x money"
MaxSupernova ยท 3 points ยท Posted at 16:35:14 on May 25, 2016 ยท (Permalink)
Money isn't the root of all evil.
The love of money is the root of all evil.
DrSandbags ยท 3 points ยท Posted at 18:53:57 on May 25, 2016 ยท (Permalink)
You can't spell "The love of money is the root of all evil" without "money is the root of all evil"!
zombie_dbaseIV ยท 1 points ยท Posted at 18:15:16 on May 25, 2016 ยท (Permalink)
Sorry, but according to the Bible it's the "love of money" that's the root of all evil.
KarlKastor ยท 1 points ยท Posted at 19:03:22 on May 25, 2016 ยท (Permalink)
I once showed this to a friend in class, then the teacher came around and looked at it. He said I had defined everything in such a way that it works and that I won't impress any girls with it. I had forgotten to tell him that this is based of proverbs. (which I had told my friend while I wrote it)
Sarkasian ยท 1 points ยท Posted at 20:09:11 on May 25, 2016 ยท (Permalink)
Except that time and money is written as time + money, so that particular joke doesn't work
supremecrafters ยท 1 points ยท Posted at 20:26:06 on May 25, 2016 ยท (Permalink)
Knowledge = Power
Power = Work/Time
Time = Money
Knowledge = Work/Money
Therefore, as knowledge approaches zero, work done also approaches zero and money earned approaches infinity. This is called the Dilbert Principle, and it explains both why upper management tends to be the least intelligent part of the company, and why my knowledge is undefined.
In a similar vein:
Books = Knowledge
Knowledge = Power
Power = Energy
Energy = Matter
Matter = Mass
Therefore, all libraries are just genteel black holes that know how to read.
culb77 ยท 1 points ยท Posted at 15:51:22 on May 25, 2016 ยท (Permalink)
This is brilliant.
amodia_x ยท 12 points ยท Posted at 21:01:37 on May 25, 2016 ยท (Permalink)
The word bed looks like a bed.. Sorry, I was never any good with math. I'm sorry.
-Tesserex- ยท 3 points ยท Posted at 13:56:30 on May 25, 2016 ยท (Permalink)
The Borsuk-Ulam theorem. It says that any function mapping an n-sphere to n-space has a set of antipodal points of the same value. So in the case of an ordinary sphere in our world (a 2-sphere), any function that maps a point on the surface to two variables will have points on opposite ends with the same values.
For example, take the Earth as a sphere. If you pick any two numerical values, for example, temperature and air pressure, there's always at least one set of points on opposite sides of the earth with the exact same value for both of them. You can say that about any two things about the Earth, as long as the function is continuous.
HanLeonSolo ยท 3 points ยท Posted at 14:45:49 on May 25, 2016 ยท (Permalink)
That I have only have to take 4 more semesters worth
[deleted] ยท 3 points ยท Posted at 14:50:22 on May 25, 2016 ยท (Permalink)
22/7 is closer to pi than 3.14 is
graaahh ยท 2 points ยท Posted at 17:49:21 on May 25, 2016 ยท (Permalink)
And 355/113 is even closer. But IIRC there's no better fraction for pi than that with a denominator that's under 5 or 6 digits.
Meese057 ยท 3 points ยท Posted at 15:08:52 on May 25, 2016 ยท (Permalink)
If you want to see if you can factor a three out of a number, add up the digits that make it up, and if they add up to a factor of three then you can factor a three out.
Ex: 117: 1 + 1 + 7 = 9 (divisible by three) 117/3 = 39
Ex2: 40044: 4 + 4 + 4 =12 (divisible by three) 40044/3 = 13,348
Virtuallyalive ยท 3 points ยท Posted at 15:28:19 on May 25, 2016 ยท (Permalink)
1+2+3+4+5.... = -1/12
PersonUsingAComputer ยท 3 points ยท Posted at 18:52:44 on May 25, 2016 ยท (Permalink)
For a certain nonstandard definition of "+" and "=", sure. Under the usual definition of an infinite sum, 1+2+3... does not converge to anything.
[deleted] ยท 1 points ยท Posted at 15:31:19 on May 25, 2016 ยท (Permalink)
[deleted]
Virtuallyalive ยท 2 points ยท Posted at 15:36:35 on May 25, 2016 ยท (Permalink)
Yes, there's a numberphile video on it.
[deleted] ยท 1 points ยท Posted at 18:42:21 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 19:37:19 on May 25, 2016 ยท (Permalink)
The result is meaningless, since you can't sum an divergent series (the sum just keeps going up and up, tending to infinity, since that's the definition of a divergent series.) The people who made that sum were applying techniques used to sum convergent series.
brufleth ยท 3 points ยท Posted at 15:54:30 on May 25, 2016 ยท (Permalink)
If the sum of the digits in a number are divisible by three then the number is divisible by three.
Exmple:
13459614
1+3+4+5+9+6+1+4 = 33
3+3 = 6
So 13459614 is divisible by 3.
_NW_ ยท 1 points ยท Posted at 18:57:57 on May 25, 2016 ยท (Permalink)
This is also true for 9. It's also true for every factor of (N-1) in a base N system.
ktisis ยท 3 points ยท Posted at 16:06:29 on May 25, 2016 ยท (Permalink)
987654321 / 123456789 is almost exactly 8.
I_FAP_TO_LOL_HENTAI ยท 3 points ยท Posted at 16:43:53 on May 25, 2016 ยท (Permalink)
This thread made me realize how dumb I actually am.
Slacker5001 ยท 1 points ยท Posted at 18:35:32 on May 25, 2016 ยท (Permalink)
No worries at all. A lot of these seemingly random facts are more like math parlor tricks or stuff that I didn't learn until a much higher level of math as a math major. So not stuff that most people would know unless they are pursuing a degree in math, which is very excessive by most standards.
[deleted] ยท 1 points ยท Posted at 00:17:11 on May 26, 2016 ยท (Permalink)
It has nothing to do with intelligence. People good at math simply care more and spend more time doing it.
[deleted] ยท 3 points ยท Posted at 17:03:42 on May 25, 2016 ยท (Permalink)
If the sum of a numbers digits is a multiple of 3 that number is divisible by 3.
Idiotnextdoor_2 ยท 2 points ยท Posted at 17:22:52 on May 25, 2016 ยท (Permalink)
Also called the divisibility test for 3.
If a number is even it is divisible by two, obviously.
4 is complicated, let's just say if you divide x by 2 and the result is even then the x number is divisible by 4. (Just something I thought on the fly, let me know if it doesn't work on any positive integer).
In a number If the digit in the units place is 5 or 0 then the number is divisible by 5.
If a number is even and divisible by 3 is divisible by 6
Don't know shit about 7.
If you divide x by 2 and the result is divisible by 4 then it's divisible by 8. (Same as 4).
Don't know shit about 9 either.
If a number has 0 in units place is divisible by 10
Searching4Ecstasy ยท 3 points ยท Posted at 17:06:02 on May 25, 2016 ยท (Permalink)
Spelling BooB and he'll on calculators!
thatspunny ยท 3 points ยท Posted at 17:17:00 on May 25, 2016 ยท (Permalink)
Gabriel's Horn: A structure than can be filled with paint (finite volume) but can never be painted (infinite surface area).
epsiloon ยท 3 points ยท Posted at 17:31:07 on May 25, 2016 ยท (Permalink)
if you want to multiply any number by 5... add a zero and divide by 2
for example: 5*142= 1420/2=710
i always find dividing by 2 is easier for me
WeenisWrinkle ยท 3 points ยท Posted at 18:49:13 on May 25, 2016 ยท (Permalink)*
.999999999... (repeating) is exactly equal to the number 1, mathematically. It's not "close", it literally equals 1.
Simple way to visualize it is with a fraction. 1/3 is the number 1 divided exactly 3 times. Each 1/3 is exactly .3333... (repeating). .3333.... times 3 = .9999...
1/3 x 3 รท .999999...
1/3 x 3 = 1
D-Shap ยท 1 points ยท Posted at 23:45:27 on May 25, 2016 ยท (Permalink)
Not when working with nonstandard analysis and hyperreal numbers
MopsyWT ยท 3 points ยท Posted at 18:59:58 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers to infinity is -1/12.
Sheriff_K ยท 3 points ยท Posted at 19:19:16 on May 25, 2016 ยท (Permalink)
1+2+3+4... repeated to infinity = -1/12
20mcgug ยท 2 points ยท Posted at 19:46:37 on May 25, 2016 ยท (Permalink)
Can confirm
SentientDust ยท 3 points ยท Posted at 20:24:34 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers, from one to infinity is -1/12. That's negative one twelfth. And it;s not just a math trick, apparently they use that identity in String Theory.
machingunwhhore ยท 3 points ยท Posted at 20:28:34 on May 25, 2016 ยท (Permalink)
One night while trying to sleep I discovered that if you know the square of a number but not the square of the number before or after it you can find it easily. Ex) 132=169 142=? To find the square of 14 all you do is add the square root of the number you know and the number you want to know together. 13+14=27 Then add that sum to the square you already know. 27+169=196 142=196 This works for any two squares, if the roots are only 1 number away. You can also go back if you 142 and want to find 13, you just add 14 and 13 then subtract from 196.
To put it in a formula: X(1)2=Y X(2)+1 or -12=Z Add X1 and X2 together Then use the same sign you did when adding or subtracting 1 to X Sum of X1 and X2 added or subtracted to Y and that Equals Z
X(1)+X(2)+Y=Z
teyxen ยท 2 points ยท Posted at 20:33:34 on May 25, 2016 ยท (Permalink)
To put it another way,
(x + 1)2 = x2 + 2x + 1 = x2 + x + (x + 1)
machingunwhhore ยท 2 points ยท Posted at 21:00:24 on May 25, 2016 ยท (Permalink)
Yeah, I wrote the equation myself so it was a bit sloppy.
Dom_Flannel_Guy ยท 3 points ยท Posted at 20:50:44 on May 25, 2016 ยท (Permalink)
8008 on a calculator says boob
[deleted] ยท 3 points ยท Posted at 21:09:43 on May 25, 2016 ยท (Permalink)*
If p is a prime number > 3 then ( p2 ) -1 is a multiple of 12.
I know the explanation. But it still baffles me that something as complex as the prime numbers can have such an elegantly simple pattern.
_diabeetus ยท 3 points ยท Posted at 21:15:10 on May 25, 2016 ยท (Permalink)
If you write "-2-2x=" on a piece of paper, it will make a sound similar to the Mary Poppins song, "chim chimney"
TestiTag ยท 3 points ยท Posted at 21:23:58 on May 25, 2016 ยท (Permalink)
There are 10 000,000,000,000,000,000,000,000,000,000 particles in the universe that we can observe.
Your momma took the ugly ones and put them into one nerd.
crawlerz2468 ยท 3 points ยท Posted at 21:27:02 on May 25, 2016 ยท (Permalink)
You can multiply by 9 very simply on your finger. Just bend the finger number that you're multiplying 9 by and you get the result. 2 x 9? Bend finger #2 and count 1 to the left and 8 to the right. 18.
Mister_Loki ยท 3 points ยท Posted at 21:30:56 on May 25, 2016 ยท (Permalink)
Please Excuse My Dear Aunt Sally
Lovett1328 ยท 1 points ยท Posted at 01:42:28 on May 26, 2016 ยท (Permalink)
Please Excuse My Dope Ass Swag
TooLazyToBeClever ยท 3 points ยท Posted at 21:51:36 on May 25, 2016 ยท (Permalink)
Math dries out your mouth, causing your teeth to crumble away.
dmr83457 ยท 3 points ยท Posted at 22:02:58 on May 25, 2016 ยท (Permalink)
1 = .9 repeating
xuz7 ยท 3 points ยท Posted at 22:03:17 on May 25, 2016 ยท (Permalink)
That some countries say math and others say maths
[deleted] ยท 3 points ยท Posted at 22:04:18 on May 25, 2016 ยท (Permalink)
You can figure out any if any number is divisible by 3 by adding its digits together, they will be also be a multiple of three.
12=>1+2 = 3
18=>1+8 = 9 = 3*3
114=>1+1+4 = 6 = 3*2
9696=> 9+6+9+6 = 30 = 3*10
This process can be done multiple times on large numbers in order to get to a smaller multiple of three.
98886=> 9+8+8+8+6 = 39 => 3+9 = 12 => 1+2 = 3
bdoerksen ยท 3 points ยท Posted at 22:08:56 on May 25, 2016 ยท (Permalink)
My fact is that maths as plural is historically incorrect. It's meant to be mathematics.
Uncle_Skeeter ยท 3 points ยท Posted at 23:14:43 on May 25, 2016 ยท (Permalink)
Getting a C- in Cal 3 means you passed Cal 3.
gwalker4 ยท 2 points ยท Posted at 23:17:22 on May 25, 2016 ยท (Permalink)
I love you
Uncle_Skeeter ยท 2 points ยท Posted at 02:39:01 on May 26, 2016 ยท (Permalink)
Thanks!
:D
On_top_of_the_world ยท 3 points ยท Posted at 23:37:02 on May 25, 2016 ยท (Permalink)
To find the square of a number that ends with 5: Take the digits other than 5 as a single number and multiply it with the next consecutive number. Place 25 after the product and you have your square.
Example, 15x15 = (1x2)25 = 225
25x25 = (2x3)25 = 625
35x35 = (3x4)25 = 1225
HappynessMovement ยท 3 points ยท Posted at 23:40:40 on May 25, 2016 ยท (Permalink)
This is probably here already, but if it isn't:
x % of y = y % of x
So 10% of 50 is 50% of 10.
spartanburt ยท 1 points ยท Posted at 03:11:25 on May 26, 2016 ยท (Permalink)
Just the regular commutative property with an extra 100 thrown in.
milkbottle ยท 3 points ยท Posted at 00:41:14 on May 26, 2016 ยท (Permalink)
x% of y = y% of x.
First time seeing that blew my then 13 year old mind.
spartanburt ยท 1 points ยท Posted at 02:56:52 on May 26, 2016 ยท (Permalink)
Just think of it as the regular commutative property, only with an extra 100 thrown in.
yosarian77 ยท 3 points ยท Posted at 01:35:45 on May 26, 2016 ยท (Permalink)
No pigeonhole theorem? Actually it's not that exciting but it's one of the only things I can remember from my math degree.
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
DeathBefore ยท 3 points ยท Posted at 02:48:59 on May 26, 2016 ยท (Permalink)
If you get enough people to hold hands a cross the entire circumference of the equator, many of them will drown.
Flying_goomba ยท 3 points ยท Posted at 03:19:34 on May 26, 2016 ยท (Permalink)
42 = 16
24 = 16
I'm a simple man.
amathus4321 ยท 3 points ยท Posted at 05:31:19 on May 26, 2016 ยท (Permalink)
You're all nerds, and I'm super jealous. I suck at all things math. I want to be smart, too.
Zarco19 ยท 3 points ยท Posted at 05:42:55 on May 26, 2016 ยท (Permalink)
A fun one nobody has mentioned: Euler's Identity.
epi x i + 1 = 0
Where e is the natural base 2.718... , pi is the circle ratio 3.14... , and i is the imaginary unit sqrt(-1).
(i.e. epi x i = -1)
Written like this, though, it can be said to relate the 5 most important numbers in math. This is one of those facts that seems staggering when you first learn it. A number to an imaginary power? What could that even mean to multiply a number by itself an imaginary number of times? Yet, somehow, if that imaginary number is pi times i, we not only get an answer, but a negative answer, and one that is nicely equal to an integer.
But really, it's a core fact in complex analysis and can be understood in a pretty geometric way.
Basically, it stems from the fact that ei x theta = cos(theta) + i sin(theta). This identity says that to take an imaginary exponent, rather that move outward on the imaginary plane (like we might for ex), we instead move around in a circle, perpendicular to how we would otherwise. This kind of makes sense, since i represents rotating by 90 degrees on the complex plane.
A more detailed proof of this fact can be given by expanding the taylor series (basically an infinite polynomial that adds up to your function) of an exponential function with an imaginary argument. When you break the series into real and imaginary terms, you end up with the series for cosine and sine easily, since the signs of in are the same as the signs in the derivatives of sin and cosine. There's another easy proof starting with the polar definition of a complex number, taking a derivative, and solving the differential equation, and I've even seen some cool geometric proofs. The crux of them all is that if you want complex exponents to have consistent properties that align with real ones, they HAVE to equal cosine plus i sine. Anything else is incongruent with the properties of exponents.
Ultimately, though, this identity says that an imaginary exponent is a rotation in the complex plane. If we start at 1 and go pi around (half a circle), we end up opposite where we started, at -1. Similarly you can see that e0 = 1, epi/2 x i = i, e2pi x i = 1. You can even raise the middle one to the ith power to get that ii = e-pi/2.... a real number.
From this ability to relate complex exponents to complex numbers, we actually learn a lot about complex numbers as a whole, and it opens the door to redefining functions as properties in general. It's a cool fact that looks flashy, has interesting math to back it up, and is actually extremely important and useful.
rustinhieber42 ยท 3 points ยท Posted at 07:08:50 on May 26, 2016 ยท (Permalink)
eฯi = -1
Euler's Identity. Amazing.
[deleted] ยท 3 points ยท Posted at 07:09:05 on May 26, 2016 ยท (Permalink)
Nullstellensatz
presciiient ยท 3 points ยท Posted at 09:39:14 on May 26, 2016 ยท (Permalink)
The difference between successive squares increases by two as you go along.
For example, the difference between 1 (1 squared) and 4 (2 squared) is 3, while the difference between 4 (2 squared) and 9 (3 squared) is 5 (2 more than 3). This follows suit as the difference between 9 (3 squared) and 16 (4 squared) is 7 (2 more than 5). As far as I know, this continues endlessly
Makhiel ยท 1 points ยท Posted at 13:22:33 on May 26, 2016 ยท (Permalink)
The difference between n2 and (n+1)2 is 2n + 1, so yeah, if you raise n by 1 the difference raises by 2, larger number are not going to break it. :)
[deleted] ยท 7 points ยท Posted at 13:09:31 on May 25, 2016 ยท (Permalink)*
that in any room with 6 people at least 3 people know each other or at least 3 people don't
edit: correction to the statement of the result
ZizekIsMyDad ยท 3 points ยท Posted at 18:09:34 on May 25, 2016 ยท (Permalink)
Hmm... You phrased the theorem wrong, it's "at least three people know each other, or at least three people don't know each other", which isn't that meaningful or interesting when you think about it. You could pretty much say "in a room with 6 people, all of them might know each other, or none of them, or any combination thereof".
I think it's actually more interesting in the graph theory context (if you're into that kind of thing), which is, "if you have 6 interconnected points and you colour each line one of two colours, there's is no way to avoid forming a triangle with one of the colours".
[deleted] ยท 1 points ยท Posted at 19:10:11 on May 25, 2016 ยท (Permalink)
I think this is why it's interesting though because you're right - it's a pretty uninteresting fact in itself and fairly obvious, but its the beginnings of a whole area of maths, namely Ramsey theory which is fascinating. For example you can prove the result that for any n and sufficiently large prime p there is a non-trivial solution to the Fermat equation modulo p using Ramsey theory.
graaahh ยท 1 points ยท Posted at 17:47:31 on May 25, 2016 ยท (Permalink)
I'm having trouble imagining how that could possibly not be the case. If three people know each other, then it works. And if no group of three people all know each other, then that means 4 or more don't.
[deleted] ยท 2 points ยท Posted at 19:32:19 on May 25, 2016 ยท (Permalink)
you're right, but the question becomes very non-obvious as soon as you ask the same for 4 people. I.e how many people do you need in a room such that at least 4 people know each other or at least 4 people don't know each other (it's 18 btw). Call this the 4th Ramsey number R(4,4). R(5,5) lies somewhere between 43 and 49 (currently unknown).
There's a really great proof using the probabilistic method due to Erdos which gives a lower bound on the Ramsey number for any R(k,k) for any k.
graaahh ยท 1 points ยท Posted at 19:55:05 on May 25, 2016 ยท (Permalink)
Oh, okay, that is pretty unintuitive when you take it higher than 3. Wasn't expecting that, very interesting!
ZizekIsMyDad ยท 0 points ยท Posted at 18:11:30 on May 25, 2016 ยท (Permalink)
I said this in a different reply to this guy:
mandyrooba ยท 1 points ยท Posted at 18:48:02 on May 25, 2016 ยท (Permalink)
This was the only buried one that wasn't a repeat and it deserves to be higher.
maz-o ยท 1 points ยท Posted at 19:23:32 on May 25, 2016 ยท (Permalink)
What if persons A,B,C all know each other, but D,E,F don't know anybody.
[deleted] ยท 1 points ยท Posted at 19:34:10 on May 25, 2016 ยท (Permalink)
That doesn't contradict the result.
knewreddituser ยท 3 points ยท Posted at 12:55:34 on May 25, 2016 ยท (Permalink)
Where if you want to see if any number is a multiple of 3, you can add each individual number together, and if they come out to a multiple of 3, then the origional number does, as well. For example, you can tell that 45243912 is a multiple of 3 because 4+5+2+4+3+9+1+2=30
Zywakem ยท 1 points ยท Posted at 14:03:24 on May 25, 2016 ยท (Permalink)
That method is called the digital root I think.
I_swear_I_am_working ยท 5 points ยท Posted at 17:01:35 on May 25, 2016 ยท (Permalink)
My favorite (and most used) math fact is that you can instantly tell if a number is divisible by 3 by adding the numerals until they are a single digit.
21 -> 2+1 -> 3
345 -> 3+4+5 -> 12 -> 1+2 ->3
23593728 -> 2+3+5+9+3+7+2+8 -> 39 -> 3+9 -> 12 -> 1+2 -> 3
Rinse and repeat!
hailey998 ยท 1 points ยท Posted at 17:06:10 on May 25, 2016 ยท (Permalink)
Pretty crazy!!!
pertante ยท 1 points ยท Posted at 17:11:07 on May 25, 2016 ยท (Permalink)
For anything that sums to either 6 or 9 is also divisible by 3.
Spring-HeeledJim ยท 4 points ยท Posted at 10:26:27 on May 26, 2016 ยท (Permalink)
I'm quite late but I have a brilliant maths fact But there isn't enough space in this text box for me to tell you
idothingsheren ยท 2 points ยท Posted at 05:25:43 on May 28, 2016 ยท (Permalink)
u/Spring-HeeledJim's last comment
anoobitch ยท 8 points ยท Posted at 13:06:09 on May 25, 2016 ยท (Permalink)
0.9999 (repeating, of course) equals exactly 1
acejohn ยท 4 points ยท Posted at 13:50:06 on May 25, 2016 ยท (Permalink)
God dammit Leroy.
Turdsworth ยท -4 points ยท Posted at 17:47:07 on May 25, 2016 ยท (Permalink)
Only to computer. There are infinitely many numbers. These two don't equal each other.
anoobitch ยท 5 points ยท Posted at 18:08:16 on May 25, 2016 ยท (Permalink)
no actually those two are just different notations for the exact same value. There are infinite number of nines so you cannot name a single value between those two numbers.
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 21:50:24 on May 25, 2016 ยท (Permalink)
You are confusing the map with the land. The land is the real numbers. The map is the decimal representations of them. There happen to be two decimal representations for the number 1. In fact there are two decimal representations for any real number which has a finite length decimal expansion: just reduce the last digit by 1 and add infinitely many 9s to the end. It is possible to show that these two decimal expansions represent exactly the same number.
yaniniwaa ยท 6 points ยท Posted at 16:12:54 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7+........ = -1/12.
[deleted] ยท 2 points ยท Posted at 00:38:54 on May 26, 2016 ยท (Permalink)
yea, i know theres a video that says it, but i don't buy it. thats not how addition works.
mathteacher85 ยท 7 points ยท Posted at 13:23:29 on May 25, 2016 ยท (Permalink)
.9999999... is exactly equal to 1
go2kejdz ยท 2 points ยท Posted at 14:06:17 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36=666
Spacefiish ยท 2 points ยท Posted at 14:16:27 on May 25, 2016 ยท (Permalink)
1/9801, in decimal form, contains every number from 00 to 99...except for 98. So it looks like (0.0001020304...969799) and then it repeats. There's a Numberphile video about it, but I'm on mobile so I can't link it.
musicotic ยท 1 points ยท Posted at 23:49:34 on May 25, 2016 ยท (Permalink)
There is also a mathcounts video on it
[deleted] ยท 2 points ยท Posted at 14:20:04 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 16:16:02 on May 25, 2016 ยท (Permalink)
Also 7 24 25
scunliffe ยท 2 points ยท Posted at 17:30:20 on May 25, 2016 ยท (Permalink)
And the 3 x 4 x 5 triangle for ensuring 90 degree angles.
yarinpaul ยท 2 points ยท Posted at 14:23:10 on May 25, 2016 ยท (Permalink)
Not really math, but:
take any number, count the # of letters in it.
Take that number of letters and count the number of letters that the number contains.
Continue and yuo'll always get 4.
examples:
12 -> t w e l v e ->
5 -> f i v e ->
4
522 -> five hundred and twenty two ->
23 -> twenty three ->
11 -> eleven ->
6 -> six ->
3 -> five ->
5 -> five ->
4
estifu ยท 2 points ยท Posted at 17:31:02 on May 25, 2016 ยท (Permalink)
You left out a step in your first example. "Twelve" has six letters, "six" has three, "three" has five.
icantcontrolmyself ยท 1 points ยท Posted at 16:30:46 on May 25, 2016 ยท (Permalink)
Can you explain this a little better? I am still not understanding
contentsugar ยท 1 points ยท Posted at 18:18:52 on May 25, 2016 ยท (Permalink)
Take any number, write it out. Count the number of letters. Write that number out. Rinse, lather and repeat til you get to four.
Nistua1 ยท 1 points ยท Posted at 19:50:20 on May 25, 2016 ยท (Permalink)
That's because 4 is the only number, that has as many letters as it's value.
[deleted] ยท 1 points ยท Posted at 19:51:44 on May 25, 2016 ยท (Permalink)
The only values where this sequence terminates (by which I mean, it will loop back to the same value as before) are those in which the number of letters in a number equals the number itself. As far as I can see, this is only true for four.
This is a cool trick by the way.
Incomingdessert ยท 2 points ยท Posted at 14:30:43 on May 25, 2016 ยท (Permalink)
A magic number is a number where all of the number's factors (excluding the number itself) add up to give that number. For example, 6 is a magic number because 3+2+1 = 6. 496 is also a magic number. This simply blew my mind when I was 10 and still does to this day now that I'm 20.
auntfaintly ยท 1 points ยท Posted at 16:20:57 on May 25, 2016 ยท (Permalink)
Never heard these called magic numbers, always called them perfect numbers. :). I liked them too. 6. 28, 496....
Similarly "weird numbers": the sum of all of their factors (including 1 but not the number itself) is larger than the number but no combination of its factors adds up to the number itself. 70 is the smallest, they get very big quickly.
This sort of stuff is sometimes called "recreational number theory"
Incomingdessert ยท 1 points ยท Posted at 17:56:55 on May 25, 2016 ยท (Permalink)
Oh cool I think I'll have to use that one!
awepicness ยท 2 points ยท Posted at 14:36:48 on May 25, 2016 ยท (Permalink)
I really like the repeating decimal of 1/998001. It goes .001002003004 and so on until 999 but skips over 998, and then it repeats starting at 001 again!
HailOurDearLordHelix ยท 2 points ยท Posted at 14:45:23 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4... = -1/12 through Riemann normalization or something like that. It's apparently measurable in physics too.
Nighthawk0973 ยท 2 points ยท Posted at 14:57:35 on May 25, 2016 ยท (Permalink)
Mine is about probability. It's known by many as Godwin's Law.
According to Godwin's Law the longer an internet discussion goes on the closer the probability of a user mentioning Hitler or Nazis gets closer to one.
Minkar ยท 1 points ยท Posted at 21:36:36 on May 25, 2016 ยท (Permalink)
doesnt that also imply the probability of a user mentioning [insert topic] goes to one?
D-Shap ยท 1 points ยท Posted at 23:50:38 on May 25, 2016 ยท (Permalink)
Yes, and the fact that this law is often mentioned in reddit discussions also increases the chance of it occurring.
Ncurran ยท 2 points ยท Posted at 14:57:57 on May 25, 2016 ยท (Permalink)
That European people say maths and North American people say math.
dalisu ยท 2 points ยท Posted at 15:01:20 on May 25, 2016 ยท (Permalink)
6 is afraid of 7.
Minkar ยท 1 points ยท Posted at 21:36:57 on May 25, 2016 ยท (Permalink)
because 7 8 10
(in base 9)
vespertili0 ยท 2 points ยท Posted at 15:01:26 on May 25, 2016 ยท (Permalink)
0 x 0 = 0, 1 x 1 = 1 but 2 x 2 != 2
musicotic ยท 2 points ยท Posted at 23:50:19 on May 25, 2016 ยท (Permalink)
b/c x2=x-> x2-x=0-> x(x-1)=0->x=0,x=1
[deleted] ยท 2 points ยท Posted at 15:12:59 on May 25, 2016 ยท (Permalink)
Look up Banach-Tarski paradox. Basically you can cut a sphere up into 5 parts, rearrange them and make 2 identical spheres as the original
FunkyFortuneNone ยท 2 points ยท Posted at 15:14:33 on May 25, 2016 ยท (Permalink)
Noether's Theorem
This is perhaps a small amount of hyperbole but I'd consider this theorem to be the bedrock upon which we understand our physical world. Considering the importance that symmetries end up having in our understanding of the physical world around us it might not be as much hyperbole as you'd think though...
hornet54 ยท 2 points ยท Posted at 15:17:29 on May 25, 2016 ยท (Permalink)
The Banach-Tarski paradox is pretty cool. IE you can decompose a ball of given radius into two balls of equal radii.
Rajaden ยท 2 points ยท Posted at 15:26:49 on May 25, 2016 ยท (Permalink)
Hm. It appears no one has said the BanachโTarski paradox yet. Absolutely fascinating.
hi_from_brian ยท 2 points ยท Posted at 15:31:59 on May 25, 2016 ยท (Permalink)
That we have, and use, two different concepts of zero. When we count upwards we do not start at 0, but at 1. However, if we wanted to count down from 30, we would start from 30 rather than 29.
This makes the first unit of an upwards count a whole one, and the first unit of a downwards count empty, or null.
ChrisMusix ยท 2 points ยท Posted at 15:32:24 on May 25, 2016 ยท (Permalink)
That .99999... = 1
LoveHaightLove ยท 2 points ยท Posted at 15:37:41 on May 25, 2016 ยท (Permalink)*
Probably that every squared number is the previous square plus the next odd number in series. 1ยฒ=0ยฒ+1, 2ยฒ=1ยฒ+3, 3ยฒ=2ยฒ+5 etc.
Demonstrated by: xยฒ=((x-1)ยฒ)+2x-1
If you simplify the second half it's xยฒ=xยฒ
(might reformat when I get home from work, probably won't)
Edit: formatting
Echo8me ยท 2 points ยท Posted at 15:39:32 on May 25, 2016 ยท (Permalink)
Your formatting is messed up. Try putting spaces between things you don't want raised.
LoveHaightLove ยท 2 points ยท Posted at 23:26:48 on May 25, 2016 ยท (Permalink)
Holy it was more messed up than I thought. I had planned on changing it, but jesus it was fucked.
[deleted] ยท 2 points ยท Posted at 15:45:34 on May 25, 2016 ยท (Permalink)
I am obsessed with chaos. If I was going to go to grad school for math (which I considered but ultimately decided against), it would be to study chaotic dynamical systems. I love the butterfly effect (despite cringing at how it gets described/bastardized in pop culture).
Ar_Ciel ยท 2 points ยท Posted at 15:46:44 on May 25, 2016 ยท (Permalink)*
Zipf's Law applies (variation permitting) to every known language ever conceived by man!
Edit: more interesting link on the subject.
[deleted] ยท 2 points ยท Posted at 15:46:51 on May 25, 2016 ยท (Permalink)
[deleted]
Poogles86 ยท 2 points ยท Posted at 15:50:47 on May 25, 2016 ยท (Permalink)
To help more quickly determine if a number is evenly divisible by 3, add all the digits in the number, then divide. For example, 9168 would be 9+1+6+8=24. 24/3=8, and 9168/3=3056
That's the only math fact I think I know, and it's not super useful.
soggie ยท 2 points ยท Posted at 15:52:00 on May 25, 2016 ยท (Permalink)
You can go one further. 24: 2+4=6.
JJean1 ยท 2 points ยท Posted at 15:54:38 on May 25, 2016 ยท (Permalink)*
That there are always at least two points on the Earth diametrically opposite each other (antipodal points) with the exact same temperature and barometric pressure. A good explanation can be found here.
culb77 ยท 2 points ยท Posted at 15:56:43 on May 25, 2016 ยท (Permalink)
If you were to receive $100 for every second since Christ was born, it still wouldn't cover 1/3 of the US national debt.
[deleted] ยท 2 points ยท Posted at 15:58:29 on May 25, 2016 ยท (Permalink)
I have no idea what's going on in this thread.
Slacker5001 ยท 1 points ยท Posted at 19:44:56 on May 25, 2016 ยท (Permalink)
Don't feel bad at all. A lot of the comments in here are either simple math "parlor tricks" that aren't really part of standard math education or higher level stuff that I only learned after taking classes as a math major. So most people will not know or ever encounter most of the stuff mentioned in the comments.
ColonelToaster ยท 2 points ยท Posted at 16:06:09 on May 25, 2016 ยท (Permalink)
Indiana tried to pass a bill to change the value of pi to about 3.2. The only reason it didn't pass is because of the intervention of a mathematics professor that happened to be in legislature that day.
redbull26 ยท 1 points ยท Posted at 16:10:06 on May 25, 2016 ยท (Permalink)
Wow, this made my head explode.
Slacker5001 ยท 1 points ยท Posted at 19:46:48 on May 25, 2016 ยท (Permalink)
I was about to be flabbergasted but the I saw it happened in the 1800's, which makes a bit more sense. Still pretty ridiculous regardless but at least it wasn't something that happened with recent politicians thank god.
Linearts ยท 2 points ยท Posted at 16:06:49 on May 25, 2016 ยท (Permalink)
The sides of a pentagon, a hexagon, and a decagon, each inscribed in congruent circles, will form a right triangle, which is also half of a golden rectangle!
Here is an illustration.
slycat34 ยท 2 points ยท Posted at 16:06:55 on May 25, 2016 ยท (Permalink)
Taken from Alex Bellos' Here's Looking at Euclid:
explanation in the next comment
slycat34 ยท 1 points ยท Posted at 16:10:26 on May 25, 2016 ยท (Permalink)
Continued from Bellos:
Hope you all enjoy as much as I did when I read it
Gangsteier ยท 2 points ยท Posted at 16:11:02 on May 25, 2016 ยท (Permalink)*
A googolplex is such a large number that if a universe were to be measured as a googolplex meters in size, you would see repetition such that there would be exact copies of yourself throughout the universe. This is because there are only so many quantum states (a limited number of ways particles can arrange themselves) in that volume of space. Numberphile does a great explanation of this on their YouTube channel. So that would suggest every other option would have been exhausted before creating duplicates. I thought about this a lot and it's actually terrifying if it holds truth. That means everything you can think of has happened in that universe once. You existing in a heavenly utopia, and the worst hell of nightmarish imagination. A kronenberg version of yourself. A constantly tortured version of yourself. You name it and the option had to be exhausted first before we can say with 100% certainty that duplicates are being created.
Edit: Minkar's question has made me realize my statement is a bit misleading as far as every other option needing to have been use first, but to say that duplication's begin to appear with 100% certainty, each quatum state would have to be used. Though duplication's could still happen before all options are used.
Minkar ยท 1 points ยท Posted at 21:45:57 on May 25, 2016 ยท (Permalink)
Why does every configuration state have to be used before a duplicate is used?
Gangsteier ยท 1 points ยท Posted at 15:48:56 on May 26, 2016 ยท (Permalink)*
If my understanding of it is correct, you techniquely dont have to exhaust every option first for it to happen, it would actually probably be very unlikely that all options are used first without duplications. But if Im imagining duplicates being made, I assume for them to start happening with absolute certainy, everything else would have to have happened as well.
Demonsguile ยท 2 points ยท Posted at 16:11:46 on May 25, 2016 ยท (Permalink)
111,111,111 x 111,111,111 = 12,345,678,987,654,321
This, I learned at Chuck E. Cheeses.
bassinastor ยท 2 points ยท Posted at 16:30:24 on May 25, 2016 ยท (Permalink)
One that I find really interesting is that .99999999999... is exactly equal to 1. There are a bunch of different ways to prove this, but I found this one on my own when I was a kid.
If you divide any number by 9 you get zero with that number repeating in the decimal places. For example, 1/9 = 0.111... 2/9 = 0.222... 3/9 = 0.333... ... On and on until you get to 9. Following this pattern you should get 9/9 = 0.999... but what do you actually end up with? Obviously 1 because a number divided by itself is 1.
It's not the most rigorous proof but as a kid I was amazed when I found it.
babaduv ยท 1 points ยท Posted at 07:44:23 on May 26, 2016 ยท (Permalink)
And 0.99999..... is 1, so we're good ;)
pm_me_ur_fav_gif ยท 2 points ยท Posted at 16:34:39 on May 25, 2016 ยท (Permalink)
Sex Panther: 60% of the time, it works all the time.
Lvnitlarge ยท 2 points ยท Posted at 16:35:04 on May 25, 2016 ยท (Permalink)
That in the US we call it just "Math". Why must it be plural?
estifu ยท 2 points ยท Posted at 17:35:59 on May 25, 2016 ยท (Permalink)
Because it's short for "mathematics."
Tramsyrev ยท 2 points ยท Posted at 16:45:36 on May 25, 2016 ยท (Permalink)
If the hight of a pizza is a and its radius is z then the formula to calculate the pizza's volume is pizz*a.
nastyjman ยท 2 points ยท Posted at 16:47:11 on May 25, 2016 ยท (Permalink)
You can find out if a series of numbers is divisible by 3 without any remainders if you add all the numbers up.
For example...
/headrollonnumpad
244895126421
Add all the numbers:
( 2 + 4 + 4 + 8 + 9 +5 + 1 + 2 + 6 + 4 + 2 + 1 )
( 48 )
( 4 + 8 )
( 12 )
( 1 + 2 )
( 3 )
Going back to the original number, when you divide that by 3, you will get 81,631,708,807.
Add those numbers up together (the 81...807), and you'll get 49, which is not divisible by 3. You'll get some remainders on that.
davidrochman ยท 2 points ยท Posted at 16:48:40 on May 25, 2016 ยท (Permalink)
Almost all numbers contain a 3.. or any other number for that matter (summarised perfectly in this video https://www.youtube.com/watch?v=UfEiJJGv4CE)
Sandal-Hat ยท 2 points ยท Posted at 16:54:14 on May 25, 2016 ยท (Permalink)
You can add up all the numbers from 1 to x by dividing x by 2 and then multiplying it by 1 plus X. (works best for even number X's but you can just add half of X rounded up to do odd numbers)
So for 1 to 500.
500 divided by 2 = 250
1 plus 500 = 501
250 x 501 = 125,250
doe28 ยท 1 points ยท Posted at 01:57:44 on May 26, 2016 ยท (Permalink)
I believe Gauss discovered this in elementary school when his teacher assigned busy work and had students add up the numbers 1 through 100. He saw that 1+100 = 101 2+99 = 101 . . . 50+51=101. He realized that the total would be 50*101
Hence the formula for summing from 1 to n when n is even is (n/2)*(n+1)
When dealing with odd numbers, however, you would sum 1 to n-1 and add n.
For example, for n=5, we would sum 1 to 4 and add 5.
Using the formula for even sums to sum 1 to 4 and add 5, we get (4/2)(5)+5=3*5=15.
Algebraically, ((n-1)/2)(n) +n = ((n+1)/2)(n).
So the equations for summing integers from 1 to n are: Even n: (n/2)(n+1) Odd n: ((n+1)/2)(n)
phuhcue ยท 2 points ยท Posted at 16:54:35 on May 25, 2016 ยท (Permalink)
There is an infinite amount of numbers between any two whole numbers.
Obelisp ยท 2 points ยท Posted at 17:15:21 on May 25, 2016 ยท (Permalink)
Why do people keep adding the "whole number" clarification? There's an infinite amount of numbers between any two non-equal numbers. The crazy part is that there's more irrational than rational numbers between any two numbers.
phuhcue ยท 2 points ยท Posted at 17:49:24 on May 25, 2016 ยท (Permalink)
Trying to make it simple. I am not a math guy and if I get too far away from what I understand I'll cease making sense. Thanks for expanding on this idea though.
L00pback ยท 2 points ยท Posted at 16:55:20 on May 25, 2016 ยท (Permalink)
When spelling our numbers, you would have to count to one thousand before you used the letter "A".
patolcott ยท 2 points ยท Posted at 17:00:45 on May 25, 2016 ยท (Permalink)
ei*pi = -1
ballsforhire ยท 2 points ยท Posted at 17:00:55 on May 25, 2016 ยท (Permalink)
If you take out all of your intestines and lay them end to end you will die
Sidco_cat ยท 1 points ยท Posted at 17:10:48 on May 25, 2016 ยท (Permalink)
In an interesting twist, the same is true with blood vessels.
taybul ยท 2 points ยท Posted at 17:00:56 on May 25, 2016 ยท (Permalink)
If you add all the digits of any number that's a multiple of 3, that number will also be a multiple of 3.
kane49 ยท 2 points ยท Posted at 17:01:26 on May 25, 2016 ยท (Permalink)
I only recently learned that a 0% Chance doesnt mean it can't happen, its just not very likely.
Phlum ยท 1 points ยท Posted at 17:09:24 on May 25, 2016 ยท (Permalink)
Can you explain, please?
kane49 ยท 2 points ยท Posted at 17:16:17 on May 25, 2016 ยท (Permalink)*
Oh thats easy.
Pick a number between 1 and infinity.
The chance of any number being picked is a clean 0%, you still picked one though
D-Shap ยท 1 points ยท Posted at 23:58:05 on May 25, 2016 ยท (Permalink)
Not always, when working with hyperreal numbers in nonstandard analysis, 1/infinity = infinitesimal, or .0000...1. When dividing by infinity, a nonreal number, you must use nonstandard analysis, which says that there is an infinitesimal chance that you will choose the right number.
Phlum ยท 0 points ยท Posted at 18:09:15 on May 25, 2016 ยท (Permalink)
Surely the chance is something like 0.000000000001%? Or is it the same principle that 0.9-recurring = 1?
kane49 ยท 1 points ยท Posted at 18:22:47 on May 25, 2016 ยท (Permalink)
Anything divided by infinity is 0, not a small number, just 0
Phlum ยท 1 points ยท Posted at 20:53:44 on May 25, 2016 ยท (Permalink)
I'm sure there's already been endless discussion to this effect, but even so...infinity isn't really a real number, so you can't divide by it, can you?
introvertedintooit ยท 1 points ยท Posted at 21:14:04 on May 25, 2016 ยท (Permalink)
That doesn't seem right. It seems right to say the limit of 1/x as x approaches infinity is 0. And I don't know that a limit is the same thing as a final numerical answer.
duttaub1 ยท 2 points ยท Posted at 17:04:00 on May 25, 2016 ยท (Permalink)
1 = 0.9999999....
PRGuyHere ยท 2 points ยท Posted at 17:06:06 on May 25, 2016 ยท (Permalink)
I don't understand anything in this entire thread. I'm not even sure whether any/all of the submissions are jokes. I am scared.
Source: Communications major
Kaylya ยท 2 points ยท Posted at 17:06:13 on May 25, 2016 ยท (Permalink)
Birthday Problem = It takes just 23 people to have 50% odds that 2 of them share a birthday. By 70 people, the odds are 99.9%.
Toph_er ยท 2 points ยท Posted at 17:11:55 on May 25, 2016 ยท (Permalink)
This is my second comment... But I really like math. Another cool thing is Binary, Octal and Hexadecimal forms of representing numbers. This is especially useful for computer science.
Each digit place in these systems (including decimal) have a reason why those are its places.
The number of digits available for the decimal system is 0-9, so ten different digits. We call this base ten.
For example, in decimal form the first digit is what most kids learn as the "ones place". That base is the 100 digit. As we know, 100 = 1 so the first digit is the ones digit. The second digit is our tens, therefore our digit is represented as 101. And so on.
In other forms this is the same idea. In Binary, there are two possible digits, 0, or 1. So, base 2. Which means that you ask yourself how many of that digit do I have? First digit is 20 (do I have a 1?) And the second digit is 21 (do I have a 2?) And 22 (do I have a 4).
God math is cool.
Strategist-X ยท 2 points ยท Posted at 17:13:19 on May 25, 2016 ยท (Permalink)
111,111,111x111,111,111 = 12,345,678,987,654,321
samsuh ยท 2 points ยท Posted at 17:15:26 on May 25, 2016 ยท (Permalink)
the digits in multiples of 9 add up to 9.
9x2 = 18; 1 + 8 = 9
9x3 = 27; 2 + 7 = 9
9x4 = 36; 3 + 6 = 9
etc.
Miawe ยท 2 points ยท Posted at 17:15:44 on May 25, 2016 ยท (Permalink)
To quickly calculate the sum of all the numbers from 1 to x.
If x is an even number: sum = (1+x)(x/2)
If x is an odd number: sum = x(x/2)+x
(The sum of the first and the last numbers, multiplied by half the number of elements in the sequence.)
anonymous_euonymus1 ยท 2 points ยท Posted at 17:15:53 on May 25, 2016 ยท (Permalink)
The fact that any reasonably continuous function can be written as an infinite sum of complex exponentials.
BiffSniffer ยท 2 points ยท Posted at 17:17:12 on May 25, 2016 ยท (Permalink)
I enjoy the fact that once you spend years learning Algebra, you never directly use it again until you have to help your kids learn it.
pablossjui ยท 1 points ยท Posted at 23:53:25 on May 25, 2016 ยท (Permalink)
this is not true for all people
Gedrean ยท 2 points ยท Posted at 17:17:54 on May 25, 2016 ยท (Permalink)
There are more dealing combinations in a deck of cards than atoms in our galaxy
Sidco_cat ยท 1 points ยท Posted at 17:19:46 on May 25, 2016 ยท (Permalink)
That is great
Witherpixel ยท 2 points ยท Posted at 17:18:49 on May 25, 2016 ยท (Permalink)
26 is the only number numerically placed between a 25, a square (5x5), and a cube, 27(3x3x3).
KarateF22 ยท 2 points ยท Posted at 17:21:16 on May 25, 2016 ยท (Permalink)
epi*sqrt(-1) = -1
It is just fascinating that two irrational numbers and an imaginary number can be combined in a way to produce a number as simple as -1.
[deleted] ยท 2 points ยท Posted at 17:21:47 on May 25, 2016 ยท (Permalink)
Not my favorite fact per se, but my favorite demonstration: Cutting a mobius strip down the middle
Doboh ยท 2 points ยท Posted at 17:24:39 on May 25, 2016 ยท (Permalink)
It is mathematically impossible for giant or enlarged versions of normal creatures to exist, like in movies such as "honey I blew up the kids" and others. The reason is that it fucks up the ratio of units to square units to cubic units. So say you take a human and make him twice as tall, his height is doubled but his volume is 8 times bigger because volume is measured in cubic units and 23=8. So structurally humans and other creatures are designed to only support a certain size and changing one demensional aspects of a creature changes the 3 demensional aspects at a much faster rate. So we would collapse under our own weight. Also the organs are very precisely sized compared to our bodies and if we were enlarged they would not be efflient enough to sustain the body because of the same ratio imbalance.
I hope this makes sense, there are some great articles that explain it better than me.
vickster339 ยท 2 points ยท Posted at 17:25:21 on May 25, 2016 ยท (Permalink)
The sum of a consecutive infinite series of non repeating integers = -1/12....
flyingjam ยท 1 points ยท Posted at 17:35:53 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series is -1/12. The series is quite obviously divergent.
vickster339 ยท 1 points ยท Posted at 17:37:27 on May 25, 2016 ยท (Permalink)
Im drunk, throw me a bone...
flyingjam ยท 1 points ยท Posted at 17:45:52 on May 25, 2016 ยท (Permalink)
The series's divergence should be fairly obvious. Just intuitively, if you keep adding numbers that get larger, of course it will go towards infinity.
But, there are ways to assign values to divergent series. They're not "correct", but can still be useful.
If you got this from that numberphile video, they made a followup in which they address this.
ectoplasmic42 ยท 2 points ยท Posted at 17:25:50 on May 25, 2016 ยท (Permalink)
The Multiples of 9 trick using your fingers.
xerxi ยท 2 points ยท Posted at 17:26:02 on May 25, 2016 ยท (Permalink)
1+2+3+4+5... to infinity = -1/12
Yes, the sum of sequential of all positive integers is -1/12.
I would explain it, but I learned it from here: https://www.youtube.com/watch?v=w-I6XTVZXww
sisepuede4477 ยท 1 points ยท Posted at 17:27:37 on May 25, 2016 ยท (Permalink)
If it's to infinity, you won't every get an end solution.
flyingjam ยท 1 points ยท Posted at 17:35:25 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
sisepuede4477 ยท 1 points ยท Posted at 17:35:59 on May 25, 2016 ยท (Permalink)
Saw video now so I'm back. It's been years since I took calculus(this is algebra) but I don't get it, and by the time I do, I'll be stuck trying to explain it to someone else. Lol.
dominic_se ยท 2 points ยท Posted at 17:27:03 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12
Edit: https://m.youtube.com/watch?v=w-I6XTVZXww
flyingjam ยท 1 points ยท Posted at 17:34:39 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
TheUnAndOnly ยท 2 points ยท Posted at 17:29:45 on May 25, 2016 ยท (Permalink)
Not my favourite. But 12 x 12 = 144. Which coincidentally the reverse is true of 21 x 21 = 441
goofball_jones ยท 2 points ยท Posted at 17:30:41 on May 25, 2016 ยท (Permalink)
That they say "maths" in England and "math" in the US.
SQLDave ยท 2 points ยท Posted at 17:32:53 on May 25, 2016 ยท (Permalink)
Mine too! There's a series from the BBC Look Around You which spoofs those sciency shows from the 70s. One was called "Maths" and for the longest time I thought the pluralization was part of the joke. (Here it is, by the way)
CMDR_Qardinal ยท 2 points ยท Posted at 17:32:58 on May 25, 2016 ยท (Permalink)
Nine.
Any number that you get by multiplying by nine, will add up to a multiple of nine (excuse my phrasing, maths never really was my strong point).
project_valient ยท 1 points ยท Posted at 17:40:31 on May 25, 2016 ยท (Permalink)
If you keep summing the answer to a single digit you get 9.. in your last example 2+7=9.
imaoreo ยท 2 points ยท Posted at 17:38:02 on May 25, 2016 ยท (Permalink)
2+2=4 2*2=4
gets me every time
[deleted] ยท 2 points ยท Posted at 17:39:25 on May 25, 2016 ยท (Permalink)
.999... is equal to 1
Mike_B_R ยท 2 points ยท Posted at 17:41:03 on May 25, 2016 ยท (Permalink)
Gรถdel's incompleteness theorems.
Mind fucking.
[deleted] ยท 2 points ยท Posted at 17:41:46 on May 25, 2016 ยท (Permalink)
If you transpose numbers the difference is always divisible by 9.
Example 12+34+56 = 102.
Transpose each number 21+43+65=129 Difference from the original 129-102=27 divisible by 9.
Transpose just one number 12+43+56=111 Difference from original 111-102=9
Transpose just two number 21+43+56=120 Difference from original 120-102=18
This is very useful if you have to type a set of numbers and the total doesn't agree with the first set.
murlockerLOL ยท 2 points ยท Posted at 17:42:11 on May 25, 2016 ยท (Permalink)
0!=1
Kakshoo ยท 2 points ยท Posted at 17:43:23 on May 25, 2016 ยท (Permalink)
When A is 50% bigger than B, B is ~33% smaller than A.
EarlGreyDay ยท 2 points ยท Posted at 17:43:59 on May 25, 2016 ยท (Permalink)
Every finite division ring is a field.
IAmAThorn ยท 2 points ยท Posted at 17:45:40 on May 25, 2016 ยท (Permalink)
That billion actually has 12 zeros, it's something like million1 is million, million2 is billion and million3 is trillion. It's supposed to be like this, then someone in America Fucked up and it caught on.
frankstandard ยท 2 points ยท Posted at 17:50:57 on May 25, 2016 ยท (Permalink)
142857
ButtersLeopold09 ยท 2 points ยท Posted at 17:51:36 on May 25, 2016 ยท (Permalink)
If you pick a 3 digit number (such as 123) and reverse it (now 321) and subtract the two, the two digits on the outside will always add up to 9, and the digit in the middle will always be 9. In this case, 321-123= 198
Another example: 450-54= 396
.........although I doesn't work with the same digit repeated 3 times. Obviously :)
Flocculency ยท 2 points ยท Posted at 17:51:44 on May 25, 2016 ยท (Permalink)
The 23 paradox/the birthday paradox. If there are 23 randomly selected people in a room, there is a 50% chance that two of them share the same birthday.
TheSupremist ยท 2 points ยท Posted at 17:53:45 on May 25, 2016 ยท (Permalink)
How everything eventually fits and works once you think hard enough.
Forgot-My-Name_again ยท 2 points ยท Posted at 17:55:10 on May 25, 2016 ยท (Permalink)
Im(ii )=0, Re(ii ) is irrational, and in fact transcendental.
coten0100 ยท 2 points ยท Posted at 17:55:21 on May 25, 2016 ยท (Permalink)
one infinity can be bigger than another infinity
TheRussianTerminator ยท 2 points ยท Posted at 18:02:16 on May 25, 2016 ยท (Permalink)
There are as much negative number as there are postive AND negative numbers.
[deleted] ยท 2 points ยท Posted at 18:03:41 on May 25, 2016 ยท (Permalink)
That division by zero is undefined.
perverse_sheaf ยท 2 points ยท Posted at 18:06:34 on May 25, 2016 ยท (Permalink)
The behaviour of spheres of radius one in different dimensions.
A unit sphere of dimension 1 is a line with length (1-volume) 2
A unit sphere of dimension 2 is a circle with area (2-volume) pi
A unit sphere of dimension 3 is a ball with volume (3-volume) 4/3 pi
So the volumes seem to be increasing. But they actually become smaller starting at 6 and tend to 0 for larger and larger dimensions.
[deleted] ยท 2 points ยท Posted at 18:06:45 on May 25, 2016 ยท (Permalink)
If you curve a pizza slice in one direction it can't bend in the other without tearing. Because a pizza is flat and without tearing always will be.
https://en.wikipedia.org/wiki/Theorema_Egregium
Gauss's is fairly well known in the mathematics world but this is his remarkable theorem.
IAmDanimal ยท 2 points ยท Posted at 18:11:05 on May 25, 2016 ยท (Permalink)
Clearly you've never had soggy microwave pizza for breakfast.
[deleted] ยท 2 points ยท Posted at 18:20:37 on May 25, 2016 ยท (Permalink)*
You had the opportunity to eat stale cold pizza and you heated it up?
Heathen.
I once had a one night stand and had no idea where I was. Half naked I got dressed and made my way out of the bedroom to find the flat mate was reheating something, they didn't look at me and must have assumed I was whoever else lived there so they started talking at me.
I don't remember what they said as I'd just noticed the vomit on my trousers and missing shoes. I was too busy trying to work out if I would be happier if it was my own vomit or some strangers...
Finally I decided, definitely my own.
They popped something in the microwave and headed to the bathroom.
Immediately as I tried to work my way to the door a pang of hunger hit me.
By this point I had no dignity left so I popped the microwave open to find about 1/3 of a pizza some sort of meat feast. I tore the pizza in there in half and legged it out the door.
Whatever it was it was glorious and I believe helped me not have hangover gastritis/nausea. That was the one time I a pizza that had been at all reheated.
There you go, a story I've never told anyone else. Enjoy.
[deleted] ยท 2 points ยท Posted at 18:08:39 on May 25, 2016 ยท (Permalink)
.999... = 1
kazneus ยท 2 points ยท Posted at 18:11:46 on May 25, 2016 ยท (Permalink)
Probably going to get buried, but the coolest thing I've ever heard of in math (you dirty English and your extra s's) is Tarski's undefinability theorem which basically states:
It follows from Godel's Incompleteness Theorems
Anyways, it's a really powerful theorem - especially given it's connotations outside of math. That is to say it can be shown mathematically that no formalized system can formally contain it's own truth.
Another way to think of it is that it can be proven that no underlying truth cannot be completely proven by itself.
Which is just completely mind blowing if you ask me. I mean it holds for language itself.. you can't define all aspects of a language solely within the context of that language. Now it is entirely possible to prove those aspects of a language (or system of math) with a different language (or system of math). That is an acceptable consequence of the theorem.
I don't know... it just completely blows my mind. No formalized system of truths can completely contain a proof for all formal truths within that system.
Okay I'll stop rambling.
TheBonyMan ยท 2 points ยท Posted at 18:12:23 on May 25, 2016 ยท (Permalink)
There are infinite sizes of infinity.
franklywang ยท 2 points ยท Posted at 18:13:50 on May 25, 2016 ยท (Permalink)
This may be buried but one of my favorites is the contraction mapping theorem which implies that a map of the world placed on the ground will always have exactly one point which exactly aligns with the point of the world which it corresponds to.
Soviet_Cat ยท 2 points ยท Posted at 18:21:51 on May 25, 2016 ยท (Permalink)
Limit of 1x as x approaches โ is e
flyingjam ยท 2 points ยท Posted at 18:23:36 on May 25, 2016 ยท (Permalink)
Er, the limit of 1x as x->infinity is 1...
Do you mean (1 + 1/n)n as n->infinity?
cocojambles ยท 2 points ยท Posted at 18:24:40 on May 25, 2016 ยท (Permalink)
I think you mean (1 + 1/x)x
Soviet_Cat ยท 1 points ยท Posted at 19:02:26 on May 25, 2016 ยท (Permalink)
Ah yes thank you
robertjohnston276 ยท 2 points ยท Posted at 18:22:37 on May 25, 2016 ยท (Permalink)*
To find the doubling time of any given population of people or animals, you just take the growth rate and divide it into 70.
So if the population of China grows 10% every year, you just divide 70 by 10, and you get 7. Then it will take 7 years for China's population to double. (That was all made up btw that's not the actual math on China's population. Thank god.)
I think any of the mathematical constants are just so interesting. Like, how the hell did someone figure out pi? Ridiculous.
EDIT: accidentally hit send while typing.
K4mp3n ยท 1 points ยท Posted at 21:18:14 on May 25, 2016 ยท (Permalink)
pi was found by Archimedes who constructed an 97tagon where all the sides had an equal length (I don't know the english words since I am not a native speaker)
mjd638 ยท 2 points ยท Posted at 18:23:15 on May 25, 2016 ยท (Permalink)
I don't know if there is a specific name on the theorum.
But, If you take a sinusoidal signal of frequency (f) and then add together every harmonic of that signal from 1 to infinity.
Then you get a square wave of the original frequency as the result.
senatorskeletor ยท 2 points ยท Posted at 18:27:03 on May 25, 2016 ยท (Permalink)
The decimal representations of sevenths has astounded me since I discovered them. As a refresher:
1/7 = 0.142857142857... 2/7 = 0.285714285714... 3/7 = 0.428571428571... 4/7 = 0.571428571428... 5/7 = 0.714285714285... 6/7 = 0.857142857142...
Gibberish at first glance, but each fraction contains the same six digits, in the same order, in its repeating decimal form (142857), just starting with a different digit each time. How is that even possible?
BEN_therocketman ยท 2 points ยท Posted at 18:28:09 on May 25, 2016 ยท (Permalink)
4 is Numberwang!
GiggleGut ยท 2 points ยท Posted at 18:31:36 on May 25, 2016 ยท (Permalink)
Back in elementary, we learned numbers never end because you can always + 1(add 1) to the highest number you can think of.
Atomix26 ยท 2 points ยท Posted at 18:31:53 on May 25, 2016 ยท (Permalink)
If a polynomial(f(x)) of at most degree "n" has "n+1" zeros, then f(x)=0.
One can prove this just using Rolle's theorem, which states that between any two zeros of a function, there is a maximum or minimum(Exists c such that f'(c)=0, c is in [a,b])
Also, (p-1)! modulo p(the remainder function) is equal to -1 if and only if p is prime.(Wilson's theorem)
Finally, the sum of all natural numbers is equal to -1/12.
5w1m1n9 ยท 2 points ยท Posted at 18:32:36 on May 25, 2016 ยท (Permalink)
2+2=5
bitwiseshiftleft ยท 2 points ยท Posted at 18:32:58 on May 25, 2016 ยท (Permalink)
This is a little-known fact about parabolic motion and elliptical orbits.
Discounting air resistance, a thrown ball in a uniform gravitational field traces out a parabola. In geometry, a parabola is defined as the set of points which are the same distance from a particular point (the focus) and a particular line (the directrix). In this case, the directrix is horizontal because the parabola opens down. The directrix of the ball's path means something physically: the directrix represents the total energy of the ball (kinetic + gravitational potential). If at any point in its path, you redirected the ball straight upward with the same speed, it would just barely reach the directrix and then fall.
The same thing is true for planetary orbits in the 2-body problem. Discounting relativity and other planets, a planet orbits the system's center of gravity in an elliptical orbit. An ellipse is the set of points which are equidistant from a circle (I don't know a name for this, but let's call it the major circle) and a particular point inside the circle (the focus). In this case, the major circle is around the system's center of gravity. The major circle has the same significance as the directrix did: the major circle represents the total energy of the planet. If the planet's motion (and the sun's much smaller motion) were redirected exactly away from the center of mass of the system, the planet would have just enough energy to reach the major circle of its former orbit (and the sun would reach the major circle of its orbit).
Filobel ยท 2 points ยท Posted at 18:33:28 on May 25, 2016 ยท (Permalink)
I always liked the Braess' paradox, because I can bring it up whenever someone says "the solution to the traffic issues in Montreal is simple, just add more bridges!"
Basically, the paradox says that adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. In other words, adding roads can actually make the traffic worse (inversely, in some cases, you can actually improve traffic by removing roads).
Here's a theoretical example. Say 4000 people want to go from point S (start) to point E (end). There are two routes. One that goes through point A and one that goes through point B. The road that goes from S to A takes x/100 minutes to travel, where x is the number of people taking that road. The road from A to E takes 45 minutes regardless of how many people are taking it. The road from S to B also takes 45 minutes regardless, while the road from B to E takes y/100 minutes, where y is the number of people travelling that road. Basically:
S --- x/100 min ---> A --- 45 min ----> E
S --- 45 min ---> B --- x/100 min ----> E
(not sure if that's clear)
Both routes take the same total time, so we should reach an equilibrium where 2000 people take one route and 2000 people take the other. So it'll take people 2000/100 + 45 minutes = 65 minutes to go from S to E, regardless of the route they take.
Now add a road between A and B that takes a very short time to travel. Say a minute. Now, it makes no sense for any of the driver to take the direct route from S to B, because even in the worst case, where all drivers take S to A, it'll take them 4000/100 to reach A, then 1 minute to reach B from A, for a total of 41 minutes. That's shorter than 45 minutes. For the same reason, it makes no sense to take A to E. So the equilibrium is that everyone will take the route S -> A -> B -> E, which will take 81 minutes.
So adding a road between A and B adds 16 minutes travel time to everyone.
[deleted] ยท 2 points ยท Posted at 18:33:37 on May 25, 2016 ยท (Permalink)
A third and a half is a half
TimboInSpace ยท 2 points ยท Posted at 18:34:19 on May 25, 2016 ยท (Permalink)
I like that vector operations are the same in all coordinate systems, like curl, divergence, etc.
Math only really clicked for me once I realized most of my struggle was in coordinate transforms - not the concepts themselves.
ZPhox ยท 2 points ยท Posted at 18:37:35 on May 25, 2016 ยท (Permalink)
Any number that is not a decimal or fraction over 0, always equals 9 when multiplied by 9. (Add the numbers together at the end of the equations till you get a single digit)
9*83736=753867 7+5+3+8+6+7=36 3+6=9
fuzzball909 ยท 2 points ยท Posted at 18:38:36 on May 25, 2016 ยท (Permalink)
eiฯ + 1 = 0
foobar5678 ยท 2 points ยท Posted at 18:39:20 on May 25, 2016 ยท (Permalink)
0.999... = 1
There are many proofs for this, but here is the one I think best explains it. Between any two numbers, there are an infinite number of other numbers. For example, between 6.4 and 6.5, you have 6.41, 6.42, 6.421, and so on for an infinite number of numbers. But there are no numbers in between 0.9 repeating and 1. Therefore, according to the definition of a number, 0.9 repeating and 1 are the same number.
diet_pepsi_bottle ยท 2 points ยท Posted at 18:39:20 on May 25, 2016 ยท (Permalink)
.99999... = 1
illtakethebox ยท 2 points ยท Posted at 18:40:20 on May 25, 2016 ยท (Permalink)
does anyone else find it rather mindblowing that we are a species that uses imaginary concepts like this to explain our universe, and it actually works?
stwhn ยท 2 points ยท Posted at 18:41:23 on May 25, 2016 ยท (Permalink)
The volume of a pizza with radius (z) and depth (a) equal to pi ร z ร z ร a
StruckingFuggle ยท 2 points ยท Posted at 18:42:20 on May 25, 2016 ยท (Permalink)
That .9 repeating equals 1.
Wait, did you say "favorite" or "most bullshit"?
Kulaid871 ยท 2 points ยท Posted at 18:43:41 on May 25, 2016 ยท (Permalink)
Computer math and actual math may differ. 1 + 1 = 3 is possible using computers.
rumplebike ยท 2 points ยท Posted at 18:43:52 on May 25, 2016 ยท (Permalink)
We do not know if exp(pi) is irrational.
qqqqqqqq4 ยท 2 points ยท Posted at 18:44:43 on May 25, 2016 ยท (Permalink)
This one may not be the most complicated or cool to others, but I love how any number to the power of zero is 1.
CounterCulturist ยท 2 points ยท Posted at 18:45:06 on May 25, 2016 ยท (Permalink)
Simple palindromic effect from 1 base digit.
Pick any single digit number aside from 0. In this case I'll choose 5. Now create a number composed only of that digit with the digit count corresponding to number you chose which in this case would be:
55555 (a 5 digit number composed only of 5s)
Now square the number:
55555 x 55555 = 3,086,358,025
Now divide the answer by the single digit you chose, squared: 5x5 = 25 -> 3,086,358,025/25 = 123454321
As you can see we have a counting palindromic number that plateaus at the original digit and then counts back down. Works for any single digit number.
Examples:
(999999999x999999999) / 81 = 12345678987654321
(7777777x7777777) / 49 = 1234567654321
(4444x4444) / 16 = 1234321
Came up with this in pre-calculus and it has entertained me ever since.
i_think_therefore_i_ ยท 2 points ยท Posted at 18:47:08 on May 25, 2016 ยท (Permalink)
Q: If you take two apples from three apples, what have you got?
A: Two apples.
notmike11 ยท 2 points ยท Posted at 18:48:01 on May 25, 2016 ยท (Permalink)*
If you multiply a 2 digit number by 11, you can add the ones and tens digit, put it in the middle of the tens and ones digit, and have the correct answer.
Examples:
10* 11: 1+0 = 1, so 110
63* 11: 6+3 = 9, so 693
If the sum of the 1s and 10s digits is a two digit number, just subtract 10 and add 1 to the tens digit:
19* 11: 1+9 = 10, so 209
89* 11: 9+8= 17, so 979
giganticpine ยท 2 points ยท Posted at 18:49:51 on May 25, 2016 ยท (Permalink)
Sorry I'm late to the party but I had one I couldn't find in the comments:
There are only two positive integers (besides 1) that can solve the equation xy = yx
24 = 42
yoLeaveMeAlone ยท 2 points ยท Posted at 18:53:31 on May 25, 2016 ยท (Permalink)*
Euler's identity:
ei*ฯ +1 = 0
It contains the three basic mathematical operations each once (addition, multiplication, exponentiation), as well as all 5 fundamental mathematical constants each once (0, 1, e, i, ฯ).
It is widely considered the most beautiful mathematical equation.
EngelbertHerpaderp ยท 2 points ยท Posted at 18:58:10 on May 25, 2016 ยท (Permalink)
The fact I'm done with college and never have to take another goddamn math class ever again.
SugarMafia ยท 2 points ยท Posted at 19:00:13 on May 25, 2016 ยท (Permalink)
Pi is an infinitely long, random number. Meaning every combination of every number exists. So if you convert the numbers to ASCII text, your name, birthday, everything about you shows up at some point in the infinitely long list of numbers.
Guppy-Fish ยท 2 points ยท Posted at 19:01:24 on May 25, 2016 ยท (Permalink)
ei*pi + 1 = 0
[deleted] ยท 2 points ยท Posted at 19:08:32 on May 25, 2016 ยท (Permalink)
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
gbs5009 ยท 2 points ยท Posted at 19:31:50 on May 25, 2016 ยท (Permalink)*
You can also check if any number is divisible by 11 by alternating adding or subtracting the digits, and seeing if the result is zero.
1 - 2 + 1 = 0, so 121 IS divisible by eleven 2 - 1 + 1 = 0, so 231 must be as well. 8 - 2 + 3 - 8 = 1, so 8,238 is NOT divisible by eleven.
thedispatcher ยท 2 points ยท Posted at 19:08:40 on May 25, 2016 ยท (Permalink)
83% of statistics are made up.
20mcgug ยท 1 points ยท Posted at 19:50:14 on May 25, 2016 ยท (Permalink)
Actually it's 76.38%
_Sigmund_Fraud_ ยท 2 points ยท Posted at 19:09:43 on May 25, 2016 ยท (Permalink)
When there are 23 people in a room, there is a 50% chance that two have the same birthday. Increasing to 70 people gets you to 99.9%. Here is more information on it.
Major_Lee_Garsol ยท 2 points ยท Posted at 19:11:02 on May 25, 2016 ยท (Permalink)
Benford's Law : https://en.wikipedia.org/wiki/Benford%27s_law
Most numbers begin with 1.
mcdincely ยท 2 points ยท Posted at 19:11:20 on May 25, 2016 ยท (Permalink)
The "B" in Benoit B. Mandelbrot stands for Benoit B. Mandelbrot.
dannystoll84 ยท 1 points ยท Posted at 19:17:05 on May 25, 2016 ยท (Permalink)
An anagram for Banach-Tarski is spoiler
Gwinjey ยท 2 points ยท Posted at 19:14:50 on May 25, 2016 ยท (Permalink)
The fact that Americans don't call it maths
allltogethernow ยท 2 points ยท Posted at 19:17:30 on May 25, 2016 ยท (Permalink)
This is from Bertrand Russell and his realization while advancing/developing set theory.
The setup:
You can have a set of sets, like "numbers" is a set of "even numbers" and "odd numbers", which are sets, too.
You can also have a set that includes itself, like "sets that have more than 10 items", might have 11 items, then it would be inside it's own set. This stuff is all very fundamental to set theory (I wouldn't understand it if it wasn't), and in turn, all of mathematics itself, since set theory was developed as a foundation for modern mathematics.
The problem happens when you try to create a set of all "sets that don't contain themself". You can't do it. A set of sets that don't contain themself is itself a set that doesn't contain itself, and thus is a member of itself. It is a paradox.
This paradox was later evidenced to claim that there is a fundamental problem in the logical makeup of conventional "true"/"false" mathematics, and contributed to the development of a different type of math that we now use every day (because it works) called fuzzy math.
PersonUsingAComputer ยท 2 points ยท Posted at 19:30:43 on May 25, 2016 ยท (Permalink)
It's true that Russell's paradox caused problems for naive set theory and that mathematicians had to come up with something else to deal with it, but the replacement wasn't fuzzy math and the paradox doesn't reveal any sort of fundamental problem in the logic of true/false mathematics. The replacement for naive set theory was Zermelo-Fraenkel set theory, which actually gives rigorous axioms for the behavior of sets and isn't vulnerable to Russell's paradox or similar problems. There is no way to define "the set of all sets that don't contain themselves" in ZF set theory. This theory, with the Axiom of Choice added in, provides an abstract basis for almost all modern mathematics. Fuzzy logic is a perfectly valid field of mathematics, but it's not like Boolean logic is invalid or has been replaced.
allltogethernow ยท 1 points ยท Posted at 20:13:43 on May 25, 2016 ยท (Permalink)
I only claimed that it contributed to the development of fuzzy math, not that fuzzy math in any way replaces boolean logic. That's not my territory to argue. It did force the development of the axiom of choice, though, which, I am not going to pretend that I understand fully. I just find the fact that the paradox was so elegant very pleasing, and I'm not really sure (though I would like to know) what the historical controversy was motivated by when ZF set theory was initially introduced.
PersonUsingAComputer ยท 1 points ยท Posted at 20:49:51 on May 25, 2016 ยท (Permalink)
The Axiom of Choice is an entirely unrelated issue to Russell's paradox. ZF without Choice doesn't fall victim to Russell's paradox either, and if it did adding in the Axiom of Choice wouldn't save it. The Axiom of Choice was suggested because it resolves many otherwise undecidable problems that many mathematicians feel should be decidable.
[deleted] ยท 2 points ยท Posted at 19:21:50 on May 25, 2016 ยท (Permalink)
That I passed college math at all.
paanwala ยท 2 points ยท Posted at 19:22:58 on May 25, 2016 ยท (Permalink)
Four colors suffice
mykman1 ยท 2 points ยท Posted at 19:23:54 on May 25, 2016 ยท (Permalink)
There is a function with bounded derivative but that derivative is not integrable.
https://en.wikipedia.org/wiki/Volterra%27s_function
[deleted] ยท 2 points ยท Posted at 19:24:32 on May 25, 2016 ยท (Permalink)*
[deleted]
brutalyak ยท 0 points ยท Posted at 20:33:49 on May 25, 2016 ยท (Permalink)
First, the derivative calculates the slope of a tangent line, and integral calculates the area under the curve. Secondly, velocity is the first derivative of position, because it is defined that way. Lastly, calculus relates to physics so well, because it was invented by Isaac Newton to study physics.
mitten_slap ยท 2 points ยท Posted at 19:28:30 on May 25, 2016 ยท (Permalink)
That they say "Maths" in Britain when they mean "Math."
haXterix ยท 1 points ยท Posted at 19:42:58 on May 25, 2016 ยท (Permalink)*
No. "Maths" in British English is no more incorrect than "Math" in USA. You might as well say 'They say "cerveza" in Spain when they mean "beer"'.
EGRValve ยท 2 points ยท Posted at 19:34:49 on May 25, 2016 ยท (Permalink)
Using only 4 colors, you can color in any set of shapes on a plane so that no two adjacent regions have the same color.
Arphahat ยท 2 points ยท Posted at 19:40:27 on May 25, 2016 ยท (Permalink)
.9 repeating equals 1. Not "is really really close to 1," but actually is exactly equal to 1.
noirhero ยท 2 points ยท Posted at 19:43:10 on May 25, 2016 ยท (Permalink)
0.9 repeating actually equals 1.
It's simple but that's why I like it.
elplumarojo ยท 2 points ยท Posted at 19:43:56 on May 25, 2016 ยท (Permalink)
If you multiply 9 by any other number, and add up those digits, you get 9 every time.
MamuTXD ยท 2 points ยท Posted at 19:48:09 on May 25, 2016 ยท (Permalink)
6+9+(6*9)=69
ImaginationOfABrick ยท 2 points ยท Posted at 19:49:44 on May 25, 2016 ยท (Permalink)
80 divided by 81
ibrentlam ยท 2 points ยท Posted at 19:51:13 on May 25, 2016 ยท (Permalink)
There are approximately pi * 107 seconds in a year. (actual number: 31,536,000) Handy if you ever have a pi in the denominator you need to cancel.
Liebonaut ยท 2 points ยท Posted at 19:51:44 on May 25, 2016 ยท (Permalink)
If i is defined as โ-1, ii is a real number and is roughly equal to 0.208.
Proof: think of the complex coordinate plane, where each point is a number a+bi, a describes the horizontal coordinate, and b describes the vertical coordinate. Converting to polar coordinates, each point can be represented RรeiA where R is distance from the origin and A is the angle from the positive x-axis in radians.
In this case, eiฯ is the point on a circle of radius 1 (the unit circle) which is ฯ radians or 180ยฐ from the x-axis. It has a value of -1+0i, which is why eiฯ = -1.
What if we only go 90ยฐ from the x-axis? That point is on the y-axis, so it's equal to 0+1i. Also, 90ยฐ is ฯ/2 in radians, so eiฯ/2 = i.
If you raise both sides to the power of i, then ii = ei2 รฯ/2 . But i2 is -1, so ii = e-ฯ/2.
dannystoll84 ยท 1 points ยท Posted at 20:25:10 on May 25, 2016 ยท (Permalink)
... using a particular branch of the logarithm.
Liebonaut ยท 1 points ยท Posted at 12:04:07 on May 26, 2016 ยท (Permalink)
What do you mean?
dannystoll84 ยท 2 points ยท Posted at 13:47:21 on May 26, 2016 ยท (Permalink)
Essentially, complex exponention is not always uniquely defined, since the complex logarithm is not uniquely valued (since e2ฯi=1, the map z -> exp(iz) is 2ฯ-periodic, so it has no continuous global inverse). On the other hand, we may define the logarithm on large regions of the complex plane -- the maximal regions looking like the hole plane minus a ray outward from 0. The "principal branch" is defined everywhere but for the negative reals, and gives the standard real-valued logarithm when applied to a positive real. But we could of course choose infinitely many other branches defined on the same region, by simply adding 2ฯi to everything.
Now if z=ii, then log(z) = i log(i), so that z = exp(iโขlog(i)). These operations are well-defined since the complex logarithm is a right inverse, or section, of the exponential map, though it is not a left inverse (that is, log(ew) does not in general equal w). But anyway, we obtain z = exp(iโขlog(i)). Solving for w=log(i) we have exp(w)=i, so if w=a+bi, then exp(w)=eaโข(cos(b)+i sin(b))=i, so that cos(b)=0, and since ea is positive for a real, we have sin(b)>0, so sin(b)=1. Hence a=0 and b=ฯ/2+2ฯn for any n.
Thus z=exp(ฯ(1/2+2n)) is a solution to z=ii for all integers n. The principal branch of the logarithm gives n=0, so that ii=exp(ฯ/2) ~= 0.203.
Liebonaut ยท 1 points ยท Posted at 14:32:20 on May 26, 2016 ยท (Permalink)
Oh, duh! So 0.208 is a solution to z=ii, but any z=exp(ฯ/2+2ฯn) satisfies it.
dannystoll84 ยท 1 points ยท Posted at 15:23:29 on May 26, 2016 ยท (Permalink)
Indeed. Notably, all solutions are positive reals.
Borthralla ยท 2 points ยท Posted at 19:52:26 on May 25, 2016 ยท (Permalink)
If you folded a paper 92 times, it's thickness would exceed the diameter of the observable universe.
loptthetreacherous ยท 1 points ยท Posted at 20:55:22 on May 25, 2016 ยท (Permalink)
It's actually ~104 times:
Piece of paper thickness: 0.05mm
Size of observable universe: 8.8ร1026 m = 8.8ร1029 mm
(8.8x1029 )/0.05=1.76*1031
logbase2 (1.76*1031) = 103.79
Borthralla ยท 1 points ยท Posted at 21:19:11 on May 25, 2016 ยท (Permalink)
Yes, I think you're right. Another one with numbers is that 1 google raindrops would be able to fill the observable universe more than 100 trillion times.
cmnthom ยท 2 points ยท Posted at 19:57:48 on May 25, 2016 ยท (Permalink)
If you transpose numbers, the difference will always be divisible evenly by 9.
84 - 48 = 36 (4*9)
Also works with more than two digits.
654 - 456 = 198 (22*9)
546 - 465 = 81 (9*9)
9018 - 1089 = 7929 (881*9)
Ashallond ยท 2 points ยท Posted at 20:00:45 on May 25, 2016 ยท (Permalink)
Euler's Equation.
ei*pi +1= 0.
Simple equations that have the five basis numbers in complex mathematics all in one equation.
ebbomega ยท 2 points ยท Posted at 20:01:26 on May 25, 2016 ยท (Permalink)
If you prove some function f(x) for x = 1, and you prove that given f(n) is true, f(n+1) must also be true, you prove it true for all positive integers.
Inductive reasoning is my favourite part of math.
loptthetreacherous ยท 1 points ยท Posted at 20:41:41 on May 25, 2016 ยท (Permalink)
When I first learned about inductive reasoning, it blew my mind. As a kid, I always thought "how do they know that's true for every number", but it's so simple.
qwertyphant ยท 2 points ยท Posted at 20:06:53 on May 25, 2016 ยท (Permalink)
Numberphile's Youtube Channel
jigielnik ยท 2 points ยท Posted at 20:15:18 on May 25, 2016 ยท (Permalink)
The fact that British people call it "maths"
dao2 ยท 2 points ยท Posted at 20:15:31 on May 25, 2016 ยท (Permalink)
That most of it can be done on a calculator.
demafrost ยท 2 points ยท Posted at 20:17:58 on May 25, 2016 ยท (Permalink)
My favorite math fact is that in the UK they call it "maths"
StevenXC ยท 2 points ยท Posted at 20:18:04 on May 25, 2016 ยท (Permalink)
Late to the party, but if you believe the Axiom of Choice...
Infinitely many mathematicians wake up blindfolded in a room. They are told that each mathematician is wearing a either a black or white hat. They will be given time to strategize while blindfolded (and have infinite memory, etc. etc.). Once their blindfolds are removed, they will be able to see every other mathematician's hat color, but they cannot communicate. Then, they must all simultaneously guess the color of their own hat. If infinitely many of the mathematicians guess incorrectly, they will all be executed; otherwise, they all survive.
There exists a strategy which guarantees that these mathematicians will survive.
StevenXC ยท 1 points ยท Posted at 22:17:21 on May 25, 2016 ยท (Permalink)*
The solution (spoilers):
The mathematicians apply the following equivalence relation on hattings: say two hattings are equivalent if they differ by only finitely many hats. Then, they may use the choice function from the Axiom of Choice to identify a representative for each equivalence class of hattings. So, when they can see each other, they have enough information (every hat but their own) to identify the representative for the equivalence class of hattings which includes their actual hatting. So, each person should guess their hat based on that representative hatting, which differs only finitely often from the actual hatting. Thus they survive to be kidnapped another day.
Atheist_Simon_Haddad ยท 2 points ยท Posted at 20:22:07 on May 25, 2016 ยท (Permalink)
The sum of any two consecutive triangular numbers is a square number.
SuperSaiyanSandwich ยท 2 points ยท Posted at 20:23:23 on May 25, 2016 ยท (Permalink)
This thread is very old and likely dead but I noticed a number pattern at a very young age I'm still fond of. If you add every successive odd number you always get a perfect square.
1 + 3 = 4 ... 4 + 5 = 9 ... 9 + 7 = 16 ... 16 + 9 = 25 etc.
Does anyone know if there's some kind of theorem or law for this or anything? It's pretty trivial observation so I know someone's seen it before, just didn't know if it was useful in any way.
loptthetreacherous ยท 3 points ยท Posted at 20:32:34 on May 25, 2016 ยท (Permalink)
Here is the proof of it.
SuperSaiyanSandwich ยท 2 points ยท Posted at 20:36:11 on May 25, 2016 ยท (Permalink)
Awesome! Thank you. 5th grade me with the shower thought actually did come up with something interesting haha
HoboMasta ยท 2 points ยท Posted at 20:38:08 on May 25, 2016 ยท (Permalink)*
It could be useful if you don't know a biggish number's square.
The pattern you recognized follows the form:
(nยฒ) + (2n + 1) = (n+1)ยฒ
So for example someone asks you what is 61ยฒ. You probably don't know that off the top of your head, but 60ยฒ (3600), is simple to remember.
So you just do 3600 + ( 2*60 + 1) = 3721 which is 61ยฒ.
It's easy to multiple a number by 2 and add 1. Just add that to the previous square and you have the next square.
tl;dr If you know the previous number's square, you can find the next number's square relatively simply.
SuperSaiyanSandwich ยท 2 points ยท Posted at 20:39:54 on May 25, 2016 ยท (Permalink)
Very cool. Had not thought of that application, thanks!
hpennco ยท 2 points ยท Posted at 20:26:02 on May 25, 2016 ยท (Permalink)
Multiplying numbers by 11
25*11 is 275, take the first number, 2, then add 1st and 2nd 7 then 3rd number 5
you can do it with larger numbers and when 2 numbers are over 10, just carry it just as with addition
49*11 is 539
jlog2304 ยท 2 points ยท Posted at 20:26:06 on May 25, 2016 ยท (Permalink)
One of my favourite facts is the birthday problem, which says that in a group of 23 people there is a c.51% chance that any two people share a birthday
Shophaune ยท 2 points ยท Posted at 20:27:42 on May 25, 2016 ยท (Permalink)
1 + Omega =/= Omega + 1
j4c0p ยท 2 points ยท Posted at 20:31:43 on May 25, 2016 ยท (Permalink)
When you celebrate 27th birthday it should be BIG party.
It is the last time you will have nn years .
DaDarkDragon ยท 2 points ยท Posted at 20:33:08 on May 25, 2016 ยท (Permalink)
5318008
mchubbuck ยท 2 points ยท Posted at 20:36:35 on May 25, 2016 ยท (Permalink)
That .99999.... is really just equal to 1
X = .9999...
10X = 9.9999...
10X-X = (9.9999...)-(.9999...)
9X = 9
X = 1
Calculus teacher showed us that a couple years ago, and my mind was blown
res30stupid ยท 2 points ยท Posted at 20:37:15 on May 25, 2016 ยท (Permalink)
Digital root, where you repeatedly add up a series of numerical digits until you get a single digit. For example, 2 + 4 + 5 + 7 + 8 = 26, then 2 + 6 = 8. So in this case, Digital Root = 8.
But it goes beyond that. If you laid out the numbers of base-10, 0-9, it'd show that 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45, then 4 + 5 = 9.
But if you were to go above base-10 into base-20, which would use a in place of the traditional number 10, b = 11, c = 12, converting them back into base 10 and getting the letters' digital roots then the digital root would, until j, would match with the traditional numerical cypher of the letters.
a = 10, 1 + 0 = 1. b = 11, 1 + 1 = 2.
Also, the digital root of Supercalifragilisticexpialidocious is 1.
Translated from base-36 to base-10, supercalifragilisticexpialidocious = 65791925216734442002988169043447582627179158156970580. Adding the digits together, the sum is 244.
2 + 4 + 4 = 10, 1 + 0 = 1.
And for those who spotted the reference in the first sum... well done.
red_hare ยท 2 points ยท Posted at 20:39:21 on May 25, 2016 ยท (Permalink)
The birthday problem states that with just 23 people you have a 50% chance of at least two people sharing the same birthday.
With a real random sample of people however, the probability is higher because birthdays aren't uniformly random. C-sections are rarely scheduled for weekends or holidays.
Megacherv ยท 2 points ยท Posted at 20:44:55 on May 25, 2016 ยท (Permalink)
I love that the sum of the sequence of all positive integers (I.e. Every positive whole number added together) is neither positive, nor is it an integer. It's -1/12.
https://www.youtube.com/watch?v=w-I6XTVZXww for an explanation
ihatedogs2 ยท 2 points ยท Posted at 20:48:13 on May 25, 2016 ยท (Permalink)
0.999999999... is exactly equal to 1. Don't believe me? Let's say n = 0.999999999... Then 10*n = 9.99999999... But 9 + n also equals 9.999999999... Therefore 10n = 9 + n so 9n = 9 and n = 1.
EthansBroadcast ยท 2 points ยท Posted at 20:50:29 on May 25, 2016 ยท (Permalink)
Negative minus Negative equals a Positive which is completely opposite of real life lol
MrBenBlanco ยท 2 points ยท Posted at 20:52:02 on May 25, 2016 ยท (Permalink)
60 percent of the time, it works every time.
_emordnilaP ยท 2 points ยท Posted at 21:05:49 on May 25, 2016 ยท (Permalink)
Late to the party but I still love this one.
If the digits of a certain number add up to a number divisible by three, than than the original number is divisible by three.
Ex: 1,578. 1+5+7+8=21 21รท3=7 1578รท3=526
PM_ME_UR_GALLADE ยท 2 points ยท Posted at 21:09:56 on May 25, 2016 ยท (Permalink)
-40ยฐ is the same in Fahrenheit and Celsius.
danwhite89 ยท 2 points ยท Posted at 21:16:19 on May 25, 2016 ยท (Permalink)
Don't know if it's been posted cos there's 8525 posts so far, but...
Hey diddle diddle, the medianโs the middle,
You add then divide for the mean,
The mode is the one that you see the most,
And the range is the difference between.
[deleted] ยท 2 points ยท Posted at 21:18:51 on May 25, 2016 ยท (Permalink)
1+1=2
gbtimmon ยท 2 points ยท Posted at 21:22:01 on May 25, 2016 ยท (Permalink)*
1 = .999999 repeating
TheAmbivalante ยท 1 points ยท Posted at 21:43:52 on May 25, 2016 ยท (Permalink)
The Repating Theorem
Willy-FR ยท 2 points ยท Posted at 21:24:28 on May 25, 2016 ยท (Permalink)
It keeps you up all night.
Oh wait.
Math.
Right.
Never mind.
NatasEvoli ยท 2 points ยท Posted at 21:24:55 on May 25, 2016 ยท (Permalink)
.999(repeating) and 1 are the exact same number and there is no way mathematically to disprove that.
eightk1ll ยท 2 points ยท Posted at 21:26:15 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers equals -1/12
johnb51654 ยท 2 points ยท Posted at 21:26:17 on May 25, 2016 ยท (Permalink)
9 is cool. Multiply nine by anything and take the outcome and ad the two numbers together and they always make nine. Example - 9x3=27, 2+7=9. 9x5=45, 4+5=9.
MustangTech ยท 1 points ยท Posted at 21:29:34 on May 25, 2016 ยท (Permalink)
thats an extension of the trick to see if a number is divisible by three, because 32 is 9
johnb51654 ยท 1 points ยท Posted at 21:34:18 on May 25, 2016 ยท (Permalink)
Guess what.
SlinkiusMaximus ยท 2 points ยท Posted at 21:28:21 on May 25, 2016 ยท (Permalink)
I consider myself a fairly intelligent person (perhaps that's a mistake), but I don't understand most of these...
Kronos111 ยท 2 points ยท Posted at 21:31:33 on May 25, 2016 ยท (Permalink)
90% of statistics posted in reddit comments are totally made up.
needMastersSupport ยท 2 points ยท Posted at 21:32:53 on May 25, 2016 ยท (Permalink)*
For any real number N, N=(N-1)+(N+1)/2.
That is FACT, my friend, obvious TRUTH, and you can test it out your self with pen and paper, any number, pick any positive number that is REAL, and there you are. You think about that. You put that in your pipe and smoke it.
Don't listen to these "fractionists" or "calculars", you work it out for yourself using basic Pythagorean Principles, which are explained ONE TWO THREE in my Pythagorean Principles for Life, available for a love donation, or no donation at all, all you have to do is ask, My Friend, and the secrets of the Universe can be yours, don't listen to these other Charlatans, they pronounce "GOD particles" swarming around you, taking away your Free Will, do not listen to them, ORDER NOW my GUARANTEED MATHEMATICS based on Pythagoras, only $1 thin dollar postage paid. Step right up, all orders insured.
feistyfoodie ยท 2 points ยท Posted at 21:33:40 on May 25, 2016 ยท (Permalink)
Numbers in all languages are the same.
{Yes, this is a movie reference.}
[deleted] ยท 2 points ยท Posted at 21:53:48 on May 25, 2016 ยท (Permalink)
0.999...(recurring) and 1 are the same number.
prototype31695 ยท 2 points ยท Posted at 21:57:13 on May 25, 2016 ยท (Permalink)
The transitive property. Makes me feel better about myself sometimes.
I high fived a girls hand. Her hand has touched her boob, By the transitive property, I high fived her boob.
chickenboy2064 ยท 2 points ยท Posted at 21:59:15 on May 25, 2016 ยท (Permalink)
.99999... = 1
It doesn't approach 1, it is the exact same fucking thing as 1.
rinzler83 ยท 2 points ยท Posted at 21:59:16 on May 25, 2016 ยท (Permalink)
That this similar thread got posted like a week ago and have many of the same responses.
BassoVoce ยท 2 points ยท Posted at 22:00:41 on May 25, 2016 ยท (Permalink)
One million seconds is about 11.5 days.
One billion seconds is about 31.7 YEARS.
[deleted] ยท 2 points ยท Posted at 22:02:46 on May 25, 2016 ยท (Permalink)
0! = 1
00 is undefined (one would think 1 going by the exponent; 0 otherwise)
craaaaazy1 ยท 2 points ยท Posted at 22:04:17 on May 25, 2016 ยท (Permalink)
111,111,111 X 111,111,111 = 12345678987654321
VelourFogg ยท 2 points ยท Posted at 22:05:40 on May 25, 2016 ยท (Permalink)
As an avid board gamer, non-transitive dice blow my mind. Basically it's pools of one or more dice that exhibit a kind of rock -paper-scissors behavior. Dice A beats dice B, dice B beats dice C, and C beats A. It's gets even weirder when you add more dice pools or 2 dice per pool. Here's a video that illustrates it better than I can explain http://youtube.com/watch?v=zWUrwhaqq_c
TheSilverNoble ยท 2 points ยท Posted at 22:09:41 on May 25, 2016 ยท (Permalink)
That in some places it's called "maths."
joker_of_the_deck ยท 2 points ยท Posted at 22:18:49 on May 25, 2016 ยท (Permalink)
"base 10" is a misnomer.
if, say, we used 7 digits throughout our history instead of our 10 digits, our number line would go, '0,1,2,3,4,5,6,10,11,12,13,14,15,16,20...โ; becoming our 'base 10'.
fun fact: our weeks are in base 7. I guess Monday would be the 0.
lazyl ยท 2 points ยท Posted at 22:44:50 on May 25, 2016 ยท (Permalink)*
It's not a misnomer. It is correctly named 'base 10'. Your point is just that all base systems, when described using a number from their own base, would always be referred to as 'base 10'. Still an interesting observation though.
loptthetreacherous ยท 1 points ยท Posted at 22:39:53 on May 25, 2016 ยท (Permalink)
You're wrong, base 10 is correct. When you say "base x" the x is always said in base 10.
In your example, you said if we used base 7 throughout our history we would still say base 10, of course because then when we say "base x", the x would always be in base 7.
joker_of_the_deck ยท 1 points ยท Posted at 22:44:49 on May 25, 2016 ยท (Permalink)
we call it base 7 because we speak in base 10. what would we call it if we spoke in base 7?
loptthetreacherous ยท 1 points ยท Posted at 22:53:30 on May 25, 2016 ยท (Permalink)
Base 13
dgriffith ยท 1 points ยท Posted at 22:41:41 on May 25, 2016 ยท (Permalink)
No, it would be called "base 7".
eg. "base 2" (binary) signifies that there are 2 symbols in use, 0 and 1.
"base 8" (octal) signifies that there are 8 symbols in use, 0-7.
"base 10" (decimal) signifies that there are 10 symbols in use, 0 to 9.
"base 16" (hexadecimal) signifies that there are 16 symbols in use, 0-9 and A-F.
"10" in any base signifies that you've reached the extent of your available symbols and you're back to the first one (0), with an overflow count in the column to the left.
(And Excel has a setting that lets you start numbered days of the week with zero on either Monday or Sunday)
joker_of_the_deck ยท 1 points ยท Posted at 22:44:37 on May 25, 2016 ยท (Permalink)
we call it base 7 because we speak in base 10. what would we call it if we spoke in base 7?
Motivatedformyfuture ยท 2 points ยท Posted at 22:19:35 on May 25, 2016 ยท (Permalink)
There is a curve called a cycloid in which no matter where you start a ball on this curve it will take the same amount of time to get to the end whether it starts 800 miles away or 5 inches. (while in a vacuum and friction is not a factor)
lazyl ยท 1 points ยท Posted at 22:39:57 on May 25, 2016 ยท (Permalink)
I assume you mean a ball accelerated only by gravity? Interesting.
Motivatedformyfuture ยท 1 points ยท Posted at 00:30:18 on May 26, 2016 ยท (Permalink)
That is correct. A mathematician (in the last 200-300 years? I don't remember anyway grandfather clocks were still a thing. The problem with them was that if you didn't start the pendulum at the right spot it wouldn't keep good time.
This mathematician designed a pendulum that followed a cycloid curve so it didn't matter where the pendulum was started. That said it was far too expensive to produce but interesting none the less.
Lotion-in-the-Basket ยท 2 points ยท Posted at 22:24:57 on May 25, 2016 ยท (Permalink)
0! = 1
Proof:
bobofthecpu ยท 2 points ยท Posted at 22:29:44 on May 25, 2016 ยท (Permalink)
I love epi*i+1=0 because it contains all the most important numbers, and after I took my first complex variables class, I was blown away by how this comes about, and how it should be written epi*i= -1
Dr_Scientist_ ยท 2 points ยท Posted at 22:36:42 on May 25, 2016 ยท (Permalink)
One and the square root of two have no common multiples. If you started counting numbers 1, 2, 3 and so on - and I started counting sqrt 2, 2 times sqrt 2, 3 times sqrt 2 and so on we would never say the same number.
I remember staying up at night thinking about it. There must be some way to rationalize sqrt 2. Sqrt 2 squared is two after all. But one sqrt 2 times isn't a multiple of one.
If you drew a line horizontally and a second line from the same point diagonally at 45 degrees, then marked out one inch intervals on both lines - there would NEVER be a point at which the intervals line up vertically. Never. Surely they would meet once in all the infinity numbers but they wont.
mikecheck0123 ยท 2 points ยท Posted at 22:40:17 on May 25, 2016 ยท (Permalink)
If a pizza has radius 'z' and depth 'a', it's volume is measure as pizz*a.
604WORLDWIDE ยท 2 points ยท Posted at 22:51:00 on May 25, 2016 ยท (Permalink)
One learned from blackjack training years ago. If you have 3 consecutive numbers (ex. 6,7,8) you can always multiply the middle number by 3 to get the total (7x3=21 or 6+7+8= 21)
Unrelated gambling fun fact: if you take the numbers on a roulette wheel 1-36 and add them (1+2+3...all the way to 36) the number you end up with is the mark of the beast 666. ๐น
Edit: added "by 3"
Pianohombre ยท 2 points ยท Posted at 22:53:41 on May 25, 2016 ยท (Permalink)
This makes me feel dumb
daneskiu ยท 2 points ยท Posted at 22:54:02 on May 25, 2016 ยท (Permalink)
If you want to create Artificial Intelligence, learn differential equations.
samlee405 ยท 2 points ยท Posted at 22:55:52 on May 25, 2016 ยท (Permalink)
The Banach-Tarski Theorem states that a sphere of any given size can be broken apart and rearranged in such away such that you obtain two spheres of equivalent size to the first.
Zaculus ยท 2 points ยท Posted at 23:00:23 on May 25, 2016 ยท (Permalink)
The Fourier transform is an automorphism of L2
MindlessTime ยท 2 points ยท Posted at 23:03:50 on May 25, 2016 ยท (Permalink)
Definitely Benford's Law. It states that for many, commonly-occurring collections of numbers there is a 30% chance that the first digit is 1, a smaller chance that the first digit is 2...and the least likely chance that the first digit is 9.
This seems like it should't make sense. Intuition suggests that numbers are just as likely to start with 1 as with 8 or 9 or 5 or any other one-digit number. But they don't. This has been found to be true of a wide range of seemingly random numbers, such as randomly selected address numbers within a large city, populations of animal species, and most notably amounts from a collection of invoices. In fact, forensic accountants will look at a large group of invoice totals, and if far fewer or far more than 30% of them don't have 1 as the first digit, it's flagged as potential fraud.
It mathematical proof has to do with the size of the interval between the logarithm of numbers. But generally speaking, most numbers start with 1.
thekyledavid ยท 2 points ยท Posted at 23:06:42 on May 25, 2016 ยท (Permalink)
If you take any number, shuffle the digits and subtract the 2 numbers, the answer will always be a multiple of 9.
For example, i'll take the number of present upvotes, 4665. If I were to shuffle that number to say, 6456, then I would do 6456-4665=1791. And 1791 is a mulitple of 9.
In case you think the was just lucky, I'll take the number of present comments, 9778, make it 7897, do 9778-7897=1881. And 1881 is a multiple of 9.
Try it yourself
itsjakeandelwood ยท 2 points ยท Posted at 23:12:46 on May 25, 2016 ยท (Permalink)
Late to the party here, but if you want to divide any number by five, double it and move the decimal one place to the left. Ex: 41 / 5 = 8.2
If you want to multiply any number by five, cut it in half and then move the decimal one place to the right. Ex: 38 * 5 = 190
butter69popcorn ยท 2 points ยท Posted at 23:14:31 on May 25, 2016 ยท (Permalink)
The number of ways a deck of cards can be shuffled is 52!, which is 8 x 1067, so each time you shuffle a deck of cards, there is an overwhelming probability that they are in that particular order for the first time in history.
iWheatMan ยท 1 points ยท Posted at 23:18:02 on May 25, 2016 ยท (Permalink)
If you haven't already, watch VSauce's 'Math magic' video on YouTube. This is included on there in much higher detail.
Tegatime ยท 2 points ยท Posted at 23:14:56 on May 25, 2016 ยท (Permalink)
11 to any power gives you the coefficients for the corresponding exponential expansion. In layman's terms: 111= 11. (X+y)1= x+y. 112= 121. (X+y)2= x2+2xy+y2 113= 1331 (X+y)3= x3+3x2y+3xy2+y3
And so on and so forth. A bit of a higher lever nerd thing I discovered one day when I was bullshitting on my calculator instead of paying attention.
Tristan_Truelove ยท 2 points ยท Posted at 23:15:02 on May 25, 2016 ยท (Permalink)
1+1= Window
M3at_Waffle ยท 2 points ยท Posted at 23:15:28 on May 25, 2016 ยท (Permalink)
If you have a number whose individual numbers add up to a multiple of 3, the parent number is also a multiple of, and thereby divisible by, 3.
e.g. 159. 1+5+9=15, which is a multiple of 3, so 159 is as well (3*53=159 or 159/3=53)
It works with bigger numbers too, like 17,653,821. 1+7+6+5+3+8+2+1=33
17,653,821/3=5,884,607
That's just some nifty shit right there!
TheRealSaltyChips ยท 2 points ยท Posted at 23:16:43 on May 25, 2016 ยท (Permalink)
forty is the the only number that is spelled alphabetically
PM_me_your_McRibs ยท 2 points ยท Posted at 23:25:18 on May 25, 2016 ยท (Permalink)
Frivolous Theorem of Arithmetic: Almost all natural numbers are very, very, very large.
implicature ยท 1 points ยท Posted at 00:56:22 on May 26, 2016 ยท (Permalink)
"almost all" with respect to which measure? :P
(but yes, this is one of my favorites as well)
Jj2589710 ยท 2 points ยท Posted at 23:32:00 on May 25, 2016 ยท (Permalink)
8*7=56
[deleted] ยท 2 points ยท Posted at 23:38:25 on May 25, 2016 ยท (Permalink)
Will Rogers phenomenonThe effect will occur when both of these conditions are met:
The element being moved is below average for its current set. Removing it will, by definition, raise the average of the remaining elements. The element being moved is above the current average of the set it is entering. Adding it to the new set will, by definition, raise the average.
GreatlyUnknown ยท 2 points ยท Posted at 23:41:56 on May 25, 2016 ยท (Permalink)
That infinite amounts come in different sizes.
alphacentauri14 ยท 2 points ยท Posted at 23:43:06 on May 25, 2016 ยท (Permalink)
There are so many combinations possible in a deck of cards that every time you shuffle it you have most likely created a combination that has never been seen before and will never be seen again. 52! is a ridiculously big number.
Questioning_Mind ยท 2 points ยท Posted at 23:49:22 on May 25, 2016 ยท (Permalink)
B4โขI4Qโข(ru/18)โขQtฯ
kcg5 ยท 2 points ยท Posted at 00:01:31 on May 26, 2016 ยท (Permalink)
The number of combinations a deck of cards can be is called "52!" More combinations than stars in the sky. There is a good chance the deck you have at home is in an order never before seen on earth....
Superdorps ยท 1 points ยท Posted at 06:48:50 on May 26, 2016 ยท (Permalink)
Ha! Joke's on you, I never opened that deck!
Markr1957 ยท 2 points ยท Posted at 00:18:16 on May 26, 2016 ยท (Permalink)
ei*pi + 1 = 0
_Bucket_Of_Truth_ ยท 2 points ยท Posted at 00:20:24 on May 26, 2016 ยท (Permalink)
24 is the highest number
Highbard ยท 2 points ยท Posted at 00:27:10 on May 26, 2016 ยท (Permalink)
If you laid all of the worlds politicians end-to-end around the equator, most of them would drown.
GuyNamedWhatever ยท 2 points ยท Posted at 00:36:24 on May 26, 2016 ยท (Permalink)
Tupper's self-referential formula. Very simply put, a formula that visually reproduces itself once graphed.
strykerius1992 ยท 2 points ยท Posted at 00:57:41 on May 26, 2016 ยท (Permalink)
There are more attoseconds (10-18 s) in a second than there have been seconds since the universe began. An attosecond is the general timescale on which we can observe electron dynamics.
Heronda ยท 2 points ยท Posted at 00:58:50 on May 26, 2016 ยท (Permalink)
taylor series yass
Buburubu ยท 2 points ยท Posted at 01:00:38 on May 26, 2016 ยท (Permalink)
There is a uniformly curved line that somehow joins up with itself every time, and mathematicians refer to it as a "circle".
Coequalizer ยท 2 points ยท Posted at 01:25:17 on May 26, 2016 ยท (Permalink)
Universal objects are unique up to unique isomorphism. It makes it easy to see that certain constructions in mathematics are the "right" ones, and really the only way of doing it.
joesatmoes ยท 2 points ยท Posted at 02:34:18 on May 26, 2016 ยท (Permalink)
That if you type 5318008 on an old calculator and flip it over it spells boobies.
joesatmoes ยท 1 points ยท Posted at 02:35:37 on May 26, 2016 ยท (Permalink)
I'm so mature
Usagii_YO ยท 1 points ยท Posted at 11:05:05 on May 26, 2016 ยท (Permalink)
Asshole and boobies were the fun ones to spell.
joesatmoes ยท 1 points ยท Posted at 13:41:24 on May 26, 2016 ยท (Permalink)
Woah. How do you spell Asshole in a calc?
[deleted] ยท 2 points ยท Posted at 02:56:19 on May 26, 2016 ยท (Permalink)
Turn the 6 upside down its a 9 now
Damn_Poop_Again ยท 2 points ยท Posted at 03:58:16 on May 26, 2016 ยท (Permalink)
Sheldon: "The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
Thatmanylives ยท 2 points ยท Posted at 03:58:22 on May 26, 2016 ยท (Permalink)
Commenting to find later. These are so cool!!
GokuMoto ยท 1 points ยท Posted at 05:14:43 on May 26, 2016 ยท (Permalink)
you know you can save a whole thread now without a comment
Thatmanylives ยท 1 points ยท Posted at 14:06:52 on June 16, 2016 ยท (Permalink)
I did not know that, but I will Google and learn how to do that so I don't have so many obscure comments, thank you!
GokuMoto ยท 1 points ยท Posted at 14:30:35 on June 16, 2016 ยท (Permalink)
Click the save button...
Dogswearingsocks ยท 2 points ยท Posted at 04:26:09 on May 26, 2016 ยท (Permalink)
Zipf's law is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution. Zipf's law states that the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc. https://en.wikipedia.org/wiki/Zipf's_law
johnjullies ยท 2 points ยท Posted at 05:15:46 on May 26, 2016 ยท (Permalink)
When you generally talk about math, people find it boring. Tell it as a maths fact and people will be amazed.
DarwinYogi ยท 2 points ยท Posted at 06:09:17 on May 26, 2016 ยท (Permalink)
The sum of any two consecutive numbers is equal to the difference of their squares.
[deleted] ยท 2 points ยท Posted at 06:21:18 on May 26, 2016 ยท (Permalink)
Not really a fact, but my favorite graph is f(x)= ( x - x2 )x-1
pongze ยท 2 points ยท Posted at 08:10:34 on May 26, 2016 ยท (Permalink)*
Squared integers can be found by adding the relative odd number 1->3->5->7->9->11->...2n-1 Formula is actually something like: n2 = (n-1)2 + 2(n-1)+1 where n>0
0+1=12 , 1+3=22 , 4+5=32, 9+7=42
I figured this out back around Sophomore year of highschool and never told anybody. Once I learned about sequences it didn't really feel all that special.
tummyisrumblin ยท 2 points ยท Posted at 08:58:44 on May 26, 2016 ยท (Permalink)
alternate interior angles that rule in geometry has helped me in the most random of times during college engineering courses.
kaitmoe ยท 2 points ยท Posted at 12:57:57 on May 26, 2016 ยท (Permalink)
58008
The-Dismal-Scientist ยท 2 points ยท Posted at 13:38:13 on May 26, 2016 ยท (Permalink)
There are more real numbers between 0 and 1 than integers between 0 and infinity.
TakeOutTacos ยท 2 points ยท Posted at 14:59:03 on May 26, 2016 ยท (Permalink)
The number 1 squared can be extrapolated to create some cool palindromes
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
1111112 = 12345654321
11111112 = 1234567654321
111111112 = 123456787654321
1111111112 = 12345678987654321
Got the one with 9 digits off of a Snapple fact and wondered if I could generate some of the other numbers, and thus I learned this!
iSquanch ยท 1 points ยท Posted at 15:29:36 on May 26, 2016 ยท (Permalink)
The powers of 11 make up Pascal's triangle. 110 = 1 111 = 11 112 = 121 113 = 1331 And so on
[deleted] ยท 2 points ยท Posted at 05:17:31 on May 27, 2016 ยท (Permalink)
apoorvm91 ยท 2 points ยท Posted at 21:31:22 on May 27, 2016 ยท (Permalink)*
Tupper's Self-Referential Formula.
Consider this amazing formula:
{1\over 2} < \left\lfloor \mathrm{mod}\left(\left\lfloor {y \over 17} \right\rfloor 2{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2\right)\right\rfloor
Just realized that Reddit doesn't implement LaTeX form. Copy-paste the above formula here to see the actual form.
or as plaintext,
1/2 < floor(mod(floor(y/17)*2-17 * floor(x-mod(floor(y), 17)),2))
If you plot the above inequality for 0โคxโค105 and kโคyโคk+16 where k equals to the following 543-digit integer:
960 939 379 918 958 884 971 672 962 127 852 754 715 004 339 660 129 306 651 505 519 271 702 802 395 266 424 689 642 842 174 350 718 121 267 153 782 770 623 355 993 237 280 874 144 307 891 325 963 941 337 723 487 857 735 749 823 926 629 715 517 173 716 995 165 232 890 538 221 612 403 238 855 866 184 013 235 585 136 048 828 693 337 902 491 454 229 288 667 081 096 184 496 091 705 183 454 067 827 731 551 705 405 381 627 380 967 602 565 625 016 981 482 083 418 783 163 849 115 590 225 610 003 652 351 370 343 874 461 848 378 737 238 198 224 849 863 465 033 159 410 054 974 700 593 138 339 226 497 249 461 751 545 728 366 702 369 745 461 014 655 997 933 798 537 483 143 786 841 806 593 422 227 898 388 722 980 000 748 404 719
You will get the formula as the plot.
A video by the Numberphile here. I was first introduced to this number in the book "Things to make and do in the Fourth Dimension" by Matt Parker ( /u/standupmaths ). I would recommend this book to almost everybody on this subreddit.
standupmaths ยท 2 points ยท Posted at 15:29:08 on May 30, 2016 ยท (Permalink)
Thanks!
Ogurac ยท 7 points ยท Posted at 14:12:01 on May 25, 2016 ยท (Permalink)*
The Monty Hall problem is quite nice.
Response : you should switch
BOOM, mind blown
PS : I also like the fact that 0.99999... = 1 (but i'm not entirely sure it's correct; according to wikipedia it is but last time I checked I remember the article was less final about it)
EDIT : forgot to tell you that 1 + 2 + 3 + 4 + ... = -1/12
FeelsBadMan
TheSirusKing ยท 3 points ยท Posted at 16:14:04 on May 25, 2016 ยท (Permalink)
0.9999... definitely is 1, its an identity.
1+2+3+4+... is also not -1/12, the number has a relation to the series but they are not equal.
GokuMoto ยท -2 points ยท Posted at 17:11:27 on May 25, 2016 ยท (Permalink)
it was presented wrong. the sum of infinity is -1/12
explanation
TheSirusKing ยท 2 points ยท Posted at 17:24:31 on May 25, 2016 ยท (Permalink)*
Except it isn't. Its not actually EQUAL to the sum, just related to it. Obviously 1+2+3+4... is divergent and thus tends to infinity. Numberphiles methods usually exploit a different use of the equals sign, meaning; "is assigned to", which in his case relates the value of a function to a series.
bsievers ยท 2 points ยท Posted at 16:33:34 on May 25, 2016 ยท (Permalink)
That is 100% correct, just like saying 3/3=1 or 5*1/5=1. There's absolutely no question to it's finality. Unless we're discussing hyperreal numbers.
Ogurac ยท 1 points ยท Posted at 16:48:54 on May 25, 2016 ยท (Permalink)
ty for the confirmation
kogasapls ยท 1 points ยท Posted at 17:49:20 on May 25, 2016 ยท (Permalink)
Unless you change the definition of 0.999..., it's still 1 in the hyperreals.
bsievers ยท 1 points ยท Posted at 18:07:52 on May 25, 2016 ยท (Permalink)
The way it was taught to me in college was that this is the exact kind of situation where hyperreals diverge from the set of real numbers, i.e. .999...=1-h where h is the infinitesimal.
kogasapls ยท 1 points ยท Posted at 18:16:43 on May 25, 2016 ยท (Permalink)
You could define 0.999... to be infinitesimally less than 1, but typically it's just defined as the limit of partial sums of 9 * 10-x .
overconvergent ยท 2 points ยท Posted at 23:42:32 on May 25, 2016 ยท (Permalink)
This is not true, as the wiki article you linked to explicitly states.
bunker_man ยท 3 points ยท Posted at 13:51:34 on May 25, 2016 ยท (Permalink)
This is more of a physics fact, but the idea most people have of what particles are is wrong. They aren't tiny balls. Those are just graphs used to describe them to you in high school textbooks. They have no size at all. They're points. And so by extension their only real properties are mathematical / informational properties. Because all they are are "values" associated with a space. In a sense, the universe is made of math / information.
andinuad ยท 1 points ยท Posted at 16:00:11 on May 25, 2016 ยท (Permalink)
What is an "informational property" and why isn't "size" a such property?
bunker_man ยท 1 points ยท Posted at 17:51:18 on May 25, 2016 ยท (Permalink)
Because their size is zero. (fundamental particles that is). Size is an emergent property that comes from structure. Particles with no size can still be distances from eachother, and relate from that distance, and so size comes from relation, which becomes structure. It works similarly to how most people will learn in high school, except that particles aren't just very small, but have no size at all.
Their properties are informational, because "matter" as classically understood doesn't exist. Its an emergent property of relation. Fundamental particles don't have properties like size or shape or "texture." All those properties only exist for structure. The only properties fundamental particles have are informational ones. Since they aren't "solids" in the way that sience used to think existed before the early 1900s, their properties don't refer to anything solid, but to pure abstraction. The values are just data that exists in that location more or less.
andinuad ยท 1 points ยท Posted at 18:05:19 on May 25, 2016 ยท (Permalink)
From what you are writing it sounds like "the set of all informational properties" and "the set of all emergent properties" are distinct sets. Could you though be a bit more precise or maybe even give a definition for what an "informational property" is?
bunker_man ยท 1 points ยท Posted at 18:27:22 on May 25, 2016 ยท (Permalink)
I can't really be precise because its not something science can directly measure. They can only describe it by analogy / how it works. Saying what it "is" is speculative philosophy in a way. How it works is what I described already. The only properties particles have are specific "values" that say how it relates to things. Its not itself a solid, because its sizeless. Particles are just a special case of what energy is doing. And energy isn't a thing either. Just an abstraction of potential and value. So it makes more sense to describe it as data than anything else. But we can't really know what that "means" directly.
The difference between fundamental particles themselves, and emergent structure is that things like texture can only be properties of things with shape or size. But particles have neither. But their relations add up to it by being in different places.
https://www.indigo.com/images/products/caffeine-molecule-structure-model-kit-62206A.jpg
Like look at a chemical model. Obviously you know that the sticks don't refer to literal material things. They're just structural relations that say what's happening. The point is that the balls are more or less the same way. They're basically locations that provide the ability to generate the relations between them. At the end of it all you have a bigger shape. The shape can interact in ways with even bigger shapes, etc. And that's where structure comes from.
andinuad ยท 1 points ยท Posted at 18:49:36 on May 25, 2016 ยท (Permalink)
So spin of a particle would not then be an informational property? Because there certainly exists particles for which we can measure their spin.
bunker_man ยท 1 points ยท Posted at 19:00:35 on May 25, 2016 ยท (Permalink)
It is. The "value" can be measured, but not what it actually "is" doing so to speak. The measurement is indirect, rather than direct like with macro scale things. The key word there was directly, not measure. There's a limit on our ability to fully understand the "nature" of things. Because beyond a certain point we can only really understand them in terms of effects.
andinuad ยท 1 points ยท Posted at 19:11:14 on May 25, 2016 ยท (Permalink)
Have a hard time to understand what "directly" would mean in this context and why it is an important distinction.
Isn't it just enough that we design a model with a certain amount of parameters that to great accuracy describes phenomena in nature? Then whenever we experimentally find something that our model cannot currently explain, we try to expand the model or make corrections to it and then see if the new model is in agreement with experimental results?
bunker_man ยท 2 points ยท Posted at 19:40:18 on May 25, 2016 ยท (Permalink)
That's enough if all you're trying to do is get results that you can interact with. But it doesn't always tell you what's happening. Take quantum indeterminism and decoherence for example. The reason we don't really know what's happening is because all we know is that the particle should be in multiple places at once, but when we check its only in one. If you decide to stop there you don't need to know what causes this, since it doesn't change what you're likely to measure in the immediate sense.
But there's multiple theories about the fundamental nature of what's going on. Does reality just "delete" the data of its extra locations and reset it when that happens? Or the more bizarre many worlds theory where the collapse simply never happens, but there's split worlds where many different versions of us observed different results? Or maybe indeterminism doesn't exist in the first place, and how the particle moves is deterministic, but impossible for us to know, since its evolution is related to all other particles in the universe in a way that is impossible to predict in the small scale? These are things that experiments as of yet are something we have no way of using to find the answer to. Since all of those theories will look the same to us when we check. This is an example of our inability to directly understand the nature of what's going on. Its one of the many times that that's the case when interacting with quantum things. we can measure the effects, but something underlies the effects that we can't really directly see.
But just describing how something works / its effects doesn't always tell you its nature. At the point where you're describing fundamental interactions, you can only really describe them informationally. Information has a definition in physics, but its not clear if these mathematical properties of particles are themselves identical with what we call information or not. Or what the difference would even be.
Something that's probably more intuitive to understand is imagine we were in the matrix. We could do science and discover how things act, but from inside the system we'd be fundamentally unable to understand some aspects of the nature of the world. Its "real" nature would be a code on a computer. But that's something that to us is fundamentally un-seeable. We can only see what the code generates in relation. This is an apt comparison, since "code" is similar to the mathematical properties of particles. We know what it looks like its -doing- from our perspective. But we're not able to see it directly in any kind of way that lets us confirm absolutely its nature entirely. There's a surprisingly larger amount of times this is the case than one would think when on the quantum level. Making it the type of thing that the ore one knows about the more they realize how much we don't know about.
andinuad ยท 1 points ยท Posted at 19:51:27 on May 25, 2016 ยท (Permalink)
Thank you!
[deleted] ยท 3 points ยท Posted at 14:38:12 on May 25, 2016 ยท (Permalink)
[deleted]
jet_so ยท 3 points ยท Posted at 17:14:15 on May 25, 2016 ยท (Permalink)*
There is only one way to arrange zero things, you don't
baconaro ยท 1 points ยท Posted at 17:37:05 on May 25, 2016 ยท (Permalink)
FTFY
Machtung7 ยท 1 points ยท Posted at 17:41:38 on May 25, 2016 ยท (Permalink)*
Similarly, n0 = 1.
Edit: for n != 0 (thank you u/DubiousCosmos)
DubiousCosmos ยท 2 points ยท Posted at 19:30:29 on May 25, 2016 ยท (Permalink)
For non-zero n. 00 is indeterminite.
Machtung7 ยท 1 points ยท Posted at 20:36:41 on May 25, 2016 ยท (Permalink)
Thank you. I remember 00 being an interesting topic.
[deleted] ยท 0 points ยท Posted at 15:10:51 on May 25, 2016 ยท (Permalink)*
[deleted]
TheSirusKing ยท 2 points ยท Posted at 16:16:30 on May 25, 2016 ยท (Permalink)
3*(3-1)! = 6, not 3.
mr_ewe ยท 3 points ยท Posted at 18:18:07 on May 25, 2016 ยท (Permalink)
Maybe it should be n!, 3!, And 1! On the left?
So 1!=1(1-1)!=1(0)!=1
1(0)!=1
Divide both sides by 1
0!=1
TheSirusKing ยท 1 points ยท Posted at 21:15:11 on May 25, 2016 ยท (Permalink)
Yeah, n!=n*(n-1)! works fine.
big-blue-balls ยท 2 points ยท Posted at 18:06:55 on May 25, 2016 ยท (Permalink)
I'm scared if you're an engineer.
skordge ยท 2 points ยท Posted at 10:47:49 on May 26, 2016 ยท (Permalink)
eiฯ + 1 = 0
A specific case of Euler's formula (x = ฯ). Look how beautiful it is! It's got a zero, a one, the square root of -1, Euler's constant and pi very neatly packed!
Huomenna ยท 3 points ยท Posted at 13:36:52 on May 25, 2016 ยท (Permalink)
If you ask someone to think of a number between 1 and a 100, the number that is most thought about is 37
galacticdick ยท 3 points ยท Posted at 14:05:37 on May 25, 2016 ยท (Permalink)
If you add an infinite series in a different order, you can get a completely different answer, or no answer at all (I.e. Trails off to infinity). Good old Riemann.
locotxwork ยท 2 points ยท Posted at 14:38:37 on May 25, 2016 ยท (Permalink)
Woah woah . . say what !?
ben1996123 ยท 1 points ยท Posted at 18:27:32 on May 25, 2016 ยท (Permalink)
1 - 1/2 + 1/3 - 1/4 + 1/5 - ... = log(2) = about 0.6931471805599
by rearranging the terms:
1 - 1/2 - 1/4 + 1/3 - 1/6 - 1/8 + 1/5 - 1/10 - 1/12 + 1/7 - ... = 1/2 log(2) = about 0.3465735901799
locotxwork ยท 1 points ยท Posted at 19:03:16 on May 25, 2016 ยท (Permalink)
WOW . . this . . I did not know
BrahquinPhoenix ยท 4 points ยท Posted at 14:56:26 on May 25, 2016 ยท (Permalink)
If you write 3.14 on paper and look at it in the mirror it spells PIE
idothingsheren ยท 1 points ยท Posted at 05:29:17 on May 28, 2016 ยท (Permalink)
If you write PIE on a piece of paper and look at it from just the right angle, it looks like PIE
BrahquinPhoenix ยท 2 points ยท Posted at 03:04:04 on May 29, 2016 ยท (Permalink)
No it doesnt, it looks like a piece of paper at a weird angle
-d0ubt ยท 2 points ยท Posted at 15:20:52 on May 25, 2016 ยท (Permalink)
If there radius of a pizza is said to be 'z' and the height of the pizza is said to be 'a', Then (assuming the pizza is a perfect cylinder) the equation of the pizza can be defined as Pizz*a.
MHG73 ยท 3 points ยท Posted at 15:25:11 on May 25, 2016 ยท (Permalink)
The number 73 is the 21st prime number. It's opposite, 37, is the 12th prime number.
TrekkiMonstr ยท 3 points ยท Posted at 16:54:23 on May 25, 2016 ยท (Permalink)
ei*ฯ = -1
Cause fuck any intuitive sense of mathematics...
Slacker5001 ยท 3 points ยท Posted at 18:41:39 on May 25, 2016 ยท (Permalink)
It's mind blowing at first but the proof is deceptively simple in the end which is also part of how mind blowing it is. Just throw some numbers in Euler's formula and boom, magic.
TrekkiMonstr ยท 2 points ยท Posted at 21:06:20 on May 25, 2016 ยท (Permalink)
Yeah but I'm a sophomore in high school; I'm only in Honors Algebra II. So for me, you've just passed the buck to proving Euler's formula.
Slacker5001 ยท 1 points ยท Posted at 21:42:29 on May 25, 2016 ยท (Permalink)
That actually isn't too crazy difficult either though definitely not something you'd touch on as a Sophomore in high school. Though would probably lead down more "rabbit hole" well how do you prove this stuff.
The only new thing you would probably need to know is what a power series it. Which is just a special way to express some equation as a sum of an infinite number for fractions. You can see some examples here. From there it's just simple math.
eix = 1 + ix + (ix2 / 2!) + (ix3 / 3!)...
= 1 + ix - (x2 / 2!) - (ix3 / 3!) + ...
Sort out the terms from here into the power series for sin(x) and cos(x)
= [1 - (x2 / 2!) + ... ] + [ix - (ix3 / 3!) + ... ]
= [1 - (x2 / 2!) + ... ] + i*[x - (x3 / 3!) + ... ]
= cos(x) + i*sin(x)
And there you go, just some simple algebra and some knowledge of a few special equations. Why power series work is something I've never learned myself so I don't feel comfortable explaining it. But you use them every now and then after learning them to prove a few things.
adamkw94 ยท 3 points ยท Posted at 16:59:46 on May 25, 2016 ยท (Permalink)
-e-ipi = 1
gcbeehler5 ยท 3 points ยท Posted at 17:33:33 on May 25, 2016 ยท (Permalink)
The square root of 69 is eight something. (say it out loud.)
EnterraCreator ยท 2 points ยท Posted at 17:48:10 on May 25, 2016 ยท (Permalink)
I get it.
SillyFlyGuy ยท 2 points ยท Posted at 20:11:24 on May 25, 2016 ยท (Permalink)
It's funny because it's true. To fully kill the joke: โ69 = 8.306623862918075
REMagic42 ยท 2 points ยท Posted at 20:13:45 on May 25, 2016 ยท (Permalink)
i don't get it
gcbeehler5 ยท 1 points ยท Posted at 02:08:28 on May 26, 2016 ยท (Permalink)
If said out loud it would sound like 'ate something'. 69, ate something. Get it?
jaykaysian ยท 3 points ยท Posted at 22:09:10 on May 25, 2016 ยท (Permalink)
3.14 mirrored spells PI.E
I_could_be_right ยท 4 points ยท Posted at 11:37:49 on May 25, 2016 ยท (Permalink)
I like that 7 ate 9.
ktkps ยท -3 points ยท Posted at 12:14:54 on May 25, 2016 ยท (Permalink)
7 6 ate - Yoda
TigerBeetle ยท 7 points ยท Posted at 15:12:16 on May 25, 2016 ยท (Permalink)*
The sum of all positive integers is -1/12
(sometimes, kind of)
Links:
https://www.youtube.com/watch?v=w-I6XTVZXww
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Perry0485 ยท 6 points ยท Posted at 17:33:47 on May 25, 2016 ยท (Permalink)
This is very misleading.
Edit: I suggest watching this: https://www.youtube.com/watch?v=jcKRGpMiVTw if you want to know what -1/12 really means in this context.
k-selectride ยท 2 points ยท Posted at 19:38:30 on May 25, 2016 ยท (Permalink)
If you use a different definition to an infinite sum instead of the one most people are used to, which is the limit of a sequence of partial sums.
emhcee ยท 1 points ยท Posted at 01:06:19 on May 26, 2016 ยท (Permalink)
If this one's interesting to folks, here's another good explanation of how this is (and kind of mostly isn't) for real.
PinguinRS ยท 4 points ยท Posted at 13:42:04 on May 25, 2016 ยท (Permalink)
Not really a maths fact but this. http://puu.sh/p4CXu.png
[deleted] ยท 4 points ยท Posted at 13:34:52 on May 25, 2016 ยท (Permalink)
[deleted]
TheNaughtyMonkey ยท 1 points ยท Posted at 17:25:48 on May 25, 2016 ยท (Permalink)
Not bad, but how about this?
Take the first three odd numbers and write each one twice
113355
Now divide the second three by the first three.
335/113
That is Pi to the 6th decimal place.
Did I blow your mind?
[deleted] ยท 2 points ยท Posted at 13:39:39 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 14:18:43 on May 25, 2016 ยท (Permalink)
This is called the "four color theorem" and it was the first theorem to be proven using a computer.
cowjk ยท 2 points ยท Posted at 14:09:10 on May 25, 2016 ยท (Permalink)
2 + 0 = 2
[deleted] ยท 2 points ยท Posted at 13:49:00 on May 25, 2016 ยท (Permalink)
Hopefully I describe this properly...
For continuous functions, the inner product of two functions u and v is the integral on [a,b] of u(x)v(x).
This ties together linear algebra and calculus fairly neatly.
Aliudnomen ยท 6 points ยท Posted at 15:41:48 on May 25, 2016 ยท (Permalink)
Not continuous; square integrable; โซ |f(x)|2 dx < โ (over [a,b] of course).
Also, this is just one of many possible inner products. It just happens to be a particularly useful one (it's the standard L2 inner product).
[deleted] ยท 1 points ยท Posted at 16:13:38 on May 25, 2016 ยท (Permalink)
Ugh. I knew I was going to screw it up.
It's still a super interesting relationship to me, though, because it seems very... "fundamental".
Pingu1807 ยท 2 points ยท Posted at 13:54:39 on May 25, 2016 ยท (Permalink)
x = 16sin3t
y = 13cost-5cos(2t)-2cos(3t)-cos(4t). The equation for a love heart graph. Not really interesting but kinda useful I suppose
user808a ยท 1 points ยท Posted at 16:20:41 on May 25, 2016 ยท (Permalink)
Wolframalpha plot
adruven ยท 2 points ยท Posted at 14:06:19 on May 25, 2016 ยท (Permalink)
4!! is fairly close to 1 mol (6.20*1023 instead of 6.02 *1023 ).
ben1996123 ยท 2 points ยท Posted at 18:29:21 on May 25, 2016 ยท (Permalink)
4!! = 8 :^)
adruven ยท 1 points ยท Posted at 20:09:02 on May 25, 2016 ยท (Permalink)
I don't understand the reasoning here, care to explain?
ben1996123 ยท 2 points ยท Posted at 20:14:58 on May 25, 2016 ยท (Permalink)
x!! is the double factorial, x(x-2)(x-4)... down to 1 or 2, so 4!! = 4*2 = 8
adruven ยท 1 points ยท Posted at 20:30:27 on May 25, 2016 ยท (Permalink)
Huh, didn't know that. I meant (4!)! - is that the correct notation for 4 factorial, factorial (24!)?
ben1996123 ยท 1 points ยท Posted at 20:32:41 on May 25, 2016 ยท (Permalink)
yes.
bearsnchairs ยท 1 points ยท Posted at 15:48:13 on May 25, 2016 ยท (Permalink)
Avogadro's number more specifically. A mol is a quantity of things, not a number.
2nd_law_is_empirical ยท 2 points ยท Posted at 14:33:01 on May 25, 2016 ยท (Permalink)
The Pigeonhole Principle : So simple, yet the basis of so much higher maths.
_NW_ ยท 3 points ยท Posted at 18:51:21 on May 25, 2016 ยท (Permalink)
By the Pigeonhole Principle, there are two people in NYC that have the same number of hairs on their head.
Danhulud ยท 2 points ยท Posted at 15:06:32 on May 25, 2016 ยท (Permalink)
TIL I know very little about Maths.
Slacker5001 ยท 1 points ยท Posted at 18:31:00 on May 25, 2016 ยท (Permalink)
No worries! A lot of this is stuff that I never even thought about until I'd started doing higher level classes as a math major. Most of it is not stuff that people would regularly just know.
Smailien ยท 2 points ยท Posted at 15:44:22 on May 25, 2016 ยท (Permalink)
1 * 9 = 09 (0 + 9 = 9)
2 * 9 = 18 (1 + 8 = 9)
3 * 9 = 27 (2 + 7 = 9)
4 * 9 = 36 (3 + 6 = 9)
5 * 9 = 45 (4 + 5 = 9)
6 * 9 = 54 (5 + 4 = 9)
7 * 9 = 63 (6 + 3 = 9)
8 * 9 = 72 (7 + 2 = 9)
9 * 9 = 81 (8 + 1 = 9)
10 * 9 = 90 (9 + 0 = 9)
3xistentialPrimate ยท 2 points ยท Posted at 16:22:03 on May 25, 2016 ยท (Permalink)
That it's pronounced math! Filthy limey
J_Neal24 ยท 2 points ยท Posted at 16:22:08 on May 25, 2016 ยท (Permalink)
Any even number greater than two is the sum of two prime numbers. I'm pretty sure that's why they know there is an infinite number of prime numbers.
elspazzo ยท 1 points ยท Posted at 16:48:33 on May 25, 2016 ยท (Permalink)*
Not really. What about 28? Or 8?Edit: I shouldn't try to math early in the morning.
Nicko265 ยท 3 points ยท Posted at 17:22:15 on May 25, 2016 ยท (Permalink)
17 + 11, 5 + 3.
This is the believed to be the case all the way to 4*1018 Goldbach's conjecture.
ApertureBear ยท 2 points ยท Posted at 18:26:52 on May 25, 2016 ยท (Permalink)
17 and 11. 1 and 7. You didn't really think about this before you posted, did you?
elspazzo ยท 1 points ยท Posted at 19:32:12 on May 25, 2016 ยท (Permalink)
While I agree with you and retracted my statement, 1 technically isn't prime.
ApertureBear ยท 2 points ยท Posted at 19:35:03 on May 25, 2016 ยท (Permalink)
3 and 5, then. Good catch :)
J_Neal24 ยท 1 points ยท Posted at 17:42:29 on May 25, 2016 ยท (Permalink)
8 = 5+3 28 = 23 + 5
ben1996123 ยท 1 points ยท Posted at 18:31:36 on May 25, 2016 ยท (Permalink)
the fact that there are an infinite amount of prime numbers is very simple and can be proved in 1 sentence. every even number greater than 2 being the sum of 2 primes is an open problem that has been unsolved for hundreds of years.
lanemik ยท 2 points ยท Posted at 16:44:15 on May 25, 2016 ยท (Permalink)
The cardinality of a set S is strictly less than the cardinality of the power set of S. This seems intuitive for sets with a finite number of elements because the power set of S is the set of all subsets of S. So if S = {0,1,2}, then the power set of S is P(S) = {{}, {0}, {1}, {2}, {0,1}, {0,2}, {1,2}, {0,1,2}}. Note that |S| = 3 and |P(S)| = 23 = 8.
What isn't obvious, but what is true, is that even if S has an infinite number of elements, P(S) has more elements. If S is the set of all Natural Numbers, an infinite set, then the power set has yet more elements in it. The consequence is that there are different sizes of infinity!
magicfinbow ยท 2 points ยท Posted at 17:01:25 on May 25, 2016 ยท (Permalink)
If you have 23 people in a room, you have a greater than 50% chance that 2 will share a birthday.
Sidco_cat ยท 1 points ยท Posted at 17:09:43 on May 25, 2016 ยท (Permalink)
that is awesome!
cloverrace ยท 2 points ยท Posted at 17:01:36 on May 25, 2016 ยท (Permalink)
The only even prime number is 2.
GokuMoto ยท 1 points ยท Posted at 03:48:46 on May 26, 2016 ยท (Permalink)
mainly due to the fact to be considered prime it can only have factors of itself and 1. all even numbers have 2 for a factor. since 2's only factors are 1 and 2 it makes it a prime number
cloverrace ยท 1 points ยท Posted at 18:40:52 on May 26, 2016 ยท (Permalink)
yep. That's why it is my favourite maths fact. :-)
GokuMoto ยท 1 points ยท Posted at 19:44:31 on May 26, 2016 ยท (Permalink)
yup
downloads-cars ยท 2 points ยท Posted at 17:02:19 on May 25, 2016 ยท (Permalink)
For the same reason .999...9 = 1, Throwing an infinitely sharp dart at the real number line could NEVER result in said dart hitting a whole number. The probability of doing so is exactly 0.
You just have to ignore the fact that you have an infinitely sharp dart.
ObviousPenguin ยท 1 points ยท Posted at 17:40:01 on May 25, 2016 ยท (Permalink)
Even better, it will never hit a rational number either; that is, any number that can be represented as a fraction. This is because for each rational number, there are an infinite number of irrational reals.
But the best part is despite all of this, there is always a rational number between two irrationals (so numbers "alternate" between rational and irrational)
toaderina ยท 2 points ยท Posted at 01:09:36 on May 26, 2016 ยท (Permalink)
Similarly (and even better I think), is that if you separate the numbers into algebraic vs. transcendental, the probability of hitting an algebraic number is also 0.
downloads-cars ยท 1 points ยท Posted at 19:36:03 on May 25, 2016 ยท (Permalink)
Good point! I love infinity!
Elpresidente80 ยท 2 points ยท Posted at 17:09:25 on May 25, 2016 ยท (Permalink)
I would say the number pi is the most interesting thing. It is infinite and contains every combination of numbers possible. Everyones birthdate, telephone number, social security number, or anything appears in it at some point. There used to be a website where you could look them up at.
ThePlatitudePlatypus ยท 2 points ยท Posted at 17:16:33 on May 25, 2016 ยท (Permalink)
In America, we say "math"
Hopeful_Swine ยท 2 points ยท Posted at 17:23:43 on May 25, 2016 ยท (Permalink)
If you began shuffling a deck of 52 playing cards in a new, random order every second since the beginning of the universe over 13 billion years ago, you would be nowhere near finished. The Universe is about 1018 seconds old. And there are over 8x1067 ways to rearrange a deck of cards.
Kendallkolenik ยท 2 points ยท Posted at 17:37:04 on May 25, 2016 ยท (Permalink)
7 x 3 = 21
Jordaneer ยท 2 points ยท Posted at 18:13:00 on May 25, 2016 ยท (Permalink)
That my girlfriend is the exact same as โ-100
A perfect 10, but still totally imaginary.
orangebagel ยท 2 points ยท Posted at 18:44:14 on May 25, 2016 ยท (Permalink)
92 is half of 99
tamparnguy2 ยท 2 points ยท Posted at 22:06:48 on May 25, 2016 ยท (Permalink)
If you take 1 of something and add another and another, the sum total will increase by one. Evey time! Trust me, It's Science.
andesz ยท 2 points ยท Posted at 10:48:37 on May 26, 2016 ยท (Permalink)
Euler's identity: the single most beautiful thing i've ever seen ei*pi = -1
serac145 ยท 2 points ยท Posted at 11:46:30 on May 25, 2016 ยท (Permalink)
You can turn a sphere inside out
ktkps ยท 2 points ยท Posted at 12:16:23 on May 25, 2016 ยท (Permalink)
that's what my grandma used to say
[deleted] ยท 2 points ยท Posted at 16:24:06 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=sKqt6e7EcCs https://www.youtube.com/watch?v=x7d13SgqUXg
Lyress ยท 1 points ยท Posted at 14:11:01 on May 25, 2016 ยท (Permalink)
You can also work with objects in an infinite amount of dimensions.
das_hansl ยท 2 points ยท Posted at 13:43:13 on May 25, 2016 ยท (Permalink)
(X-A).(X-B).(X-C).(X-D) ... (X-Z) = 0.
billym32 ยท 1 points ยท Posted at 14:39:19 on May 25, 2016 ยท (Permalink)
7 ate 9
actual_factual_bear ยท 1 points ยท Posted at 16:56:55 on May 25, 2016 ยท (Permalink)
6 7 ate
pucatown ยท 3 points ยท Posted at 14:59:27 on May 25, 2016 ยท (Permalink)
0! (Zero factorial) = 1. It seems wierd because not only is it a mind bender, but also the notation 0!=1 looks like it could be the logical operator != (does not equal). So it looks like it's saying 0 does not equal 1.
scatpack ยท 3 points ยท Posted at 15:09:23 on May 25, 2016 ยท (Permalink)
The ratio of the total length of ANY river and the total source length (point a to b) = Pi
The total length of ANY river (the distance you would travel as you sailed down it) and the straight line distance from begining to end. (as the crows fly, etc) = Pi
kieranvs ยท 8 points ยท Posted at 17:04:29 on May 25, 2016 ยท (Permalink)
This is clearly not the case. Just consider a hypothetical straight river.
scatpack ยท 1 points ยท Posted at 17:34:56 on June 15, 2016 ยท (Permalink)
http://www.joyofpi.com/pifacts3.html
kieranvs ยท 1 points ยท Posted at 00:01:44 on June 16, 2016 ยท (Permalink)
From your source:
Whereas your comment emphasized 'any' twice.
jevans102 ยท 1 points ยท Posted at 23:21:40 on May 25, 2016 ยท (Permalink)
Might be true if we don't think mathematically. The way water flow doesn't allow most rivers to be straight AFAIK. They will normally develop the back and forth pattern.
rmfei ยท 3 points ยท Posted at 23:50:25 on May 25, 2016 ยท (Permalink)
The shape of a river depends on lots and lots of factors, and it changes over time as the banks are eroded by the flowing water. It's very hard to believe that this relationship would always be even approximately correct.
scatpack ยท 1 points ยท Posted at 17:34:46 on June 15, 2016 ยท (Permalink)
http://www.joyofpi.com/pifacts3.html
rrussell1 ยท 2 points ยท Posted at 22:30:45 on May 25, 2016 ยท (Permalink)
Doesnt this assume that the river is made up from circle arcs? Which is... Completely wrong.
Jager1966 ยท 1 points ยท Posted at 15:12:12 on May 25, 2016 ยท (Permalink)
Any way to verify this? Fascinating.
[deleted] ยท 2 points ยท Posted at 15:41:31 on May 25, 2016 ยท (Permalink)
https://github.com/lsjroberts/pi-me-a-river
random_fucktuation ยท 1 points ยท Posted at 19:24:45 on May 25, 2016 ยท (Permalink)
This verifies that it's not true.
[deleted] ยท 2 points ยท Posted at 21:44:30 on May 25, 2016 ยท (Permalink)
You would be correct sir :) Posted solely for the purpose of allowing @jager1966 to verify. Erosion alters bends in the river sometimes significantly and thus sinuosity will be altered so no river would stay the same. While it sounded reasonable, the data collected thus far shows that even the average is not Pi....
PronouncedOiler ยท 1 points ยท Posted at 17:03:21 on May 25, 2016 ยท (Permalink)
Source?
scatpack ยท 1 points ยท Posted at 17:35:40 on June 15, 2016 ยท (Permalink)
http://www.joyofpi.com/pifacts3.html
"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14, which is close to the value of the number pi... The ratio of pi is most commonly found for rivers flowing across very gently sloping planes, such as those found in Brazil or the Siberian tundra."
[deleted] ยท 2 points ยท Posted at 15:07:58 on May 25, 2016 ยท (Permalink)
5318008
Now hold your screen upside down.
Infinite_Bananas ยท 1 points ยท Posted at 16:04:34 on May 25, 2016 ยท (Permalink)
hur hur hur
steviewonderous ยท 1 points ยท Posted at 14:27:23 on May 25, 2016 ยท (Permalink)
The fact that they call it "maths" in some places
Wassayingboourns ยท 0 points ยท Posted at 14:57:29 on May 25, 2016 ยท (Permalink)
I searched down this page for 10 minutes to find this comment just so I could un-downvote you, and of course the score is hidden.
GravityTracker ยท 0 points ยท Posted at 16:15:24 on May 25, 2016 ยท (Permalink)
If you took the probability of Neil Patrick Harris having sex with Honey Boo Boo's mom, and divide that by the number of atoms in the universe, you still have more fucks than I give about college basketball.
rage-rally-repeat ยท 1 points ยท Posted at 13:42:48 on May 25, 2016 ยท (Permalink)
x% of y = y% of x
c00yt825 ยท 1 points ยท Posted at 13:51:08 on May 25, 2016 ยท (Permalink)
To find out if a number can be divided by 3 just add all the digits together and see if those can be divided by 3.
km89 ยท 1 points ยท Posted at 14:03:26 on May 25, 2016 ยท (Permalink)
The antiderivative of the circumference of a circle is the area of that same circle.
And the antiderivative of the surface area of a sphere is that same sphere's volume.
Sorathez ยท 1 points ยท Posted at 20:55:56 on May 25, 2016 ยท (Permalink)
"Antiderivative"? What are you gonna go about calling division the "multiplicative inverse"? In this house we call it the integral.
boriherter ยท 1 points ยท Posted at 14:05:44 on May 25, 2016 ยท (Permalink)
Any number whose digits add up to 9 is divisible by 9. ie, 81, 72, 603, 5004, 12321, 111111111 etc
Zywakem ยท 1 points ยท Posted at 14:05:55 on May 25, 2016 ยท (Permalink)
Four is the only number in the English language to have the same number of letters as the number itself.
Forty is the only one to have all its letters in alphabetical order.
Murderous Maths anyone?
[deleted] ยท 1 points ยท Posted at 14:08:39 on May 25, 2016 ยท (Permalink)
[deleted]
Arcola56 ยท 1 points ยท Posted at 14:19:22 on May 25, 2016 ยท (Permalink)
Uhhh. What? 1/0 is not infinity. The limit of 1/n as n approaches 0 is infinity but that's all. 1/0 is not a solvable problem.
Gazzamate ยท 1 points ยท Posted at 14:11:44 on May 25, 2016 ยท (Permalink)*
A faster way to multiply by Nine is to put both your hands in front of you. Now, say you want to multiply 3 by 9. from left to right, count to your third finger. Put that one down. The finger you put down now creates a border between the tens and ones. The tens will be on the left, while the ones will be on the right. You have 2 fingers on the left, and 7 on the right. Hence the answer is 27.
Unfortunately, this only works up to 9x10...
Unless you have more fingers.babecafe ยท 1 points ยท Posted at 14:15:31 on May 25, 2016 ยท (Permalink)
9x => (10-1)x => 10x - x => (x-1) in tens place, (10-x) in ones place.
It doesn't help to have more fingers.
Gazzamate ยท 1 points ยท Posted at 14:17:56 on May 25, 2016 ยท (Permalink)
...That's true.
Warrior__Maiden ยท 1 points ยท Posted at 14:14:07 on May 25, 2016 ยท (Permalink)
When I was a kid I was fascinated being 7 years old and realizing that halfway through the 9 times table the numbers are inverse after 5 X.
CircleJerkAmbassador ยท 1 points ยท Posted at 14:14:48 on May 25, 2016 ยท (Permalink)
There's a method for testing divisibility by any prime number.
Take any prime number and mulitply it by whatever single digit number you need to make the ones place a 9. Add 1 and divide by 10.
The resulting number is what you can multiply the last digit of a number and add it to the rest of the digits. If the resulting number is divisible by your prime, then the whole original number is. If you're not sure, you can always do the trick over and over again.
For 13
Multiply 13 * 3 to get 39. 39 + 1 = 40. 40/10 = 4.
So take 169, 132 , 169 so 9 * 4 = 36. 36 +16 = 52
52 is 13 * 4, but if you still weren't sure try it again
52, take 2 * 4, get 8. 8 + 5 = 13. 13 is definitely a multiple of 13, so 169 is a multiple of 13 as well.
angle4evur ยท 1 points ยท Posted at 14:16:46 on May 25, 2016 ยท (Permalink)
Euler's identity is pretty cool. It leads to the odd equation eฯi = -1.
babecafe ยท 1 points ยท Posted at 14:18:03 on May 25, 2016 ยท (Permalink)
exp(i*PI) + 1 = 0
KTcrazy ยท 1 points ยท Posted at 14:18:34 on May 25, 2016 ยท (Permalink)
There are 97,000 sneezes per second on Earth. This is assuming that there are 1.2 sneezes per person per day.
chaosbutters ยท 1 points ยท Posted at 14:20:27 on May 25, 2016 ยท (Permalink)
If you have 23 people in a room, there is a 50% chance 2 of them have the same birthday. 70 people gives you a 99.9%
NSquared98 ยท 1 points ยท Posted at 14:20:41 on May 25, 2016 ยท (Permalink)
After high school and college I won't have to touch higher level math ever again.
Guttgupp ยท 1 points ยท Posted at 14:21:53 on May 25, 2016 ยท (Permalink)
22 / 7 is closer to pi than 3.14 is
Guttgupp ยท 2 points ยท Posted at 14:22:30 on May 25, 2016 ยท (Permalink)
and 355 / 113 is even closer
Guttgupp ยท 2 points ยท Posted at 14:22:50 on May 25, 2016 ยท (Permalink)*
I just realized that I reply to my own comments
FeelsBadMan
wolftooth21 ยท 1 points ยท Posted at 14:23:49 on May 25, 2016 ยท (Permalink)
The largest number to ever be used constructively in math is called graham's number. To find the number, arrow notation is used, where an arrow represent putting a number to a power. Call g1= 3333, now repeat this where g2 has a g1 amount of arrows! Now repeat this until you reach g64. https://www.youtube.com/watch?v=XTeJ64KD5cg
wanmoar ยท 1 points ยท Posted at 14:27:24 on May 25, 2016 ยท (Permalink)
the sum of the digits for any number obtained after multiplication by 9, is 9
for example.
9 * 7 = 63 = 6+3 = 9
9 * 65468 = 589212 = 5+8+9+2+1+2 = 27 = 2+7 = 9
[deleted] ยท 1 points ยท Posted at 14:29:08 on May 25, 2016 ยท (Permalink)
This was said below
GravediggerHound ยท 1 points ยท Posted at 14:30:09 on May 25, 2016 ยท (Permalink)
X squared = (x-1)squared + y.
Y= X equivalent odd number.
Too put it simple: 2 squared = (2-1)squared + 3
You can do this for any number it never fails.
I got to this conclusion by myself.
Echung97 ยท 1 points ยท Posted at 14:30:18 on May 25, 2016 ยท (Permalink)
.999 repeating is equal to 1.
And that there are different infinities of different sizes.
jabba_the_wut ยท 1 points ยท Posted at 14:31:29 on May 25, 2016 ยท (Permalink)
1+1=2
the_drew ยท 1 points ยท Posted at 14:32:04 on May 25, 2016 ยท (Permalink)
2 is a prime number.
auntfaintly ยท 1 points ยท Posted at 16:21:55 on May 25, 2016 ยท (Permalink)
Only even prime number.
FrareBear ยท 1 points ยท Posted at 14:32:34 on May 25, 2016 ยท (Permalink)
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
Not really a math fact just a very pleasing pattern.
DuncanEastwood ยท 1 points ยท Posted at 14:32:38 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=GFLkou8NvJo
aezyph ยท 1 points ยท Posted at 14:34:19 on May 25, 2016 ยท (Permalink)
i don't understand any of these..
mikronaut ยท 1 points ยท Posted at 14:34:28 on May 25, 2016 ยท (Permalink)
196... It's a weird number.
https://en.wikipedia.org/wiki/196_(number)
parkourben99 ยท 1 points ยท Posted at 14:34:49 on May 25, 2016 ยท (Permalink)
If is seems to easy then it's most likely wrong.
mkicon ยท 1 points ยท Posted at 14:35:53 on May 25, 2016 ยท (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
iamnos ยท 1 points ยท Posted at 14:35:59 on May 25, 2016 ยท (Permalink)
Late to the party, but...
To determine if any number is divisible by 3, add up the individual numbers and see if the result is divisible by 3.
ie: Is 1584 divisible by 3? 1+5+8+4 = 18. 18 is divisible by 3 so, 1584 is.
It scales as well. In the above example, if you weren't sure if 18 was divisible by 3, you could do 1+8=9 and 9 is divisible by 3, so both 18 and 1584 are.
auntfaintly ยท 1 points ยท Posted at 16:38:50 on May 25, 2016 ยท (Permalink)
That was very useful in middle and high school. I was all over divisibility rules.
Works for 9, summing the digits works for 9
2 and 5 are easy, last digit is divisible by 2 or 5 respectively
11: add the first digit subtract the second add the third, etc. is the result divisible by 11? Example: 25795: 2 - 5 + 7 - 9 + 5 = 0 11*0=11 so yes 25795 is divisible by 11
22578: 2-2+5-7+8 =6 not divisible by 11
7 is less fun
Enginerd951 ยท 1 points ยท Posted at 14:37:11 on May 25, 2016 ยท (Permalink)
You can have finite areas under curves that decay to zero over infinity.
BrahmsAllDay ยท 1 points ยท Posted at 14:38:07 on May 25, 2016 ยท (Permalink)
Take a square, divide into thirds length and width wise. You now have 9 squares. Punch out the middle square. Repeat the process with the remaining 8 squares ad infinitum. The resulting shape has an infinite perimeter but exactly 0 area.
DocBalls ยท 1 points ยท Posted at 14:38:11 on May 25, 2016 ยท (Permalink)
Realize that any decision or question you need answered in your life, math will provide your answer, just finding the correct formula is your path to success.
teetetotte ยท 1 points ยท Posted at 14:39:25 on May 25, 2016 ยท (Permalink)
0.999999... == 1
How? well,
0.11111... = 1/9
9 * 0.11111... = 9 * 1/9
0.99999... = 1
KapnKrumpin ยท 1 points ยท Posted at 14:39:35 on May 25, 2016 ยท (Permalink)
epi*i=-1
A mathematical expression that, at first glance makes absolutely no sense. An irrational number raised to the power of another irrational number times an imaginary number equals an even, negative number.
Additionally, you can't raise a number to a power and get a negative number. the closest you can theoretically get is zero.
Yet, this is a mathematically accurate formula. Plug it into any scientific calculator.
In my high school calculus class, I was told that a mathematician had it inscribed on his grave because it was so absurd. Not sure if that's true, though.
Finchyy ยท 1 points ยท Posted at 14:39:42 on May 25, 2016 ยท (Permalink)
The digital roots of a sequence of square numbers are palindromic.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289
1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1
Also, the digital root of any multiple of 9 is 9.
Kulaid871 ยท 1 points ยท Posted at 14:40:25 on May 25, 2016 ยท (Permalink)
Base 12 was used before and arguably is better, and ppl argue to change our base 10 system to it.
-jFk- ยท 1 points ยท Posted at 14:42:43 on May 25, 2016 ยท (Permalink)
It makes sense to choose the other door.
TheRiverOtter ยท 1 points ยท Posted at 14:42:56 on May 25, 2016 ยท (Permalink)
There is not a googol of anything in the universe. Source.
Zonemasta8 ยท 1 points ยท Posted at 14:43:23 on May 25, 2016 ยท (Permalink)
I swear I saw this exact thread with the exact anwsers about 4 days ago.
ghillerd ยท 1 points ยท Posted at 14:44:00 on May 25, 2016 ยท (Permalink)
36 is the sum of the first three cube numbers and the product of the first three square numbers. Also, it's the 8th triangular number and the 6th square number, being the smallest number other than 1 that's both, and it's the only one that's both who's square root is also triangular (again, excluding 1). It's 13-gonal. It's semiperfect because 6, 12, and 18 all divide into it, and when summed give 36. It's the sum of twin primes (17 and 19).
chadiman ยท 1 points ยท Posted at 14:44:32 on May 25, 2016 ยท (Permalink)
The fact that I just finished my last exam of this year. Until August that is where I will have to resit them.
cthulu0 ยท 1 points ยท Posted at 14:44:38 on May 25, 2016 ยท (Permalink)
Because there ~11million people in New York City, and the average human has way less than 11 millions hairs on his head, there are at least 2 people in NYC with the EXACT same number of hairs on their heads.
This is the pigeon hole principle.
_Eerie ยท 1 points ยท Posted at 16:20:07 on May 25, 2016 ยท (Permalink)
Can you prove this theory?
cthulu0 ยท 1 points ยท Posted at 19:56:20 on May 25, 2016 ยท (Permalink)
The pigeonhole principle is an established long ago proven mathematical theorem. It is also intuitive to understand. It states that if you have N holes and more than N pigeons which you are trying to put in the holes, then at least one hole will have 2 pigeons in it.
dick_freud ยท 1 points ยท Posted at 14:44:39 on May 25, 2016 ยท (Permalink)
i'm a big fan of the classic: multiply any number by 9 and the sum of all the digits in the answer always equals 9 (when you keep adding the digits to the point of having only 1 digit obviously). even works with decimals. eg. 113.9486 x 9 = 1025.5374 -> add that shit up and get 27 -> 2+7=9
Cruithne ยท 1 points ยท Posted at 14:45:31 on May 25, 2016 ยท (Permalink)
The harmonic series (1/1 + 1/2 + 1/3 + 1/4...) diverges (reaches infinity). The harmonic series missing any integer converges. Like, if you take out all the numbers with a 9 in them it never gets higher than 23. It doesn't have to be 9- as long as something is missing, it won't reach infinity.
flabbergastedrhino ยท 1 points ยท Posted at 14:45:52 on May 25, 2016 ยท (Permalink)
Central limit theorem truly portrays the beauty of numbers
REDace0 ยท 1 points ยท Posted at 14:46:00 on May 25, 2016 ยท (Permalink)
Almost all natural numbers are very very large.
(For whatever reasonable definition of "almost all" and "very very large" you care to make.)
diz4 ยท 1 points ยท Posted at 14:47:16 on May 25, 2016 ยท (Permalink)
I've always loved the Pythagorean Theorum a2 + b2 = c2
marpro15 ยท 1 points ยท Posted at 14:47:19 on May 25, 2016 ยท (Permalink)
If you want to know the square of a number, say 13, simply take the sqaure of the previous number, which is in this case 144 and add the number and the previous number to the square of the previous number, which means 12 + 13 + 144 = 169 = the square of 13
M_Night_Shamylan ยท 1 points ยท Posted at 14:47:54 on May 25, 2016 ยท (Permalink)
That 6 is afraid of 7 because 7 ate 9
neuropathica ยท 1 points ยท Posted at 14:48:38 on May 25, 2016 ยท (Permalink)
Zero times anything is zero
mynewaccount_420 ยท 1 points ยท Posted at 14:48:39 on May 25, 2016 ยท (Permalink)
Add up the digits of any number. If they add up to a multiple of 3, than the original number is also a multiple of 3.
i.e. 81 --> 8 + 1 = 9
Lacrimocyka ยท 1 points ยท Posted at 14:48:45 on May 25, 2016 ยท (Permalink)*
number 6174.) 1 - Take any four-digit number, using at least two different digits. (Leading zeros are allowed.) 2 - Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. 3 - Subtract the smaller number from the bigger number. 4 - Go back to step 2. The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations.
tck91 ยท 1 points ยท Posted at 14:49:04 on May 25, 2016 ยท (Permalink)
I LIVE FOR OBSCURE MATH FACTS.
8 x 12 = 102 - 22 = 96
That is: any two numbers multiplied equals the midpoint number squared minus (the distance between the higher/lower number and the midpoint) squared.
44 x 92 = 682 - 242
37 x 72 = 54.52 - 17.52
17.24 x 35.648 = 28.4442 - 9.2042
:) edited for word
Mikezster ยท 1 points ยท Posted at 14:49:12 on May 25, 2016 ยท (Permalink)
0.9 recurring is equal to one.
ndividualistic ยท 1 points ยท Posted at 14:50:11 on May 25, 2016 ยท (Permalink)
Math answers have no grey area (unless you get into higher mathematical functions). This makes me extremely happy. Edit: I can't spell.
Maninhartsford ยท 1 points ยท Posted at 14:50:14 on May 25, 2016 ยท (Permalink)
I don't have to do it anymore.
EHG123 ยท 1 points ยท Posted at 14:50:20 on May 25, 2016 ยท (Permalink)
The first isomorphism theorem
uwagapies ยท 1 points ยท Posted at 14:50:53 on May 25, 2016 ยท (Permalink)
Aleph Null, and transfinite numbers.
mercyful_fade ยท 1 points ยท Posted at 14:51:17 on May 25, 2016 ยท (Permalink)
That one about birthdays, that it's highly likely to have two people with the same bday when there's only like 50 or 100 people in a room.
rawrdid ยท 1 points ยท Posted at 14:51:38 on May 25, 2016 ยท (Permalink)
I give exactly 0 fucks! Amazing!
LoneWanderer520 ยท 1 points ยท Posted at 14:51:44 on May 25, 2016 ยท (Permalink)
2+2=4
MeNotSanta ยท 1 points ยท Posted at 14:51:46 on May 25, 2016 ยท (Permalink)
If you don't fuck math, math will fuck you!
[deleted] ยท 1 points ยท Posted at 14:51:57 on May 25, 2016 ยท (Permalink)
If you multiply eleven times another two digit number and to get the answer you can put the two digits at the front and end, then the middle digit will be the sum of both numbes(requires rounding after a certain point.)
I noticed it once while bored on a road trip.
majorwtf ยท 1 points ยท Posted at 14:52:12 on May 25, 2016 ยท (Permalink)
ฮฑยณฮฒCosฮผr2Secโ
[deleted] ยท 1 points ยท Posted at 14:52:32 on May 25, 2016 ยท (Permalink)
To within half a percent, pi seconds is a nano-century.
Globertbaratheon ยท 1 points ยท Posted at 14:53:02 on May 25, 2016 ยท (Permalink)
Multiplying by 9 can give you a factor that sums to 9. For example 9X9=81 8+1=9, 9X17=153 1+5+3=9, 9X11=99 9+9=18 1+8=9. Always helped me know if I multiplied by 9 correctly
AUS_Doug ยท 1 points ยท Posted at 14:53:34 on May 25, 2016 ยท (Permalink)*
Collatz Conjecture
Take any whole number.
If it's odd, multiply by 3 and add 1.
If it's even, divided it by 2.
Repeat and eventually you'll get to 1.
Example:
Start at 3 -> 3x3+1 = 10 -> 5 -> 5x3+1 = 16 -> 8 -> 4 -> 2 -> 1
They've proved this true (i.e. you won't get stuck in a loop) for every number up to (quite) a large number.
OtisTheZombie ยท 1 points ยท Posted at 14:54:13 on May 25, 2016 ยท (Permalink)
0.9 (repeating) is the same as 1.
slabby ยท 1 points ยท Posted at 14:54:51 on May 25, 2016 ยท (Permalink)
That there is not just one math, but in fact several different kinds of maths.
CosineTau ยท 1 points ยท Posted at 14:54:57 on May 25, 2016 ยท (Permalink)
The archimedean property is pretty legit.
I also really like isomorphisms in groups.
TheWillRogers ยท 1 points ยท Posted at 14:55:41 on May 25, 2016 ยท (Permalink)
I may be in graduate math classes, but set(2)/2 =1/sqrt2 will always bow my mind
my_work_acccnt ยท 1 points ยท Posted at 14:56:33 on May 25, 2016 ยท (Permalink)
.99999 (repeating) = 1
1/3 = .33333 repeating
2/3 = .66666 repeating
logic says next step is 3/3 = .99999 repeating, but we know any number divided by itself is equal to 1.
ask-a-local ยท 1 points ยท Posted at 14:56:35 on May 25, 2016 ยท (Permalink)
I've always loved the pigeonhole principle because it is so darned useful.
Put simply: if you have more pigeons than pigeonholes then at least one of the pigeonholes contains more than one pigeon.
The simple formulation might seem like it is too obvious to be useful, but it can be generalised into forms that are useful for solving problems involving probabilities and infinite sets.
Dima0425 ยท 1 points ยท Posted at 14:57:04 on May 25, 2016 ยท (Permalink)
The sum of any two prime number will always equal an even number.
Icko_ ยท 2 points ยท Posted at 15:05:43 on May 25, 2016 ยท (Permalink)
lol no - 2+3 = 5
LightningThieff ยท 1 points ยท Posted at 14:57:13 on May 25, 2016 ยท (Permalink)
Pythagoras (known most notably for the pythagorean thereom) believed beans were evil and this led to is death.
He thought beans pulled evil up from hell. An angry group of folks who disagreed with his work were after him one day and it was between them and a field of beans. He chose death.
Pink_Cleats ยท 1 points ยท Posted at 14:58:13 on May 25, 2016 ยท (Permalink)
Pi = ln (-1)/sqrt (-1)
I couldn't believe it when I saw the proof, but it blew my mind
tinkrman ยท 1 points ยท Posted at 14:58:24 on May 25, 2016 ยท (Permalink)
Take any 4 digit number, with at least one digit different than the others. (eg 3324) Arrange the digits in descending order (4332), and ascending order (2334), Find the difference (4332-2334 = 1998). Now repeat the process with 1998, eventually you will end up with: 6174
Kaprekar's constant
Romulus_Novus ยท 1 points ยท Posted at 14:59:21 on May 25, 2016 ยท (Permalink)
The Monty Hall Problem
omegaxysgaming ยท 1 points ยท Posted at 14:59:49 on May 25, 2016 ยท (Permalink)
111,111,111 * 111,111,111 gives you 12345678987654321
Sailormercuryaz ยท 1 points ยท Posted at 14:59:54 on May 25, 2016 ยท (Permalink)
7 8 9
Stink-Finger ยท 1 points ยท Posted at 15:00:53 on May 25, 2016 ยท (Permalink)
Any number who's components add up to 9 is divisible by 9.
2079 = 2 + 0 + 7 + 9 = 18 18 = 1 + 8 = 9
2079 is divisible by 9
voidFunction ยท 1 points ยท Posted at 15:01:13 on May 25, 2016 ยท (Permalink)
Start with an integer. Then, create a new integer that has the same number of digits as the original but is composed of nines. Divide the original by the new number, and you'll get a decimal number that is the first integer repeated indefinitely.
123 / 999 = 0.123123123123123...
80 / 99 = 0.808080808080808080...
jungl3j1m ยท 1 points ยท Posted at 15:01:27 on May 25, 2016 ยท (Permalink)
My favorite math non-fact is:
Proof that 2 = 1.
Assume that we have two variables a and b, and that: a = b
Multiply both sides by a to get: a2 = ab
Subtract b2 from both sides to get: a2 - b2 = ab - b2
This is the tricky part: Factor the left side (using FOIL from algebra) to get (a + b)(a - b) and factor out b from the right side to get b(a - b). If you're not sure how FOIL or factoring works, don't worryโyou can check that this all works by multiplying everything out to see that it matches. The end result is that our equation has become: (a + b)(a - b) = b(a - b)
Since (a - b) appears on both sides, we can cancel it to get: a + b = b
Since a = b (that's the assumption we started with), we can substitute b in for a to get: b + b = b
Combining the two terms on the left gives us: 2b = b
Since b appears on both sides, we can divide through by b to get: 2 = 1
bigdon199 ยท 2 points ยท Posted at 15:11:08 on May 25, 2016 ยท (Permalink)*
for those who aren't sure on this one, the trick is if a=b then a-b=0 so if you divide by (a-b) to cancel it out you're dividing by 0 which of course doesn't work.
jungl3j1m ยท 1 points ยท Posted at 15:18:53 on May 25, 2016 ยท (Permalink)
Needs spoiler tag.
bigdon199 ยท 1 points ยท Posted at 15:23:42 on May 25, 2016 ยท (Permalink)
you're right - sorry about that
[deleted] ยท 1 points ยท Posted at 15:02:13 on May 25, 2016 ยท (Permalink)
Scott Steiner has a 141 2/3 percent chance of beating Samoa Joe at Sacrifice.
q1w2e3r4t5z ยท 1 points ยท Posted at 15:02:47 on May 25, 2016 ยท (Permalink)
You can write all the numbers up to 999 without using the letter "a"
Like: One, two, three etc.
ollinarg_relyt ยท 1 points ยท Posted at 15:02:50 on May 25, 2016 ยท (Permalink)
111,111 x 111,111= 12345654321
Super simple one but for some reason I always found it to be really interesting.
Quuantix ยท 1 points ยท Posted at 15:03:15 on May 25, 2016 ยท (Permalink)
The proof based around Graham's number is so interesting. It is so incredibly large that if your mind tried to comprehend it, you would die of a brain overload. It is bigger than googolplexgoogolplex. If you learn up on the actual application of this number, you will be astounded at how unnecessarily big this number is for the app.
cucufag ยท 1 points ยท Posted at 15:03:15 on May 25, 2016 ยท (Permalink)
0.999... = 1
https://en.wikipedia.org/wiki/0.999...
Infinity is fun to talk about, and even though I've discussed this topic plenty of times, I still sometimes have a hard time grasping the concept. Most people struggle when they first learn about it as well.
captaineighttrack ยท 1 points ยท Posted at 15:03:22 on May 25, 2016 ยท (Permalink)
42
phenry1110 ยท 1 points ยท Posted at 15:03:32 on May 25, 2016 ยท (Permalink)
Not a fact but a fun proof. It will sometimes take a while for a person to catch the problem with this proof of 1=0
x = y. Then x2 = xy. Subtract the same thing from both sides: x2 - y2 = xy - y2. Dividing by (x-y), obtain x + y = y. Since x = y, we see that 2 y = y. Thus 2 = 1, since we started with y nonzero. Subtracting 1 from both sides, 1 = 0.
jknowlton ยท 1 points ยท Posted at 15:04:05 on May 25, 2016 ยท (Permalink)
The size of the set of all negative integers is equal to the set of all integers. That is, there are as many negative whole numbers as negative and positive integers. You can prove this by creating a bijective function (a one to one function) between the two sets.
Also it's math, not maths.
ComputerGeek516 ยท 1 points ยท Posted at 15:05:08 on May 25, 2016 ยท (Permalink)
That 2+2=5
ylmcc ยท 1 points ยท Posted at 15:05:09 on May 25, 2016 ยท (Permalink)
If it's very easy in an exam it's probably wrong too
rordooger ยท 1 points ยท Posted at 15:05:17 on May 25, 2016 ยท (Permalink)
99.99% of statistics are made up on the spot
Jddevos ยท 1 points ยท Posted at 15:15:12 on May 25, 2016 ยท (Permalink)
99.97% actually. Common mistake.
ComaToys ยท 1 points ยท Posted at 15:05:33 on May 25, 2016 ยท (Permalink)
An oldy but a goody.
The sum of individual numbers in a multiple of three will always add up to another multiple of three.
98754037690 x 3
296262113070
2+9+6+2+6+2+1+1+3+0+7+0 = 39
3+9 = 12
1+2 = 3
nehala ยท 1 points ยท Posted at 15:05:43 on May 25, 2016 ยท (Permalink)
By some interpretations and measures in physics, 1+2+3+4+5+6....+ infinity is -1/12.
https://www.youtube.com/watch?v=w-I6XTVZXww
Tinkletyme ยท 1 points ยท Posted at 15:05:49 on May 25, 2016 ยท (Permalink)
That if you add a bed, subtract clothes, divide her legs, you will multiply.
Joker1337 ยท 1 points ยท Posted at 15:06:16 on May 25, 2016 ยท (Permalink)
The Golden Ratio (ฮฆ) can be derived from the Fibonacci sequence (1, 1, 2, 3, 5, 8...) by alternatively adding and subtracting the ratio of subsequent values in the sequence:
vulp ยท 1 points ยท Posted at 15:06:26 on May 25, 2016 ยท (Permalink)
The square root of 69 is ate something.
IncognitoAnonymous ยท 1 points ยท Posted at 15:06:28 on May 25, 2016 ยท (Permalink)
111 111 111 * 111 111 111 = 123 456 789 876 543 21
meatb4ll ยท 1 points ยท Posted at 15:06:28 on May 25, 2016 ยท (Permalink)
Everything applies to everything else. When I learn combinatorics, I use stuff from analysis to solve problems. In representations, I needed combinatorics. And analysis used pieces of both. And everything is kind of multiple ways of looking at one problem at higher levels and that's sort cool.
Take voting theory - there are equivalent explanations both geometrically and abstract algebraically, and that's super cool!
Tivia ยท 1 points ยท Posted at 15:07:25 on May 25, 2016 ยท (Permalink)
That no matter what common core claims, 2 + 2 = 4 and be damned at how you arrived at the answer.
Joeg332 ยท 1 points ยท Posted at 15:07:55 on May 25, 2016 ยท (Permalink)
There are different sizes of infinity some are larger than others
3lectricboy ยท 1 points ยท Posted at 15:08:56 on May 25, 2016 ยท (Permalink)*
If you add up every number from 1 to infinity, the answer is -1/12. This is not a trick or play on words, and nobody knows why it works. The proof is relativity simple to understand too.
sauce
redditisadamndrug ยท 1 points ยท Posted at 16:17:19 on May 25, 2016 ยท (Permalink)
If you add up every number from 1 to infinity, AN answer is -1/12.
Another answer is that it is divergent and does not sum to a finite number. It all depends on your definition of "infinite sum".
[deleted] ยท 1 points ยท Posted at 15:09:07 on May 25, 2016 ยท (Permalink)
That there's a phone app that uses the camera to solve complex math problems.
growol ยท 1 points ยท Posted at 15:09:49 on May 25, 2016 ยท (Permalink)
You should always check your math because sometimes the product of two negative integers is a positive number.
MrNogi ยท 1 points ยท Posted at 15:10:12 on May 25, 2016 ยท (Permalink)
I'm probably a little late but: If you times 37 by multiples of 3 you get a really cool pattern of numbers
For example, 37 x 3 = 111, 37 x 6 = 222 and so on
gypsymoth94 ยท 1 points ยท Posted at 15:11:06 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is equal to -1/12. Blows my mind. It even has some useful applications in physics.
i.e. 1+2+3+4+5+6... = -1/12
redditisadamndrug ยท 1 points ยท Posted at 16:17:38 on May 25, 2016 ยท (Permalink)
If you add up every number from 1 to infinity, AN answer is -1/12.
Another answer is that it is divergent and does not sum to a finite number. It all depends on your definition of "infinite sum".
723723 ยท 1 points ยท Posted at 15:11:12 on May 25, 2016 ยท (Permalink)
This one is guaranteed to blow your mind!! The rule is anything x 9 when you add the sum will = 9. let me give you an example.
9x2=18.... 1+8=9
9x34=306.... 3+0+6=9
9x1025=9225... 9+2+2+5=18... 1+8=9
9x123456789=1,111,111,101 thats 9 ones!
try it with any number, if you need help let me know.
Zakimaruu ยท 1 points ยท Posted at 15:11:12 on May 25, 2016 ยท (Permalink)
On Earth, Affix a cord/rope between two points, no matter how taught you pull that cord/rope, it will never be a straight line/plane, there will always be a sag.
More of a physics example, but the math behind it is pretty cool.
ย As you pull tighter the sag gets less, but it's a function of 1/force, so to get zero sag you need infinite force.
drdugong727 ยท 1 points ยท Posted at 15:11:35 on May 25, 2016 ยท (Permalink)
.999999 forever (.9 repeating I don't know how to type that symbol) equals 1.
Not approximately 1, but exactly equals 1.
Best example I have to explain it is: 1/3 equals .3 repeating (most everyone understands and agrees with this). 1/3 plus 1/3 therefore equals .6 repeating. And 1/3 plus 1/3 plus 1/3 equals .9 repeating which also equals 3/3. Boom 3/3 equals 1 equals .9 repeating.
fbb755 ยท 1 points ยท Posted at 15:11:43 on May 25, 2016 ยท (Permalink)
The Pigeonhole Principle allows us to say with certainty things such as "There are at least two people in the city of New York who share the same number of hairs on their head" and "In a packed Carnegie Hall performance, there will be two people who have the same first and last initials."
These sound counterintuitive, but the Pigeonhole Principle is very simple, and seems obvious once you hear the explanation.
https://en.m.wikipedia.org/wiki/Pigeonhole_principle
Randy__Bobandy ยท 1 points ยท Posted at 15:11:46 on May 25, 2016 ยท (Permalink)
xlogY = ylogX
iSkyal ยท 1 points ยท Posted at 15:11:52 on May 25, 2016 ยท (Permalink)
That 0.999999... = 1
FuckingGOTim ยท 1 points ยท Posted at 15:35:25 on May 25, 2016 ยท (Permalink)
Is there any reason for this? Me and a friend were trying to figure out why 1/3+1/3+1/3=1 but if you take the decimals of each (0.333...+0.333...+0.333...) it would never reach 1 because they are all repeating infinitely.
redditisadamndrug ยท 1 points ยท Posted at 16:25:02 on May 25, 2016 ยท (Permalink)
You have to look at it from the perspective of
"If 0.999... represented a real number, which real number would it represent?"
You find that the only answer that makes sense is that 0.999... = 1.
In the real numbers there is no such thing as an infinitesimal difference, and so 1 - 0.999... = 0.000... = 0 thus they represent the same number along with many other factors.
Lots of people are assuming that 0.333... = 1/3 but if you can truly convince yourself that they are equal then along the way you should have convinced yourself that 0.999... = 1.
FuckingGOTim ยท 1 points ยท Posted at 16:27:52 on May 25, 2016 ยท (Permalink)
Huh, makes sense! Thanks!
iSkyal ยท 1 points ยท Posted at 01:23:39 on May 27, 2016 ยท (Permalink)
There are good videos on youtube that explain it very well and also if you type 0. 99999999999999 on a modern calculator and press enter it will say 1
GameRender ยท 1 points ยท Posted at 15:12:00 on May 25, 2016 ยท (Permalink)
In base. 13, 6x9=42
Katur ยท 1 points ยท Posted at 15:12:03 on May 25, 2016 ยท (Permalink)*
You can see multiple of 9 on your hands.
So for example 9 x 7. That would be your right index finger(7, from left to right) and you'd have 6 fingers to the left (including your left hand) and 3 to the right making the answer 63.
TimeToSackUp ยท 1 points ยท Posted at 15:12:09 on May 25, 2016 ยท (Permalink)*
9x1= 9 9= 9
9x2=18 1+8=9
9x3= 27 2+7=9
9x4=36 3+6=9
9x5=45 4+5=9
9x6=54 5+4=9
9x7=63 6+3=9
9x8=72 7+2=9
9x9=81 9+1=9
9x10=90 9+0=9
9x11=99 9+9=18 1+8=9
9x12=108 1+8=9
9x13=117 1+1+7=9
9x14=126 1+2+6=9
9x15=135 1+3+5=9
9x16=144 1+4+4=9
9x17=153 1+5+3=9
9x18=162 1+6+2=9
9x19=171 1+7+1=9
9x20=180 1+8+0=9
...
Thewhiteguccimane ยท 1 points ยท Posted at 15:12:31 on May 25, 2016 ยท (Permalink)
There are infinite numbers between 1 and 2, but none of them are 3
DoesntFearZeus ยท 1 points ยท Posted at 15:12:35 on May 25, 2016 ยท (Permalink)
The square of any number is:
(2 times every number less than the number summed) + the number.
5x5 = 1+1+2+2+3+3+4+4+5 = 25
And you can use this to get. The square of a number is the square of the number less than it, plus the number less than it plus the number.
5x5 = (4x4) +4+5 = 16 + 4 + 5 = 25
So if you know
25x25 = 625
Then
26x26 = 625 + 25 + 26 = 676
Then
29x29 = (30x30) - 30 - 29 = 900 - 30 - 29 = 841
Helps a lot with weird squares near easy squares.
Sometime during JHS or HS I figured this out. I'm sure I'm not the first one to do it, but I've never ran across it something they teach people in school. Made test on squares easier.
nottheavgjoe ยท 1 points ยท Posted at 15:12:40 on May 25, 2016 ยท (Permalink)
Simple facts: The sum of the first N odd numbers equals N-squared The sum of any three consecutive integers is always a multiple of 3 The sum of three consecutive integers, where the middle integer is a multiple of 3, is always a multiple of 9 (duh!)
40yearsoftrees ยท 1 points ยท Posted at 15:13:18 on May 25, 2016 ยท (Permalink)
Illegal prime numbers! https://www.reddit.com/r/todayilearned/comments/3flxj8/til_illegal_prime_numbers_exist_first_illegal/
Noctudeit ยท 1 points ยท Posted at 15:13:21 on May 25, 2016 ยท (Permalink)
The fact that mathematics is not a plural word, and therefore the appropriate short form is "math" not "maths".
sortior ยท 1 points ยท Posted at 15:14:22 on May 25, 2016 ยท (Permalink)
The square root of 69 is eight something...
MjolnirDK ยท 1 points ยท Posted at 15:14:54 on May 25, 2016 ยท (Permalink)
The size of graham's number
Darkeden251 ยท 1 points ยท Posted at 15:14:59 on May 25, 2016 ยท (Permalink)
Any number consisting only of 1s squared will result in an answer consisting of numbers in order, counting up then down.
Ex: 12 is 1, 112 is 121, 1112 is 12321, and so on.
bigdon199 ยท 1 points ยท Posted at 15:15:25 on May 25, 2016 ยท (Permalink)
lots of great maths facts from these guys https://www.youtube.com/user/numberphile
listix ยท 1 points ยท Posted at 15:15:55 on May 25, 2016 ยท (Permalink)
I like 1/4999 and 1/9997 but my favorite one is 1/998001. You might need wolfram alpha to check those.
dierubikdie ยท 1 points ยท Posted at 15:15:58 on May 25, 2016 ยท (Permalink)
142857 + 142857 = 285714
285714 + 142857 = 425871
428571 + 142857 = 571428
571428 + 142857 = 714285
714285 + 142857 = 857142
857142 + 142857 = 999999
1/7 is a hell of a fraction.
polytopic ยท 1 points ยท Posted at 15:16:08 on May 25, 2016 ยท (Permalink)
If you take the derivative of the area of a circle with respect to its radius, you get its perimeter. d/dr (\pi r2) = 2 \pi r
Anglosaxwegian ยท 1 points ยท Posted at 15:16:09 on May 25, 2016 ยท (Permalink)
Not a fact but I have a sneaking suspicion that a new universe is created every time someone divides by zero... like a tiny big bang happens inside your calculator that is dramatically smaller than a quark. Billions of years from now your calculator will be teaming with life... unaware of how tiny they are and unaware that other life forms are relatively close to them in proximity... Are we inside a calculator right now? O___O
Tavyr ยท 1 points ยท Posted at 15:16:35 on May 25, 2016 ยท (Permalink)
In the game Set, when the properties of each card are expressed as a vector of integers mod 3, a "set" is formed when sum of the vectors on three cards is the zero vector.
Dereg5 ยท 1 points ยท Posted at 15:16:38 on May 25, 2016 ยท (Permalink)
111,111,111ร111,111,111= 12,345,678,987,654,321
devonha ยท 1 points ยท Posted at 15:16:53 on May 25, 2016 ยท (Permalink)
The Four Color Theorem.
You can fill in any map (and have no adjacent bodies with the same color) with only four colors.
David21444 ยท 1 points ยท Posted at 15:16:53 on May 25, 2016 ยท (Permalink)
If you start at 0 and every odd number, +1, 3 5 7 9 11 You get a perfect square every time
gagsy92 ยท 1 points ยท Posted at 15:17:38 on May 25, 2016 ยท (Permalink)
Pretty simple one but to find out if a number is divisible by 3, just add all the digits together until you're left with a single digit, if that digit is divisible by 3, the original number is.
Example A: 2,375,274 = 2+3+7+5+2+7+4 = 30 = 3+0 = 3 = Divisible by 3.
Example B: 2,654,984 = 2+6+5+4+9+8+4 = 38 = 3+8 = 11 = 1+1 = 2 = Not divisible by 3.
PunctuationsOptional ยท 1 points ยท Posted at 15:17:54 on May 25, 2016 ยท (Permalink)
All these squares make a circle.
drmmrpngn ยท 1 points ยท Posted at 15:18:17 on May 25, 2016 ยท (Permalink)
111,111,111 x 111,111,111=12,345,678,987,654,321
razzec_phone ยท 1 points ยท Posted at 15:19:34 on May 25, 2016 ยท (Permalink)
144 is Gross
[deleted] ยท 1 points ยท Posted at 17:30:57 on May 25, 2016 ยท (Permalink)
Eew
NobGoblin64 ยท 1 points ยท Posted at 15:19:35 on May 25, 2016 ยท (Permalink)
If you have at least 1 threesome your average number of partners during sex will always be above 1.
GreyZeint ยท 1 points ยท Posted at 15:20:10 on May 25, 2016 ยท (Permalink)
Late to the party, but here we go.
If you take some building blocks and make a flat square out of them, some squares can be disassembled into two smaller squares using every block. A well known example of this is that a 5x5 square can be disassembled into a 3x3 and a 4x4 square. This is obvious because 32 + 42 = 52 . It can be relatively easily shown that there are infinitely many different squares with that property.
However, if you were to try the same with cubes you would not succeed, since no cube can be disassembled into two smaller cubes using every building block. This is a consequence of one of the most famous theorems called Fermat's Last Theorem. It states that the equation an + bn = cn , where a, b, c and n are positive integers, has no solution for n > 2. The theorem was conjectured in the 1600s by Pierre de Fermat but not proven until 1994 by Andrew Wiles.
cnk93 ยท 1 points ยท Posted at 15:20:16 on May 25, 2016 ยท (Permalink)*
None. None of the math facts are my favorite.
Source: I have dyscalculia.
pleasedontkillmyvibe ยท 1 points ยท Posted at 15:20:26 on May 25, 2016 ยท (Permalink)
That there is an 82% chance that using any of these math facts on your first date, won't get you laid.
tychonov ยท 1 points ยท Posted at 15:20:31 on May 25, 2016 ยท (Permalink)
I think no one has yet mentioned the Borwein integrals. I would write the integrals in this post if I knew how to include LaTeX conveniently.
Firebelley ยท 1 points ยท Posted at 15:20:43 on May 25, 2016 ยท (Permalink)
Apparently .99999999999999999.... = 1
https://en.wikipedia.org/wiki/0.999...#Proofs
KosherHitler ยท 1 points ยท Posted at 15:21:04 on May 25, 2016 ยท (Permalink)
1x1=2 Thanks Terrance Howard, you crazy fuck!
nietzescher ยท 1 points ยท Posted at 15:21:54 on May 25, 2016 ยท (Permalink)
The number of prime numbers up to some integer N is, roughly, N divided by the number of digits of N.
TenTonneMackerel ยท 1 points ยท Posted at 15:21:56 on May 25, 2016 ยท (Permalink)
4 is the only number where the amount of letters required to spell it out are equal to its value.
Retbull ยท 1 points ยท Posted at 15:21:58 on May 25, 2016 ยท (Permalink)
Godels incompleteness theorem. Given a system of operators you will always find that a paradox arises.
ecafyelims ยท 1 points ยท Posted at 15:21:58 on May 25, 2016 ยท (Permalink)
Even though i is an imaginary number, ei*pi is real (-1).
RadicalLemma ยท 1 points ยท Posted at 15:21:59 on May 25, 2016 ยท (Permalink)
If you chose two random positive integers, the probability that these two numbers have no common factor greater than 1 is 6/(pi2)
onboarderror ยท 1 points ยท Posted at 15:22:42 on May 25, 2016 ยท (Permalink)
you will die
_Eerie ยท 1 points ยท Posted at 16:32:34 on May 25, 2016 ยท (Permalink)
It's a biology fact, not maths fact.
onboarderror ยท 1 points ยท Posted at 17:34:49 on May 25, 2016 ยท (Permalink)
If I add "statistically speaking" to that it is :)
ElderlyPowerUser ยท 1 points ยท Posted at 15:23:05 on May 25, 2016 ยท (Permalink)
I am done taking math courses for the rest of my life.
zweigraf ยท 1 points ยท Posted at 15:23:11 on May 25, 2016 ยท (Permalink)
One of paper equals 4 of coin. Works every time!
thegreatestajax ยท 1 points ยท Posted at 15:23:46 on May 25, 2016 ยท (Permalink)
In the UK they call it maths.
boozeviking ยท 1 points ยท Posted at 15:23:57 on May 25, 2016 ยท (Permalink)
Pi is exactly 3!
xHeroOfWar022 ยท 1 points ยท Posted at 15:24:04 on May 25, 2016 ยท (Permalink)
666+666+666+6+6+6=666
conalfisher ยท 1 points ยท Posted at 15:24:25 on May 25, 2016 ยท (Permalink)
111,111,111 X 111,11,111= 12345678987654321
yagidy ยท 1 points ยท Posted at 15:24:40 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers = -(1/12)
Electric27 ยท 1 points ยท Posted at 15:24:49 on May 25, 2016 ยท (Permalink)
epi*I=-1. It's weird but plug it into your calculator
littlespoon22 ยท 1 points ยท Posted at 15:24:56 on May 25, 2016 ยท (Permalink)
There are the same number of prime numbers as even numbers.
Quadrapangle ยท 1 points ยท Posted at 15:25:37 on May 25, 2016 ยท (Permalink)
The fact that one class can change my gpa so much
seditive26114 ยท 1 points ยท Posted at 15:25:39 on May 25, 2016 ยท (Permalink)
That everything we know can be broken down into numbers and measured. That these numbers can justify peoples entire existence. They make or break how things work. Can be repeated and replicated by anyone who wants to try.
Also 69 is a sex thing and that is cool too.
No_God_For_Me_Thanks ยท 1 points ยท Posted at 15:25:47 on May 25, 2016 ยท (Permalink)
Saw this on reddit a few months ago. 10! = 6 Weeks
kerapang ยท 1 points ยท Posted at 15:25:49 on May 25, 2016 ยท (Permalink)*
I figured this one out of in fifth grade Any number squared is +2 the number squared before it. That's confusing so here's an example:
1x1=1 2x2=4 4-1=3
2x2=4 3x3=9 9-4= 5
3x3=9 4x4=16 16-9= 7
I've only ever tried it up to ~152 but it's true throughout.
EDIT: Reddit doesn't allow the carrot symbol so I used "X"
kyew ยท 1 points ยท Posted at 15:54:08 on May 25, 2016 ยท (Permalink)
Use a backslash to escape carets: "\^"
[deleted] ยท 1 points ยท Posted at 15:25:51 on May 25, 2016 ยท (Permalink)
Sacred geometry
MrDylanMoore ยท 1 points ยท Posted at 15:26:18 on May 25, 2016 ยท (Permalink)
That there's no 's' at the end of the word 'math.'
[deleted] ยท 1 points ยท Posted at 15:26:31 on May 25, 2016 ยท (Permalink)
The fact that is isn't plural in the United States. It's Math.
Project2r ยท 1 points ยท Posted at 15:26:46 on May 25, 2016 ยท (Permalink)
You can theoretically turn a 3d sphere inside out.
But not a 2d circle.
corndoggy67 ยท 1 points ยท Posted at 15:27:03 on May 25, 2016 ยท (Permalink)
X%of Y is equal to Y% of X
hard9649 ยท 1 points ยท Posted at 15:27:18 on May 25, 2016 ยท (Permalink)
1/9= 0.111111...
2/9= 0.222222...
3/9= 0.333333...
4/9= 0.444444...
5/9= 0.555555...
6/9= 0.666666...
7/9= 0.777777...
8/9= 0.888888
9/9= 0.999999 and also 1
SigurdZS ยท 1 points ยท Posted at 15:27:23 on May 25, 2016 ยท (Permalink)*
Ever been sitting at a cafรฉ table outside and been annoyed with your chair or table being wobbly?
Well you can fix it. With math.
movesaround ยท 1 points ยท Posted at 15:28:00 on May 25, 2016 ยท (Permalink)
The fact that you can tell right away whether someone is from America or GB by whether they say math or maths. On the odd occasion it might be a jabroni that goes to Princeton saying "maths".
[deleted] ยท 1 points ยท Posted at 15:28:27 on May 25, 2016 ยท (Permalink)
Riemann's Rearrangement Theorem: You can rearrange the terms of certain infinite series to get any number you want.
It's more detailed, but I'm not going to really about those details.
Lackeycharms ยท 1 points ยท Posted at 15:28:43 on May 25, 2016 ยท (Permalink)
You can never mathematically reach a door by going half the distance each time.
iam8up ยท 1 points ยท Posted at 15:28:49 on May 25, 2016 ยท (Permalink)
To come up with the volume of pizza it is pizz*a.
bustakapinyoass ยท 1 points ยท Posted at 15:29:01 on May 25, 2016 ยท (Permalink)
I've always liked that if you lose a bet, but then offer a another bet that is double the previous one, and repeat this until you finally win, you will walk away with a net gain.
I bet and lost $1, putting my overall at -$1. Then I bet $2 and lose, putting me at -$3. Then $4, putting me at -$7, etc until I finally win a bit and leave with $1.
The only downside is this assumes you have an infinite amount of money to bet with!
PM-ME_YOUR-DREAMS ยท 1 points ยท Posted at 15:29:11 on May 25, 2016 ยท (Permalink)
9 times any number, excluding 1 and 0, will still equal nine when the two digits are added together. Example... 9x9=81 8+1=9
austinlambert03 ยท 1 points ยท Posted at 15:29:11 on May 25, 2016 ยท (Permalink)
Sure it's not fancy, but 2 + 2 always equals 4, but sometimes equals fish.
fameistheproduct ยท 1 points ยท Posted at 15:31:21 on May 25, 2016 ยท (Permalink)
Sometimes, 2+2 equals 5.
FarSightXR-20 ยท 1 points ยท Posted at 15:29:43 on May 25, 2016 ยท (Permalink)
Maths has to be the worst fucking word in the world.
PAxlFitz ยท 1 points ยท Posted at 15:29:54 on May 25, 2016 ยท (Permalink)
Pi is exaclty 3!
ashesarise ยท 1 points ยท Posted at 15:30:30 on May 25, 2016 ยท (Permalink)
I get irrationally upset when I see "Math" referred to as "Maths". Its not called "Histories" is called "History". Its not called "Englishes" its called "English". Its not called "Sciences" its called "Science".
ThorinDev ยท 1 points ยท Posted at 15:30:44 on May 25, 2016 ยท (Permalink)
If X is irrational than X0.5 will be too. Hi Portal 2 Fans!
ectish ยท 1 points ยท Posted at 15:31:11 on May 25, 2016 ยท (Permalink)*
Nevemind
ClintRasiert ยท 1 points ยท Posted at 15:33:03 on May 25, 2016 ยท (Permalink)
What? No, it's not.
ectish ยท 1 points ยท Posted at 15:52:47 on May 25, 2016 ยท (Permalink)
Shit, highschool was too long ago.
drylandshark ยท 1 points ยท Posted at 15:31:47 on May 25, 2016 ยท (Permalink)
Mine
mikeash ยท 1 points ยท Posted at 15:31:50 on May 25, 2016 ยท (Permalink)
eฯ - ฯ = 20. This is hard to calculate properly, and most calculators will get it slightly off.
hasib1986 ยท 1 points ยท Posted at 15:32:09 on May 25, 2016 ยท (Permalink)
Take both your hands, not the palm side but the other side, like as if your looking at them, and from left to right you can easily do your 9 times table. So from the left if you put down your pinkie, you've got 9 fingers left meaning 1 times 9 equals 9. Then lift your pinkie back up and put down your wedding ring finger (also from the left), you will have your pinkie representing 1 and apart from your wedding finger which is down you will have 8 fingers left to the right i.e 2 times equals 18 and so on. :)
SiVGiV ยท 1 points ยท Posted at 15:55:41 on May 25, 2016 ยท (Permalink)
Also this
cboski ยท 1 points ยท Posted at 15:32:15 on May 25, 2016 ยท (Permalink)
The conversion factor between kilometers and miles is approximately the same as the factor affecting the Fibronacci's sequence. So when you have 1 1 2 3 5 8... 2 miles = 3 Km, 3 mi = 4.8 Km and 5 mi = 8 Km
SiVGiV ยท 1 points ยท Posted at 15:56:42 on May 25, 2016 ยท (Permalink)
This one's useful
no_en ยท 1 points ยท Posted at 15:32:16 on May 25, 2016 ยท (Permalink)
The sum of the positive natural numbers is -1/12
Jonusious ยท 1 points ยท Posted at 15:32:40 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers on to infinity is equal to -1/12.
cherz007 ยท 1 points ยท Posted at 15:32:52 on May 25, 2016 ยท (Permalink)
You can always determine if a number X is divisible by three by adding up the digits in the number X. If the sum of those digits is divisible by three, then X is divisible by three.
TH-42PWD8UK ยท 1 points ยท Posted at 15:32:52 on May 25, 2016 ยท (Permalink)
ELI5: up until a year ago it was math, now everybody has to gurgle out the word "maths".
Kandyman_12 ยท 1 points ยท Posted at 15:32:53 on May 25, 2016 ยท (Permalink)*
Whatever you do, maths will ruin your life.
OSUNOOB1 ยท 1 points ยท Posted at 15:33:04 on May 25, 2016 ยท (Permalink)
In a graph or any sort of diagram where lines are connected to each other with dots AKA vertices. If those vertices all have even degrees meaning they have an even number of lines connecting to other vertices than there exista an eulerian cycle where basically you can start at any vertice go through every possible line (edge) connecting the vertices ONCE and still go back to the original
pokemonpasta ยท 1 points ยท Posted at 15:33:07 on May 25, 2016 ยท (Permalink)
Get a calculator and keep divide 1 by 3, then the result of that, etc.
1/3 = 0.3333333...
/3 = 0.11111111...
/3 = 0.0370370370370...
/3 = 0.01234567901...
That's the last of the interesting ones tbh, but I thought that was pretty cool
simmelianben ยท 1 points ยท Posted at 15:33:09 on May 25, 2016 ยท (Permalink)
It's possible to count to 242 on one hand and 59048 on 2 hands if you use trinary.
Example:
Each knuckle is the next power of three and each full extension is the previous power of three*2.
queazan ยท 1 points ยท Posted at 15:33:10 on May 25, 2016 ยท (Permalink)
That the coefficients of binomial expansion as demonstrated by Pascal's triangle also perfectly dictate the probabilities of head/tail counts when flipping coins so long as you don't eliminate overcount. Interpret by summing up each row of pascal's triangle and treating each digit in a row as a single event's probability out of the sum. So:
When flipping a one-sided coin, every flip will always give you 1, out of 1 possible outcome. When flipping a single two sided coin, there is a 1 in 2 probability of one head, and 1 in 2 probability of one tail. When flipping two double-sided coins, there is a 1 in 4 possibility of two heads, 2 in 4 possibility of one head and one tail, 1 in 4 possibility of two tails. And for 3 double-sided coins, 1 in 8 chance of three tails, 3 in 8 chance of one head two tails, 3 in 8 chance of two head one tail, and 1 in 8 chance of all tails.
Or:
1
11
121
1331
It's trivial, but it absolutely enchants me that a simple observation about binomial expansion applies to binary probabilities. I believe (though I haven't tried to prove) that similar would hold for trinomial expansion and probabilities where each element has three outcomes, as the expansions really are just enumerating all possible outcomes of a given n-ary equation, I think, which is basically the same thing as simple probabilities.
[deleted] ยท 1 points ยท Posted at 16:52:42 on May 25, 2016 ยท (Permalink)
that's probably why it's called a binomial probablity. I thought about that fact and it was plenty clear to me that it's not a coincidence and there is plenty reaspn why.
queazan ยท 1 points ยท Posted at 18:13:40 on May 25, 2016 ยท (Permalink)
That's basically what I was getting at when I said that expansions are just enumerating all possible outcomes, and why I'm moderately sure it'll apply to trinomial and upwards expansions. I've just learned over time that when it comes to math, I should never assume that I know what the hell I'm doing :P
And I know it's not "coincidence", but I still find it enchanting. It's one of the wonderful things about math - that you can prove one thing many different ways, and each of those ways interrelate and shine a little more light on some phenomena underneath the thing you're looking at. I just feel that this is a wonderfully clear example of it.
[deleted] ยท 1 points ยท Posted at 18:28:32 on May 25, 2016 ยท (Permalink)
haha we can totally agree on that. I think I'm just less enchanted by that example. I thought for a bit, huh, and then it makes sense to me. The thing that really strike me was all the construct they used in Real Analysis and further down some Banach space stuff. It's just so fascinating but difficult to wrap my head around at the same time.
I took Statistical Inference the same semester as Functional Analysis. That's probably one of the reasons that I found statistics way easier. A binomial distribution, after all, is still quite straightforward, compared to an infinite dimensional Hilbert space or something like that.
queazan ยท 1 points ยท Posted at 18:37:02 on May 25, 2016 ยท (Permalink)
That's completely fair. It's a very subjective thing, I think. I mean, in general I love any example where one particular mathematical concept or idea ties directly in to another one. And I don't have the statistical background that you have - I did mostly calc and discrete mathematics.
I think, too, for me it's more impactful because it was something I worked out on the side of something else. A few of my coworkers had invented some silly betting game, where they flipped a set number of coins and tried to guess whether more would be heads or tails. That got me thinking about probability, and working out the statistics of their game...which in turn lead me to realizing the correlation between binomial expansion and binomial probabilities.
So maybe a big chunk of it for me is that "I came up with it myself" (which, I mean, I know I didn't come up with it first but you know what I mean) - it was that sort of "bolt out of the blue" that made me go "oh shit, bitchez, these maths are totally insane".
Note: I did not actually say that to my coworkers, but I really wish I had.
[deleted] ยท 1 points ยท Posted at 19:09:17 on May 25, 2016 ยท (Permalink)
haha. THAT IS REALLY NEAT. You know if you were born 500 years early it would be queazan distribution instead of Bernoulli distribution! What is neat, is that modern statistics/probability theory is indeed founded on gambling, either throwing a coin, or a die.
I can see where that comes from :) I think it really takes a genius to actually found things. It's really easy to understand, nowadays, why it is a Bernoulli distribution. But whoever comes up with it themselves are genius, imo.
lowlightsource ยท 1 points ยท Posted at 15:33:13 on May 25, 2016 ยท (Permalink)
12345679 x 8 = 98765432
BlueKlay ยท 1 points ยท Posted at 15:33:56 on May 25, 2016 ยท (Permalink)
Take any number and add the digits up, then subtract that number from the original. It will always be divisible by 9.
Ex: 23,045
2+3+0+4+5=14
23,045-14=23,031
23,031/9=2,559
[deleted] ยท 1 points ยท Posted at 16:51:35 on May 25, 2016 ยท (Permalink)
it is fascinating until you think about the proof. suppose the number is two digit. 10x+y. what you did is basically (X+y)-(10x+y) = -9x. of course it's divisible by 9.
ShadeofIcarus ยท 1 points ยท Posted at 15:34:14 on May 25, 2016 ยท (Permalink)
.9 repeating is equal to 1.
1/3 = .3 repeating.
1/3*3 = 1
.3 repeating * 3 = .9 repeating
OnlyMath ยท 1 points ยท Posted at 15:34:15 on May 25, 2016 ยท (Permalink)
There are infinite degrees of infinity.
Also our basic number sets were essentially built upon the existence of an empty set.
[deleted] ยท 1 points ยท Posted at 15:34:44 on May 25, 2016 ยท (Permalink)
The amount of times this question was asked this month > The amount of times a question should be asked on ask reddit in one month
[deleted] ยท 1 points ยท Posted at 15:35:10 on May 25, 2016 ยท (Permalink)
22รท7 is really close to Pi.
FilemonNeira ยท 1 points ยท Posted at 15:35:16 on May 25, 2016 ยท (Permalink)
Doing the best at each step doesn't guarantee the best at the end.
Simple example: Suppose we have coins of value 1,10,25 and we want to get a value with as few coins as possible. If you always take the largest possible value, called greedy, you may fail. Say you want 31, if you are greedy you get 25,1,1,1,1,1,1 but the optimal is 10,10,10,1.
In fact, is very rare that a greedy algorithm produces the actual optimal.
[deleted] ยท 1 points ยท Posted at 15:35:19 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 2 points ยท Posted at 15:58:48 on May 25, 2016 ยท (Permalink)
Uh, we can definately prove that 1+1=2. I've done it myself even, it isn't that difficult if you've done a bit of set theory.
[deleted] ยท 1 points ยท Posted at 18:31:35 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 2 points ยท Posted at 18:34:58 on May 25, 2016 ยท (Permalink)
It is proven that peano arithmetic=>1+1=2, or ZFC=>1+1=2. What do you mean by proven? Of course it has to start from axioms, you can't prove anything without axioms. For a start, you need axioms to define 1,2,+ and =.
[deleted] ยท 2 points ยท Posted at 16:49:01 on May 25, 2016 ยท (Permalink)
I remember that argument from college in Real Analysis. that was when I realized that I can never be a mathematician. I can learn but I'm not that smart to come up with something like that lol
pedrobeara ยท 1 points ยท Posted at 15:38:44 on May 25, 2016 ยท (Permalink)
1 added to 1 is not going to make 11 is it?
FTWwings ยท 1 points ยท Posted at 15:47:58 on May 25, 2016 ยท (Permalink)*
this looks interesting , tell me more about not proving 1 + 1
highenergyAdam ยท 1 points ยท Posted at 15:35:20 on May 25, 2016 ยท (Permalink)
The integral of circumference becomes the area of a circle. Pretty neat how formulas for shapes all connect with calculus.
wuop ยท 1 points ยท Posted at 15:35:38 on May 25, 2016 ยท (Permalink)
That Zeno's Paradox is an easy way to remember geometric summation.
DaJoW ยท 1 points ยท Posted at 15:35:38 on May 25, 2016 ยท (Permalink)
If you add all natural numbers (1+2+3+4+...) the sum is -1/12.
6010_new_aquarius ยท 1 points ยท Posted at 15:35:40 on May 25, 2016 ยท (Permalink)
Godel's Incompleteness Theorem
Sixpool965 ยท 1 points ยท Posted at 15:35:41 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is equal to -1/12. There is a very cool numberphile video about this on YouTube.com/watch?v=w-I6XTVZxww
bli ยท 1 points ยท Posted at 15:35:59 on May 25, 2016 ยท (Permalink)
Given natural numbers r and s (for s<r) where one is odd, one is even, and their greatest common factor is 1:
You can generate every reduced pythagorean triple as: r2 - s2 ; 2rs ; r2 + s2
tjdavids ยท 1 points ยท Posted at 15:36:34 on May 25, 2016 ยท (Permalink)
That if you have a series of all positive integers ascending (1+2+3+4+5+6+7+8+9...) and you need to do algebra on it you can just replace the series with -1/12.
WorthyPython ยท 1 points ยท Posted at 15:36:38 on May 25, 2016 ยท (Permalink)
a straight line is just a circle with infinite radius
rtfmnoob ยท 1 points ยท Posted at 15:36:40 on May 25, 2016 ยท (Permalink)
Gabriel's horn. Otherwise known as the infinite paint can. With infinite surface area but finite volume. It can't hold enough paint to paint the outside of its own paint container! Gabriel's horn!
Edit: Format and spell
[deleted] ยท 1 points ยท Posted at 16:46:49 on May 25, 2016 ยท (Permalink)
is it a similar idea to Cantor's set where it is not countable but the length of the set is 0?
rtfmnoob ยท 1 points ยท Posted at 18:40:12 on May 25, 2016 ยท (Permalink)
I'll have to dig into Cantors set. I haven't head of it before. The idea is that essentially a molecule of paint will get stuck near the the narrow end of the funnel. But the surface area continues on to infinity but there is no more volume that can squeeze past the circumference of a molecule in the funnel.
[deleted] ยท 2 points ยท Posted at 19:06:27 on May 25, 2016 ยท (Permalink)
ah I see. Interesting. Cantor set has a similar idea on 1d I think, where you can have infinite amount of numbers, but the length of the set itself is 0 because it is nowhere dense or something. https://en.wikipedia.org/wiki/Cantor_set
Atlasony ยท 1 points ยท Posted at 15:37:28 on May 25, 2016 ยท (Permalink)
You can actually divide by zero.
PYbusiness ยท 1 points ยท Posted at 15:37:51 on May 25, 2016 ยท (Permalink)
Isn't this only true if you assume winds operate in two dimensions? If winds move other than parallel to the surface, you can have winds everywhere, I would have thought.
DiabloCanyonOne ยท 1 points ยท Posted at 15:38:35 on May 25, 2016 ยท (Permalink)
sqrt(2) = 2 * sin(pi/4)
I understand the connection, but I always thought it was kinda neat...
mishaxz ยท 1 points ยท Posted at 15:38:50 on May 25, 2016 ยท (Permalink)
Are there programs that can calculate proofs?I mean figure out the proof for some problems?
[deleted] ยท 1 points ยท Posted at 16:45:21 on May 25, 2016 ยท (Permalink)
depends on what kind of problems I think. algorithms won't help you once you set into abstract math (iirc).
CactrotRunner ยท 1 points ยท Posted at 15:39:03 on May 25, 2016 ยท (Permalink)
I never understood why, perhaps an expert can ELI5, but if 1/3 + 1/3 + 1/3 = 1 and 1/3 = .3333(repeating) then why does .3333 + .3333 + .3333 = .9999 (repeating), and not 1.
I understand they're infinitely close, but they aren't equal which upsets me.
[deleted] ยท 1 points ยท Posted at 15:46:05 on May 25, 2016 ยท (Permalink)
They are not infinitely close, they happen to be the same number! We sometimes are blown out by that, but there's no rule that says that a number has an unique way of writing it down (for example, it's crystal clear that 1/2 = 0.5).
About 0.9999... (with an infinite trail of 9's) being the same than 1, what you said is just one of the multiple proofs of it. There are many ways of proving it, my personal favourite being that if two numbers are different, there's always a different number in the middle (for example, as 0.5372 is different than 0.5373 we can find a number in the middle, such as (0.5372+0.5373)/2). As there is no number between 0.999... and 1, we can conclude that they are the same number.
canalis ยท 1 points ยท Posted at 15:48:06 on May 25, 2016 ยท (Permalink)
No ELI5, but 1/3 is not actually equal to 0.33333333... The difference is just infinitely small and thus does not matter mathematically.
So 3 x 0.3333333333... Is infinitely close to 1 but never actually 1, kinda like an asymptote that gets ever closer to 1
TalksInMaths ยท 1 points ยท Posted at 15:48:55 on May 25, 2016 ยท (Permalink)
They are equal, and you just described one of the proofs. They're "infinitely close" meaning that the difference between them is smaller than any real number, so the difference between them is zero.
1-0.9 = 0.1
1-0.99 = 0.01
1-0.999 = 0.001
...
1-0.999... = 0
TreeEyedRaven ยท 1 points ยท Posted at 15:39:30 on May 25, 2016 ยท (Permalink)
I wish I could find the exact quote, it was something along the lines of: "Nothing is more equal than a set of parallels" which was how the equals sign was conceived. I remember it was from a book call "against the gods" I read about 10 years ago
theflyingspaghetti ยท 1 points ยท Posted at 15:40:08 on May 25, 2016 ยท (Permalink)
144 is the 12th Fibonnaci number, it is also 12 squared, it is also the only square Fibonnaci number.
moomsy ยท 1 points ยท Posted at 15:40:27 on May 25, 2016 ยท (Permalink)
I guess just the fact that infinity is everywhere if you look for it. Any space between two integers/points can be cut in half an infinite amount of times. The existence of asymptotes is probably the coolest thing I can think of.
Numerate ยท 1 points ยท Posted at 15:40:49 on May 25, 2016 ยท (Permalink)
1 + 2 = 3 4 + 5 + 6 = 7 + 8
As you may have guessed, it keeps going: 9 + 10 + 11 + 12 = 13 + 14 + 15 Et cetera
Expressed generally, for any natural number n: (n2) + (n2+1) + (n2+2) + ... + (n2+n) = (n2+n+1) + (n2+n+2) + ... + (n2 + 2*n)
Once you express it in the general form like this, you can prove it with induction. I had a lot of fun with this when I first saw the original statement of two equations. Nerd-sniped me for a good hour playing with it.
Seventy9Inchez ยท 1 points ยท Posted at 15:41:28 on May 25, 2016 ยท (Permalink)*
Probably a bit late to the party, but I love how you can use the Fibonacci sequence to convert miles to km and vice versa.
Here's how:
The Fibonacci sequence goes as known like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Take two consecutive numbers, let's say 5 and 8. There's actually 5 miles in 8 kilometers. This happens because the ratio between two consecutive numbers in the sequence closes up on the golden ratio, which is 1,618. Coincidentally, there are 1,609 km in a mile, so there you go!
Indie_Dev ยท 1 points ยท Posted at 15:41:40 on May 25, 2016 ยท (Permalink)
That the sum of all whole numbers is -1/12
Here's a video that explains it. It's a very well known fact and is used in many areas of physics where it works flawlessly.
[deleted] ยท 1 points ยท Posted at 16:40:56 on May 25, 2016 ยท (Permalink)
you'll learn what exactly is sum_(I=1)an as n goes to infinity in first semester as a math major.
stevenmc ยท 1 points ยท Posted at 15:41:42 on May 25, 2016 ยท (Permalink)
If you drop a stone on the ground, it must first fall half way.
To continue to the ground, it must first fall half way again.
Repeat.
Does the stone ever mathematically hit the ground?
turtlepie ยท 1 points ยท Posted at 15:41:57 on May 25, 2016 ยท (Permalink)*
. 9999 (repeating) = 1
1/3 =. 3333 (repeating)
3(1/3) = 3(.3333 repeating)
1=.9999 (repeating)
SlightlyBreezy ยท 1 points ยท Posted at 15:42:01 on May 25, 2016 ยท (Permalink)
My favorite is simple 0+x=x 0*x=0 00=1 Zero is my favorite its almost always a small quirk in math
le-secret-account ยท 1 points ยท Posted at 15:42:08 on May 25, 2016 ยท (Permalink)
I can find the number of your mother in the decimals of pi
MT_Flesch ยท 1 points ยท Posted at 15:42:33 on May 25, 2016 ยท (Permalink)
pie are squared
Tactical_Wolf ยท 1 points ยท Posted at 15:42:33 on May 25, 2016 ยท (Permalink)
Four is the only number with the same number of letters as it's numerical value.
[deleted] ยท 2 points ยท Posted at 15:45:30 on May 25, 2016 ยท (Permalink)
So has five. Edit. Did a recount. Incorrect. Edit2. Wait three does too. Edit3. Shit
terminalvelocit3 ยท 1 points ยท Posted at 15:42:41 on May 25, 2016 ยท (Permalink)
...333333 = -1/3 Assume that ...333333 = x Thus,
...333330 = 10x
...333333 = x
-...00003 = 9x
Dividing by 9 gives us
-1/3 = x
[deleted] ยท 1 points ยท Posted at 16:39:04 on May 25, 2016 ยท (Permalink)
this means you don't know how to do math.
terminalvelocit3 ยท 1 points ยท Posted at 17:08:12 on May 25, 2016 ยท (Permalink)*
It's legit.
It uses the same logic as /u/kimera-houjuu 's comment.
mikdavi84 ยท 1 points ยท Posted at 15:42:43 on May 25, 2016 ยท (Permalink)
That if you drop the 's' from the end of it, it 100% removes your chance of sounding like a gross foreigner
suzie42Q ยท 1 points ยท Posted at 15:42:53 on May 25, 2016 ยท (Permalink)
Zeno's paradox. All motion is impossible, in order to go from point A to point B you have to go halfway (point C). In order to go from point A to point C, you must go halfway (point D), this can be duplicated infinite times therefore, theoretically you will never make it from point A to point B.
But obviously we all can make it from point A to point B, but it's a fun.
dawrastler ยท 1 points ยท Posted at 15:43:14 on May 25, 2016 ยท (Permalink)
0 factorial is 1
42nd_towel ยท 1 points ยท Posted at 15:43:20 on May 25, 2016 ยท (Permalink)
The fact that 0.999999(repeating) is equal to 1. Due to limits and infinity and all that. This can be demonstrated intuitively by thinking about the fractions 1/3 and 2/3. They are 0.3333(repeating) and 0.6666(repeating). So then 3/3 should be equal to 0.9999(repeating) if you multiply, say, 1/3 times 3. And also equal to 1.
theLEVIATHAN06 ยท 1 points ยท Posted at 15:43:40 on May 25, 2016 ยท (Permalink)
My favorite math fact is that I'm fucking terrible at it.
TarekAbb ยท 1 points ยท Posted at 15:44:12 on May 25, 2016 ยท (Permalink)
knowing that you can never really prove that a square is a square. try to look up mathematical and philosophical proofs that a square has right angles and is equal on both sides, most proofs will reach a point where you have to assume that an infinity it would withstand but we don't get to that infinity we just say that assuming we get there it will be square. When i learned that you can never really say a square is a square my mind was blown
ur_labia_my_INBOX ยท 1 points ยท Posted at 15:44:37 on May 25, 2016 ยท (Permalink)
Pick a number in your head. Add 6 to that number, then subtract 2, divide by 3 and add 19.
mcmcc ยท 1 points ยท Posted at 15:44:51 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + ... = -1/12
Similarly, 1 + 1 + 1 + 1 + ... = -1/2
jywn4679 ยท 1 points ยท Posted at 15:56:31 on May 25, 2016 ยท (Permalink)
Not true.
wdr1 ยท 1 points ยท Posted at 15:44:52 on May 25, 2016 ยท (Permalink)
.999999... Is exactly equal to 1.0
IrregardingGrammar ยท 1 points ยท Posted at 15:45:12 on May 25, 2016 ยท (Permalink)
My favorite math fact is someone saying "maths" immediately makes them seem like a pretentious tryhard.
[deleted] ยท 1 points ยท Posted at 15:45:13 on May 25, 2016 ยท (Permalink)
Top notch thread, guys.
jborbz ยท 1 points ยท Posted at 15:45:32 on May 25, 2016 ยท (Permalink)
That boobs trick on a calculator is pretty rad.
Vaelik ยท 1 points ยท Posted at 15:45:45 on May 25, 2016 ยท (Permalink)
You actually can divide by zero. Thank you dividing by conjugate.
Deni_Dana ยท 1 points ยท Posted at 15:45:45 on May 25, 2016 ยท (Permalink)
x% of y is y% of x
DaddyCatALSO ยท 1 points ยท Posted at 15:45:53 on May 25, 2016 ยท (Permalink)
The formula for finding the area of a larger square from unit squares.
eitoadyaso ยท 1 points ยท Posted at 15:46:33 on May 25, 2016 ยท (Permalink)
In the UK, they call "math" "maths"!
TheIncredibleWalrus ยท 1 points ยท Posted at 15:46:48 on May 25, 2016 ยท (Permalink)
Any integer modulo 10 will give you the last digit of this integer
(Meaning: if you divide an integer with 10 the remaining number will always be it's last digit).
This might sound really simple and obvious but I don't think many people realize it.
It can have many applications, especially in Computer Science and various algorithms. For example, if you add two integers of any size the last digit of that sum will be the last digit of the sum of the two numbers modulo, etc.
rauschen ยท 1 points ยท Posted at 15:46:54 on May 25, 2016 ยท (Permalink)
When choosing colours for different regions on a map, you only need four different colours to ensure that no two adjacent regions have the same colour!
If you wanna read more
[deleted] ยท 1 points ยท Posted at 15:46:57 on May 25, 2016 ยท (Permalink)
Every Prime Number, except for 2 and 3, is one more or one less than a multiple of 6.
brokenha_lo ยท 1 points ยท Posted at 15:47:31 on May 25, 2016 ยท (Permalink)
There are more unique arrangements in a deck of playing cards than there are atoms in our solar system.
[deleted] ยท 1 points ยท Posted at 15:47:53 on May 25, 2016 ยท (Permalink)
The Fibonacci sequence has actually nothing to do with the Golden Ratio.
CatSoul_ ยท 1 points ยท Posted at 15:49:04 on May 25, 2016 ยท (Permalink)
How can this thread make it to the frontpage almost every week
SomanydynamoS ยท 1 points ยท Posted at 15:49:10 on May 25, 2016 ยท (Permalink)
If you add up all the positive intergers, i.e 1+2+3+4...etc. to infinity, you get -1/12 as the sum. This still blows my mind. Proof: https://www.youtube.com/watch?v=w-I6XTVZXww
jywn4679 ยท 2 points ยท Posted at 15:56:10 on May 25, 2016 ยท (Permalink)
Not true, the sum obviously diverges.
SomanydynamoS ยท 1 points ยท Posted at 15:59:46 on May 25, 2016 ยท (Permalink)
explain please
jywn4679 ยท 2 points ยท Posted at 16:02:05 on May 25, 2016 ยท (Permalink)
A sum diverges if it keeps getting bigger and bigger, and is not bounded. The sum in question if clearly not bounded, since if it was bounded by x then just let N be any integer larger than x, and then 1+2+...+N>x. It can be proven that divergent series don't converge.
What converge means is that the sum keeps getting closer to some value. This sum actually just gets further and further away from -1/12, so it certainly doesn't converge to it.
SomanydynamoS ยท 1 points ยท Posted at 16:06:58 on May 25, 2016 ยท (Permalink)
Did you watch the video? It looks like this is an accepted answer for the sum of all positive integers, and its used effectively in physics calculations. Infinity doesn't always give intuitive answers.
jywn4679 ยท 1 points ยท Posted at 16:09:26 on May 25, 2016 ยท (Permalink)
I've seen the video before, it's wrong because you cannot manipulate infinite series like that.
In some contexts it makes sense to assign 1+2+3+... the value -1/12, but the sum absolutely does not equal -1/12 under the normal definitions of sum and converge.
It is not an accepted answer. This isn't a time when infinity is unintuitive.
SomanydynamoS ยท 1 points ยท Posted at 16:15:22 on May 25, 2016 ยท (Permalink)
BTW, I'm not arguing, I'm genuinely curious if you had more information. I found this video because I subscribe to numberphile and thought it was cool.
jywn4679 ยท 2 points ยท Posted at 16:19:33 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/askscience/comments/3v9kd7/why_is_12345_112/cxlwu3g
He explains it fairly well I think. The key idea is that (as the video sort of shows) IF 1+2+3+... had a value, THEN that value would be -1/12. For there we pretend that it converges and see what we can do with it.
As for the applications to physics, in some calculations someone ended up with the result 1+2+3+..., but this would have made no sense since they know the answer to their problem could not be infinity. They plugged in the value of -1/12 and suddenly it all works. I don't think it is fully understood why it works, but physics is more concerned with making things work than knowing why.
SomanydynamoS ยท 1 points ยท Posted at 16:26:48 on May 25, 2016 ยท (Permalink)
Interesting, thanks!
[deleted] ยท 1 points ยท Posted at 16:34:39 on May 25, 2016 ยท (Permalink)
the sum doesn't exist. for a limit to exist, it must converge. in this case it doesn't even converge and therefore the limit doesn't exist.
the video is not true.
tallpapab ยท 1 points ยท Posted at 15:49:34 on May 25, 2016 ยท (Permalink)
One favorite is that nobody says "maths" in the US.
VCRPornAddict ยท 0 points ยท Posted at 15:50:06 on May 25, 2016 ยท (Permalink)
Who gives a fuck? Are you honestly that naive to think Americans are the only people that browse reddit?
tallpapab ยท 1 points ยท Posted at 15:59:31 on May 25, 2016 ยท (Permalink)
Well, Mr. Potty Mouth, I merely find it amusing that in the American colonies they think of "Math" as a singular subject whereas in other places it's often rendered as if it were a plural. What an odd conclusion you jump to, thinking that I must not realize that Yankees are not the entirety of Reddit. Carry on with your VCR pornography, oh confident one.
VCRPornAddict ยท 2 points ยท Posted at 16:32:11 on May 25, 2016 ยท (Permalink)
Well I'll give you the benefit of the doubt as per your intentions with your original comment, but the way you wrote it certainly suggested a passive aggressive tone. You can bet that I'll continue with my VCR pornos.
Ibarfd ยท 1 points ยท Posted at 15:49:36 on May 25, 2016 ยท (Permalink)
That pie r squared even though pies are round.
[deleted] ยท 1 points ยท Posted at 15:49:39 on May 25, 2016 ยท (Permalink)
If you add the single digits of any number together and then subtract it from the original number you will always get a multiple of 9.
Ex: 23 2+3=5 23-5=18
Its great for simple magic tricks that give people the feeling that they have some control.
incathuga ยท 1 points ยท Posted at 15:50:09 on May 25, 2016 ยท (Permalink)
Borsuk-Ulam: Given a continuous function f from the sphere to the plane, there exist points x and -x on the sphere such that f(x) = f(-x).
Example in plain English: There are two points exactly opposite of each other on the Earth with the same temperature and air pressure.
The fun thing about this is that the proof doesn't use what you might expect (ie, calculus); it uses topology and group theory, which are about space and number systems and are in some sense about as far from calculus as you can get in the realm of math.
[deleted] ยท 1 points ยท Posted at 15:50:24 on May 25, 2016 ยท (Permalink)
The pattern of seeds in sunflowers, as well as many other plant life follows the Fibonacci sequence
Erch ยท 1 points ยท Posted at 15:57:15 on May 25, 2016 ยท (Permalink)
The "steel ball run" series of Jojo's bizarre adventure used the Fibonacci sequence as a mechanic for super powers. Shit was cray.
[deleted] ยท 1 points ยท Posted at 16:22:33 on May 25, 2016 ยท (Permalink)
I'm not into anime but interesting. I'll have to look it up
Erch ยท 1 points ยท Posted at 18:04:27 on May 25, 2016 ยท (Permalink)
Well, that series is only in the manga so far. The anime is catching up pretty quickly though (25 years worth of comics being turning into television takes a while). To sum it up though: the two protagonists have the ability to throw objects -mostly steel balls-, at the "golden ratio"... somehow. This somehow grants them the ability to do all kinds of things. Yeah... Jojo's bizarre adventure is pretty weird.
DHELMET47 ยท 1 points ยท Posted at 15:50:26 on May 25, 2016 ยท (Permalink)
ei = pi
texasjoe ยท 1 points ยท Posted at 15:50:33 on May 25, 2016 ยท (Permalink)
Really elementary level one, here. If you spread all of your fingers out, you have the basic times table for the number 9. What's 4*9? Pull down your fourth finger from the left and count the remaining fingers on the left and right side to get the tens and ones value respectively. Kid me hated nine multiplication until I was taught this.
lazyant ยท 1 points ยท Posted at 15:50:51 on May 25, 2016 ยท (Permalink)
A 2-dimensional being could prove that 3 dimensions exist, some theorem in my topology class.
AlwaysInnocent ยท 1 points ยท Posted at 15:51:45 on May 25, 2016 ยท (Permalink)
22/7 is a better approximation for pi than 3.14
TalksInMaths ยท 1 points ยท Posted at 15:51:50 on May 25, 2016 ยท (Permalink)
The uncountability of the reals.
inika101 ยท 1 points ยท Posted at 15:51:59 on May 25, 2016 ยท (Permalink)
1/2 = 3/6
Now add the numerators 1 + 3 = 4
Now add the denominators 2 + 6 = 8
Then divide the answers 4/8 = 1/2 = 3/6
[deleted] ยท 1 points ยท Posted at 16:31:15 on May 25, 2016 ยท (Permalink)
if a/b = C/d, then (a+C)/(b+d)= a/b.
I learned it in elementary school. the proof is dead simple.
[deleted] ยท 1 points ยท Posted at 15:52:01 on May 25, 2016 ยท (Permalink)
1+1=window
loklok90 ยท 1 points ยท Posted at 15:52:16 on May 25, 2016 ยท (Permalink)
x = 0.999...
10x = 9.999...
10x = 9 + x
9x = 9
x = 1
Therefore: 0.9999... = 1
kingsoloman28 ยท 1 points ยท Posted at 15:52:31 on May 25, 2016 ยท (Permalink)
The probablity of a random number containing a 3 (this can be substituted for any number 1-9) that is less than 10x is equal to (10x - 9x )/ 10x which approaches one as x increases.
[deleted] ยท 1 points ยท Posted at 15:52:32 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers 1+2+3+4....=-1/12
That's a sum from positive 1 to positive infinity mind you.
jywn4679 ยท 1 points ยท Posted at 15:55:46 on May 25, 2016 ยท (Permalink)
Not true.
[deleted] ยท 1 points ยท Posted at 16:29:44 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
jywn4679 ยท 1 points ยท Posted at 16:30:41 on May 25, 2016 ยท (Permalink)
Did you actually read even the intro to that article? It clearly states the series diverges, and can be assigned the value -1/12.
[deleted] ยท 1 points ยท Posted at 16:37:30 on May 25, 2016 ยท (Permalink)
Yes, and I'm very proud of you having read words too.
Doesn't strike you as even a bit interesting that the sum of all positive integers, up to infinity, can be assigned a value at all, and that it's a negative one, and a fraction at that? And this is done using standard methods used for solving many traditional mathematical series, and that the result is also used in other high level mathematics and physics problems? Or do you just want to sound like you have a big peepee on the internet?
jywn4679 ยท 1 points ยท Posted at 16:39:32 on May 25, 2016 ยท (Permalink)
In some sense the series can be assigned any value you want. Giving it this value is interesting for other reasons, as are the physical applications. However it is still very false under convensional definitions.
And the standard emthods used are used wrongly, they only apply to covnergent series.
[deleted] ยท 1 points ยท Posted at 15:52:43 on May 25, 2016 ยท (Permalink)
.999999 = 1
x=.999999 10x= 9.99999
then subtract the first equation from the second aaand just like magic...
10x-x=9.99999-.999999 9x=9 x=1
KeatingOrRoark ยท 1 points ยท Posted at 15:52:45 on May 25, 2016 ยท (Permalink)
Being able to do the multiples of 9 on your hands.
avshockey ยท 1 points ยท Posted at 15:52:48 on May 25, 2016 ยท (Permalink)*
epi*i+1=0. Math is strange since all these "special" numbers e, pi, sqrt -1, 1, and 0 can all be related by a relatively simple equation!
eXLoV3 ยท 1 points ยท Posted at 15:53:33 on May 25, 2016 ยท (Permalink)*
I hope i'm not late to the party, but the graphic for the ecuation (ex - e-x )/2 looks like a neckless and the ecuation is called the neckless ecuation. I find it cute.
not_gern_blanston ยท 1 points ยท Posted at 15:53:53 on May 25, 2016 ยท (Permalink)
I hope this is on-topic can somebody help me with this? this always has me scratching my head. if you stand in front of a wall and move halfway towards the wall from where you are standing, and do it an infinite amount of times, you will never reach the wall. can somebody explain this like I'm five?
[deleted] ยท 1 points ยท Posted at 16:28:21 on May 25, 2016 ยท (Permalink)
think of it as distance left. the first time you move, you have half distance left. the second time, you still have half of half. each time you move, there is some distance left not covered. no matter how many times you move, the distance not covered is still there, therefore, you can grt infinitely close, but never really reach it.
not_gern_blanston ยท 1 points ยท Posted at 16:54:32 on May 25, 2016 ยท (Permalink)
thank you for this. I kind of get that I guess were still has me scratching my head is the fact that you will never reach it. at some point you will be down to a space smaller than an atom and I guess it brings to mind how small a space can be cut in half yet never get there! Thanks
Vpie649 ยท 1 points ยท Posted at 15:54:03 on May 25, 2016 ยท (Permalink)
.9 repeating = 1
Hellcowz ยท 1 points ยท Posted at 15:54:04 on May 25, 2016 ยท (Permalink)
The mystery of 3 6 9
GoldenSpiral20 ยท 1 points ยท Posted at 15:54:07 on May 25, 2016 ยท (Permalink)
6 is a perfect number. 6's divisors are 3, 2, & 1, and 3+2+1= 6.
ticknosto ยท 1 points ยท Posted at 15:54:09 on May 25, 2016 ยท (Permalink)
Benford's law says that naturally occurring leading numbers are more likely to be small (i.e. 1 is more common than 2 is more common than 3...)
Things like electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants all follow this rule and it's not fully understood why.
Benford's law is regularly used to detect fraud by large financial institutions and has been in used as evidence in criminal cases.
jdf06007 ยท 1 points ยท Posted at 15:54:14 on May 25, 2016 ยท (Permalink)
I'm late to this, but there is a geometric shape that exists (Gabriel's Horn) that has a finite volume but an infinite surface area. In other words, you could fill with paint, but never paint it.
teh_g ยท 1 points ยท Posted at 15:54:33 on May 25, 2016 ยท (Permalink)
In America we call it math.
LEEVINNNN ยท 1 points ยท Posted at 15:54:38 on May 25, 2016 ยท (Permalink)
Mine is that in the land of the free, and the home of the brave, we just call it "math"
atw527 ยท 1 points ยท Posted at 15:54:44 on May 25, 2016 ยท (Permalink)
http://imgs.xkcd.com/comics/e_to_the_pi_minus_pi.png
NinjaoftheNorth ยท 1 points ยท Posted at 15:54:49 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers (1 + 2 + 3 + 4...) is -(1/12). See the Wikipedia article on it, or the Numberphile video.
MagikarpCan ยท 1 points ยท Posted at 15:55:14 on May 25, 2016 ยท (Permalink)*
Infinities are funny. They make weird things happen.
For example:
There are as many even numbers as there are counting numbers (1, 2, 3, etc.). There are also as many multiples of three as there are counting numbers. There are also as many multiples of one hundred as there are counting numbers.
This actually applies to multiples of any integer except zero. (Integers are the positive and negative counting numbers, and zero.) Multiples of googol? There are as many of those as there are counting numbers. Multiples of Graham's Number? Same thing. We can do this because we never run out of multiples of a given a nonzero integer.
Speaking of integers, there are as many of those as counting numbers. We can go further. You know rational numbers? Numbers that can be represented by fractions? Turns out there are as many of those as there are counting numbers. What about the rational numbers between 0 and 1? There are an infinite number of those, right? Yep, and there are as many of those as there are counting numbers.
All these sets (multiples of a given integer, the integers themselves, rationals, rationals within an interval) are called "countably infinite" because they are the same size as the set of counting numbers. You can do this trick with any countably-infinite set.
Let's try going one step further. Let's take the real numbers, which are the rational numbers and the irrationals. (Irrationals are numbers that can't be represented by fractions, like pi or e or the golden ratio.) Are there as many of those as there are counting numbers? No. There are actually more of them. It turns out that the set of real numbers is bigger than the set of counting numbers. This set is uncountably infinite. You could say that "its infinity is bigger than the infinity of the counting numbers."
But this means that there are more than one kinds of infinity, right? And since there are more than one, we can talk about how many there are, right? Yes, and this brings me to the fact I actually wanted to share.
There are so many infinities that there there is no infinity large enough to describe it.
[deleted] ยท 1 points ยท Posted at 15:55:18 on May 25, 2016 ยท (Permalink)
The way you can shuffle a pack of cards (52!) is huge. From http://czep.net/weblog/52cards.html and much more fun to tell at parties than just the 'when you shuffle a pack it has never been in that order ever':
NotPercyChuggs ยท 1 points ยท Posted at 15:55:34 on May 25, 2016 ยท (Permalink)
That I don't need that shit at all in my line of work.
vprufus7 ยท 1 points ยท Posted at 15:56:13 on May 25, 2016 ยท (Permalink)
The difference of the squares of any two prime numbers greater than 3 is a multiple of 24.
schoolsbelly ยท 1 points ยท Posted at 15:56:16 on May 25, 2016 ยท (Permalink)
I don't like this thread
exoxe ยท 1 points ยท Posted at 15:56:33 on May 25, 2016 ยท (Permalink)
0 = 1 if 1 = 0
UNBR34K4BL3 ยท 1 points ยท Posted at 15:56:35 on May 25, 2016 ยท (Permalink)
0.999... is exactly equal to 1
If you don't believe it, you're wrong
cjdoyle ยท 1 points ยท Posted at 15:56:41 on May 25, 2016 ยท (Permalink)
I don't know why but the word "maths", just doesn't sound right to me, it sounds like something incomplete.
I stick with mathematics
perhaps it's my nature as a silly american
How2Smash ยท 1 points ยท Posted at 15:57:00 on May 25, 2016 ยท (Permalink)
If you count the letters of a number then count the letters of that number and repeat that, you will always end at four.
Example:
11 -> 6 -> 3 -> 5 -> 4
King-Kunta24 ยท 1 points ยท Posted at 15:57:17 on May 25, 2016 ยท (Permalink)
1+1= Window
kyew ยท 1 points ยท Posted at 15:57:26 on May 25, 2016 ยท (Permalink)
Most numbers start with 1
buckingATniqqaz ยท 1 points ยท Posted at 15:57:29 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers (1, 2, 3, 4, ...) is -1/12
scumbag-reddit ยท 1 points ยท Posted at 15:57:30 on May 25, 2016 ยท (Permalink)
Damn Brits and their 'maths'
Sarah728 ยท 1 points ยท Posted at 15:57:31 on May 25, 2016 ยท (Permalink)
A million seconds is around 11 days and a billion seconds is about 31 years
[deleted] ยท 1 points ยท Posted at 15:57:35 on May 25, 2016 ยท (Permalink)
0.(9) = 1
https://en.wikipedia.org/wiki/0.999...
[deleted] ยท 1 points ยท Posted at 15:57:39 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6... = -1/12
Berlinia ยท 1 points ยท Posted at 15:57:48 on May 25, 2016 ยท (Permalink)*
There is a type of number called trancendental number. e and ฯ are trancendentals. The funny thing about trancendentals is that:
a) They are the only type of numbers that are truly infinite (so infinite and uncountable). So the reason the real line has infinite amounts of numbers in it (uncountably) is because of those little fuckers, that are absurdly difficult to detect.
b) We know relatively little about them. Proving a number is trancedental is absurdly difficult. Only recently it was proven that ex is one of those, but e + ฯ may or may not be!
BazingaSLC ยท 1 points ยท Posted at 15:57:49 on May 25, 2016 ยท (Permalink)
The Birthday Problem in statistics where if there are 23 people in a room there's a 50% chance two share a birthday
https://en.m.wikipedia.org/wiki/Birthday_problem
Vaxtin ยท 1 points ยท Posted at 15:57:50 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7+8+9...= -1/12
All positive integers added together equals a negative fraction... blows my mind.
Here's the proof: (Numberphile) https://www.youtube.com/watch?v=w-I6XTVZXww
8mins long
Feiyue ยท 1 points ยท Posted at 15:58:13 on May 25, 2016 ยท (Permalink)
All of the positive integers added together equals minus one twelfth.
1+2+3+4+5... = -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
TrapperJon ยท 1 points ยท Posted at 15:58:25 on May 25, 2016 ยท (Permalink)
111,111 x 111,111= 12345678987664321
downingp ยท 1 points ยท Posted at 15:58:33 on May 25, 2016 ยท (Permalink)*
111111 * 111111 = 12345654321
11111 * 11111 = 123454321
1111 * 1111 = 1234321
111 * 111 = 12321
11 * 11 = 121
deltora ยท 1 points ยท Posted at 15:58:38 on May 25, 2016 ยท (Permalink)
2 2 is the same as 2 x 2
BazingaSLC ยท 1 points ยท Posted at 15:58:49 on May 25, 2016 ยท (Permalink)
Proof .9 repeating actually equals 1.
https://en.m.wikipedia.org/wiki/0.999...
I-Am-the-Snuggler ยท 1 points ยท Posted at 15:58:57 on May 25, 2016 ยท (Permalink)
My favorite fact is that in the US we refer to as math, and pretty much everywhere else it's referred to as maths.
thegraaayghost ยท 1 points ยท Posted at 15:59:07 on May 25, 2016 ยท (Permalink)
I like the divisibility rule of 3.
Any number that is a multiple of 3 will always have digits that sum to a multiple of 3.
The digits of 15 sum to 6. The digits of 336 sum to 12. The digits of 450087 sum to 24.
It's a somewhat useful trick if you're trying to factor a number.
The same thing works with 9.
mathprof ยท 1 points ยท Posted at 15:59:08 on May 25, 2016 ยท (Permalink)
There are as many real numbers in the interval [0, 1] as there are on the rest of the entire (infinite) number line. This works for any interval you choose.
capilot ยท 1 points ยท Posted at 15:59:31 on May 25, 2016 ยท (Permalink)
eiฯ = -1
Tenth grade, thought I knew a lot of math (champion of the math team). Heard this tidbit, went to my math teacher. He goes "Really?", does some math I couldn't begin to follow, and then says "Huh, I'll be damned, it is."
That's when I realized I wasn't nearly as smart as I thought I was.
Fredricothealien ยท 1 points ยท Posted at 15:59:46 on May 25, 2016 ยท (Permalink)
Europeans will never have a pi day
Trowbee ยท 1 points ยท Posted at 16:14:59 on May 25, 2016 ยท (Permalink)
We have 22nd July though
Fredricothealien ยท 1 points ยท Posted at 19:19:47 on May 25, 2016 ยท (Permalink)
It's supposedly closer to 21.0
MuckingAbout ยท 1 points ยท Posted at 15:59:48 on May 25, 2016 ยท (Permalink)
1 is the loneliest numbers. It's even worse than 2.
BazingaSLC ยท 1 points ยท Posted at 16:00:13 on May 25, 2016 ยท (Permalink)
In topography, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
https://en.m.wikipedia.org/wiki/Four_color_theorem
JackParagon ยท 1 points ยท Posted at 16:00:58 on May 25, 2016 ยท (Permalink)
That everything fits together perfectly makes sense..
OR when no ones looking.. You just do whatever you want and say it makes sense (goddamn you Euclid guy)
Wideandtight ยท 1 points ยท Posted at 16:01:02 on May 25, 2016 ยท (Permalink)
Gabriel's horn is a mathematical Construct with infinite Surface area and finite volume . Suppose you want to paint the inside of the horn, all You'd need is a finite Volume of paint to fill it to full and coat the sides . But since the Surface area is infinity , You just painted an infinite Surface with a finite amount of paint '
tasty-fish-bits ยท 1 points ยท Posted at 16:01:25 on May 25, 2016 ยท (Permalink)
ej*pi+1=0
SupersonicEmbryonic ยท 1 points ยท Posted at 16:01:39 on May 25, 2016 ยท (Permalink)
The fact that people elsewhere call it "Maths", when in the US we just call it "Math"
this_onlyforamoment ยท 1 points ยท Posted at 16:01:43 on May 25, 2016 ยท (Permalink)
commenting as a bookmark
Ioseb ยท 1 points ยท Posted at 16:01:44 on May 25, 2016 ยท (Permalink)
It's maybe already been posted. But based on quantum mechanics and black holes and stuff, if you'd walk a googolplex meters straight out from where you are and into space, chances are you'd eventually stumble upon an exact copy of yourself. Mathematically speaking of course.
ZbaconZ ยท 1 points ยท Posted at 16:01:48 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers starting at 1 = -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
It's kinda iffy, and the math basically requires combining two entirely different studies of math, but it shows up in quantum physics a bunch.
agamemnomnom ยท 1 points ยท Posted at 16:01:49 on May 25, 2016 ยท (Permalink)
I've always like Kaprekar's constant. Rearrange any 4 digit number, not starting with zero, into descending order minus ascending order. Get the sum and rearrange them again. And you will always eventually reach 6174.
Ex.
5432 โ 2345 = 3087 8730 โ 0378 = 8352 8532 โ 2358 = 6174 7641 โ 1467 = 6174
pjokinen ยท 1 points ยท Posted at 16:01:49 on May 25, 2016 ยท (Permalink)
epi*i = -1
Crazy to think that those three very important figures equal such a mundane number when arranged like this
MoneyIsTiming ยท 1 points ยท Posted at 16:02:02 on May 25, 2016 ยท (Permalink)
52! is the number of combinations that a deck of 52 cards can be shuffled into. 52! is such an enormous number that humans can't comprehend its size. It is estimated that if there were a billion stars with a billion planets each with 1 million people in each planet shuffling a deck of cards 1,000 times per second, orders of cards would just now start repeating if they have been shuffling since the time the first deck of cards was created.
FoolishChemist ยท 1 points ยท Posted at 16:02:17 on May 25, 2016 ยท (Permalink)
102 + 112 + 122 = 132 + 142
Hablodicaprio ยท 1 points ยท Posted at 16:03:11 on May 25, 2016 ยท (Permalink)
That it's my last year of math in school. Feels good.
fabulous_frolicker ยท 1 points ยท Posted at 16:03:21 on May 25, 2016 ยท (Permalink)
0.999 repeating infinitely is =1. Our teacher blew the classes mind with the proof since no one believed it.
Jmsaint ยท 1 points ยท Posted at 16:03:52 on May 25, 2016 ยท (Permalink)
The sum of all positive intergers (1+2+3+.... Up to infinity) is -1/12
(Well kinda)
http://www.smithsonianmag.com/smart-news/great-debate-over-whether-1234-112-180949559/
kroxigor01 ยท 1 points ยท Posted at 16:04:09 on May 25, 2016 ยท (Permalink)
-2sin666 degrees = phi
fatclownbaby ยท 1 points ยท Posted at 16:04:12 on May 25, 2016 ยท (Permalink)
Birthday paradox.
23 people in a room, there is a 50% chance two people share a birthday.
70 people in a room and it's 99.9%
dingboodle ยท 1 points ยท Posted at 16:04:49 on May 25, 2016 ยท (Permalink)
TIL I didn't learn nearly enough math in school.
[deleted] ยท 1 points ยท Posted at 16:04:55 on May 25, 2016 ยท (Permalink)*
The sum of all natural number equals -1/12
1+2+3+4+5+6+7+......=-1/12
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_โฏ
Rowfl ยท 1 points ยท Posted at 16:07:59 on May 25, 2016 ยท (Permalink)
How o.O
Elegant427 ยท 1 points ยท Posted at 16:04:57 on May 25, 2016 ยท (Permalink)*
{ [ 12 + 144 + 20 + 3 * โ(4) ] / 7 } + 5 * 11 = 9ยฒ + 0
Edit: Formatting messed it up.
Editยฒ: Someone beat me to it... :(
raxacorico_4 ยท 1 points ยท Posted at 16:05:03 on May 25, 2016 ยท (Permalink)
That it is all a theory. Math has yet to be truly proven.
jordawesome ยท 1 points ยท Posted at 16:05:15 on May 25, 2016 ยท (Permalink)
The sum of all positive whole numbers from 1 onward has a finite, non positive result: -1/12.
1 + 2 + 3 + 4 + .... = -1/12.
FromOuterSuburbia ยท 1 points ยท Posted at 16:05:17 on May 25, 2016 ยท (Permalink)
If you have a set a containing n + 1 positive integers, there will be two numbers i and j in the set such that i โ j is divisible by n.
It's cooler if you actually try it yourself. I'll pick n to equal 3. Just thinking of completely random numbers off the top of my head:
a = { 172; 11; 61,726,632; 650,213 }
Allow i = 650,213, j = 11
i โ j = 650,213 โ 11 = 650,202
650,202 / n = 650,202 / 3 = 216,734
gillyboatbruff ยท 1 points ยท Posted at 16:05:28 on May 25, 2016 ยท (Permalink)
0.99999999..... equals exactly one.
phroggish_one ยท 1 points ยท Posted at 16:05:56 on May 25, 2016 ยท (Permalink)
The Rule of Threes is my personal favorite.
wiivile ยท 1 points ยท Posted at 16:06:02 on May 25, 2016 ยท (Permalink)
The title of this thread is too British for me to respond.
t3rneado ยท 1 points ยท Posted at 16:06:03 on May 25, 2016 ยท (Permalink)
ITT: /r/theydidthemath
CavalEAR ยท 1 points ยท Posted at 16:06:37 on May 25, 2016 ยท (Permalink)*
With any two digit number.
x+y=n
x-y= z
n+z=t
t/2=x (or y depending on which is the bigger number between x and y)
n-z=r
r/2=y (or x depending on which is the bigger number between x and y)
Gandeloft ยท 1 points ยท Posted at 16:06:39 on May 25, 2016 ยท (Permalink)
1+1=2..
in8nirvana ยท 1 points ยท Posted at 16:06:48 on May 25, 2016 ยท (Permalink)
The sum of the powers of 2 from 0 to (n-1) is equal to (2 to the nth power) minus 1.
ArtchR ยท 1 points ยท Posted at 16:06:58 on May 25, 2016 ยท (Permalink)
That 1 = 0,999...
x = 0,999 / 10x = 9,999... / 10x - x = 9,999... -0,999... / 9x = 9 / x = 1/ 1 = 0,999...
Goretho ยท 1 points ยท Posted at 16:07:24 on May 25, 2016 ยท (Permalink)
You can get someone to name any number and you can easily tell if it is evenly divided with 9.
Take 2386 for example. (2386 / 9) = 265.11111
But 2376 is evenly divided. (2376 / 9) = 264
How can you tell?
Add 2 + 3 + 7 + 6 = 18
Since 18 is evenly divided by 9, so is the entire number. Great little party trick!
Edit: Easier to read
nil_von_9wo ยท 1 points ยท Posted at 16:07:57 on May 25, 2016 ยท (Permalink)
Multiply 9 by any non-zero integer. If there is more than one digit, add these digits to each other, repeating until reduced to one digit. The result will be 9.
hamsterish ยท 1 points ยท Posted at 16:07:58 on May 25, 2016 ยท (Permalink)
Law of Nines: Take any random list of numbers, from 2 numbers to ....however many. Calculate the sum of the individual numbers and take it away from the original number. The answer will always be a multiple of 9. Add all the numbers of the answer and they will also be a multiple of 9, etc.
379372649 = 3+7+9+3+7+2+6+4+9 = 50
379372649-50 = 379372599 = 9 x 42152511
3+7+9+3+7+2+5+9+9 = 54
5+4=9
It stems from the structure of base 10. If we counted in base 9, it would be called the Law of Eights :D
SpicyMax ยท 1 points ยท Posted at 16:08:12 on May 25, 2016 ยท (Permalink)
This math poem http://i.imgur.com/NFxLEq7.png
wyrmsonmorkeleb ยท 1 points ยท Posted at 16:08:37 on May 25, 2016 ยท (Permalink)
aln b = bln a
Bluemer2 ยท 1 points ยท Posted at 16:09:12 on May 25, 2016 ยท (Permalink)
That the sum 1+2+3+4+......=-1/12
BOSTONF4N ยท 1 points ยท Posted at 16:09:14 on May 25, 2016 ยท (Permalink)
If you multiply something by 5. you can add a 0 to the other number and find half.
LordTengil ยท 1 points ยท Posted at 16:09:26 on May 25, 2016 ยท (Permalink)
That there are an equal amount of numbers between 1 and 2 as ther are numbers between 1 and 3.
For everyone that thinks this is obviously bullshit, real numbers are weird. Cardinality, how you measure how large a set is, is also very weird when dealing with infinites. It has a very intutive interpretation: Two sets have an equal amount of numbers if you can somehow pair them up, one by one, so that you use all numbers in both sets. But the conclusions you reach are weird.
mhordeuxlol ยท 1 points ยท Posted at 16:09:28 on May 25, 2016 ยท (Permalink)
Since the sequence of numbers in Pi's decimals is chaotic and infinite you can pick whatever number you want with how many digit you want and you'll find it somewhere in the decimals of Pi
tommasz ยท 1 points ยท Posted at 16:09:49 on May 25, 2016 ยท (Permalink)
2 is the only even prime number.
lxBATESxl ยท 1 points ยท Posted at 16:10:10 on May 25, 2016 ยท (Permalink)
x0 = 1
Proof is rather straight-forward seeing that
x-2 = 1/(xx) x-1 = 1/x x0 = ? x1 = x x2 = xx x3 = xxx
[deleted] ยท 1 points ยท Posted at 16:10:15 on May 25, 2016 ยท (Permalink)
Math is bullshit and is the work of the devil.
random_us3rname ยท 1 points ยท Posted at 16:10:47 on May 25, 2016 ยท (Permalink)
Many of the good ones have already been mentioned but one rather basic thing I haven't seen in this thread yet:
To find out whether a number is divisible by 9 just calculate the sum of the digits and see whether that is divisible by 9. Also works for 3. For 11 you have to calculate an alternating sum of the digits like 6809 would be 9-0+8-6=11 which is divisible by 11 and so is 6809.
JComposer84 ยท 1 points ยท Posted at 16:10:49 on May 25, 2016 ยท (Permalink)
I used to have a teacher who's license tag read: SQRT-1 People would say "what does squirt one mean?" Square Root of Negative 1! The Imaginary Number he would say.
A neat and helpful little math trick for everyday life. If you get paid hourly, and want to know how much you make per year, you take your hourly wage and multiply it by 2, and add 3 zeros. Therefore if you make $20 / hr, you roughly make $40k per year (if you work 40 hours a week)
xShuksanCat ยท 1 points ยท Posted at 16:10:58 on May 25, 2016 ยท (Permalink)
Two is the only integer that doesn't have the letter "e" in it.
Invader9292 ยท 1 points ยท Posted at 19:03:45 on May 25, 2016 ยท (Permalink)
Four? six? thirty-two, etc.. ?
xShuksanCat ยท 1 points ยท Posted at 20:33:26 on May 25, 2016 ยท (Permalink)
Sorry, prime number.
gologologolo ยท 1 points ยท Posted at 16:11:03 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+... into infinity is equal to -1/12
https://youtu.be/w-I6XTVZXww
cnwilks ยท 1 points ยท Posted at 16:11:11 on May 25, 2016 ยท (Permalink)
I'm not sure that this fits, but I've always enjoyed the puzzle of the three businessmen who show up to a hotel, and there's only one room left. The room rate is $30, and each of them put in $10 a piece.
After they get to their room, the desk clerk realized that the room rate was only $25, so he sends $5 to the room with the bellhop. He gives them the $5, and they give him a $2 tip, and pocket $1 each.
That means that each of them paid $9 for their share of them room, which adds up to $27, and when you add the $2 tip back in, it amounts to $29. Where did the other dollar go?
washheightsboy3 ยท 3 points ยท Posted at 16:43:00 on May 25, 2016 ยท (Permalink)
Check the couch cushions. Always at least a dollar in there.
misdirected985 ยท 2 points ยท Posted at 16:16:51 on May 25, 2016 ยท (Permalink)
Nah bro
Neurokarma ยท 2 points ยท Posted at 16:47:51 on May 25, 2016 ยท (Permalink)
You don't add the 2 you subtract to get 25
SweetLenore ยท 1 points ยท Posted at 16:23:32 on May 25, 2016 ยท (Permalink)
No it would be $9 and some change they each paid which would add up to $28.
vckadath ยท 1 points ยท Posted at 16:11:11 on May 25, 2016 ยท (Permalink)
Saw this on reddit last year: 111,111,111 x 111,111,111 = 12345678987654321
chill3willy ยท 1 points ยท Posted at 16:11:36 on May 25, 2016 ยท (Permalink)
Magic number 9
h-jay ยท 1 points ยท Posted at 16:11:58 on May 25, 2016 ยท (Permalink)*
The positional representation of any rational number is non-unique.
All integers have two representations in any base. E.g. 1=0.(9)=0.99999... in base 10, or 1=0.(1)=0.11111... in base 2.
All rationals have at least one base where their positional representation is non-unique. E.g. for one third, 0.1=0.0(2)=0.02222... in base 3.
This is important because there are silly arguments about whether 0.9999... "really" is 1. Such arguments are usually drawn out, not-to-the-point and often incorrect unless one first explicitly acknowledges the non-uniqueness of positional representation in such cases. The reasoning should be, then, whether 0.(9) can express any number other than 1, while still maintaining the semantics of the positional representation. The answer is: no.
idiputchko ยท 1 points ยท Posted at 16:12:19 on May 25, 2016 ยท (Permalink)
Not saying Maths.
Thassodar ยท 1 points ยท Posted at 16:12:31 on May 25, 2016 ยท (Permalink)
The fact that math and maths is grammatically correct when referring to mathematics.
jbloom3 ยท 1 points ยท Posted at 16:12:34 on May 25, 2016 ยท (Permalink)
Look up numberphile on youtube. They have tons of cool math videos
draycel ยท 1 points ยท Posted at 16:12:40 on May 25, 2016 ยท (Permalink)*
12 time 12 is 144. 21 times 21 is 441. 13 times 13 is 169 and 31 times 31 is 961. 14 times 14 is 196, 41 times 41? You guessed it! 1681.
mkomaha ยท 1 points ยท Posted at 16:12:44 on May 25, 2016 ยท (Permalink)
There are over 18 Quintilian planets in No Man's Sky because of maths....
bigalsplaypen ยท 1 points ยท Posted at 16:12:45 on May 25, 2016 ยท (Permalink)
That there's only one of them.
chill3willy ยท 1 points ยท Posted at 16:12:50 on May 25, 2016 ยท (Permalink)
If you turn 8 sideways, it becomes infinity.
C0ltFury ยท 1 points ยท Posted at 16:12:53 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers, for example 1,2,3,4.... to infinity can be proved using summation equations to, in fact, equal -1/12
It is a statement used in string theory a lot.
Source: https://youtu.be/w-I6XTVZXww
plippel ยท 1 points ยท Posted at 16:13:07 on May 25, 2016 ยท (Permalink)
So many patterns, see them all?
CptHampton ยท 1 points ยท Posted at 16:13:51 on May 25, 2016 ยท (Permalink)
The sum of all positive integers (1+2+3+4...) is -1/12
JustForArkona ยท 1 points ยท Posted at 16:13:54 on May 25, 2016 ยท (Permalink)
e i * pi + 1 = 0
poizon_elff ยท 1 points ยท Posted at 16:14:02 on May 25, 2016 ยท (Permalink)
The sum of n odd numbers, starting from 1, is n2. 1+3+5+7+9=25, which is 52.
eceuiuc ยท 1 points ยท Posted at 16:14:10 on May 25, 2016 ยท (Permalink)
Given an alphabet A of size k, it is possible to construct a sequence that contains all possible subsequences of length n in A exactly once. These sequences are known as De Bruijn sequences and are always of length kn.
SteveBloke ยท 1 points ยท Posted at 16:14:14 on May 25, 2016 ยท (Permalink)
When counting 0 to infinity there are as many even numbers as there are numbers.
jimmythefrenchfry ยท 1 points ยท Posted at 16:14:37 on May 25, 2016 ยท (Permalink)
That 0 equals eI*Pi
(Euler's Formula.)
There's so much of everything in that equation: 0 is defined, e looks like a grand wizard using I and Pi to get 0. Though it's in polar format, it can be rearranged in rectangular trig format.
Stare at that equation long enough, you start to realize that math with real numbers (or what we just call numbers). May be a very very small part of what is really out there.
davidmirkin ยท 1 points ยท Posted at 16:14:39 on May 25, 2016 ยท (Permalink)
If you draw lines on paper which are two matchstick lengths apart, there is exactly pi chance a matchstick you drop onto the paper will lie across that line. This is know as Buffon's Needle if you wish to Google it.
The_mingthing ยท 1 points ยท Posted at 16:14:53 on May 25, 2016 ยท (Permalink)
One millimiter of water occupies one cubic centimeter, weighs one gram, requires one calorie to heat up one degree centigrade, which is one percent of the difference between its freezing point and its boiling point.
Read it on a reddit post once...
Galt42 ยท 1 points ยท Posted at 16:14:54 on May 25, 2016 ยท (Permalink)
Euler's identity:
ei*ฯ + 1 = 0
It's insane because the 3 constants have nothing to do with one another, and it uses every level of mathematical operations through exponents.
[deleted] ยท 1 points ยท Posted at 16:15:05 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Millennium_Prize_Problems
Solve any of the problems listed there and you receive one million dollars as well as a Field's Medal which is the mathematics equivalent to the Nobel prize.
One of the problems, the Poincarรฉ conjecture, was solved earlier in the century by a Russian mathematician who refused to accept the money or the prize.
Generally speaking the problems are all incredibly difficult to solve. People have devoted their entire life to just one small part of each of these problems and made little progress.
Here is a video explaining the Riemann Hypothesis, one of the millennium prize problems. Even if you do not have a math background this video is quite easy to understand, as it was made so that pretty much anyone can watch it: https://www.youtube.com/watch?v=d6c6uIyieoo
scoobysimon ยท 1 points ยท Posted at 16:15:09 on May 25, 2016 ยท (Permalink)
That the moon is almost exactly 400 times smaller than the sun, but the sun is 400 times further away, making them seem almost exactly the same size in the sky. Such a random coincidence, though I know not strictly a maths fact.
FanOfLemons ยท 1 points ยท Posted at 16:15:56 on May 25, 2016 ยท (Permalink)
There are more numbers between 0 and 1 than there are whole numbers greater than 1.
Joniden ยท 1 points ยท Posted at 16:16:18 on May 25, 2016 ยท (Permalink)
I have not used anything I learned in Algebra 2 since high school. THAT is a fact.
Ezemity ยท 1 points ยท Posted at 16:16:33 on May 25, 2016 ยท (Permalink)
That (n3)-((n-1)3) will always produce a prime ie (999) - (888) = 217 factor(217) = 1, 217,
RealTerranceHoward ยท 1 points ยท Posted at 16:16:36 on May 25, 2016 ยท (Permalink)
โ2 = 1.
bsievers ยท 1 points ยท Posted at 17:11:35 on May 25, 2016 ยท (Permalink)
It's true. The proof is as complex as it is rigorous, and requires learning a bit of new math, but this could change the entire future of the world. It would blow Pythagoras' mind if he could see it.
ManBearPig1865 ยท 1 points ยท Posted at 20:16:41 on May 25, 2016 ยท (Permalink)
Newton's and Einstein's too!
Grey_Haze ยท 1 points ยท Posted at 16:16:49 on May 25, 2016 ยท (Permalink)
22/7 is close enough to Pi for many calculations
UrNotFly ยท 1 points ยท Posted at 16:17:02 on May 25, 2016 ยท (Permalink)
Two negatives make a positive. Makes me happy for whatever reason.
[deleted] ยท 1 points ยท Posted at 16:17:09 on May 25, 2016 ยท (Permalink)
The fact that 90% of all these facts are pulled from a single youtube channel
GotchaBackJack ยท 1 points ยท Posted at 16:17:48 on May 25, 2016 ยท (Permalink)
42 is the answer to all
[deleted] ยท 1 points ยท Posted at 16:17:49 on May 25, 2016 ยท (Permalink)
The probability of this becoming a click bait article like every other big ask edit is near 1.
Yandrak666 ยท 1 points ยท Posted at 16:17:52 on May 25, 2016 ยท (Permalink)
What is the biggest number u can think of ? Like a Number with 10 Billion zeros ?
Thats nothing compared to Grahams number.
hellABunk ยท 1 points ยท Posted at 16:18:04 on May 25, 2016 ยท (Permalink)
1,2,34.
conuly ยท 1 points ยท Posted at 16:18:22 on May 25, 2016 ยท (Permalink)
1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...
justworkingmovealong ยท 1 points ยท Posted at 16:18:42 on May 25, 2016 ยท (Permalink)
The limit of a donut is the hole
tucan110 ยท 1 points ยท Posted at 16:18:47 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12 Proof (sorta): https://www.youtube.com/watch?v=w-I6XTVZXww
TheDecagon ยท 1 points ยท Posted at 16:19:06 on May 25, 2016 ยท (Permalink)
It's probably buried in here somewhere, but just in case it's not mine is
1 + 2 + 3 + 4 + 5 + ... = -1/12
Obligatory numberphile explanation video
Tsquare43 ยท 1 points ยท Posted at 16:19:07 on May 25, 2016 ยท (Permalink)
This thread is making my brain hurt.
whittlemedownz ยท 1 points ยท Posted at 16:19:21 on May 25, 2016 ยท (Permalink)
You know the Pythagorean theorem: the square of the length of the long side of a right triangle is equal to the sum of the squares of the lengths of the other two sides. It turns out this works for arbitrary dimensional objects. If you have a k-dimensional parallelogram in n-dimensional space, the square of the k-volume of that parallelogram is equal to the sum of the squares of the k-volumes of the projections of that parallelogram into all of the k-dimensional planes in the n-dimensional space.
robogo ยท 1 points ยท Posted at 16:19:35 on May 25, 2016 ยท (Permalink)
In some cases, it can be proven that 1+1=3. Or 0.
DenizenPrime ยท 1 points ยท Posted at 16:19:44 on May 25, 2016 ยท (Permalink)
The Fibonacci Sequence (1 1 2 3 5 8 ...) can be used to roughly and easily convert between miles and kilometers and vice versa.
3 mi is about 5 km, 5 mi is about 8 km, and so on. A bit down the line we see adjacent terms 196418 and 317811. Well, 196418 miles is 316104.13 km, a percent error of only 0.54%. Sure it's not accurate enough for science, but for most applications it's close enough.
Epshimzok ยท 1 points ยท Posted at 16:19:45 on May 25, 2016 ยท (Permalink)
1 = .999999.....
x = .999999..... 10x = 9.99999..... x = .99999..... 1 = .99999.....
goldieH96 ยท 1 points ยท Posted at 16:19:46 on May 25, 2016 ยท (Permalink)
The sum of 1 through infinity is -1/12
ogresan ยท 1 points ยท Posted at 16:19:47 on May 25, 2016 ยท (Permalink)
If the universe is infinite, then absolutely everything you can imagine IS happening somewhere.
ShmanDoe ยท 1 points ยท Posted at 16:19:56 on May 25, 2016 ยท (Permalink)
I'm not a big fan of math, but I have to admit that the Fibonacci number sequence is amazing. The fact that it pops up all over in nature, like in flowers and snail shells is so fascinating.
bennyboy82 ยท 1 points ยท Posted at 16:20:18 on May 25, 2016 ยท (Permalink)
T W E L V E. That's six.
But still
6 = six s i x = 3 3 = 5 5 = five five = 4
PuddingT ยท 1 points ยท Posted at 16:20:19 on May 25, 2016 ยท (Permalink)
7 ate 9
uzi ยท 1 points ยท Posted at 16:20:21 on May 25, 2016 ยท (Permalink)
Checking if a number is divisible by the first twelve numbers:
BONUS: I didn't say anyone mention the investor favorite Rule of 72 ... if you want to know how long it'll take to double your money when growing a consistent percentage, divide 72 by it. So if you're getting 15% a year, then it'll take 72/15 or roughly 5 years. Getting 8%? Then it'll be more like 9 years.
REEE_PM_ME_YOUR_TISM ยท 1 points ยท Posted at 16:20:24 on May 25, 2016 ยท (Permalink)
fuck math.
eltoro ยท 1 points ยท Posted at 16:20:34 on May 25, 2016 ยท (Permalink)*
Take any four-digit number. (EDIT: excluding repdigits) Follow these steps:
Make two versions of the number, one with the digits sorted in descending order, the other with digits in ascending order (drop leading zeros).
Subtract the second from the first.
Take the new number you get from subtracting, and repeat steps 1-3.
Factoid: you will eventually reach 6174 in seven steps or less.
ApertureBear ยท 1 points ยท Posted at 18:30:17 on May 25, 2016 ยท (Permalink)
1111 - 1111 = 0. Huh.
eltoro ยท 1 points ยท Posted at 00:36:43 on May 26, 2016 ยท (Permalink)
Okay, you got me. It does work for non-repdigits though.
SaggingZebra ยท 1 points ยท Posted at 16:20:53 on May 25, 2016 ยท (Permalink)
My favorite is called the everything formula. Watch for the explanation and enjoy.
washheightsboy3 ยท 1 points ยท Posted at 16:20:59 on May 25, 2016 ยท (Permalink)
One is the loneliest number that you'll ever do Two can be as bad as one It's the loneliest number since the number one
Read more: Three Dog Night - One (is The Loneliest Number) Lyrics | MetroLyrics
cntdlxe ยท 1 points ยท Posted at 16:21:00 on May 25, 2016 ยท (Permalink)
2+2 is 4
bitbybitbybitcoin ยท 1 points ยท Posted at 16:21:09 on May 25, 2016 ยท (Permalink)
2+2=5. Thanks, George Orwell!
Sunbeamdreaming ยท 1 points ยท Posted at 16:21:15 on May 25, 2016 ยท (Permalink)
0.3* + 0.3* + 0.3* = 1 1/3 + 1/3 + 1/3 = 1 0.9* = 1
*= recurring (Which basically means continues forever)
xmod14 ยท 1 points ยท Posted at 16:21:38 on May 25, 2016 ยท (Permalink)
There's only one answer.
coyotes_ate_your_cat ยท 1 points ยท Posted at 16:21:41 on May 25, 2016 ยท (Permalink)
1/3 = .333333333... and 1 = 1/3+1/3+1/3 so: 1 = 0.33333...+0.33333....+0.333333... Therefore 1 = 0.9999999999...
ristoman ยท 1 points ยท Posted at 16:22:04 on May 25, 2016 ยท (Permalink)*
You can write any power of 10 by only using a single digit that isn't 1 or 0.
lundse ยท 1 points ยท Posted at 16:22:18 on May 25, 2016 ยท (Permalink)
Euler's identity is... suspicious-looking. I don't get the implications, I'm not saying it proves anything.
It's just looks too perfect. Like it's up to something.
Slightly_Stoopid_ ยท 1 points ยท Posted at 16:22:25 on May 25, 2016 ยท (Permalink)
Math fact: math is for men
PillowDrool ยท 1 points ยท Posted at 16:22:30 on May 25, 2016 ยท (Permalink)
That 2+2 is in fact 4.
stenrude ยท 1 points ยท Posted at 16:22:48 on May 25, 2016 ยท (Permalink)
If you add up all the natural numbers from 1 to infinity, the sum is -1/12.
zakkwaldo ยท 1 points ยท Posted at 16:22:58 on May 25, 2016 ยท (Permalink)
Not really a fact, but I've always been the fan of The integral of son(X)cos(X)dx
[deleted] ยท 1 points ยท Posted at 16:23:09 on May 25, 2016 ยท (Permalink)
Numbers are infinite, so any sound you make is eventually a number. fhqwhgads!
AHappyLurker ยท 1 points ยท Posted at 16:23:18 on May 25, 2016 ยท (Permalink)
Its not necessarily a fact, more of a mind bender and it has a special name, but I've forgot it. It goes something like this:
A man has a bag of potatoes weighing 100kg. These potatoes are 99% water. He goes home and dries them out, so that they are now 98% water. He reweighs them, how much do they weigh now?
The answer is 50kg.
ApertureBear ยท 1 points ยท Posted at 18:24:29 on May 25, 2016 ยท (Permalink)
That makes sense. 99% of the weight of the potatoes is water. So the potatoes are 1kg potato and 99kg water. In order for the potatoes to be 98% water, they would need to be 1kg potatoes and 49kg water.
AHappyLurker ยท 1 points ยท Posted at 18:31:22 on May 25, 2016 ยท (Permalink)
exactly, but it seems counter intuitive at first
ApertureBear ยท 1 points ยท Posted at 18:34:57 on May 25, 2016 ยท (Permalink)
Thanks for making me think :)
AHappyLurker ยท 1 points ยท Posted at 18:54:09 on May 25, 2016 ยท (Permalink)
np :)
Destiny_Gene ยท 1 points ยท Posted at 16:24:14 on May 25, 2016 ยท (Permalink)
The theory of higher dimensions such as 4D and 5D can actually be simply explained by adding perspective lines in a 2D representation. I'm on a phone so I can't hyperlink images.
Say for example I have a 2D drawing of a box and to make it 3D, the vertices of the corners of two boxes need to be connected to make a simple cube. To make the cube 4D, another cube can be placed inside it with all of the two sets of corners connected by another set of lines, making the well known hyper cube or tesseract of the Avengers. It can be converted to 5D with a heck lot more lines and so on.
Pretty interesting to apply it as a possible link to parallel universes like pages of a book if multiple 3 dimensional planes formally existed.
[deleted] ยท 1 points ยท Posted at 16:24:16 on May 25, 2016 ยท (Permalink)
This is kind of unrelated, but whenever I try to make a text post on any sub-thread it says "that sub Reddit only allows text posts" but my post is only text.
F0sh ยท 1 points ยท Posted at 16:24:27 on May 25, 2016 ยท (Permalink)
That there are different sizes of infinity. A very clever madman named Georg Cantor proved it using a method called diagonalisation. There's a proof on Wikipedia and I wrote an explanation about it a while ago too.
It's a pretty simple argument but it's quite astounding because people tend to think of infinity as being bigger than anything - so how could there be something even bigger? Well, countable infinity is only bigger than all the finite stuff - that's the key :)
stigmaboy ยท 1 points ยท Posted at 16:25:05 on May 25, 2016 ยท (Permalink)
If you add up all the positive numbers from 1 to infinite, the sum comes out to -1/12.
That or ei*pi = 1
scotscott ยท 1 points ยท Posted at 16:25:46 on May 25, 2016 ยท (Permalink)
One is the loneliest number
Turbojelly ยท 1 points ยท Posted at 16:25:47 on May 25, 2016 ยท (Permalink)
Graham's Number
This is a number that is so big that to fully write it out, using 1 atom in the universe for each number in the sequence. You would run out of atoms in the Universe before you finished writing it down.
This is a great video explaining it: https://www.youtube.com/watch?v=GuigptwlVHo
InertInertia ยท 1 points ยท Posted at 16:25:51 on May 25, 2016 ยท (Permalink)
That there are more combinations of playing cards than there are years that the universe has existed. Way more.
[deleted] ยท 1 points ยท Posted at 16:26:22 on May 25, 2016 ยท (Permalink)
There are different sizes of infinity
IAMBACKYOUBANDME ยท 1 points ยท Posted at 16:26:36 on May 25, 2016 ยท (Permalink)
1+1 =2
guitarbassguy ยท 1 points ยท Posted at 16:26:53 on May 25, 2016 ยท (Permalink)
1/89 is the Fibonacci sequence in decimal form.
MischeviousMacaque ยท 1 points ยท Posted at 16:26:55 on May 25, 2016 ยท (Permalink)
The fact that there are different sizes of infinity. This is my favorite mathematical argument from real analysis. You'd think that infinity is simply infinity, because it is freaking infinite, but no!
Let's say we have the integers: {1,2,3... n, such that n goes to infinity}. Now let's say we only consider the even number (i.e. 2, 4, 6...) one would think there might be "half" as many even numbers as there are integers, but no there are still an infinite number of even numbers and in fact we can write the even numbers as {2, 4... 2*n}, there is an even number that corresponds to every integer n. These sets have the same cardinality, the same size (countably infinite).
You can cary this out for any multiples of integers (3n, 4n... and eventually n*n or n2) there is still a 1 to 1 correspondence, there is an integer corresponding to every square. We can take this further to n3, n4, etc all having a 1 to 1 correspondence with the integers. These are all countably infinite sets!
Now this is where things get tricky. If you think of n as a set of countably infinite things, the 2n is two of those sets, 3n is 3, n2 is a countably infinite number of countably infinite sets kind of like an infinite square like:
1 2 3 4 ... n -> infinite times
2 4 6 8 ... 2*n->
3 6 9 12 ... 3*n
...
...
1 4 9 16 ... n2
Bare with me now. Then n3 is like a giant cube, a countably infinite number of a countably infinite number of countably infinite sets. Yet it still has the same cardinality of just one countably infinite set. Now take this to the extreme, what about ninfinity ? That would be a countably infinite number of a countably infinite number ....of a countably infinite number of countably infinite sets. This my friends is what we call uncountably infinite and is the cardinality of the Real numbers.
I apologize if that makes no sense, I did my best trying to explain this in words on Reddit. The point is there are different sizes of infinity, and that is freaking crazy.
Skeptic1222 ยท 1 points ยท Posted at 16:27:03 on May 25, 2016 ยท (Permalink)
If a piece of paper is .1 mm thick, folding it 50 times makes it 250 times thicker, and you get 112 million km (80 million miles), or .75 AU (the distance from the earth to the sun).
itsjustawizard ยท 1 points ยท Posted at 16:27:14 on May 25, 2016 ยท (Permalink)
cosine is the derivative of sine
uhhhclem ยท 1 points ยท Posted at 16:27:37 on May 25, 2016 ยท (Permalink)
If you're impressed by how big factorials get, wait until you discover Knuth's up arrow notation and Graham's number.
DownVotingCats ยท 1 points ยท Posted at 16:27:42 on May 25, 2016 ยท (Permalink)
I prefer my facts to be about cats.
Trummelumsk ยท 1 points ยท Posted at 16:28:07 on May 25, 2016 ยท (Permalink)
The Mandelbrot set --> f_c(z)=z2+c
bg-j38 ยท 1 points ยท Posted at 16:28:18 on May 25, 2016 ยท (Permalink)
Dec 25 = Oct 31
In other words, 25 in base 10 (decimal) equals 31 in base 8 (octal). Christmas = Halloween. Jack Skelington is coming.
AlreadySleepy ยท 1 points ยท Posted at 16:28:21 on May 25, 2016 ยท (Permalink)
Math is discovered, not invented.
[deleted] ยท 1 points ยท Posted at 16:30:14 on May 25, 2016 ยท (Permalink)
The formula or whatever that proves anything to the power of 0 becomes one. Not sure if that's how it works, but it made sense to me.
ReverendSaintJay ยท 1 points ยท Posted at 16:30:18 on May 25, 2016 ยท (Permalink)
My 3rd grade teacher was wrong, I DO have a calculator in my pocket wherever I go.
rdogg4 ยท 1 points ยท Posted at 16:30:23 on May 25, 2016 ยท (Permalink)
"Benford's law, also called the first-digit law, is a phenomenological law about the frequency distribution of leading digits in many (but not all) real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.[1] For example, in sets which obey the law, the number 1 appears as the most significant digit about 30% of the time, while 9 appears as the most significant digit less than 5% of the time. By contrast, if the digits were distributed uniformly, they would each occur about 11.1% of the time.[2] Benford's law also makes (different) predictions about the distribution of second digits, third digits, digit combinations, and so on."
https://en.m.wikipedia.org/wiki/Benford%27s_law
bearzog ยท 1 points ยท Posted at 16:30:31 on May 25, 2016 ยท (Permalink)
My favorite ones involve some sort of paradox/counterintuitive result:
Monty Hall Problem You should switch.
Birthday Problem It only takes 23 people in a room to have >50% chance of two people sharing a birthday.
Brouwer Fixed Point Theorem If you take a map of the USA to any point in the country, there will always be a point on the map that represents that exact point in the country.
Four Color Theorem No matter how a map is drawn, with just 4 colors, you will always be able to color each region such that it is not the same color as any region it touches.
0.999... = 1 Since there is no number between 0.999... and 1, they are actually the same number! (By 0.999..., I mean a number with 9's repeating infinitely; e.g., the limit of 0.9, 0.99, 0.999, ....)
Seilu_NA ยท 1 points ยท Posted at 16:30:51 on May 25, 2016 ยท (Permalink)
There are more ways to rearrange a standard deck if cards than there are atoms in the world.
[deleted] ยท 1 points ยท Posted at 16:30:57 on May 25, 2016 ยท (Permalink)
0.9 repeating = 1
It's not infinitely close to 1. It is 1.
sufferpuppet ยท 2 points ยท Posted at 16:43:21 on May 25, 2016 ยท (Permalink)
Then why don't you write 1 that way all the time? Stupid base 10 system.
[deleted] ยท 2 points ยท Posted at 17:03:22 on May 25, 2016 ยท (Permalink)
Who says I don't! The utility companis complains every time I do it on their checks.
TurtleSmile1 ยท 1 points ยท Posted at 16:31:20 on May 25, 2016 ยท (Permalink)
The difference between the square of consecutive numbers is the same as the sum of those consecutive numbers.
Example: The square of 30 is 900. The square of 29 is 841. 30+29=59, which is 900-841. It's a quick and relatively easy way to find the square of large numbers without a calculator, assuming they're near to an easily-calcuable square.
smep ยท 1 points ยท Posted at 16:31:27 on May 25, 2016 ยท (Permalink)
e raised to the pi*i minus one is equal to 0.
epi*i-1=0
Uthak ยท 1 points ยท Posted at 16:31:34 on May 25, 2016 ยท (Permalink)
If you pay attention and take good notes in class, its not fucking hard.
Valveq0 ยท 1 points ยท Posted at 16:31:54 on May 25, 2016 ยท (Permalink)
Legendre's constant
macromort ยท 1 points ยท Posted at 16:32:09 on May 25, 2016 ยท (Permalink)
That 'math' doesn't have an 's' in it.
TatsumakiTed ยท 1 points ยท Posted at 16:32:16 on May 25, 2016 ยท (Permalink)
Half of one times half of one, equals one quarter of one.
TaedW ยท 1 points ยท Posted at 16:32:48 on May 25, 2016 ยท (Permalink)
There are pi (ฯ) seconds in a nano-century.
siraolo ยท 1 points ยท Posted at 16:32:54 on May 25, 2016 ยท (Permalink)*
Mine is pretty simple.
1=.99999 repeating . It speaks to me of the uncertainty of numerical values, given the limitations of humanity to quantify the infinite.
the_mojonaut ยท 1 points ยท Posted at 16:33:01 on May 25, 2016 ยท (Permalink)
14*5=25
https://youtu.be/t8XMeocLflc
Panhead09 ยท 1 points ยท Posted at 16:33:03 on May 25, 2016 ยท (Permalink)
This one.
JakDrako ยท 1 points ยท Posted at 17:05:50 on May 25, 2016 ยท (Permalink)
TIL a dozen dozens is a gross.
bonzo0884 ยท 1 points ยท Posted at 16:33:07 on May 25, 2016 ยท (Permalink)
epi*i = -1
https://www.youtube.com/watch?v=F_0yfvm0UoU
yeah_well_no ยท 1 points ยท Posted at 16:33:17 on May 25, 2016 ยท (Permalink)
My favorite fact about Math is propably that, despite everything is thought up and defined by Humans, it applies to everything we do and everything we do can be calculated.
The_Doctor-_- ยท 1 points ยท Posted at 16:33:26 on May 25, 2016 ยท (Permalink)
You can't divide anything by zero.
[deleted] ยท 1 points ยท Posted at 16:33:31 on May 25, 2016 ยท (Permalink)
69=6*9+6+9
learath ยท 1 points ยท Posted at 16:33:33 on May 25, 2016 ยท (Permalink)
That it's called "math".
That there are patterns to primes.
historyisaweapon ยท 1 points ยท Posted at 16:33:34 on May 25, 2016 ยท (Permalink)
0.9999... = 1
saello ยท 1 points ยท Posted at 16:33:36 on May 25, 2016 ยท (Permalink)
I always found the fact that every multiple of 9 the answer will add to 9 to be pretty cool. For example 3x9 = 27 and 2+7 = 9. This holds true on a larger scale 458 627x9 = 4 127 643 and 4+1+2+7+6+4+3 = 27 and then 2+7 = 9. Try it out with any random number multiplied by 9 and eventually the answer will add to 9.
Shayde505 ยท 1 points ยท Posted at 16:33:43 on May 25, 2016 ยท (Permalink)
My favourite math fact is that since I've graduated high school I haven't had to use pythagorean theorem nearly as often as the teacher implied I would.... I do however need to learn how to do taxes..
EpicGuard ยท 1 points ยท Posted at 16:34:09 on May 25, 2016 ยท (Permalink)
It's probably not as interesting as the others here, but I really loved finding out that in calculus you find the instantaneous rate of change for a function by basically faking a distance equation from beginner's algebra. It's just rise over run and you pretend there's a run instead of a zero.
Steve_the_Stevedore ยท 1 points ยท Posted at 16:34:22 on May 25, 2016 ยท (Permalink)
You can mathrmatically show that there will be always be at least two spots on earth with the exact same temparature and pressure whicb are perfectly opposite of eachother:
Let's say you had a globe with the temperatures at every point on it marked. and now let's say the tempeatur at the north pole was -10ยฐ while it was -40 at the south pole. Now you had a copy of the globe but instead of having the temperature on it it had the temperature differnce between the point you are looking at and the point on the opposite side of the earth. So the north pole would have -10- (-40)=+30 and the south pole would have -30. Now consider that temperature is a continous function. That means that whichever way you take on you second globe from one pole to the other you will pass a point where the function is zero.
So we have established that there is some kind of "ring" around the earth where the difference between the temperature on opposing sides of the globe is zero. There are infinitly many of these points.
Now we do the same for atmospheric pressure. We get a second ring. Each point of these rings (by way of their construction) has another point of the respective ring on exactly the other side of the globe. If you put two rings with this property on a sphere like our globe they will always have at least two intersecting points. These points will be on the exact opposite side of the globe.
So there will always be a pair of points with exactly the same pressure and temperature that are on the exact opposite side from eachother.
Ratmotored57 ยท 1 points ยท Posted at 16:34:41 on May 25, 2016 ยท (Permalink)
Two thirds of four fifths of fuck all is in fact....zero.
[deleted] ยท 1 points ยท Posted at 16:34:53 on May 25, 2016 ยท (Permalink)
.99999 repeating is exactly equal to 1
elspazzo ยท 1 points ยท Posted at 16:34:53 on May 25, 2016 ยท (Permalink)
A dozen, a gross, and a score,
Plus three times the square root of four,
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.
PestySwami ยท 1 points ยท Posted at 16:35:01 on May 25, 2016 ยท (Permalink)
50% of people struggle with maths. That's almost half.
IdentiFriedRice ยท 1 points ยท Posted at 16:35:13 on May 25, 2016 ยท (Permalink)
Fact: No matter how much I study, I always do better when I don't study.
MaysonD ยท 1 points ยท Posted at 16:35:21 on May 25, 2016 ยท (Permalink)
Kind of hard to explain without pictures, but there's an easy tip for multiplying by nine.
Take 9*6 for example. You could lower the six to a five, and add the number that would add to nine. So 54 is the answer.
9*7. 63
9*1. Would be zero and add a nine. 09.
9*9. 81
ApertureBear ยท 1 points ยท Posted at 18:12:43 on May 25, 2016 ยท (Permalink)
Why wouldn't you just multiply the 6 by 10 and then subtract 6? This works beyond the single-digit times table.
MaysonD ยท 1 points ยท Posted at 18:29:35 on May 25, 2016 ยท (Permalink)
That works too, but this thread isn't about the easiest way to math, but the cool tricks you can do with it.
ApertureBear ยท 1 points ยท Posted at 18:35:14 on May 25, 2016 ยท (Permalink)
Okay :)
Yell0w68 ยท 1 points ยท Posted at 16:35:21 on May 25, 2016 ยท (Permalink)
Benford's law, which basically says that in many naturally occurring lists of numbers, around 30% of the numbers start with a 1 and less than 5% of them starts with a 9. For example the Fibonacci numbers.
IWatchGifsForWayToo ยท 1 points ยท Posted at 16:35:48 on May 25, 2016 ยท (Permalink)
If there are 23 people in a room, there is a 50% chance that two of those people will have the same birthday. It's called the birthday problem and by the time there are 50 people in the room, there is a 97% chance that two people share a birthday.
Thanatoshi ยท 1 points ยท Posted at 16:35:49 on May 25, 2016 ยท (Permalink)
I don't know what this means, but I figured out that if this equation is the same as n2
|n-10| = a
If a > 10: 100+21(a)+(a(a-1)
You just switch the additions to subtractions if a < 10.
I don't know if anyone else enjoys useless math facts, but I definitely so. Especially if I figure them out myself.
ydubs ยท 1 points ยท Posted at 16:35:56 on May 25, 2016 ยท (Permalink)
My favorite math fact that I love is that
2 = (34 )(34) - (43 )(43)
This equation in addition to looking pretty also modes 2pi to four digits of accuracy as you can see here:
https://drive.google.com/file/d/0B_3HLelJejwQUEhXUXJneDBUYjQ/view
It's components also model protonic mass to seven digits of accuracy, shown here:
https://drive.google.com/file/d/0B_3HLelJejwQT25qVDdvR3JXMTA/view
In fact, I have been tempted to think these equations which I produced are actually quantum models but I haven't been able to prove it. For example, the 2 fits into any physics equation that has a two in it and there are numerous occurrences of a 2 -- such as when something is squared or rooted, like the speed of light. The other thing is that there is particle wave duality -- perhaps this equation models the co-existence of a particle and a wave which are mathematical symmetric of each other? The other thing is the components 3 and 4 represent space and time, which is really physics-y. And other stuff too!
thethunderbirdguy ยท 1 points ยท Posted at 16:36:01 on May 25, 2016 ยท (Permalink)
The Fibonacci series! Present everywhere!
somerandomguy02 ยท 1 points ยท Posted at 16:36:23 on May 25, 2016 ยท (Permalink)
That math is not plural.
[deleted] ยท 1 points ยท Posted at 16:37:39 on May 25, 2016 ยท (Permalink)
Figures don't lie but liars figure.
[deleted] ยท 1 points ยท Posted at 16:37:45 on May 25, 2016 ยท (Permalink)
The probability of randomly selecting a rational number from the set of all real numbers bounded by two points is zero, even though there are infinitely many rational numbers within that set.
Love_And_Light33 ยท 1 points ยท Posted at 16:37:45 on May 25, 2016 ยท (Permalink)
If you add up the mass of quantum vacuum fluctuations (packed in a holographic interference pattern, totally space filling - colloquially known as the flower of life) that fit in the sphere of the proton, you yield 1055 grams.
This is the exact estimated mass of the observable Universe.
belarius ยท 1 points ยท Posted at 16:38:00 on May 25, 2016 ยท (Permalink)
If you write out the Stern-Brocot sequence, and make a fraction out of each consecutive pair of numbers in the sequence, you'll list out every possible fraction exactly once, in its most reduced form.
nyrangers30 ยท 1 points ยท Posted at 16:38:15 on May 25, 2016 ยท (Permalink)
.9999999 (infinitely) = 1
jonker5101 ยท 1 points ยท Posted at 16:38:19 on May 25, 2016 ยท (Permalink)
If you have 20 minutes, check out Vsauce's "Math Magic" video. Pretty awesome stuff.
kvachon ยท 1 points ยท Posted at 16:38:50 on May 25, 2016 ยท (Permalink)
That the concept of Zero exists. Must of been a bitch to explain/define.
8002reverse ยท 1 points ยท Posted at 16:38:52 on May 25, 2016 ยท (Permalink)
If five is too much and two is itself two few, what is enough?
Jcbarona23 ยท 1 points ยท Posted at 16:39:03 on May 25, 2016 ยท (Permalink)
In *string* theory, 1+1+1+1+... = - 1/12 (iirc)
K281067 ยท 1 points ยท Posted at 16:40:08 on May 25, 2016 ยท (Permalink)
There is such a thing as a matrix exponential that can be interesting
benartmao ยท 1 points ยท Posted at 16:40:12 on May 25, 2016 ยท (Permalink)
I've never felt stupidar.....
IncommendatusZ ยท 1 points ยท Posted at 16:40:14 on May 25, 2016 ยท (Permalink)
0.999... (repeating) is equal to 1.
kungfooe ยท 1 points ยท Posted at 16:40:19 on May 25, 2016 ยท (Permalink)
I really like Hilbert's Infinity Hotel Problem.
Basically, this thing messes with your mind because we're so used to the size of finite numbers (i.e., if you were counting, you could eventually count up to this number) that when we try to deal with the size of infinity it messes with our thinking because our finite number thinking "breaks" in multiple cases.
Russglish21 ยท 1 points ยท Posted at 16:40:22 on May 25, 2016 ยท (Permalink)
That various infinities are larger/[equal to] than each other. It's simple, but I always liked the proof and thought it was cool.
Goodgardo ยท 1 points ยท Posted at 16:40:51 on May 25, 2016 ยท (Permalink)
705600 divided by the current year.
auntfaintly ยท 1 points ยท Posted at 16:41:03 on May 25, 2016 ยท (Permalink)
Monte Carlo integration. If your calculus teacher asks you how to go about integrating something and you don't have a clue, just yell "Monte Carlo Integration!"
Kilieks ยท 1 points ยท Posted at 16:41:06 on May 25, 2016 ยท (Permalink)
3โโโ3+1
Your turn Graham
lazespud2 ยท 1 points ยท Posted at 16:41:07 on May 25, 2016 ยท (Permalink)
The fact that they call it "maths" in the UK and "math" in the US. Definitely one of my favorite Britishisms; right up there with "boot" for "trunk" in a car.
SyntheticGod8 ยท 1 points ยท Posted at 16:49:21 on May 25, 2016 ยท (Permalink)
Next you'll be telling me you put your car in a fancy garage, not a "car hole".
lazespud2 ยท 1 points ยท Posted at 16:52:34 on May 25, 2016 ยท (Permalink)
oh the dream of a fancy carhole... sadly I just have a carport.
KarmaUK ยท 1 points ยท Posted at 17:00:28 on May 25, 2016 ยท (Permalink)
It's obvious to me, you're teaching a range of branches of mathematics, not just one math, but lots of maths :) Geometry, Algebra, etc...
lazespud2 ยท 1 points ยท Posted at 17:06:37 on May 25, 2016 ยท (Permalink)
I don't disagree pretty much at all; as I said, it's my fave "Britishism".
but to the typical american it definitely sounds weird! : )
OnePunkArmy ยท 1 points ยท Posted at 16:41:28 on May 25, 2016 ยท (Permalink)
With the exception of 2 and 3, all prime numbers are exactly 1 away from a multiple of 6.
c3534l ยท 1 points ยท Posted at 16:41:37 on May 25, 2016 ยท (Permalink)
Gรถdel's incompleteness theorems:
There is no algorithm which can prove all facts about the natural numbers that is not also occasionally wrong.
There is no way for logic to prove that it is, itself, logically consistent.
alligatorslap ยท 1 points ยท Posted at 16:42:22 on May 25, 2016 ยท (Permalink)
The continuum hypothesis.
This video explains it pretty well in layman's terms: https://www.youtube.com/watch?v=UPA3bwVVzGI
[deleted] ยท 1 points ยท Posted at 16:42:28 on May 25, 2016 ยท (Permalink)
[deleted]
Obelisp ยท 1 points ยท Posted at 17:20:59 on May 25, 2016 ยท (Permalink)
What's funny is that statement is true, but only vacuously true. It's also true that if you divide by 0, you'll become a trillionaire.
Kropduster01 ยท 1 points ยท Posted at 16:43:21 on May 25, 2016 ยท (Permalink)
1/3=0.333333 2/3=0.666666 3/3=0.9999999 0.999999=1
criscorock ยท 1 points ยท Posted at 16:43:28 on May 25, 2016 ยท (Permalink)
If you get 1% better at something every day (compared to the previous day), by the end of the year, you'll be thirty-eight times as good as you were on the first day! :D
oldKing_Cole ยท 1 points ยท Posted at 16:44:12 on May 25, 2016 ยท (Permalink)
.9999999 repeating = 1
Take 1) x=.99999... 2) 10x=9.99999... Second equation minus the first equation gives us 9x=9. Therefore, x=1!
sdub76 ยท 1 points ยท Posted at 16:44:18 on May 25, 2016 ยท (Permalink)
My all time favorite is that all multiples of nine have digits that add up to nine if you continue to collapse them.
9*4157 = 37,413 โ 3+7+4+1+3 = 18 โ 1+8 = 9
Similarly, all multiples of 3 add up to 3,6, or 9. Makes it easy to tell if something is quickly divisible.
3*487 = 1,461 โ 1+4+6+1 = 12 โ 1+2 = 3
Blew my 9 year old mind many moons ago.
evilzombiesnoman ยท 1 points ยท Posted at 16:44:53 on May 25, 2016 ยท (Permalink)
This thread is amazing
comforteagle99 ยท 1 points ยท Posted at 16:44:56 on May 25, 2016 ยท (Permalink)
There are just as many prime numbers as even numbers.
xxAkirhaxx ยท 1 points ยท Posted at 16:45:06 on May 25, 2016 ยท (Permalink)
There are as many even or odd integers as integers themselves because if n represents all integers, then 2n represents all even integers, and 2n-1 represents all odd integers. The relation of f (n) = 2n or f (n) = 2n -1 is bijective. So the sets are of equal size.
phillies1989 ยท 1 points ยท Posted at 16:46:05 on May 25, 2016 ยท (Permalink)
My favorite is that there is no solution we know of yet tonthe traveling salesman problem and if that problem ever gets figured out all the cryptography and other math problems in P=NP will go from thousands of years to crack to days or hours.
Ganaraska-Rivers ยท 1 points ยท Posted at 16:46:34 on May 25, 2016 ยท (Permalink)
Compound interest, or the exponential function. Non mathematicians (and even some mathematicians) overlook this in every day life.
For an example, practically every government and central bank in the world aims to create inflation of 2% a year as a matter of policy. They usually run a little higher, on average.
Now calculate what this will do to the value of your money, or the price of anything you buy, over the course of your lifetime. Or over 10, 20 or 50 years.
This crops up all the time in ways we don't think of.
Wiknetti ยท 1 points ยท Posted at 16:46:34 on May 25, 2016 ยท (Permalink)
C=ฯd - Cherry pie delicious
A=ฯr2 - Apple pies are too
V=ฯr2h - Vegetable pies are too horrible (I love spinach-feta pie though... no maths for that, just food.)
Gpop007 ยท 1 points ยท Posted at 16:46:35 on May 25, 2016 ยท (Permalink)
My favourite number is 23.
StockmanBaxter ยท 1 points ยท Posted at 16:47:40 on May 25, 2016 ยท (Permalink)
That I do actually walk around with a calculator everywhere I go!
HandiCapablePanda ยท 1 points ยท Posted at 16:48:13 on May 25, 2016 ยท (Permalink)*
An easy trick to multiply by 11s.
For example 11 x 54 = 594. You add the digits that are being multiplied to 11. In this case 5+4=9. Insert the resulting sum between the original numbers. With larger numbers it gets more complicated.
11 x 56 = 616. You must "carry" the additional number to the first digit.
11 x 125 = 1375: take the first and last numbers, those will stay the same. Then start adding. 1+2=3. 2+5=7. Add these, in order, with the first and last numbers. 1,375.
hesafunnyone ยท 1 points ยท Posted at 16:48:16 on May 25, 2016 ยท (Permalink)
I love pi. 3.1452 is amazing. I work with diameter and radius frequently so I use it often but I still think it's a neat string of numbers.
IthiQQ ยท 1 points ยท Posted at 16:48:27 on May 25, 2016 ยท (Permalink)
12 =1
22 =1+2+1
32 =1+2+3+2+1
42 =1+2+3+4+3+2+1
52 =1+2+3+4+5+4+3+2+1
62 =1+2+3+4+5+6+5+4+3+2+1
...
Etc.
So in short (n+1)2 =n2 +n+(n+1), or alternatively (n+1)2 =n2 +2n+1.
ominousfire ยท 1 points ยท Posted at 16:49:20 on May 25, 2016 ยท (Permalink)
Probably a bit late but here's one:
In math-eese: The result of the recursive summing of digits is path independent.
In English: If I have a number and I add its digits together, and add those digits together, until I have a single digit, the order in which I add the digits does not matter. In fact, I do not have to finish summing the whole number before I add them together. If you don't get what I'm on about heres an example: http://i.imgur.com/nNUSqqj.png
There's a whole bunch of other cool stuff about that, such as the digit 9 does not have any result on the output number unless the number is 9. Ie: 1,999,999 --> 1. Same goes for any combination of numbers that add up to 9. This fact only applies in base 10.
The resulting number for any non zero positive integer is additionally given by n mod 9, but if the result of that is zero, then the actual result is 9. The general rule is n mod base of n - 1, but a zero result results in the base minus one.
EDIT: forgot two words.
[deleted] ยท 1 points ยท Posted at 16:49:39 on May 25, 2016 ยท (Permalink)
The sum of all odd numbers up to any 2N+1 where N is an integer results in a perfect square.
2(0)+1=1
1+2(1)+1=4
4+2(2)+1=9
etc.
NidfridLeoman ยท 1 points ยท Posted at 16:49:52 on May 25, 2016 ยท (Permalink)
There are 360 distinct ways to arrange the letters in the word circle.
herrmann-the-german ยท 1 points ยท Posted at 16:50:08 on May 25, 2016 ยท (Permalink)
Any positive number minus its cross sum is divisible by nine.
dajewsualsuspect ยท 1 points ยท Posted at 16:50:22 on May 25, 2016 ยท (Permalink)
My favorite is the 11 times table. Just add two sides of the # together and put it in the middle of the #.....example 11x25= 275 2+5=7
or 11x65=715 6+5=11 carry your 1 715
jimmy_bean ยท 1 points ยท Posted at 16:50:29 on May 25, 2016 ยท (Permalink)
At what size lottery, or lottery ticket price per, does buying every possible combination (guaranteeing a win) become feasible?
ImPixxel ยท 1 points ยท Posted at 16:50:38 on May 25, 2016 ยท (Permalink)
MA I m...V ESN I ## Xxx z Xxx zzszz z Hz; xx;xxx;iiio
ImPixxel ยท 1 points ยท Posted at 01:23:36 on May 27, 2016 ยท (Permalink)
...my ass posted to reddit. Wow. This is a new one.
First it ordered pizza, now this?
Stopkilling0 ยท 1 points ยท Posted at 16:51:09 on May 25, 2016 ยท (Permalink)
(1/3) * 3 = 1.
(1/3) = 0.3 repeating.
0.3 repeating * 3 = 0.9 repeating.
0.9 repeating does not equal one. But it does.
Pun_In_Ten_Did ยท 1 points ยท Posted at 16:51:48 on May 25, 2016 ยท (Permalink)
Take any 3 digit number and key it into a calculator.
Now, enter it again.
Divide by 13.
Divide by 11.
Divide by 7.
You will get your original three digit number back
:p
damianstuart ยท 1 points ยท Posted at 16:52:12 on May 25, 2016 ยท (Permalink)
3+4 CAN = 5.
In vector math.
kirbstompin ยท 1 points ยท Posted at 16:52:16 on May 25, 2016 ยท (Permalink)
That math is called maths in other countries
pyrojoe121 ยท 1 points ยท Posted at 16:52:33 on May 25, 2016 ยท (Permalink)
That .9999999...=1. Not that it is very, very close to 1, but it is equal to it.
lockedinaroom ยท 1 points ยท Posted at 16:52:39 on May 25, 2016 ยท (Permalink)
ii is a real number.
good_vibes_maad_city ยท 1 points ยท Posted at 16:52:51 on May 25, 2016 ยท (Permalink)
Sacred Geometry:
8 Earth years are roughly equal to 13 Venus years, meaning the two planets approximately trace out this pattern with 5-fold symmetry as they orbit the Sun.
[deleted] ยท 1 points ยท Posted at 16:52:52 on May 25, 2016 ยท (Permalink)
That there probably is no function that returns all primes, or that e or Pi are irrational. Mathematics is the science of pure logic, there is nothing more universally true than it.... and still - it's a pure chaotos and an unordered mess!!!
madMambo ยท 1 points ยท Posted at 16:53:02 on May 25, 2016 ยท (Permalink)
Pi is the amount of times you can wrap the diameter of a circle around it.
Rsaesha ยท 1 points ยท Posted at 16:53:02 on May 25, 2016 ยท (Permalink)
0.999... (recurring) is provably equal to 1.
factanonverba_n ยท 1 points ยท Posted at 16:53:03 on May 25, 2016 ยท (Permalink)
eiฯ +1=0
The five most important numbers in math, i, ฯ, e, 1, and 0 are all in the same equation.
[deleted] ยท 1 points ยท Posted at 16:53:28 on May 25, 2016 ยท (Permalink)*
Any power of 11 can be written as a sum of the pascal numbers in the respective digits place... for instance:
115 = 1 * 105 + 5 * 104 + 10 * 103 + 10 * 10 2 + 5 * 101 + 1 * 100
Not shocking, but proud I found it out myself after the first couple classes of number theory.
You_Lack_Hatred ยท 1 points ยท Posted at 16:53:45 on May 25, 2016 ยท (Permalink)
Both 0.99999999___ and 1.000___00001 are equivalent to the number 1. This is because the number 1 is the only real number that is unprovable to exist.
Zeptic ยท 1 points ยท Posted at 16:54:03 on May 25, 2016 ยท (Permalink)
Math is just a concept of numbers thought up by humans. They don't actually mean anything to people who don't understand their significance. Say for example 8 x 2 = 16, that would be completely useless to a child, but to someone who understands it, it actually means something.
It completely blows my mind, honestly.
Lazynerd44 ยท 1 points ยท Posted at 16:54:07 on May 25, 2016 ยท (Permalink)
1+1=2
pm8k ยท 1 points ยท Posted at 16:54:25 on May 25, 2016 ยท (Permalink)
e-i*pi + 1 = 0
A nice concise formula using the major constants, symbols, and numbers of mathematics
SlrowS ยท 1 points ยท Posted at 16:55:09 on May 25, 2016 ยท (Permalink)
I don't do math, but reading these answers makes me feel somewhat more intelligent
baldman1 ยท 1 points ยท Posted at 16:55:21 on May 25, 2016 ยท (Permalink)
If you ride a bike around a circular track, starting from a standstill and coming to a stop at the point you started, no matter how fast you go and how you vary your speed during the bike ride (no going backwards though), there will always be two spots directly opposite each other on the circle where your speed was the same. (the speed needs to vary Continuously though. Instantly accelerating to the speed of light or whatever is cheating.)
[deleted] ยท 1 points ยท Posted at 16:55:55 on May 25, 2016 ยท (Permalink)
Fermat's last conjecture
[deleted] ยท 1 points ยท Posted at 16:56:19 on May 25, 2016 ยท (Permalink)
Fave fact: Americans think "maths" is incorrect shorthand for mathematics
rearless ยท 1 points ยท Posted at 16:56:37 on May 25, 2016 ยท (Permalink)
Take ANY three digit number, repeat it so it is a 6 digit number. For example 123123. That number will always be divisible by 13. The result is always divisible by 11. And that result is always divisible by 7 and you get back to your original three digit number.
Examples:
123 123123/13= 9471 9471/11=861 861/7=123
924 924924/13=71148 71148/11=6468 6468/7=924
The hint is 13 * 11 * 7 = 1001
sparkymist ยท 1 points ยท Posted at 16:56:49 on May 25, 2016 ยท (Permalink)
Nothing, nothing at all, maths suck...
Well the fact that I don't have to do anymore classes is the best ever.
_FadedRoyalty ยท 1 points ยท Posted at 16:56:56 on May 25, 2016 ยท (Permalink)
That when i was in high school, math was my favorite & best subject. Now I'm just lost
RodrigoBravo ยท 1 points ยท Posted at 16:57:28 on May 25, 2016 ยท (Permalink)
9x2= 18 1+8= 9
the addition of the result of a number multiplied by 9 will always be 9.
danidzs ยท 1 points ยท Posted at 16:57:29 on May 25, 2016 ยท (Permalink)
If you type 58008 on a calculator and turn it around something magical happens
Splitz300 ยท 1 points ยท Posted at 16:57:55 on May 25, 2016 ยท (Permalink)
ITT: People smarter than me.
ep311 ยท 1 points ยท Posted at 16:58:16 on May 25, 2016 ยท (Permalink)
3ยฒ + 4ยฒ = 5ยฒ
Thompy ยท 1 points ยท Posted at 16:58:46 on May 25, 2016 ยท (Permalink)
68+1=69 ...heh
Lady_Anarchy ยท 1 points ยท Posted at 16:58:55 on May 25, 2016 ยท (Permalink)
it exists.
HarryPotHead45 ยท 1 points ยท Posted at 16:59:07 on May 25, 2016 ยท (Permalink)
My dad always told my brother and I this story to see if we had an answer.
3 guys are stranded but then find a hotel in a blizzard, the manager charges them $10 each for their room, total being $30. Bellhop takes them up to their room, when he comes back down the manager says he feels bad for the guys and takes $5 off and tells the bellhop to give it back to the guys. On his way up to the room, he figues he can't split $5 equally for the 3 guys, so he keeps $2 and gives each one back $1. So if each man is given back $1, they essentially paid $9 each, so $9ร3 is $27 and the bellhop kept $2, what happened to the last dollar?
Being a little kid, it stumped us.
Sidco_cat ยท 1 points ยท Posted at 17:12:38 on May 25, 2016 ยท (Permalink)
I'm stumped.
pertante ยท 1 points ยท Posted at 17:16:45 on May 25, 2016 ยท (Permalink)
The hotel did.
[deleted] ยท 1 points ยท Posted at 16:59:16 on May 25, 2016 ยท (Permalink)
British say "maths" and Americans say "math"
NickAppleese ยท 1 points ยท Posted at 16:59:55 on May 25, 2016 ยท (Permalink)
Not a mathematician, but I like cross canceling, eg 140/100% = x/34%. I find that I've used that formula in daily life more than anything else. Math was my favorite subject, though I sucked at it. =/
Sitk042 ยท 1 points ยท Posted at 17:00:00 on May 25, 2016 ยท (Permalink)
For Any number divisible by 9, if you add up its digits, their total will be a number divisible by 9. 3 * 9 = 27, 2 + 7 = 9; 42 * 9 = 378, 3 + 7 + 8 = 18...
[deleted] ยท 1 points ยท Posted at 17:00:15 on May 25, 2016 ยท (Permalink)*
2x +2x =2x+1 works But 3x +3x =3x+1 does not work But 3x +3x +3x =3x+1 does work And so on 4x +4x +4x +4x =4x+1 Edit: Added some spaces so it looked correct Edit no 2: math was wrong, now isn't.
DarkIntent ยท 1 points ยท Posted at 17:00:45 on May 25, 2016 ยท (Permalink)
There is a theorem called the fixed point theorem which states that:
Here is a basic example:
Boring but how about a cool application. The function (projection) that sends spherical coordinates in space to a 2d image (map) is continuous (I hope...). This is why it's possible to read a "You are here" sign at the mall or airport and you actually are. Seems obvious but this is why.
Sorry if my math is rusty, it's been a while.
Links:
http://mathworld.wolfram.com/BrouwerFixedPointTheorem.html http://mathworld.wolfram.com/FixedPointTheorem.html
caposhitliner ยท 1 points ยท Posted at 17:01:53 on May 25, 2016 ยท (Permalink)
phi.
RicardoMgl ยท 1 points ยท Posted at 17:02:25 on May 25, 2016 ยท (Permalink)
0,9999... = 1
_AISP ยท 1 points ยท Posted at 17:02:31 on May 25, 2016 ยท (Permalink)
A circle whose diameter is the length of a side of a square takes up ~78.5% or pi/4 of the area of that square.
roh8880 ยท 1 points ยท Posted at 17:02:52 on May 25, 2016 ยท (Permalink)
I think this qualifies.
mrshibx ยท 1 points ยท Posted at 17:03:23 on May 25, 2016 ยท (Permalink)
The Godel incompleteness theorems
[deleted] ยท 1 points ยท Posted at 17:03:38 on May 25, 2016 ยท (Permalink)
0.9 recurring is equal to 1.0
birdie_sparrows ยท 1 points ยท Posted at 17:03:48 on May 25, 2016 ยท (Permalink)
crumbs
YouWillRememberMe ยท 1 points ยท Posted at 17:04:49 on May 25, 2016 ยท (Permalink)
That we really cannot comprehend infinity. For example, 1 is exactly equal to .9 repeating.
Here are the details about it the proof
Dima0425 ยท 1 points ยท Posted at 17:05:26 on May 25, 2016 ยท (Permalink)
2 is not a prime number
xXZHeatWaveZXx ยท 1 points ยท Posted at 17:05:35 on May 25, 2016 ยท (Permalink)
I forget how, but mathematically you can make one sphere into two spheres identical to the first.
Aominee ยท 1 points ยท Posted at 17:05:50 on May 25, 2016 ยท (Permalink)
What's 9 + 10?
TheGaz ยท 1 points ยท Posted at 17:06:10 on May 25, 2016 ยท (Permalink)
The space between two whole numbers contains an infinite amount of numbers.
1 + 1 = 2, but the space between 1 and 2 contains 1.0000000001, 1.0000000002, 1.0000000003 etc.
judo_panda ยท 1 points ยท Posted at 17:06:33 on May 25, 2016 ยท (Permalink)
32 + 42 = 52 or X2 + Y2 = Z2
I was playing around with squares when we first learned them in elementary, brought that to the teacher and she showed that to the class, claiming she had never seen that before. Don't know how truthful she was about that though.
flyingjam ยท 1 points ยท Posted at 17:42:27 on May 25, 2016 ยท (Permalink)
Yeah, that's a Pythagorean triple. Others include 5, 12, 13 and 8,15,17.
judo_panda ยท 1 points ยท Posted at 17:49:35 on May 25, 2016 ยท (Permalink)
Gotcha. Around the same time, I found that the difference between each square sum is the sum of both squares.....
Works with every pair of consecutive squares
lukebaker94 ยท 1 points ยท Posted at 17:06:48 on May 25, 2016 ยท (Permalink)
5318008
Idiotnextdoor_2 ยท 1 points ยท Posted at 17:06:51 on May 25, 2016 ยท (Permalink)
I suck at it.
ElagabalusRex ยท 1 points ยท Posted at 17:07:26 on May 25, 2016 ยท (Permalink)
The whole field of cardinality is weird. For example, there are as many even numbers as there are odd or even numbers.
Sidco_cat ยท 1 points ยท Posted at 17:07:42 on May 25, 2016 ยท (Permalink)
I love that you can help a kid learn their multiplication tables with the 9 trick with your fingers.
https://www.youtube.com/watch?v=AnsoxGqDOoo
Ialdabaoloth ยท 1 points ยท Posted at 17:07:45 on May 25, 2016 ยท (Permalink)
This one is from an old PC game - Rama.
If you start with the number 41, and add increments of 2*n, the series you produce: 41, 43, 47, 53, 61, 71, etc. is one of the longest running series of primes!
McSquiggglez ยท 1 points ยท Posted at 17:08:13 on May 25, 2016 ยท (Permalink)
Feel a bit late, but there are more real numbers between 0-1 then there are integers. The set of integers between -infinity and +infinity is smaller than the set of real numbers between 0 and 1. And while on infinity, the sum of all positive integers is a negative fraction.
Apofis ยท 1 points ยท Posted at 17:08:35 on May 25, 2016 ยท (Permalink)*
There are no general solutions in radicals for polynomial equations of degree more than 4. Polynomials are one of the most fundamental things in mathematics and computing in general, because computers can evaluate them simply. However, finding all roots analytically can be difficult for polynomials of high degree. Luckily we have efficient and stable numerical algorithm for finding all roots of polynomials. Its name is "QR iteration", and it is an algorithm for finding all eigenvalues of a matrix, but can be used to find roots of polynomials as well.
praetorian_ ยท 1 points ยท Posted at 17:08:45 on May 25, 2016 ยท (Permalink)
Conisder the set of all boring numbers. Define it however you like. Within that set there must be a smallest number, which is officially the smallest boring number. That makes it interesting, so we must remove it from the set. Now consider the rest of that set, there is now a new smallest number of the set. Repeat ad infinitum and we can conlude that there are no boring numbers and hence ALL NUMBERS ARE INTERESTING.
YAY Maths! FML
[deleted] ยท 1 points ยท Posted at 17:09:23 on May 25, 2016 ยท (Permalink)
Happy Numbers - take the digits of any number, square all of them and add them together - repeat until the sum of the squares of the digits equals 1, or the system loops endlessly in a cycle which does not include 1 (thus meaning the number is a sad number) - absolutely 0 mathematical use (it's part of maths known as "recreational mathematics"), but it's a pretty interesting way to pass time if you have nothing else to do (and like maths)
completely-ineffable ยท 1 points ยท Posted at 17:09:25 on May 25, 2016 ยท (Permalink)
Two structures (in the same signature) have the same theory if and only if they have isomorphic ultrapowers [Sh:13].
PhysicsVanAwesome ยท 1 points ยท Posted at 17:09:37 on May 25, 2016 ยท (Permalink)
By using analytic continuation of the Riemann Zeta function, you can prove that the sum of all the natural numbers (1+2+3+4+.....) is equal to -(1/12). It is a very important result that is famous in analysis and has physical significance in quantum field theory and string theory.
See Zeta Regularization. :D
Deep_Black_Joe ยท 1 points ยท Posted at 17:09:45 on May 25, 2016 ยท (Permalink)
x=0.999...
10x=9.999...
10x-x=9x
9x=9.0
x=1.0
Syfawx ยท 1 points ยท Posted at 17:09:47 on May 25, 2016 ยท (Permalink)*
that 0.999... is actually 1.
edit: Proof -
let's make 0.99... x
therefore 10x = 9.99...
and 10x-x=9
therefore 9x=9, therefore x=1
tah dah!
edit 2: for some people who don't understand what the ellipsis means, it means a recurring number.
amahumahaba ยท 0 points ยท Posted at 17:20:17 on May 25, 2016 ยท (Permalink)*
10 x 0.99 is not 9.99.
I understand that this is supposed to be a joke, but its way too painful to see this stuff brainfuck a bunch of people.
e: Alternatively, if this is a scenario where you are subscribed to this idea, as some are, something being mathematically correct while factually incorrect simply proves the faults within our own system.
Syfawx ยท 1 points ยท Posted at 17:36:34 on May 25, 2016 ยท (Permalink)
Firstly, it is, and i think i made it pretty clear by adding an ellipsis instead of the dot on top of the number to show it is recurring. An ellipsis is commonly used instead of a dot anyway. 10 x 0.99... is 9.99...
This isn't supposed to be a joke - it's an actual mathematical phenomenon. Look it up for yourself before writing so passively agressive.
amahumahaba ยท 1 points ยท Posted at 17:43:27 on May 25, 2016 ยท (Permalink)
I am familiar with it. I understand the logic of it(Not having seen someone use an ellipsis to show repeating, i've always seen it with the line above(which obviously is not something that we have immediate access to at a keyboard, thats my own bad) I assumed it was strictly .99). Currently considered a phenomenon by many, yes, But plugging something into a system that is clearly not built to handle it and deciding that it is fact is ridiculous to me. Based on how we handle numbers, yes this can be argued to be "accurate" or "correct", but the real fact is that we clearly have just reached a limit of our own system or understanding.
Syfawx ยท 1 points ยท Posted at 17:48:25 on May 25, 2016 ยท (Permalink)
But that's exactly why its my favourite maths fact - because it is so clearly ridiculous is our minds but logic tells us differently and it shows a flaw in our numbering system.
amahumahaba ยท 0 points ยท Posted at 17:54:52 on May 25, 2016 ยท (Permalink)
I can agree with that. I mean, it certainly is interesting that we have managed to break our own number system. Fantastic really. People all too much just assume things like this are perfect because that is what they grew up with, but something like this can hopefully help show people that the system simply isn't complete. What i don't care for is that it is always presented as something that is "proving" something that isn't true when the majority of people do not understand that proving something mathematically is not the same as proving it factually, and because that isn't usually mentioned as it is brought up in the context of fucking with peoples head(which is usually fun to me), they accept it because "the system works"
cmsimike ยท 1 points ยท Posted at 17:09:53 on May 25, 2016 ยท (Permalink)
1) There are different sizes of infinity
2) .9999999999999 (repeating) equals 1
[deleted] ยท 1 points ยท Posted at 17:09:57 on May 25, 2016 ยท (Permalink)
0.9999... = 1
[deleted] ยท 1 points ยท Posted at 17:10:22 on May 25, 2016 ยท (Permalink)
If you were to write out the longest, most complex mathematical equation on a single chalkboard with an unlimited amount of chalk, you would be wasting your time.
Saytahri ยท 1 points ยท Posted at 17:10:56 on May 25, 2016 ยท (Permalink)
Unintuitive probability is great.
Let's play a game. It's not very fun, but it goes like this:
I have 2 coins. I will flip both coins (both at once each time) without you seeing until I get at least one heads.
I have the coins in front of me, one covered by each hand.
I reveal a heads (if they are both heads I pick randomly).
So you now have a revealed heads, and a hand covering the other coin.
What is the probability that the other coin is heads?
It's not 1/2. It's 1/3.
Jaarl ยท 1 points ยท Posted at 17:11:04 on May 25, 2016 ยท (Permalink)
Im not sure if this is common knowledge, but I cant find any info on it... if you have a number where all the digits add up to 9 ex. 400302 (4+0+0+3+0+2=9) then it is divisable by 9
nyctob0t ยท 1 points ยท Posted at 17:11:04 on May 25, 2016 ยท (Permalink)*
4+4+4=12
Altemus_Prime93 ยท 1 points ยท Posted at 17:11:13 on May 25, 2016 ยท (Permalink)
If you add every positive whole number to infinity ie: 1+2+3+4+5+...You get -1/12
sadmafioso ยท 1 points ยท Posted at 17:16:35 on May 25, 2016 ยท (Permalink)
This is not precisely true. The series diverges. However, there is a way to assign -1/12 to that sequence of numbers that is consistent with some useful mathematical operations.
AurelianoTampa ยท 1 points ยท Posted at 17:11:42 on May 25, 2016 ยท (Permalink)
The potato paradox. More about how we conceptualize numbers than being a neat math fact:
Fred brings home 100 lbs of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then lets them dehydrate overnight so that they consist of 98 percent water the next day. What is their new weight?
50 lbs.
serial_crusher ยท 1 points ยท Posted at 17:11:46 on May 25, 2016 ยท (Permalink)
I still can't get over the fact that 0.9999(infinity repeating 9s) is equal to 1. Everything I know about real numbers is a lie.
Burukai ยท 1 points ยท Posted at 17:53:36 on May 25, 2016 ยท (Permalink)
Is actually equal to 1 or is it just impossible to say how much less than 1 it is making it essentially equal to 1.
serial_crusher ยท 1 points ยท Posted at 18:11:18 on May 25, 2016 ยท (Permalink)
Actually equal to. http://www.purplemath.com/modules/howcan1.htm
The notion that it's "impossible to say" is kind of a misconception about the way infinity works. Like people want to assume reality has some hard limit where eventually there will just stop being another 9, because it's easier to comprehend things that way, but it's not the case. In truth, we know how much infinity is, and that answer is... well, infinity.
[deleted] ยท 1 points ยท Posted at 17:11:50 on May 25, 2016 ยท (Permalink)
231 seconds is about 68 years.
263 seconds is older than the universe
Korrendus_Hunt ยท 1 points ยท Posted at 17:12:07 on May 25, 2016 ยท (Permalink)
If you take the length of a river (as the crow flies) from its source to its mouth and multiply by pi, you get an almost exact measurement of its total length including the meanders.
efurnit ยท 1 points ยท Posted at 17:12:08 on May 25, 2016 ยท (Permalink)
ITT: Arithmetic, not math
Joblaska ยท 1 points ยท Posted at 17:32:07 on May 25, 2016 ยท (Permalink)
arithmetic is a branch of math
Andonly ยท 1 points ยท Posted at 17:12:17 on May 25, 2016 ยท (Permalink)
789 and was not punished! What kind of screwed up system is this?
VatoGringo ยท 1 points ยท Posted at 17:12:39 on May 25, 2016 ยท (Permalink)
There is no lift circulation around the trailing edge of an airfoil.
Katastic_Voyage ยท 1 points ยท Posted at 17:13:04 on May 25, 2016 ยท (Permalink)
Ham sandwich theorem
VMorkva ยท 1 points ยท Posted at 17:13:52 on May 25, 2016 ยท (Permalink)
That I'm failing math.
ianmelanson ยท 1 points ยท Posted at 17:14:24 on May 25, 2016 ยท (Permalink)
My favorite maths fact is that British people say maths instead of math
marlow41 ยท 1 points ยท Posted at 17:14:39 on May 25, 2016 ยท (Permalink)
The Cool Ninja Theorem.
[deleted] ยท 1 points ยท Posted at 17:14:50 on May 25, 2016 ยท (Permalink)
a simple one - that you can do your nine times tables on your hands by raising them in front of you fingers splayed out and lower the digit you are multiplying by 9. Any fingers to the left are in the 10's and to the right are in the 1's. Works up to 9x10 obviously.
Darkseer89 ยท 1 points ยท Posted at 17:14:51 on May 25, 2016 ยท (Permalink)
2+1 = OK
Bronsonite ยท 1 points ยท Posted at 17:14:56 on May 25, 2016 ยท (Permalink)
There are an infinite number between 1 and 2.
Lefty_22 ยท 1 points ยท Posted at 17:15:06 on May 25, 2016 ยท (Permalink)
Input + Generation = Output + Accumulation + Consumption
joje0904 ยท 1 points ยท Posted at 17:15:12 on May 25, 2016 ยท (Permalink)
I haven't seen this yet and I'm sure it's going to stay buried but I have to put it anyway.
1+2+3+4+... summed all the way to infinity equals -1/12
don't believe me?
flyingjam ยท 1 points ยท Posted at 17:38:29 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
goodtwitch ยท 1 points ยท Posted at 17:15:25 on May 25, 2016 ยท (Permalink)
The Triangle of Power is great, because it ties together logarithms, exponential functions and cube roots all in one symbol.
reallyrabidbilly ยท 1 points ยท Posted at 17:15:41 on May 25, 2016 ยท (Permalink)
my favorite maths fact? that almost everybody else hates it and I dont.
MateuszToosh ยท 1 points ยท Posted at 17:15:43 on May 25, 2016 ยท (Permalink)
Pugs were bread to take down lions.
CaptainJoemama77 ยท 1 points ยท Posted at 17:16:18 on May 25, 2016 ยท (Permalink)
That between 0-1 there is Infinity numbers. Idk it just always blow my mind
Adsefer ยท 1 points ยท Posted at 17:16:39 on May 25, 2016 ยท (Permalink)
All nine times tables add up too 9, eh 81 8+1 = 9
kripticblade ยท 1 points ยท Posted at 17:17:13 on May 25, 2016 ยท (Permalink)
Pythagorean theorem: a2 + b2 = c2.... it's actually helped me out a few times.
TheKingPug ยท 1 points ยท Posted at 17:17:15 on May 25, 2016 ยท (Permalink)
That .9999 repeating is in fact equal to 1.
klparrot ยท 1 points ยท Posted at 17:17:29 on May 25, 2016 ยท (Permalink)
If you cut a hollow sphere into slices horizontally, the surface area of each slice is in consistent proportion to its height.
cordobamd ยท 1 points ยท Posted at 17:18:34 on May 25, 2016 ยท (Permalink)
1 is the loneliest number :(
danhakimi ยท 1 points ยท Posted at 17:19:00 on May 25, 2016 ยท (Permalink)
The fact that it's "math," not "maths." Get off my reddit, you this is America's reddit!
UNIScienceGuy ยท 1 points ยท Posted at 17:19:00 on May 25, 2016 ยท (Permalink)
https://en.m.wikipedia.org/wiki/Pizza_theorem
kaajukatli ยท 1 points ยท Posted at 17:19:12 on May 25, 2016 ยท (Permalink)
The Pigeonhole Principle
Simply put, if there are 9 holes and 10 pigeons, then at least one hole has more than one pigeon.
lurgi ยท 1 points ยท Posted at 17:19:15 on May 25, 2016 ยท (Permalink)
Between any pair of distinct rational numbers there is an irrational number. Between any pair of distinct irrational numbers there is a rational number. Yet there are more irrational numbers than rational numbers.
Mars2050orbust ยท 1 points ยท Posted at 17:19:25 on May 25, 2016 ยท (Permalink)
Chiming in late, but 111, 222, 333, 444, 555, 666, 777, 888, and 999 are all divisible by 3.
I found this out while counting down from 999 in multiples of 3 to fall asleep at night. It didn't help much.
kuzism ยท 1 points ยท Posted at 17:19:31 on May 25, 2016 ยท (Permalink)
5 out of 4 people have trouble with fractions and spelling favorites.
Healfwer ยท 1 points ยท Posted at 17:20:14 on May 25, 2016 ยท (Permalink)
2+2 =4
2ร2 =4
22 =4
Ynwe ยท 1 points ยท Posted at 17:20:18 on May 25, 2016 ยท (Permalink)
that P = NP
ctahoem ยท 1 points ยท Posted at 17:20:34 on May 25, 2016 ยท (Permalink)
There is an infinite amount of numbers between any two numbers
heisenbug ยท 1 points ยท Posted at 17:23:39 on May 25, 2016 ยท (Permalink)
pooponagoose ยท 1 points ยท Posted at 17:24:10 on May 25, 2016 ยท (Permalink)
https://keepitmooovin.files.wordpress.com/2014/09/tim-and-eric-mind-explosion-gif-41769.gif?w=292&h=214
austinnormancore ยท 1 points ยท Posted at 17:20:40 on May 25, 2016 ยท (Permalink)
It's easy to see one and one make two, two and one make three
beastium ยท 1 points ยท Posted at 17:20:57 on May 25, 2016 ยท (Permalink)
The number 9 both exists and doesn't - if you add up the sum of any whole number, the digital root (sum of all the single digit numbers) will be the same with or without the 9's.
Mendokusai137 ยท 1 points ยท Posted at 17:21:08 on May 25, 2016 ยท (Permalink)
That you guys say maths instead if math.
MeEvilBob ยท 1 points ยท Posted at 17:21:54 on May 25, 2016 ยท (Permalink)
80085
mtthwschwtzr ยท 1 points ยท Posted at 17:22:09 on May 25, 2016 ยท (Permalink)
The sum of all real numbers is -1/12!
[deleted] ยท 1 points ยท Posted at 17:22:11 on May 25, 2016 ยท (Permalink)
[deleted]
flyingjam ยท 1 points ยท Posted at 17:37:30 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
The numberphile video is very misleading. They later made a follow-up which clears some of it up. Please watch it.
gilesperkins14 ยท 1 points ยท Posted at 17:22:40 on May 25, 2016 ยท (Permalink)
The only line that doesn't pass the vertical line test is the vertical line.
p0op ยท 1 points ยท Posted at 17:22:41 on May 25, 2016 ยท (Permalink)
I don't know why I came to this thread. My high school level math from many years ago is gone and all this is confusing and scary.
Minecraftshenanigans ยท 1 points ยท Posted at 17:22:46 on May 25, 2016 ยท (Permalink)
The number four. Square root = 2. Cut it in half? 2. It's an even number, which for some reason I associate with good (odds are evil!). You can square it a bunch and those numbers are sweet as well. And 2+2=4. Everyone always comes back to it as a known fact. I just really love 4. Also I associate it with the color green, my favorite color.
crossedstaves ยท 1 points ยท Posted at 17:32:44 on May 25, 2016 ยท (Permalink)
But in china and related places, its associated with death and considered unlucky, so be careful.
Minecraftshenanigans ยท 1 points ยท Posted at 01:33:30 on May 26, 2016 ยท (Permalink)
That is unfortunate.
BuddhaRocks ยท 1 points ยท Posted at 17:22:48 on May 25, 2016 ยท (Permalink)
When you multiply by 9, the resulting numbers can be added together to equal 9.
Constant__Variables ยท 1 points ยท Posted at 17:23:07 on May 25, 2016 ยท (Permalink)
6 was scrared of 7, because 7 8 9.
[deleted] ยท 1 points ยท Posted at 17:23:14 on May 25, 2016 ยท (Permalink)
0.9 repeating = 1.
This gets a lot of people. One way to explain it is that 0.9 repeating is just another way of saying the same thing, like speaking a different language. Another way to explain it is that 0.3 repeating is 1/3, and if you add up the infinite 3s, they all become 9s but that's just like 1/3 + 1/3 +1/3. Some people still have a hard time dealing with it.
crossedstaves ยท 2 points ยท Posted at 17:29:55 on May 25, 2016 ยท (Permalink)
I prefer to think about in more abstract terms, but they might not be helpful to other people. Basically for two real numbers to be distinct, there must exist numbers between them. A single point can't have any distance, so its just the basic truth that to establish any distance between real numbers, which is to say, make them different, we need to be able to form a collection of intervening values.
Since one cannot imagine or create any number between 0.999999... and 1 there can be no distance between them, and thus they are the same. Its a conceptual argument, but its clean to me.
typhoon_2099 ยท 1 points ยท Posted at 17:23:34 on May 25, 2016 ยท (Permalink)
Using Pi accurate to 37 decimal places you can measure the circumference of the universe to within a single atom.
TheYoupi ยท 1 points ยท Posted at 17:23:38 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+....... = -1/12 If you add all the whole numbers in the world together it will add up to -1/12
flyingjam ยท 1 points ยท Posted at 17:36:21 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
anomalousBits ยท 1 points ยท Posted at 17:24:07 on May 25, 2016 ยท (Permalink)
Benford's Law states that in any large sample of numerical data, the number 1 is the leading digit about 30% of the time.
The_Reckonist ยท 1 points ยท Posted at 17:24:09 on May 25, 2016 ยท (Permalink)
1x1 = 1 2x2 = 4 4x4 =16 16x16=256 256x256=65536
Was in a bleach advert when i was a toddler. Never forgot it.
Unknownlight ยท 1 points ยท Posted at 17:24:10 on May 25, 2016 ยท (Permalink)
2 ร 11 = 22
22 ร 112 = 222
pewpewsnotqqs ยท 1 points ยท Posted at 17:24:13 on May 25, 2016 ยท (Permalink)
ei*pi
Snuffy1717 ยท 1 points ยท Posted at 17:24:21 on May 25, 2016 ยท (Permalink)
You cannot ever reach the biggest number...
AManHasSpoken ยท 1 points ยท Posted at 17:24:26 on May 25, 2016 ยท (Permalink)
The golden ratio is pretty cool. Like, seriously.
My favorite thing about it is how it works with squaring and square roots.
ฮฆ (the golden ratio) is approximately 1.618. ฮฆ2 is approximately 2.618, exactly ฮฆ+1. 1/ฮฆ is approximately 0.618, exactly ฮฆ - 1.
fredmoney91 ยท 1 points ยท Posted at 17:24:29 on May 25, 2016 ยท (Permalink)
Simple but interesting. You can see if any number is divisible by 3 if the digits added up are divisible by three. ex: 2,894 // 2+8+9+4=23// 2+3=5 not divisible by 3. 8,634,270// 8+6+3+4+2+7=30// 3+0=3 divisible by 3.
ska_Sean ยท 1 points ยท Posted at 17:24:39 on May 25, 2016 ยท (Permalink)
There are an infinite amount of number between any two number, bit the biggest amount of infinite number is between 0 and 1
CabbagedDaughter ยท 1 points ยท Posted at 17:24:41 on May 25, 2016 ยท (Permalink)
Find the fifth root of any number
[deleted] ยท 1 points ยท Posted at 17:25:43 on May 25, 2016 ยท (Permalink)
That nothing is actually random.
conman62 ยท 1 points ยท Posted at 17:25:44 on May 25, 2016 ยท (Permalink)
Figure out the next perfect square:
If you're not sure what the next perfect square is and know the previous two perfect squares, you can figure out the next one(s) by taking the difference between the previous two perfect squares. From the difference, add the next odd number to the previous perfect square.
Ex: What's the next perfect square after 169? Well 169-144=25. The next odd number is 27. 27+169 = 196, which is a perfect square of 14. What's next? 196+29= 225, which is a perfect square of 15. And so on...
I'm sure this is an actual theory somewhere, but I figured it out after reading in Steve Jobs that they used adding sequential odd number to make rounded edges instead of doing square roots: 1+3=4, 1+3+5=9, 1+3+5+7=16...
MakingSumXs ยท 1 points ยท Posted at 17:26:02 on May 25, 2016 ยท (Permalink)
"The limit does not exist"
MadMaoh ยท 1 points ยท Posted at 17:26:07 on May 25, 2016 ยท (Permalink)
For calculating tips/gratuity: 15% of $10 = 10% of $15
D_VoN ยท 1 points ยท Posted at 17:26:12 on May 25, 2016 ยท (Permalink)
I know my calculus.
U + Me = Us
ragingchestbeard ยท 1 points ยท Posted at 17:26:27 on May 25, 2016 ยท (Permalink)
x% of y = y% of x
GaslightProphet ยท 1 points ยท Posted at 17:26:41 on May 25, 2016 ยท (Permalink)
There are different sized infinities.
Basaa ยท 1 points ยท Posted at 17:26:53 on May 25, 2016 ยท (Permalink)
If you take 1 of every Euro note and coin, you have a total of โฌ888.88.
feeblegoat ยท 1 points ยท Posted at 17:26:58 on May 25, 2016 ยท (Permalink)
The coin flipping problem I solved with some of my friends at University - If I flip a coin forever, what are the odds I get one more head than tails; and what is the average number of flips? It's my favorite because it's incredibly unintuitive. The odds you will get one more heads than tails is 100%; if you flip forever, you will eventually get one more head that tails. However, the average number of flips is infinite. So yes, you will definitely get one more heads than tails... But on average it will take you an infinite amount of time :) it is so weird I love it.
permaculture ยท 1 points ยท Posted at 17:26:59 on May 25, 2016 ยท (Permalink)
It took several hundred pages in Principia Mathematica to prove the validity of the proposition 1+1=2.
hrgilbert ยท 1 points ยท Posted at 17:27:04 on May 25, 2016 ยท (Permalink)
The set of all numbers is the same size as the set of all odd (or even) numbers โ they're both infinite. One would think that the set of all numbers would be double the size of the set of only odd (or even) numbers, but all you have to do is imagine linking each number in each set together with an imaginary line. Like this:
1, 2, 3, 4, 5...
1, 3, 5, 7, 9...
No matter how high the list of all numbers gets, there will always be another odd (or even) number to "match" it with.
dyfx ยท 1 points ยท Posted at 17:27:10 on May 25, 2016 ยท (Permalink)
Imagine that you send a message of zeros and ones and every number has a 10% chance of being flipped, you can make the message redundant in such a way that the original message can be recovered with virtual certainty AND that message is only twice as long as the original. Shannon's Noisy Channel Theorem.
Katastic_Voyage ยท 1 points ยท Posted at 17:27:18 on May 25, 2016 ยท (Permalink)*
Derivatives and integrals? They don't have to be integers.
You can take one half of a derivative. You can take 3.14159... (a special constant like Pi, or e) of a derivative. You can take cos(theta) (A function!) of a derivative.
It's called Fractional Calculus and it dates back to 1695 and it will blow your freaking mind.
They also coined an operator that does both integration and differentials. Somewhat understandably called "differintegration."
Vital1ty ยท 1 points ยท Posted at 17:35:25 on May 25, 2016 ยท (Permalink)
What would be the use of taking a partial derivative? I just finished a college calculus, so I understand what I might want a regular derivative for, but in what situation would a fractional derivative be wanted?
jacobslighthouse ยท 1 points ยท Posted at 17:27:37 on May 25, 2016 ยท (Permalink)
There's no such thing as a Math Fact. There ya go all.
impalah ยท 1 points ยท Posted at 17:27:48 on May 25, 2016 ยท (Permalink)
The Buttered Cat Paradox
https://s-media-cache-ak0.pinimg.com/736x/b8/d7/5f/b8d75fb82654a929b9a193dcc0e8ea73.jpg
viperus99 ยท 1 points ยท Posted at 17:28:12 on May 25, 2016 ยท (Permalink)
a circle = Pi * r2 a perfect circle = Pi * (square 2)2 the perfect circle = 2 * Pi
Justmy2cUK ยท 1 points ยท Posted at 17:28:12 on May 25, 2016 ยท (Permalink)
N squared = the sum of the first N odd numbers
bobroxs ยท 1 points ยท Posted at 17:28:18 on May 25, 2016 ยท (Permalink)
Proving that .99999 repeating doesn't exist.
flyingjam ยท 1 points ยท Posted at 17:32:42 on May 25, 2016 ยท (Permalink)
Er, it does exists, it's the number 1.
bobroxs ยท 1 points ยท Posted at 18:18:34 on May 25, 2016 ยท (Permalink)
.9999 doesnt exist because it is a different number. It what i mean.
flyingjam ยท 1 points ยท Posted at 18:19:33 on May 25, 2016 ยท (Permalink)
I'm not sure what you're saying. It's a different number from what? And why does that make it not exist?
bobroxs ยท 1 points ยท Posted at 20:02:21 on May 25, 2016 ยท (Permalink)
Its the sum of a convergent infinite series isn't it?
flyingjam ยท 1 points ยท Posted at 20:03:40 on May 25, 2016 ยท (Permalink)
Yes, and it's equal to 1. 1 is a number which definitely exists.
bobroxs ยท 1 points ยท Posted at 20:12:33 on May 25, 2016 ยท (Permalink)
I guess I am misunderstanding. Since .9999 is equal to 1, doesn't that mean .9999 does not exist, because it is a different number?
flyingjam ยท 1 points ยท Posted at 20:14:25 on May 25, 2016 ยท (Permalink)
Er, no? .999... is just another way to represent the number 1 with our decimal system. It's like saying that the number 4/2 doesn't exist because it's equal to 2.
bobroxs ยท 1 points ยท Posted at 20:24:24 on May 25, 2016 ยท (Permalink)
Ok. That makes more sense. Sorry!
Cmac253 ยท 1 points ยท Posted at 17:28:28 on May 25, 2016 ยท (Permalink)
Fibonacci Sequence shows up in nature
[deleted] ยท 1 points ยท Posted at 17:29:20 on May 25, 2016 ยท (Permalink)
2+2=4
Justmy2cUK ยท 1 points ยท Posted at 17:29:25 on May 25, 2016 ยท (Permalink)
The is a larger infinity of bad ideas in the universe than the infinity of good ideas
[deleted] ยท 1 points ยท Posted at 17:29:44 on May 25, 2016 ยท (Permalink)
That British people call it "maths"
jrizzle86 ยท 1 points ยท Posted at 17:40:18 on May 25, 2016 ยท (Permalink)
Well Americans call Lego, Legos and so we are even
jdschultze ยท 1 points ยท Posted at 17:30:16 on May 25, 2016 ยท (Permalink)*
There is a theorem that states you are able to break apart one sphere into pieces and put it back together as two identical spheres
brotoes ยท 1 points ยท Posted at 17:48:36 on May 25, 2016 ยท (Permalink)
The axiom of choice!
Jetstreamer ยท 1 points ยท Posted at 17:30:36 on May 25, 2016 ยท (Permalink)
Why does 6 hate 7? Because 7,8,9.
brotoes ยท 1 points ยท Posted at 17:48:15 on May 25, 2016 ยท (Permalink)
Because 7 is a registered six offender.
FragranceOfPickles ยท 1 points ยท Posted at 17:31:27 on May 25, 2016 ยท (Permalink)
1-1+1-1+1-1+1-1+... = -1/4
theduderina ยท 1 points ยท Posted at 17:31:41 on May 25, 2016 ยท (Permalink)
That math is black magic
anon33249038 ยท 1 points ยท Posted at 17:31:54 on May 25, 2016 ยท (Permalink)
Here's a trick with multiplying 11s.
Take a 2 digit number: 32
32*11=352. If you and the two outside numbers of the multiplier it creates the middle number. But it goes further than that.
3243*11= 35673. Look!
First digit: 3
Second digit: 3+2=5
Third digit: 4+2=6
Fourth digit: 4+3=7
Last digit: 3.
Now if you have two digits that add up to 10, you add 1 to the previous number.
3264*11=35904
First digit: 3
2nd digit: 3+2=5
3rd digit: 6+2=8
4th digit: 6+4=10 (at this point you drop the zero and go back and add 1 to the previous number making the third digit 9)
Last digit: 4
Princeso_Bubblegum ยท 1 points ยท Posted at 17:32:06 on May 25, 2016 ยท (Permalink)*
When we talk of "squares" in algebra, it means the same thing as an actual geometric square. A common example of this is the Pythagorean Theorem: a2 + b2 = c2, that is the exact same thing as this. When ancient mathematicians squared things or took a square root, they literally were dealing with actual squares that they drew down. Ever wonder why (a+b)2 = a2 + 2ab + b2 ? Well, here you go. In fact, most of your algebra problems from high school can be drawn as pictures. Here is how medieval mathematicians solved x2 + 10x = 39.
Vihart has a good video on this.
gruffi ยท 1 points ยท Posted at 17:33:42 on May 25, 2016 ยท (Permalink)
Can any of you brainbots picture 4 points on the surface of a sphere that are all equidistant to each other across the surface of the sphere?
Griffolion ยท 1 points ยท Posted at 17:33:44 on May 25, 2016 ยท (Permalink)
I don't know if this is actually true, but I once read that every possible combination of numbers is contained within the decimals of Pi. Any mathematicians care to weigh in on that?
flyawayonmygrepher ยท 1 points ยท Posted at 17:48:14 on May 25, 2016 ยท (Permalink)
Pi is irrational, so it does not repeat or terminate. This means that somewhere in there, every sequence of numbers is contained somewhere (and an infinite number of times, in fact)
flyingjam ยท 1 points ยท Posted at 17:49:54 on May 25, 2016 ยท (Permalink)
We don't know. A number which has that property is called a normal number, and it has not been proven that pi is one.
iwhitt567 ยท 1 points ยท Posted at 17:34:11 on May 25, 2016 ยท (Permalink)*
Any power of Phi (the 'golden ratio', ~1.618) can be expressed as A(phi)+B, where A and B are not only integers, but consecutive members of the Fibonacci sequence.
On a related note, as you get deeper into the Fibonacci sequence, the ratio of ( F(n) / F(n-1) ) very quickly approaches Phi.
EDIT: For clarification, the first fact happens because Phi has a pretty unique property such that
and
bubadmt ยท 1 points ยท Posted at 17:34:25 on May 25, 2016 ยท (Permalink)
Some infinities are different, or even larger than others. I.e. an infinity series of numbers from 1-2 and all between 2-3. They are both infinite, yet the first series is different and smaller.
-hosain- ยท 1 points ยท Posted at 17:35:26 on May 25, 2016 ยท (Permalink)
Something I noticed in grade school, if you needed say 132 , but knew 122 , you could take 122 (144) add 12, then add 13, which is 169, which is 132.
x2 = (x-1)2 + (x-1) + x
1012 = 1002 + 100 + 101
1012 = 10201
Edited for format
Shengou ยท 1 points ยท Posted at 17:35:37 on May 25, 2016 ยท (Permalink)
I believe this comes from a vsauce video, but Infinities are different sizes, one such is aleph null.
CoolZGuy ยท 1 points ยท Posted at 17:35:51 on May 25, 2016 ยท (Permalink)
The sum of all positive integers equals -1/12
CoolZGuy ยท 1 points ยท Posted at 17:35:51 on May 25, 2016 ยท (Permalink)
The sum of all positive integers equals -1/12
GoredonTheDestroyer ยท 1 points ยท Posted at 17:36:02 on May 25, 2016 ยท (Permalink)
Despite what certain celebrities believe, 1x1 does not, in fact, equal 2. Why? Well, you have one group of one, and you multiply that by one, you get... One.
mzoltek ยท 1 points ยท Posted at 17:36:09 on May 25, 2016 ยท (Permalink)
Does "Please excuse my dear aunt sally" qualify?
jthoning ยท 1 points ยท Posted at 17:37:11 on May 25, 2016 ยท (Permalink)
1+2+3+4+...=-1/12 If you add together every natural number you get -1/12.
BigCthuluBurger ยท 1 points ยท Posted at 17:37:46 on May 25, 2016 ยท (Permalink)
A fact about Grahams Number..
https://www.youtube.com/watch?v=XTeJ64KD5cg
The first sentence stuck in my head since the day i saw it....
sirpootis ยท 1 points ยท Posted at 17:37:48 on May 25, 2016 ยท (Permalink)
Belphegor's Prime.
1000000000000066600000000000001
This number has a 1, followed by unlucky 13 zeroes, followed by the mark of the beast, 666, followed by unlucky 13 zeroes again, ending with 1.
It is named after a demon.
It is a prime number.
Gimli_a_Break ยท 1 points ยท Posted at 17:38:02 on May 25, 2016 ยท (Permalink)
That you people call it "maths." How many of them are there?
Ldeezy ยท 1 points ยท Posted at 17:38:26 on May 25, 2016 ยท (Permalink)
That 1 = .9999... repeating
Algebraic proof:
Let n = .999.... So 10n = 9.9999...
Subtract the first equation for n from the second
9n = 9 (repeating decimals subtract out)
Divide both sides by 9, we now get n = 1
[deleted] ยท 1 points ยท Posted at 17:38:32 on May 25, 2016 ยท (Permalink)
Mom showed me this. As an adult it doesn't do much, may have been useful as a kid... But do a column of 0-9, then after each of those do a column of 9-0... And you get the multiples of 9.
0 9
1 8
2 7
3 6
Etc.
I know this one is a simple explanation and all, and not a miracle, but still could be useful.
Bonus fact- The other one I found odd in elementary- if you add up the digits of a number, and that number is divisible by 3... The whole number will be divisible by 3.
For example- 5,622,810- the numbers add up to 24. So since 24 is divisible by 3, 3 will go into it evenly.
If not, it's not divisible by 3.
Dafuq up wit dat
[deleted] ยท 1 points ยท Posted at 17:39:11 on May 25, 2016 ยท (Permalink)
I don't know what you call this but if you swap between adding and subtracting this formula 1/(n+1) . And n starts at 0 and continue forever. You end up with 1 - 1/2 + 1/3 - 1/4 + 1/5 ... - 1/n+1. It ends up with ฯ/4.
urPenguinsRbelong2us ยท 1 points ยท Posted at 17:39:51 on May 25, 2016 ยท (Permalink)*
june 7 1967 israel killed many Americans but killed more on 9/11 and succeeded in pulling us into endless wars in the middle east now what does America get for being an ally? that is right nothing.
Dr-K-G ยท 1 points ยท Posted at 17:39:59 on May 25, 2016 ยท (Permalink)*
We don't know wether pipipipi is an integer or not.
Edit: A few more of my favorite unsolved problems:
We don't know if e+pi or e*pi is rational but we know that at least one of them has to be irrational
Can every even number greater than 2 be expressed as a sum of two primes?
A perfect number is a positive integer that is equal the sum of its proper positive divisors, for example 6 = 1+2+3 or 28 = 1+2+4+7+14. Unsolved problems: Are there odd perfect numbers? Are there infinitely many perfect numbers?
Are there infintely many twin primes? That is primes that are exactly two apart, for example (3, 5), (5, 7), (11, 13) and (17, 19).
timeemac ยท 1 points ยท Posted at 17:40:01 on May 25, 2016 ยท (Permalink)
Math is true regardless of your beliefs.
[deleted] ยท 1 points ยท Posted at 17:40:24 on May 25, 2016 ยท (Permalink)
One million seconds is eleven and a half days. One billion seconds is almost 32 years.
Not really a "maths fact". Or my favourite.
roshoka ยท 1 points ยท Posted at 17:41:10 on May 25, 2016 ยท (Permalink)
If there are 6 people in a room, you can be completely certain, without knowing a thing about any of them, that at least 3 of them know each other or at least 3 of them are strangers.
SadHoodieDude ยท 1 points ยท Posted at 17:42:05 on May 25, 2016 ยท (Permalink)
I normally hate maths but this is all very interesting to me.
poopshipdestroyer1 ยท 1 points ยท Posted at 17:42:05 on May 25, 2016 ยท (Permalink)
.9999999 repeating is equal to 1.
1/3=.333333333_ 1/3=.333333333_ 1/3=.333333333_ +___________________ 1=.99999999999_
CaptainzGreg ยท 1 points ยท Posted at 17:42:40 on May 25, 2016 ยท (Permalink)
Indeed, let x=0.9999999... Then 10x = 9.9999999... Then 10x - x = 9.9999999... - 0.9999999... Then 9x =9 So x=1
Conclusion : 1=0.9999999...
LoneMantiss ยท 1 points ยท Posted at 17:42:55 on May 25, 2016 ยท (Permalink)
That in the US they say "math" and in the UK they say "maths."
broken-imperfect ยท 1 points ยท Posted at 17:43:08 on May 25, 2016 ยท (Permalink)
THE SLOPE OF THE TANGENT LINE IS THE SAME THING AS THE FIRST DERIVATIVE
Enigmagico ยท 1 points ยท Posted at 17:43:47 on May 25, 2016 ยท (Permalink)
"Math is fucking hard"
MosquitoTerminator ยท 1 points ยท Posted at 17:43:52 on May 25, 2016 ยท (Permalink)
My favorite fact: This is the 3rd time I see this getting to the top page in the last two months.
starwars_and_guns ยท 1 points ยท Posted at 17:44:41 on May 25, 2016 ยท (Permalink)
.99999=1
Listener-of-Sithis ยท 1 points ยท Posted at 17:44:50 on May 25, 2016 ยท (Permalink)
"You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large. But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.โ
[deleted] ยท 1 points ยท Posted at 17:45:59 on May 25, 2016 ยท (Permalink)
That consecutive lottery numbers are just as probable as any other sequence.
Turdsworth ยท 1 points ยท Posted at 17:46:13 on May 25, 2016 ยท (Permalink)
A normal distribution of normal distributions is normally distributed.
bepseh ยท 1 points ยท Posted at 17:46:33 on May 25, 2016 ยท (Permalink)
theres an Infiniy between every 2 integers. or something like this.
wait..i cant remember
DiabloCanyonOne ยท 1 points ยท Posted at 17:46:42 on May 25, 2016 ยท (Permalink)
Add two to cut it in half, add one to halve it again...
Solution
Frogole ยท 1 points ยท Posted at 17:47:03 on May 25, 2016 ยท (Permalink)
I feel so sick , Go on you Gods and save humanity :)
Kakshoo ยท 1 points ยท Posted at 17:47:35 on May 25, 2016 ยท (Permalink)
(Posted already so this must be my second favourite right?)
When you tighten a rope that covers the whole equator in length(approximately 40,000km), and then lengthen the rope by 6 meters and tighten it again, so that the rope hangs in the air at an equal height the whole way, that height will be approximately 1 meter.
popemichael ยท 1 points ยท Posted at 17:47:47 on May 25, 2016 ยท (Permalink)
It's mind blowing that there are things bigger than infinity.
toml3030 ยท 1 points ยท Posted at 17:48:23 on May 25, 2016 ยท (Permalink)
Doing too much of it will mess up your gums...oh you wanted MATH facts, not METH facts.
desiag ยท 1 points ยท Posted at 17:48:34 on May 25, 2016 ยท (Permalink)
Benford's law
PushingPrawn ยท 1 points ยท Posted at 17:48:52 on May 25, 2016 ยท (Permalink)
There are infinite even numbers and infinite odd numbers
Thequeenofhearts21 ยท 1 points ยท Posted at 17:49:14 on May 25, 2016 ยท (Permalink)
Infinity is not a number. It is a kind of number, and you can count beyond the smallest infinity.
scunliffe ยท 1 points ยท Posted at 17:49:32 on May 25, 2016 ยท (Permalink)
If you ever need to calculate the SUM of numbers from 1 to N (e.g. a Bar bet) there's an easy formula for it.
e.g. if you need to count all the numbers from 1 to 100 (e.g. 1+2+3+4+5+6+7+8+9+......98+99+100)
You can spend 5min on your phone calculator or use this simple math(s) trick.
If you were to add up 2 sets of the numbers... but add it heads to tails like this...
You end up with N pairs times (N + 1). This is exactly double the amount you were trying to sum, so divide by 2 and you have your result.
[deleted] ยท 1 points ยท Posted at 17:49:47 on May 25, 2016 ยท (Permalink)
[deleted]
flyingjam ยท 1 points ยท Posted at 17:51:34 on May 25, 2016 ยท (Permalink)
Pi has not been proven to be a normal number (I.e one that contains "all" strings of digits), so we don't actually know if that's true.
[deleted] ยท 1 points ยท Posted at 18:01:41 on May 25, 2016 ยท (Permalink)
[deleted]
flyingjam ยท 2 points ยท Posted at 18:04:19 on May 25, 2016 ยท (Permalink)
The number 0.1011011101111... also has a decimal expansion that is infinitely long and never repeats, but it also never has the digit 2.
You have to prove that the number is normal, and that's no easy task.
Here's the wikipedia page for more reading:
https://en.wikipedia.org/wiki/Normal_number
lifeonbroadway ยท 1 points ยท Posted at 18:00:40 on May 25, 2016 ยท (Permalink)
Im not sure if I understood that but it made my neck tingle lol
[deleted] ยท 1 points ยท Posted at 17:49:52 on May 25, 2016 ยท (Permalink)
0.9999... being equal to 1.
1/3 = 0.3333...
2/3 = 0.6666...
3/3 = 1
valcarni ยท 1 points ยท Posted at 17:50:39 on May 25, 2016 ยท (Permalink)
111111111 x 111111111 = 12345678987654321
IskaneOnReddit ยท 1 points ยท Posted at 17:50:56 on May 25, 2016 ยท (Permalink)
That you get the frequency spectrum of a function by multiplying it with ei*o ther_stuff and integrating it.
Kasoo ยท 1 points ยท Posted at 17:51:22 on May 25, 2016 ยท (Permalink)
If you take a point called Z in the complex plane and let Z1 be Z squared plus C, and let Z2 be Z1 squared plus C, and let Z3 be Z2 squared plus C, and so on.
If the series of Z's always stays close to Z and never trends away; that point is in the Mandelbrot Set !
daynthelife ยท 1 points ยท Posted at 18:08:51 on May 25, 2016 ยท (Permalink)
No, if the sequence starting with Z=0 stays bounded then C belongs to the Mandelbrot set. You're mixing up the Mandelbrot set with the filled Julia set for f(z)=z2+c (also a fractal that often looks quite cool)
Kasoo ยท 1 points ยท Posted at 18:11:28 on May 25, 2016 ยท (Permalink)
Jonathan Coulton lied to me!
msa001 ยท 1 points ยท Posted at 17:51:26 on May 25, 2016 ยท (Permalink)
You can easily find the Nth prime number by jus <jd on dmkwke,
[deleted] ยท 1 points ยท Posted at 17:51:29 on May 25, 2016 ยท (Permalink)
[deleted]
lifeonbroadway ยท 1 points ยท Posted at 17:55:43 on May 25, 2016 ยท (Permalink)
Could you possibly explain to me how the Fibonacci sequence can be applied to many different areas of life? For example, I've heard of it somehow applying to music theory, but it's never been explained in a way I could understand...
fartmitten ยท 1 points ยท Posted at 17:51:45 on May 25, 2016 ยท (Permalink)
0.9999... = 1
majorfoodie ยท 1 points ยท Posted at 17:52:39 on May 25, 2016 ยท (Permalink)
Pi
dannystoll84 ยท 1 points ยท Posted at 17:53:52 on May 25, 2016 ยท (Permalink)
Goodstein's Theorem. Easily one of the weirdest theorems I know, and it at first seems very counterintuitive.
In layman's terms:
When we representing a number in a base (say 99 = 10200 in base 3) we are implicitly representing it as a sum of powers of the base, for instance
99 = 1โข34 + 0โข33 + 2โข32 + 0โข31 + 0โข30
= 34 + 2โข32.
A Goodstein sequence is defined as follows:
Start with any positive number n in any base b_0 > 1, and write out the base b_0 representation for n as a series as above. But don't just do that: every time you see a number greater than to b_0 in one of the exponents, also write that as a power series in b_0, and so on until all the numbers written down are at most b_0. So in our case (n_0 = 99, b_0 = 3) we have
99 = 33+1 + 2โข32.
This is called the hyper-base b_0 representation of n.
So starting with n, we write it in hyper-base b_0. Now comes the cool part: every time you see b_0 in the expansion of n, replace that with b+1. Note that "usually" this will dramatically increase the value represented. After doing this, subtract 1 to obtain a new number n_1, and if n_1 is positive, rewrite the number in hyper-base b_1 = b+1.
So in our example, we have
n_1 = 44+1 + 2โข42 - 1 = 1055
= 44+1 + 42 + 3โข4 + 3
in hyper-base b_1 = 4. We now just repeat this process. For instance, we have
n_2 = 55+1 + 52 + 3โข5 + 2 = 15688,
n_3 = 66+1 + 62 + 3โข6 + 1 = 279991,
et cetera. As you can see, these numbers increase quickly.
On the other hand, Goodstein's theorem states that no matter what our initial base is -- you could start with 1,000,000 in base 2, of you like -- the sequence will eventually terminate, i.e. n_k will equal zero for some finite k.
Somehow, once these numbers get big enough, their structure is exhausted, and they stop increasing, so we then simply subtract 1 until we reach 0.
On the other hand, the time it takes for the sequence to terminate is generally enormous. Indeed, the function giving the number of steps to terminate starting with n_0 in base 2 increases at a very rapid pace. For instance, if we start by writing n_0 = 4 in base b_0 = 2, the sequence takes 3โข2402653211 - 2 steps to reach 0, while if n_0 = 12, the number of steps needed is more than Graham's number.
But the real punchline is that while this theorem is true (according to standard set theory), it cannot be proven using the standard axioms of arithmetic. In a sense, the function described in the above paragraph grows too quickly for first order arithmetic to prove that it is finite for all n (note that it n price the function is finite for each n, by simply writing out the whole sequence, but this is quite different from proving the statement for all n simultaneously.)
cushcritter ยท 1 points ยท Posted at 17:54:28 on May 25, 2016 ยท (Permalink)
80085 looks like BOOBS in the calculator
sex_panther96 ยท 1 points ยท Posted at 17:54:28 on May 25, 2016 ยท (Permalink)
One day I wanted to know what number times 666 would equal 121212. I found that same number did some other weird things 666ร182=121212 555ร182=101010 444ร182=80808 33ร182=6006 xxx182=2x2x2x xx182=2x02x I don't know what's up with 182, but it fascinates me.
bjsy92 ยท 1 points ยท Posted at 17:54:32 on May 25, 2016 ยท (Permalink)
That it's actually math
IStoleThePies ยท 1 points ยท Posted at 17:54:42 on May 25, 2016 ยท (Permalink)
Euler's identity: Eฯi = -1.
It's brilliant and it actually makes way for other functions, like hyperbolic functions.
JimmyR42 ยท 1 points ยท Posted at 17:54:53 on May 25, 2016 ยท (Permalink)
It's more of a logical fact, but the fact that Commutativity is not universal which implies that the "frame of reference" impacts the logical axioms that rules it.
hunangsflugan ยท 1 points ยท Posted at 17:55:03 on May 25, 2016 ยท (Permalink)
Want to know if a very large number is evenly divisible by 3, 6 or 9 without using a calculator? Easy.
Lets use the number 1.709.604 as an example.
Divisible by 3
If you sum up the individual digits of the large number and the sum is divisible by 3, then the original number is also divisible by 3.
Divisible by 6
Same process as before but with an extra step.
Add up the individual digits and see if the sum is divisible by 3.
If the sum is divisible by 3 AND if the large number ends in an even number (0,2,4,6,8) then the large number is also divisible by 6.
Divisible by 9
Same process as the first one, but this time with a 9.
Add up the individual digits and see if the sum is divisible by 9
But Hunangsfluga! What if the sum of the large number is so big that I can't tell if it's divisible by three???
Don't worry. Just repeat the steps as many times as needed
This trick works really well with rounded numbers.
For example we can see straight away that 7.000.000.000.000.000 is not divisible by 3, 6 or 9 since 7+a whole lot of nothing = 7
What about 7.000.000.000.000.002 ?
You tell me...
Stroger ยท 1 points ยท Posted at 17:55:14 on May 25, 2016 ยท (Permalink)
0.999.... =1
https://en.wikipedia.org/wiki/0.999...
i-like-robots ยท 1 points ยท Posted at 17:55:21 on May 25, 2016 ยท (Permalink)
.999..... repeating equals 1.
x = .9999...
10x = 9.999...
10x - x = 9.999.... - .999....
9x = 9
x = 1
Also, this fucking bullshit: https://www.quora.com/What-is-the-most-intriguing-mathematical-concept-you-have-ever-encountered/answer/Prashanth-Ravindran-1?srid=cFJ&share=b56dbab7
crusoe ยท 1 points ยท Posted at 18:23:19 on May 25, 2016 ยท (Permalink)
1/3 = 0.333333...
3 * 1/3 = 1 = 0.3333... + 0.333... + 0.333... = 0.999....
This is only an issue because 1/3 has a repeating rep in base 10. In base 3 it looks sane
1/3 = 0.1 in base 3
0.1 + 0.1 + 0.1 = 1.0 in base 3
Neebat ยท 1 points ยท Posted at 17:55:40 on May 25, 2016 ยท (Permalink)
2+2 = 2*2 =22
justtoclick ยท 1 points ยท Posted at 17:57:49 on May 25, 2016 ยท (Permalink)
That is pretty cool...
happychineseboy ยท 1 points ยท Posted at 17:55:52 on May 25, 2016 ยท (Permalink)
St. Petersburg paradox
elkabongg ยท 1 points ยท Posted at 17:56:06 on May 25, 2016 ยท (Permalink)
There's no such thing as an exact measurement of size and distance. you can always refine the measurement to create an over/under situation.
maroney111 ยท 1 points ยท Posted at 17:56:32 on May 25, 2016 ยท (Permalink)
0 x 5,293,648,364 = 0
varmisciousknid ยท 1 points ยท Posted at 17:56:32 on May 25, 2016 ยท (Permalink)
Get a calculator that reads out a lot of digits and use it to square a number made out of 1s e.g. 111,111 or 1,111. It's neat
mr-dogshit ยท 1 points ยท Posted at 17:57:51 on May 25, 2016 ยท (Permalink)
0.999... = 1
https://upload.wikimedia.org/math/3/4/c/34cc2f375a21d5f74b6bbaef6cfe35d2.png
[deleted] ยท 1 points ยท Posted at 17:58:04 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 23:55:17 on May 27, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 03:52:18 on May 28, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 20:16:07 on May 28, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 20:21:52 on May 28, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 20:45:39 on May 28, 2016 ยท (Permalink)
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[deleted] ยท 1 points ยท Posted at 22:09:09 on May 28, 2016 ยท (Permalink)
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slowhand5 ยท 1 points ยท Posted at 17:58:10 on May 25, 2016 ยท (Permalink)
What we call "math" in the US is called "maths" in the UK.
This is both a maths fact and an Englishs fact.
cream_of_the_crap ยท 1 points ยท Posted at 17:58:57 on May 25, 2016 ยท (Permalink)
I know this thread is mainly for geniuses/brainiacs, but there's something my 5th grade Math teacher told me that has stuck in my mind forever: if you add up all the digits in a number, and the result is divisible by 3, then the whole number is divisible by 3.
103 = 1+0+3 = 4, so 103 is not divisible by 3.
105 = 1+0+5 = 6, so 105 can be divided by 3.
I know it's silly, but me being completely biased towards humanities makes me even prouder of the fact that at least I got this from elementary school mathematics :)
Budalla ยท 1 points ยท Posted at 18:00:14 on May 25, 2016 ยท (Permalink)
If you get 20 random people there's about a 50% chance of at least 2 of them sharing a birthday. The maths is easy if you calculate the chance of none of them sharing
Melba69 ยท 1 points ยท Posted at 18:00:20 on May 25, 2016 ยท (Permalink)
โ69 = eight something.
KitAndKat ยท 1 points ยท Posted at 18:00:27 on May 25, 2016 ยท (Permalink)
112 = 121
1112 = 12321
11112 = 1234321
etc. and for a sequence of N ones, this is true in every base of N+1 or more, e.g. if the 1st example is in hexadecimal, its decimal equivalent is 17x17=289.
Wanwan156 ยท 1 points ยท Posted at 18:00:37 on May 25, 2016 ยท (Permalink)
123456789x8= 987654312 So close
rosco314 ยท 1 points ยท Posted at 18:00:42 on May 25, 2016 ยท (Permalink)
Take any arbitrary number with more than 1 digit, call it xyz. Add the digits to one another (x+y+z) =s. Subtract that number from the original (xyz)-s =abc. Then add those digits, a+b+c = T. That number, T, is always evenly divisible by 9. Example: 573. Add it up 5+7+3=15. Subtract from the original 573-15=558. Add those digits, 5+5+8=18. The sum is divisible y 9! /2=2. It works! Now, please tell me why this works.
iamverymoronic ยท 1 points ยท Posted at 18:01:23 on May 25, 2016 ยท (Permalink)
I can't get high on poteneuse
bears_eat_you ยท 1 points ยท Posted at 18:01:24 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=6L0xT8lMyss
ruddyscrud ยท 1 points ยท Posted at 18:01:47 on May 25, 2016 ยท (Permalink)
Euler's identity:
eiฯ+1=0
It's just so beautiful.
Irru ยท 1 points ยท Posted at 18:01:52 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=YocQ1g5uC5s
onzie9 ยท 1 points ยท Posted at 18:01:59 on May 25, 2016 ยท (Permalink)
Take every integer, square it, and invert it. Add them all together. The answer is pi2/6. That is, 1/1+1/4+1/9+1/16+1/25+...=pi2/6.
I'm no fan of pi, but that is a decently cool place for it to show up. The two proofs I know of this fact are both found here. Euler's version is not rigorous (or, rather, it was not rigorous when he came up with it), but the Fourier transform method was solid from the start.
Rotating_Hill ยท 1 points ยท Posted at 18:02:18 on May 25, 2016 ยท (Permalink)
There are more numbers between 1 and 2, on a rational number line, than there is in the entire list of rational numbers.
Rosehodgesislyfe ยท 1 points ยท Posted at 18:02:32 on May 25, 2016 ยท (Permalink)
That it's called math not maths
martin_grosse ยท 1 points ยท Posted at 18:02:41 on May 25, 2016 ยท (Permalink)
From a mathematician's standpoint, 22 centimeters is an even number of centimeters, but a non-even (perhaps odd) number of decimeters.
ekazu129 ยท 1 points ยท Posted at 18:02:45 on May 25, 2016 ยท (Permalink)
A simple one but one I like nonetheless. The digits of any number divisible by nine (but doesn't end in 9) will add up to 9.
9+0=9 1+8=9 2+7=9 Etc.
NotSorryIfIOffendYou ยท 1 points ยท Posted at 18:03:07 on May 25, 2016 ยท (Permalink)
If you lay a map of a country down on the ground in that country there will always be one point on the map that lies exactly on its actual location in the real world. This is guaranteed in any country other than South Africa and Italy or any other I am forgetting which completely surrounds another nation.
AWebDeveloper ยท 1 points ยท Posted at 18:03:20 on May 25, 2016 ยท (Permalink)
1+2+3+4+5 = 15
This just makes me happy for some reason.
5 numbers.
3 sections.
The 3rd multiple of 5.
That's 3 different things.
Illuminartttyyyy confuhrmed!
blubbersassafras ยท 1 points ยท Posted at 18:03:36 on May 25, 2016 ยท (Permalink)
Someone else got their GCSE maths tomorrow?
Shifty_Samurai ยท 1 points ยท Posted at 18:03:54 on May 25, 2016 ยท (Permalink)
46% of people reading this statement believe it.
Roadsoda350 ยท 1 points ยท Posted at 18:04:09 on May 25, 2016 ยท (Permalink)
142857 multiplied by any whole number 1,2,3,... will give you digits that are either a permutation of 142857 or digits that can be summed to create 142857. As the numbers get higher and higher this becomes more difficult but at numbers < 20 or so it's pretty clear.
MrMoe18 ยท 1 points ยท Posted at 18:04:25 on May 25, 2016 ยท (Permalink)
0.999 repeating is equal to 1
TheJackFroster ยท 1 points ยท Posted at 18:04:35 on May 25, 2016 ยท (Permalink)
That I dont have to learn it anymore.
Sanctitty ยท 1 points ยท Posted at 18:04:52 on May 25, 2016 ยท (Permalink)
That to average guess salary real quick when someone says they make $12 an hour all you have to do is double that number and add three zeros assuming they work 40 hours a week. $12 dollars would equal to aboutish $24,000 a year before taxes and stuff. Its pretty easy and comes in handy a lot more then i thought.
irritable_sophist ยท 1 points ยท Posted at 18:29:09 on May 25, 2016 ยท (Permalink)
Or just observe that (in civilized countries anyway) there are about 2000 working hours in a year.
SickAgain ยท 1 points ยท Posted at 18:05:00 on May 25, 2016 ยท (Permalink)
If you take a calculator and type the top row of numbers backwards for example 987 and then subtract the top row of numbers but in the opposite direction for example 789, you get 198.
Now take the second row 654 and do the same, subtract the opposite, 456 you get 198.
Guess what for 321 minus 123? 198. Pretty simple but quite interesting too.
careersinscience ยท 1 points ยท Posted at 18:05:44 on May 25, 2016 ยท (Permalink)
My favorite math fact, as an American, is that the English call it "Maths." Adorable. Also, since I am American, that is the extent of my mathematical knowledge.
pinheadcamera ยท 1 points ยท Posted at 18:06:02 on May 25, 2016 ยท (Permalink)*
142,857 when multiplied by an integer (x) between 1 and 6 results in a number that has the same digit sequence, just with a shifted beginning point.
x2 = 285714 x3 = 428571 x4 = 571428 x5 = 714285 x6 = 857142
x7 is funky - it gives you 999,999
beyond that, you get the same original pattern if you ignore the first digit and add it onto the last:
x 8 = 1142856 x9 = 1285713
and so on.
EDIT: wikipedia explains it better than me. https://en.wikipedia.org/wiki/142857_(number)
THX1138special ยท 1 points ยท Posted at 18:07:08 on May 25, 2016 ยท (Permalink)
When you add the digits of the first ten multiples of 9 they equal nine. ex 9x2=18, 1+8=9. 9x4=36, 3+6=9 and so on.
kinder_teach ยท 1 points ยท Posted at 18:07:59 on May 25, 2016 ยท (Permalink)*
The progression of these numbers
1 x 1 = 1
11 x11 = 121
111 x 111 = 12,321
1111 x 1111 = 1,234,321
11111 x 11111 = 123,454,321
111111 x 111111 = 12,345,654,321
1111111 x 1111111 = 1,234,567,654,321
11111111 x 11111111 = 123,456,787,654,321
and
111111111 x 111111111 = 12,345,678,987,654,321
usernametakenbs ยท 3 points ยท Posted at 18:18:05 on May 25, 2016 ยท (Permalink)
1 x 1 = 2 is definitely my favorite fact here
kinder_teach ยท 1 points ยท Posted at 19:20:06 on May 25, 2016 ยท (Permalink)
Thanks, hit the wrong key there
Pandamana ยท 1 points ยท Posted at 18:08:18 on May 25, 2016 ยท (Permalink)
Besides Euler's formula, the other cool one I learned when studying EE was that the imaginary number i !=sqrt(-1), as I'll prove below:
if i=sqrt(-1)
i2 = sqrt(-1) x sqrt(-1) = sqrt(-1 x -1) = sqrt(1) = 1
You MUST define i as i2 = -1, not i=sqrt(-1). The truth is i is +/- sqrt(-1), but you can never know which one.
YouFeedTheFish ยท 1 points ยท Posted at 18:08:28 on May 25, 2016 ยท (Permalink)
Gabriel's Horn is a mathematical object which has a finite volume, but an infinite surface area. Mind blowing really.
daweber ยท 1 points ยท Posted at 18:08:50 on May 25, 2016 ยท (Permalink)
You can quickly find out what (9x1to9) are by putting your hands up in front of you palms towards you and putting the finger down that you are trying to multiply 9 by. For example 9x8=72 you put down your eighth finger and count the fingers before and get 7 and the fingers after and you get 2. The seven is in the tenths place and the two is in the ones place so it makes 72. If anyone doesn't understand pm me and I'll try to explain it better or I'll send pictures
CookieMafia ยท 1 points ยท Posted at 18:09:13 on May 25, 2016 ยท (Permalink)
The fact that if you were to wrap a cord around the Earth (assuming it's perfectly spherical), and then you added one metre of cord, it would be able to be lifed about 16cm uniformly (or, in other words, the Earth woul have to have a radius 16cm larger for it to be wrapped tightly). The best pat is that this doesn't depend on the radius of the sphere, so it also holds true for, say, a basketball.
Sleyck ยท 1 points ยท Posted at 18:09:27 on May 25, 2016 ยท (Permalink)
0.9999999999999.... = 1 Because periodic numbers are written dividing them in 9 so 0.9 periodic would be 9/9 and that is = 1
Schnives ยท 1 points ยท Posted at 18:09:41 on May 25, 2016 ยท (Permalink)
The fact that you can have multiple infinities, some bigger than the other.
Vsauce's video "How to Count Past Infinity" explains this very well
(I'll link l8er homies)
agangofoldwomen ยท 1 points ยท Posted at 18:09:45 on May 25, 2016 ยท (Permalink)
f=ma
or as my physics professor used to say, "f equals your ma"
CarrionSymphony ยท 1 points ยท Posted at 18:10:00 on May 25, 2016 ยท (Permalink)
That I won't have to take another maths class again in my life
[deleted] ยท 1 points ยท Posted at 18:10:18 on May 25, 2016 ยท (Permalink)
2 is the only number that is prime and even.
[deleted] ยท 1 points ยท Posted at 18:10:28 on May 25, 2016 ยท (Permalink)
1 + 1 almost always equals 2.
Mind. Blown.
Swvodoo ยท 1 points ยท Posted at 18:21:48 on May 25, 2016 ยท (Permalink)
http://www.businessinsider.com/2--2-doesnt-always-equal-4-2014-6
[deleted] ยท 1 points ยท Posted at 18:10:39 on May 25, 2016 ยท (Permalink)*
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[deleted] ยท 0 points ยท Posted at 18:16:13 on May 25, 2016 ยท (Permalink)
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dave_id87 ยท 1 points ยท Posted at 18:10:47 on May 25, 2016 ยท (Permalink)
you+me=us
qp0n ยท 1 points ยท Posted at 18:10:55 on May 25, 2016 ยท (Permalink)
"Professor Hans-Henrik Stolum, an earth scientist at Cambridge University has calculated the ratio between the actual length of rivers from source to mouth and their direct length as the crow flies. Although the ratio varies from river to river, the average value is slightly greater than 3, that is to say that the actual length is roughly three times greater than the direct distance. In fact the ratio is approximately 3.14"
TLDR; Pi is eerily found in the chaos of nature.
[deleted] ยท 1 points ยท Posted at 18:10:56 on May 25, 2016 ยท (Permalink)
Probably won't be seen but I've always liked the concept of perfect numbers and if my programming is ever branched out of web development I'd love to find ways to discover more perfect numbers, if possible, but I bet people try already and it's hard as hell.
Spicy_Shart ยท 1 points ยท Posted at 18:11:00 on May 25, 2016 ยท (Permalink)
.999999999=1
sonicmasonic ยท 1 points ยท Posted at 18:11:33 on May 25, 2016 ยท (Permalink)
In between each number, from 1-9 there are infinite numbers. It's a paradox of sorts. For instance, in between 3.1 and 3.2 is pi and so far... infinite.
[deleted] ยท 1 points ยท Posted at 18:11:42 on May 25, 2016 ยท (Permalink)
https://www.youtube.com/watch?v=Oz7d6IL2cYc
JDavies11 ยท 1 points ยท Posted at 18:11:45 on May 25, 2016 ยท (Permalink)
There is an infinite amount of numbers between 0 and 1.
This infinity is so great that it's impossible to even begin counting it since you could never find where to start, since there could be an infinite amount of zeros before the first real digit. (Ex. 0.0000...1).
Omvasu ยท 1 points ยท Posted at 18:12:11 on May 25, 2016 ยท (Permalink)
0.99999โฆโฆ=1
and the war began.
lite67 ยท 1 points ยท Posted at 18:12:19 on May 25, 2016 ยท (Permalink)
.999999_ = 1
Fudgycheeseman ยท 1 points ยท Posted at 18:13:14 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 +... etc. = - 1/12 Explanation in link: https://youtu.be/w-I6XTVZXww
(channel Numberphile explains lots of interesting math facts)
[deleted] ยท 1 points ยท Posted at 18:13:30 on May 25, 2016 ยท (Permalink)
Square numbers. Say 92 squared. 100-92 and square that equals 64. 92-8 is 84. 8464 is 92 squared.
therealdeeptoot ยท 1 points ยท Posted at 18:14:17 on May 25, 2016 ยท (Permalink)
Some people say "math" and others "maths".
shucksshuck ยท 1 points ยท Posted at 18:14:47 on May 25, 2016 ยท (Permalink)
That seven ate nine.
Slonkey ยท 1 points ยท Posted at 18:15:02 on May 25, 2016 ยท (Permalink)
More numbers contain a 3 than do not.
https://www.youtube.com/watch?v=UfEiJJGv4CE
BallsDeepinBetrayal ยท 1 points ยท Posted at 18:15:03 on May 25, 2016 ยท (Permalink)
Favourite fact is that 7 ate 9
R-M-Pitt ยท 1 points ยท Posted at 18:15:08 on May 25, 2016 ยท (Permalink)
In a group of people it is a certainty that at least two will have the same number of friends in that group.
intergalacticvoyage ยท 1 points ยท Posted at 18:15:18 on May 25, 2016 ยท (Permalink)
That there cannot be an infinite series of non-zero finite intervals regressing into the past.
TGentG ยท 1 points ยท Posted at 18:16:04 on May 25, 2016 ยท (Permalink)
Picked this one up in discrete math, the sum of all positive integers (IE 1 + 2 + 3 + 4 .... and so on) is equal to -1/12. Here's a numberphile which explains it.
itsannefrank ยท 1 points ยท Posted at 18:16:07 on May 25, 2016 ยท (Permalink)
Well, my favorite maths fact is that if you divide 2 by 2 then equally you deserve to get cancer
TANKER_01 ยท 1 points ยท Posted at 18:16:25 on May 25, 2016 ยท (Permalink)
GABRIEL'S HORN... Google it. It's a calculus awesome thing and it's my favorite math thing ever.
myk- ยท 1 points ยท Posted at 18:16:26 on May 25, 2016 ยท (Permalink)
y=mx+b
thecassabunny ยท 1 points ยท Posted at 18:16:34 on May 25, 2016 ยท (Permalink)
That 1 x 1 - 1 + 1 / 1 = 1. And the same with any number. 6 + 6 = 12 12 - 6 = 6 6 x 6 = 36 36 / 6 = 6
NameNameIsMyUsername ยท 1 points ยท Posted at 18:16:38 on May 25, 2016 ยท (Permalink)
Pi is called Pi because 3.14 reflected on a mirror looks like PIE. May sound stupid, but I only just noticed this XD
Aftermath12345 ยท 1 points ยท Posted at 18:17:06 on May 25, 2016 ยท (Permalink)
the Cauchy-Schwarz inequality
a bit cliche, but it takes some mathematical maturity to understand its importance
youngrb ยท 1 points ยท Posted at 18:17:28 on May 25, 2016 ยท (Permalink)
I have been outside more than 10,000 times.
60 years - 8 years (supervised) * 365 days * 12 times outside per day = over a quarter million times. I have ten friends. If they are all roughly the same age, that is 2.5 million visits outside. No one has been hit by a meteor.
Coincidence? Just sayin'...
SkywayTraffic ยท 1 points ยท Posted at 18:17:32 on May 25, 2016 ยท (Permalink)
TIL I'm even worse at math than I realized. Wtf are you people even talking about in this thread?
kjaeft ยท 1 points ยท Posted at 18:18:13 on May 25, 2016 ยท (Permalink)
I feel so stupid not being able to comprehend and appreciate this thread...
Noahskey ยท 1 points ยท Posted at 18:19:10 on May 25, 2016 ยท (Permalink)
Obviously the finger trick for the 9s table. Dude I live off that shit
slr162 ยท 1 points ยท Posted at 18:19:32 on May 25, 2016 ยท (Permalink)
the sum of the digits that equal a multiple of 9 always equals 9. (i.e. 9 x 123 = 1107, 1+1+0+7 = 9)
tredontho ยท 1 points ยท Posted at 18:19:46 on May 25, 2016 ยท (Permalink)
There are more numbers between 0 and 1 than there are rational numbers overall.
SmLnine ยท 1 points ยท Posted at 18:19:47 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + ... = - 1/12
Obviously the sum will keep increasing forever. But you can assign a finite value to it, and that value happens to be -1/12. If you're feeling skeptical:
graciegray ยท 1 points ยท Posted at 18:19:52 on May 25, 2016 ยท (Permalink)
If you graph y=ln(x) on 1/4 inch graph paper, with a scale of 1 integer every inch, if the paper stretched for one million miles, the graph of ln(x) would only be 24.9 inches above the x-axis!
Ln(x) is the wimpiest function ever! Yes, it is unbounded, so the y-axis technically approaches infinity, but to do so, the paper would literally stretch beyond the limits of the universe!
banjoesq ยท 1 points ยท Posted at 18:19:54 on May 25, 2016 ยท (Permalink)
All prime numbers are multiples of six plus or minus one. And the Fibonacci sequence forms a repeating pattern of 24 numbers in base (or modulo) twelve. Ok, so that's two facts. But they are related facts.
alphasquid ยท 1 points ยท Posted at 18:20:17 on May 25, 2016 ยท (Permalink)
1 x 1 = 2
_Prisoner_24601_ ยท 1 points ยท Posted at 18:20:46 on May 25, 2016 ยท (Permalink)
12345679x8=98765432
BluCynMuk ยท 1 points ยท Posted at 18:21:03 on May 25, 2016 ยท (Permalink)
That the basics will never ever ever change
SemideL ยท 1 points ยท Posted at 18:21:35 on May 25, 2016 ยท (Permalink)
The complex plane becomes a compact topological space by adding a point.
[deleted] ยท 1 points ยท Posted at 18:21:35 on May 25, 2016 ยท (Permalink)
That the correct way to spell "maths" is "math."
/s
throckmortonsign ยท 1 points ยท Posted at 18:22:12 on May 25, 2016 ยท (Permalink)
If you take powers of (2, 4, 8, 16, 32, 64, 128, 256) there is a repetition that recurs in each place (0's, 10's, 100's, etc.).
If you split the 10 digit repeating sequence into 2 of equal length you get:
It works in the 100's, 1000's place and presumably the rest of them.
cmdrsalamander ยท 1 points ยท Posted at 18:22:19 on May 25, 2016 ยท (Permalink)
867-5309
I got it. I got it.
eshemuta ยท 1 points ยท Posted at 18:22:20 on May 25, 2016 ยท (Permalink)
Fibonacci Sequence, as presented by the agents of MathNet.
bmalbert81 ยท 1 points ยท Posted at 18:23:05 on May 25, 2016 ยท (Permalink)
this is more of a tip for elementary kids. all single digit multiples of 9 equal 9 when added together. 9 x 1 = 9
9 x 2 = 18 | 1+8 =9
9 x 3 = 27 | 2+7 =9
9 x 4 = 36 | 3+6 =9
and so on
you_cant_banme ยท 1 points ยท Posted at 18:23:29 on May 25, 2016 ยท (Permalink)
Mine is that 'mathematics' is not plural, and thus should be called 'math', not 'maths'.
alflup ยท 1 points ยท Posted at 18:23:54 on May 25, 2016 ยท (Permalink)
Benford's Law
https://en.wikipedia.org/wiki/Benford%27s_law
In any base system, take base 10 for example, the first number in the base system will appear a gazillion times more than the last number in the base system in any valid statistics you take. It's how they know you faked an experiment or your experiment was flawed.
sovietshark2 ยท 1 points ยท Posted at 18:24:11 on May 25, 2016 ยท (Permalink)*
I figured this out in first grade for multiplying by 9.
If you take 9 x 5, the answer is 45. Two ways to figure this out, both the numbers (Excluding when multiplying by 11 or factors of 11), results in the numbers equaling 9 if added together.
Another cool trick is 9 x 4 = 36, take the 4, multiply it by 10 and then subtract 4 to get 36. This works for any single digit number such as 9 x 9 = 81, take 90 - 9 = 81. 9 x 8, 80 - 8 = 72 9 x 7, 70 - 7 = 63 9 x 6, 60 - 6 = 54 9 x 5 , 50 - 5 = 45 9 x 4 , 40 - 4 = 36 9 x 3, 30 - 3 = 27 9 x 2, 20 - 2 = 18
I was really good at multiplication in first grade.
Edit: I tried to explain this in front of my class and another girl did it the same way and we were both the "smart" ones so Im not sure if other people use this or not for multiplication.
MrPoletski ยท 1 points ยท Posted at 18:24:15 on May 25, 2016 ยท (Permalink)
There's fermat's last theorem which is either a tragic tale of lost mathematics that took 358 years to rediscover, or it's the most effective example of trolling in the history of mankind.
[deleted] ยท 2 points ยท Posted at 19:40:07 on May 25, 2016 ยท (Permalink)
I have evidence showing that Fermat had the proof but I'm on mobile and can't post it right now
MrPoletski ยท 2 points ยท Posted at 20:25:25 on May 25, 2016 ยท (Permalink)
RIP /u/ballinismyhobby
[deleted] ยท 1 points ยท Posted at 20:37:37 on May 25, 2016 ยท (Permalink)
:)
mrpbeaar ยท 1 points ยท Posted at 18:24:22 on May 25, 2016 ยท (Permalink)
If you add all natural numbers from 1 to infinity you get -1/12
Proof
DatMamba99 ยท 1 points ยท Posted at 18:24:28 on May 25, 2016 ยท (Permalink)
This is rather simple, but always puts it in perspective for me: $1,000,000,000(1 billion) is simply 1,000 million. When thinking about $ it seems absurd!
SurtSicario ยท 1 points ยท Posted at 18:24:51 on May 25, 2016 ยท (Permalink)
1+1=3
Ginjedai ยท 1 points ยท Posted at 18:25:02 on May 25, 2016 ยท (Permalink)
Aaaand now I feel dumb as hell.
ShowBlender ยท 1 points ยท Posted at 18:25:16 on May 25, 2016 ยท (Permalink)
I always found it odd that sequentially adding odd numbers together happens to match the values of the perfect square number set. The number set of perfect squares f(n) = n2, (0,1,4,9,16,25,36,49...) is equal to the sequential sum of the odd number set f(n) = 2n-1 (1,3,5,7,9,11) starting at 0.
0+1=1, 1+3=4, 4+5=9, 9+7=16, 16+9=25, 25+11=36.
ladydeputy ยท 1 points ยท Posted at 18:25:35 on May 25, 2016 ยท (Permalink)
pi is like the galaxy...infinite and you can find yourself (birthday) in it.
sightlab ยท 1 points ยท Posted at 18:25:39 on May 25, 2016 ยท (Permalink)
There are weird numbers: a natural number that is abundant but not semiperfect. The smallest weird number is 70.
dxfout ยท 1 points ยท Posted at 18:26:10 on May 25, 2016 ยท (Permalink)
Juvenile I know but, sorry but I gotta do it. 8=====D
NoctisRex ยท 1 points ยท Posted at 18:26:32 on May 25, 2016 ยท (Permalink)
Relevant SMBC (slightly NSFW)
Another one (SFW)
AnEvilSnowman ยท 1 points ยท Posted at 18:26:43 on May 25, 2016 ยท (Permalink)
The theorem with the most everyday applications.
https://www.youtube.com/watch?v=UXRUiTEZgbA
Chrisram88 ยท 1 points ยท Posted at 18:26:43 on May 25, 2016 ยท (Permalink)
There was a girl who was 69 lbs. She thought she was 222 fat. Drove down 51st. Went to see doctor X, took the 8 pill and became 55378008. This is when you would turn the calculator upside down and it would read boobless... Or something like that.
theforeshadowing ยท 1 points ยท Posted at 18:27:09 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers (1 + 2 + 3 + 4 ...) is -1/12
https://plus.maths.org/content/infinity-or-just-112
ampereus ยท 1 points ยท Posted at 18:27:22 on May 25, 2016 ยท (Permalink)
The sum of all integers is -1/12.
gn0xious ยท 1 points ยท Posted at 18:28:13 on May 25, 2016 ยท (Permalink)
There are more than 11,000 species of moths in the U.S. alone.
Moths make great mimics, presenting themselves as wasps, tarantulas, even praying mantis. Some moths even mimic bird droppings to make themselves appear less palatable.
Moths are important pollinators, day or night.
Some moths are born without mouths and never eat. Their sole purpose is to mate and lay eggs. Speaking of mating, males can smell a female from more than 7 miles away.
senatorskeletor ยท 1 points ยท Posted at 18:28:24 on May 25, 2016 ยท (Permalink)
This post on kottke.org blew my fucking mind.
Dast_Kook ยท 1 points ยท Posted at 18:29:06 on May 25, 2016 ยท (Permalink)
1,111,111 ร 1,111,111 = 1,234,567,654,321
[deleted] ยท 1 points ยท Posted at 18:29:13 on May 25, 2016 ยท (Permalink)
I give you three $20 notes: +3 ร +20 = +60 for you
I give you three $20 debts: +3 ร -20 = -60 for you
I take three $20 notes from you: -3 ร +20 = -60 for you
I take three $20 debts from you: -3 ร -20 = +60 for you
zigzampow ยท 1 points ยท Posted at 18:29:22 on May 25, 2016 ยท (Permalink)
2 + 2 = 4. It's (obviously) simple math, but it's fact. It's special to me because I've spent much of my life drowning in variables and non-constants, it took 30 years to realize that the stability I craved was that fact, and math, as fact, is in variable. It took me 30 years to realize that no matter how much I fight it, numbers are my favorite.
___wade_wilson___ ยท 1 points ยท Posted at 18:29:28 on May 25, 2016 ยท (Permalink)
8008
ikkonoishi ยท 1 points ยท Posted at 18:29:41 on May 25, 2016 ยท (Permalink)
For base ten the entire multiplication table can be easily memorized with two number sequences.
01234567890
03692581470
Take the number you want and find the list with it closer to the beginning or end then read every number in sequence skipping the same number that you had to skip from 0 to reach it. Each time the number you are looking at decreases you add 1 to the 10s place.
Lets take 8
8 is -1 away from 0 in this list. 01234567890
So remove every other number
024680
Count backwards
0 8 6 4 2 0
Increase 10s place every time the number decreases.
00 08 16 24 32 40
crahs8 ยท 1 points ยท Posted at 18:29:57 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5... = -1/12
It does tend to infinity, but the sum is -1/12.
Here is a video that explains it.
TheFrodo ยท 1 points ยท Posted at 18:30:30 on May 25, 2016 ยท (Permalink)
That it's called MATH
lucasjkr ยท 1 points ยท Posted at 18:30:44 on May 25, 2016 ยท (Permalink)
I have only ever needed to use Pi once in my life, and that was to calculate to price difference, per square inch, of a large circular pizza vs a rectangular party pizza. The first was over twice as expensive BTW.
And I believe that that one-time calculation likely means that I used pi one more time, on average, than the average american.
TL/DR - You can use the value of pi to calculate the value of pie.
jason9510386 ยท 1 points ยท Posted at 18:30:46 on May 25, 2016 ยท (Permalink)
It is a universal language.
And by universal I mean universal.
[deleted] ยท 1 points ยท Posted at 18:30:59 on May 25, 2016 ยท (Permalink)
The finger multiplications for 9 is my favorite... Hold up both of your hands facing you... Think of a number 1-10 to multiply by 9. So say 3. Now starting from the left most finger of your left hand (thumb). Count down to the right 3 fingers... (Middle finger) then put your middle finger down. To the left of your middle finger there are 2 raised fingers... To the right of you middle finger there are 7 including the ones on your right hand... So you have the answer 27. Works for every number 1-10
[deleted] ยท 1 points ยท Posted at 18:31:21 on May 25, 2016 ยท (Permalink)
ii is a real number (if one takes the principal value of the arg function)
Henriiiko ยท 1 points ยท Posted at 18:31:26 on May 25, 2016 ยท (Permalink)
8008135
jaded76 ยท 1 points ยท Posted at 18:32:04 on May 25, 2016 ยท (Permalink)
111,111,111*111,111,111 = 12345678987654321
RafeHaab ยท 1 points ยท Posted at 18:32:09 on May 25, 2016 ยท (Permalink)
1+1=10
There are 10 kinds of people. Those who understand this reference, and those who don't.
cartmancakes ยท 1 points ยท Posted at 18:32:13 on May 25, 2016 ยท (Permalink)
The Big Bang Theory gave a good one.
Sheldon: "The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
gnuchu ยท 1 points ยท Posted at 18:32:16 on May 25, 2016 ยท (Permalink)
11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 111111111 = 12345678987654321
prez_james_marshall ยท 1 points ยท Posted at 18:32:16 on May 25, 2016 ยท (Permalink)
That it's called math in 'murica.
voiceofnonreason ยท 1 points ยท Posted at 18:32:29 on May 25, 2016 ยท (Permalink)
.999999.... is actually equal to 1.
Because .333333..... is 1/3, so multiply it by 3 and you get .999999.... or 3/3, which simplifies to 1.
KnightsOfArgonia ยท 1 points ยท Posted at 18:32:41 on May 25, 2016 ยท (Permalink)
1800 - 666 = 1 1 3 4 ( h e l l )
The_Razor ยท 1 points ยท Posted at 18:32:44 on May 25, 2016 ยท (Permalink)
That math is called maths in other countries.
[deleted] ยท 1 points ยท Posted at 18:32:57 on May 25, 2016 ยท (Permalink)
[deleted]
flyingjam ยท 2 points ยท Posted at 18:34:41 on May 25, 2016 ยท (Permalink)
The first line of the wikipedia page is
You can, however, use certain summation methods to provide a value; these are special sums, however. The normal sum is divergent and does not have a value.
thrownthiswayorthat ยท 1 points ยท Posted at 18:33:14 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6... and so forth to infinity = -1/12
JanEric1 ยท 1 points ยท Posted at 10:16:01 on May 26, 2016 ยท (Permalink)
no
RedDwarfian ยท 1 points ยท Posted at 18:34:23 on May 25, 2016 ยท (Permalink)
The sum of digits of multiples of 9 reduce to 9 (in Base 10 systems like ours). Take 9*43 = 387. 3+8+7 = 18, 1+8 = 9. This same practice works with any multiple of 3, because 3*3 = 9. Example: 3*614 = 1842, 1+8+4+2 = 15, 1+5 = 6, which is a multiple of 3.
The interesting fact is that this expands into any base system. If you're in a Base N number system, the sum of the digits of any multiple of N-1 will add up to a multiple of N-1, eventually reducing down to N-1. In addition, the factors of N-1 hold the same property that the sum of multiples will add up to a multiple.
Take Octal, base 8. The multiples of 7 have this property, but no other single digit number does. 14 in base 8 is 016, 21 is 025, 35 is 052, and etc.
Look at Hex, base 16. The multiples of 15 (0xF) do this, but so do multiples of 3 and 5. 100000 in hex is 0x186A0. 1+8+6+A+0 = 0x19, 1+9 = A, which is 10, which is a multiple of 5.
ajdrausal ยท 1 points ยท Posted at 18:34:31 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
[deleted] ยท 1 points ยท Posted at 18:35:17 on May 25, 2016 ยท (Permalink)
Pick a number, any number will do.
Spell it out.
Count the letters.
Spell out that number.
Repeat.
Eventually you will get stuck in a loop at four.
Itsacon ยท 1 points ยท Posted at 18:36:26 on May 25, 2016 ยท (Permalink)
1+ei*pi = 0.
Seriously, 3 of the weirdest numbers in the known universe, put them together and you get -1
[deleted] ยท 1 points ยท Posted at 18:36:38 on May 25, 2016 ยท (Permalink)
One way functions haven't been proven, but, for all intents and purposes, do exist. They are used primarily for encryption all over the place.
Theoretically there's no such thing, but good luck reverse engineering a 4,096bit RSA key.
FourToTheFloor_ ยท 1 points ยท Posted at 18:36:53 on May 25, 2016 ยท (Permalink)
This has always been a favourite of mine: There are as many odd numbers in the universe, as there are odd and even numbers added together. It's a different way to describe infinity.
DingDongHelloWhoIsIt ยท 1 points ยท Posted at 18:37:03 on May 25, 2016 ยท (Permalink)
9+10=21
one50nine ยท 1 points ยท Posted at 18:37:12 on May 25, 2016 ยท (Permalink)
I think this kinda counts.
One milliliter of water is one cubic centimeter, which weighs one gram, which takes one joule to heat one degree Celsius which is one percent of the amount of energy to heat one gram of water from freezing to boiling.
(I think I've probably forgotten or messed up something. Sorry)
ZacharyL182 ยท 1 points ยท Posted at 18:37:12 on May 25, 2016 ยท (Permalink)
Multiply 12345679 by 8 and you will get 98765432!
KelRen ยท 1 points ยท Posted at 18:37:28 on May 25, 2016 ยท (Permalink)
It's the same in every country.
jwktiger ยท 1 points ยท Posted at 18:37:55 on May 25, 2016 ยท (Permalink)
Perhaps my favorite is the Alabama Paradox, in 1880 they were figuring out how many congressional districts each state would have. If there were 299 representatives Alabama would get 8 spots. But if there were 300 representatives Alabama would get ONLY 7 spots.
So going to more representatives would mean Alabama would have LESS Spots.
Wiki has a good spot on it
DrBobdave ยท 1 points ยท Posted at 18:38:53 on May 25, 2016 ยท (Permalink)
If you have 23 people in a room there is over a 50% chance that 2 of them have the same birthday.
tomsanders21 ยท 1 points ยท Posted at 18:38:58 on May 25, 2016 ยท (Permalink)
Four is the only number to have its respective number of letters in the word.
Astros_alex ยท 1 points ยท Posted at 18:39:10 on May 25, 2016 ยท (Permalink)
That the ratio of an igloo's circumference to it's diameter is Eskimo Pie
[deleted] ยท 1 points ยท Posted at 18:40:21 on May 25, 2016 ยท (Permalink)
.999 repeating = 1
[deleted] ยท 1 points ยท Posted at 18:40:33 on May 25, 2016 ยท (Permalink)*
[deleted]
icydeadpeeps ยท 1 points ยท Posted at 18:44:24 on May 25, 2016 ยท (Permalink)
I think you need to add an "in half" in there. I can fold a piece of paper 103 times without issue if I'm allowed to fold it anywhere.
Pronato ยท 1 points ยท Posted at 18:40:35 on May 25, 2016 ยท (Permalink)*
That the sum of all numbers to infinity is -1/12.
Yeah let that sink in a for minute and then watch this: https://youtu.be/w-I6XTVZXww
NefariusMarius ยท 1 points ยท Posted at 18:40:41 on May 25, 2016 ยท (Permalink)
Sin2(x) + cos2(x) = 1 has always been a life saver
studyingallnightlong ยท 1 points ยท Posted at 18:41:08 on May 25, 2016 ยท (Permalink)
the sum of all the natural numbers to infinity equals -1/12
1+2+3+4+5+6+...(to infinity) = -1/12
here's the proof https://www.youtube.com/watch?v=w-I6XTVZXww
jwor024 ยท 1 points ยท Posted at 18:42:03 on May 25, 2016 ยท (Permalink)
10 = 1
[deleted] ยท 1 points ยท Posted at 18:42:23 on May 25, 2016 ยท (Permalink)*
An infinite amount of time passes every second, so our thinking of either infinity or time are wrong.
If infinite implies something goes forever, that also implies it NEVER stops.
1=1 and 1 second = 1 second
Between every second that passes, all other variations of that second (.1 second, .11 second, .111 second, etc) happen infinitely before the next second. However, we KNOW the next second comes, we can measure it with a simple stopwatch. Infinite doesn't make any sense to me.
legoman1237 ยท 1 points ยท Posted at 18:42:46 on May 25, 2016 ยท (Permalink)*
Not sure if this is a fact, but if an equation in the form az3 + bz2 + cz + d has two complex roots and one real root, the third root can be found easily by equating -b/a to the real sum of the two known roots and the unknown root.
Example: Suppose we are given the equation z3 - 4z2 + z + 26, and that one root is 3+2i (Hence 3-2i is implied to be a root as well).
So -b/a would be -(-4)/1= 4, therefore 4= (3+2i) + (3-2i) + x (Where x is the third root).
Hence the complex parts cancel out and rearranging the real parts to obtain x we get x= -2, which is the third root.
I remember using this in my exams, much quicker method than long division
yellowbootsphotoco ยท 1 points ยท Posted at 18:42:52 on May 25, 2016 ยท (Permalink)
False.
Chap1er ยท 1 points ยท Posted at 18:42:57 on May 25, 2016 ยท (Permalink)
1729 https://en.m.wikipedia.org/wiki/1729_(number)
shakingunder ยท 1 points ยท Posted at 18:44:18 on May 25, 2016 ยท (Permalink)
Asymptotes: I can't still get my head around how they will approach to, for example; the x-axis (y=0) but never actually reach it.
itshurleytime ยท 1 points ยท Posted at 18:44:25 on May 25, 2016 ยท (Permalink)
The difference between two consecutive squared integers is the sum of the integers.
292 - 282 =28+29
(x+1)2 - x2 = 2x+1
x2 +2x+1 -x2 =2x+1
TheHamCaptain ยท 1 points ยท Posted at 18:44:31 on May 25, 2016 ยท (Permalink)
Right - I don't remember the maths and didn't understand it in the first place really but it was a cool fact and hopefully someone here can elaborate:
-1 = +1
This was told to me by my A-Level maths tutor.
snake_grillz ยท 1 points ยท Posted at 18:44:39 on May 25, 2016 ยท (Permalink)
๏ฟผ
spookje ยท 1 points ยท Posted at 18:46:22 on May 25, 2016 ยท (Permalink)
The sum of all the natural numbers up to infinity is -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
ZenosAss ยท 1 points ยท Posted at 18:46:43 on May 25, 2016 ยท (Permalink)
That the "sum" of all the natural numbers is assigned the value -1/12.
Fl4zer ยท 1 points ยท Posted at 18:47:43 on May 25, 2016 ยท (Permalink)
f' from ex is ex
ShellInTheGhost ยท 1 points ยท Posted at 18:47:44 on May 25, 2016 ยท (Permalink)
eiฯ + 1 = 0
Da_Snail ยท 1 points ยท Posted at 18:49:49 on May 25, 2016 ยท (Permalink)
I'm a little late for this thread, but my personal favorite is that anything multiplied by 5 is always half the number * 10. (Ex. 5 * 6 = 6 / 2 = 3 * 10 = 30) The opposite is also true when dividing, a number divided by 5 is always double / 10.
DCdictator ยท 1 points ยท Posted at 18:50:45 on May 25, 2016 ยท (Permalink)*
Anything that points out that as things approach infinity our ability to understand them intuitively dissolves. For instance 1+2+3+4+5+6+7... equals = -1/12
Also Bertrand's Paradox
Basically, in certain situations how you go about choosing a random value affects the probability distribution of what that value might be, even if you don't change the pool from which the value is chosen. This would seem at odds without understanding because random implies that each value has an equal likelihood of being chose, so if you were selecting a random value from 1 - 100 each value would have a 1% chance of being chosen, but in some instances this breaks down.
Take for instance a factory that assembles cubes randomly with dimensions 0 - 1 unit, so at most they would be 1x1x1 cubes and at least 0x0x0 cubes (nothing).
A consequence of this method of production is that you should expect something with a volume of 1/8 or less to occur about 1/8 times because volumes are even distributed between 0 and 1.
However, side lengths are also evenly distributed between 0 and 1 and you would expect a side length of 1/2 or less to occur half the time, but this is the same as expecting a cube of volume 1/8 to occur half the time (because volume = side length squared).
The result is that we have what are apparently different probabilities of manufacturing the same set of cubes. The explanation for why this is the case is pretty tricky, and I honestly don't have a solid enough grasp on it that I can explain it to other people without working it out as I say it.
Kittykatmeeeow ยท 1 points ยท Posted at 18:51:23 on May 25, 2016 ยท (Permalink)
When multiplying a two digit number by eleven, you add the digits and put it in between the two values to find the answer. It should look like this: xy X 11=x(x+y)y
Ex: 10x11=110 1(1+0)0= 110
13x11=143 1(1+3)3=143
52x11=572 5(5+2)2=572
It gets wonky when the middle digit is over ten, but still works. You just carry the one. 99x11=1089 9(9+9)9=9(18)9= (9+1)89=1089
66x11=726 6(6+6)6=6(12)6=(6+1)26=726
Virus64 ยท 1 points ยท Posted at 18:51:28 on May 25, 2016 ยท (Permalink)
One thousand is the first number in sequence to have the letter "a" in it.
Prettygame4Ausername ยท 1 points ยท Posted at 18:51:54 on May 25, 2016 ยท (Permalink)
So...uh....no one's going to mention ei*pi + 1 = 0
Or Euler's tetrahedronal rule ?
Or Gabriel's horn ? Infinite area, finite space ?
LiverpoolMaverick ยท 1 points ยท Posted at 18:52:07 on May 25, 2016 ยท (Permalink)
2+2=4
AlkarinValkari ยท 1 points ยท Posted at 18:52:31 on May 25, 2016 ยท (Permalink)
ITT: Things I don't understand.
x5e ยท 1 points ยท Posted at 18:52:42 on May 25, 2016 ยท (Permalink)
The imaginary number i, when raised to the power of itself, ii is a real number.
Whitewolfer ยท 1 points ยท Posted at 18:52:46 on May 25, 2016 ยท (Permalink)
That the simple pigeonhole principle is so useful for proving and solving equations in combinatorics.
LuckyEddy07 ยท 1 points ยท Posted at 18:52:58 on May 25, 2016 ยท (Permalink)
Ten, ten, ten, twenty on yo titties, bitch
Windover ยท 1 points ยท Posted at 18:53:47 on May 25, 2016 ยท (Permalink)
2 is the only number that you can multiply and add to get the same number.
2+2=4
2x2=4
Can't be done with any other number (besides 0 but like come on).
tidaljunkie ยท 1 points ยท Posted at 18:53:48 on May 25, 2016 ยท (Permalink)
That 99.9% of the time you won't have to use algebraic equations to pay $2.00 for candy at a store.
pemboo ยท 1 points ยท Posted at 18:54:00 on May 25, 2016 ยท (Permalink)
Would anyone be interested in a small series of videos outlining some of these facts with explanations and proofs? Obviously not the ones that have been done to death (ei.pi = -1)
SoundsGoodChief ยท 1 points ยท Posted at 18:54:27 on May 25, 2016 ยท (Permalink)
09+90=99; 18+81=99; 27+72=99; 36+63=99; 45+54=99
Cr3X1eUZ ยท 1 points ยท Posted at 18:54:42 on May 25, 2016 ยท (Permalink)
There's a formula that "can directly calculate the value of any given digit of PI without calculating the preceding digits."
But only in base-16.
https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
ahf95 ยท 1 points ยท Posted at 18:54:42 on May 25, 2016 ยท (Permalink)
You can't divide by 0, but you can divide by 0!
...
Sorry, I'll leave.
wozowski ยท 1 points ยท Posted at 18:55:13 on May 25, 2016 ยท (Permalink)
Not quite math, but the fact that there are as many even numbers as there are even and odd numbers combined is pretty cool.
[deleted] ยท 1 points ยท Posted at 18:55:31 on May 25, 2016 ยท (Permalink)
That adding two uneven numbers together always results in an even number.
Sublime99 ยท 1 points ยท Posted at 18:55:43 on May 25, 2016 ยท (Permalink)
The fact that the indiana general assembly Almost rounded Pi to 3.2 as an assumption to legislatively prove a method for squaring the circle Yet it was proven impossible 15 years earlier
Joshua102097 ยท 1 points ยท Posted at 18:55:45 on May 25, 2016 ยท (Permalink)
Monty Hall Paradox
ahf95 ยท 1 points ยท Posted at 18:55:49 on May 25, 2016 ยท (Permalink)
The sum of the infinite series: 1+2+3+4+5+.... is in fact -1/12.
Yup. It has been proven in many different ways.
Iliadyllic ยท 1 points ยท Posted at 18:57:15 on May 25, 2016 ยท (Permalink)
That zero raised to the zeroth power (00) is 1. Or 0. Or indeterminate. (depending on who you ask.)
AskAGinger ยท 1 points ยท Posted at 18:57:19 on May 25, 2016 ยท (Permalink)
111,111,111 * 111,111,111 = 12,345,678,987,654,321
Shelldazy62 ยท 1 points ยท Posted at 18:57:31 on May 25, 2016 ยท (Permalink)
If you multiply a number by the same number (number squared) it will always equal 1 more than the number before it and after it multiplied.
reki ยท 1 points ยท Posted at 18:57:57 on May 25, 2016 ยท (Permalink)
Bunch of interesting ones I heard from my friends. Not all of these are rigorously true, so mathematicians please excuse me if I'm butchering terms or simplifying things a bit.
1) Using bipolar coordinates, you can find the 4-volume of a 4-sphere. In fact, you can easily extend this for every even number, and you notice the constant factor of pi required increases by 1. Being a little more clever, you can actually write a formula that finds the N-volume of an N-sphere, for both odd and even N. You'll find that it ends up having a factor of piN/2 in there somewhere...the fact that you don't end up using half-powers of pi in odd-numbered dimension spheres results from the next fun fact.
2) Using the Gamma function to extend the factorial system, you find that the gamma function (and hence "factorial") of 1/2 is the square root of pi. Indeed, you find a factor of (N/2) factorial in the N-volume of an N-sphere equation as well, this cancels out nicely with the factor of a 1/2 pi you get from the other part of the equation for odd-numbered dimensions.
3) There are multiple kinds of infinities. There's countable and uncountable ones: the rationals are countable, the reals are not. More interestingly, general math assumes that the reals are of the class of the simplest uncountable infinities: aleph-1. The countable infinity is labelled aleph-0. There's an axiom we kind of just assume that there is no grade of infinity beyond aleph-0 and aleph-1, and using this system, you can generate an infinite number of sizes of infinities, labelled aleph-0, aleph-1, aleph-2, etc. But wait! That series is of itself, countable. What size of infinity is used to describe all of the set of possible infinities? Turns out, it can't be in that countable series describing sizes of infinities, because you run into contradictions. It's a whole another type of uncountable infinity.
4) While we think of the "mean" as an average of a collection of numbers, it has a mathematical definition that's formulated as an integral, making it applicable to continuous probability distributions. By messing with your probability distribution to undermine this integral definition, you can create a probability distribution that doesn't have a mean or variance (or any higher moments either): the Cauchy distribution.
5) A classic thought experiment: is it possible to hang a painting by strongs on 2 nails, such that removing either nail causes the painting to fall? How about for N nails, assuming a massless, frictionless string? The answer: yes! By creating a real-world analogue of a commutator, such as aba-1b-1, you can create such a system. It's not very practical though.
6) There are certain famous mathematical problems that have yet to be solved, such as the Riemann Hypothesis. Nobody knows if it's true or not, and we might not for some time. What we DO know, however, is that either it is true, or it's negation is true: the law of excluded middle. There are some subtleties that make this different than saying it's either true or false, but that's an issue of semantics. People have shown proofs and theorems for statements by first assuming the Riemann hypothesis is true, and using the consequences to prove the results; then, they turn around and assume the Riemann hypothesis is false and use the same consequences to prove the exact same result. Regardless of whether the Riemann hypothesis itself is true or false (or even undecidable), these theorems hold!
[deleted] ยท 1 points ยท Posted at 18:58:06 on May 25, 2016 ยท (Permalink)
I should not have got on this thread stoned.
20mcgug ยท 1 points ยท Posted at 19:52:08 on May 25, 2016 ยท (Permalink)
Username checks out
PurplePain57 ยท 1 points ยท Posted at 18:58:35 on May 25, 2016 ยท (Permalink)
That the natural logarithm is the anti-derivative of x-1, I just like how it gave me a better understanding of where e came from.
father_kipz ยท 1 points ยท Posted at 18:58:37 on May 25, 2016 ยท (Permalink)
Bedford's law basically dictates the distribution of numbers that occur as the first number in any given organic set of numbers.
https://en.m.wikipedia.org/wiki/Benford%27s_law
[deleted] ยท 1 points ยท Posted at 18:59:04 on May 25, 2016 ยท (Permalink)
Locally increasing functions are increasing.
maz-o ยท 1 points ยท Posted at 18:59:32 on May 25, 2016 ยท (Permalink)
there are different size infinites.
Krashbandofco0t ยท 1 points ยท Posted at 18:59:38 on May 25, 2016 ยท (Permalink)
3 friends split a motel room for $10 each. The manager tells them the next morning they were having holiday special and the new teller last night was unaware, then gives them 5 singles. The friends take $1 each and give $2 to the breakfast cook. Now they paid $9 each and the cook got $2, where the hell did the other $1 go?
DeltaF1 ยท 1 points ยท Posted at 19:00:04 on May 25, 2016 ยท (Permalink)
ITT: Vsauce, Michael here!
yuckypants ยท 1 points ยท Posted at 19:00:24 on May 25, 2016 ยท (Permalink)
The infinity symbol is called the lemniscate
mperklin ยท 1 points ยท Posted at 19:00:26 on May 25, 2016 ยท (Permalink)
North America uses the singular: "math" whereas Europe pluralizes their "maths"
[deleted] ยท 1 points ยท Posted at 19:01:04 on May 25, 2016 ยท (Permalink)
That people say maths in Europe but Math in America
Talking_Meat ยท 1 points ยท Posted at 19:02:50 on May 25, 2016 ยท (Permalink)
256 is a metaphor.
JavidanOfTheWest ยท 1 points ยท Posted at 19:03:07 on May 25, 2016 ยท (Permalink)
My guilty pleasure was to find a comment saying "that it's useless in the real world".
But I was not ready for so many actual maths facts.
Triapod ยท 1 points ยท Posted at 19:03:11 on May 25, 2016 ยท (Permalink)
I find seemingly trivial open problems interesting.
Here is a related fun game and solutions
TookRed ยท 1 points ยท Posted at 19:03:18 on May 25, 2016 ยท (Permalink)
I always liked the fact that there are an Infinite amount of real numbers between 0 and 1.
Daktush ยท 1 points ยท Posted at 19:03:20 on May 25, 2016 ยท (Permalink)*
1+2+3+4+5... up to infinity = -1/12
Jdrid ยท 1 points ยท Posted at 19:03:21 on May 25, 2016 ยท (Permalink)
I love the fact that -40 Celsius is equal to -40 Fahrenheit.
Scrial ยท 1 points ยท Posted at 19:03:32 on May 25, 2016 ยท (Permalink)
That Pi * 13.37 = 42 the answer to everything.
Baconguacamoleburger ยท 1 points ยท Posted at 19:03:46 on May 25, 2016 ยท (Permalink)
538008
ninjafox250 ยท 1 points ยท Posted at 19:04:25 on May 25, 2016 ยท (Permalink)
If the digits in a number can be added up to reach a number divisible by 3, then the original number is divisible by 3.
For example: 8,965,271,586: 8 + 9 =17 +6 =23 +5 =28 + 2 =30 + 7 =37 + 1 =38 + 5 =43 + 8 =51 + 6 =57. If you can't easily identify 57 as divisible by 3, you can reduce again 5+7 =12. (you should be able to identify 12 as divisible by 3, but if not, then reduce once more.... 1+2=3)
[deleted] ยท 1 points ยท Posted at 19:04:27 on May 25, 2016 ยท (Permalink)
if p and q are primes, then (p/q)(q/p)=(-1)[p-1]*[q-1] *1/4, where (p/q) and (q/p) mean "p is a square mod q" and "q is a square mod p", which each have value 1 if its true, or -1 if its not.
See: Legendre Symbol and Quadratic Reciprocity
theincourup ยท 1 points ยท Posted at 19:04:31 on May 25, 2016 ยท (Permalink)
I love that if you want to know whether a huge number is divisible by 3, just add up each digit. If that sum is divisible by 3, then the original number is also divisible by 3.
Example: Is 168354 divisible by 3? Yes, because 1+6+8+3+5+4=27, which is also divisible by 3. 168354/3 = 56118
HeadToToes ยท 1 points ยท Posted at 19:05:15 on May 25, 2016 ยท (Permalink)
80085 looks like boobs written wierdky.
HappyGoPink ยท 1 points ยท Posted at 19:05:22 on May 25, 2016 ยท (Permalink)
That math is hard.
maxquatch ยท 1 points ยท Posted at 19:06:06 on May 25, 2016 ยท (Permalink)
If the individual digits of a large number add up to a number that is divisible by three, that number as a whole is divisible by three. Example: 105: 1+0+5=6, six is divisible by three, therefore 105 is divisible by three.
[deleted] ยท 1 points ยท Posted at 19:06:09 on May 25, 2016 ยท (Permalink)
0! = 1
baconboyloiter ยท 1 points ยท Posted at 19:06:11 on May 25, 2016 ยท (Permalink)
Probably the basics of Calculus. It just seems interesting to me how position, velocity, and acceleration are all related through derivatives.
Theresmyshoe ยท 1 points ยท Posted at 19:06:19 on May 25, 2016 ยท (Permalink)
121 is a perfect square in every numeral base for which it is a valid number.
Even the negative and non-integer bases.
Scacho ยท 1 points ยท Posted at 19:06:33 on May 25, 2016 ยท (Permalink)
You can add all the digits of a number to see if it's divisible by 3.
21, 2+1=3 is divisible 342, 3+4+2=9 is divisible And so on
rielephant ยท 1 points ยท Posted at 19:06:45 on May 25, 2016 ยท (Permalink)
Leonard Euler made so many discoveries that a lot of his theorems are named after the first person after him to discover them.
gforret ยท 1 points ยท Posted at 19:07:28 on May 25, 2016 ยท (Permalink)
The fact that maths comes from mathematics which comes from the Greek mathฤmatikรก which means "all things mathematical". The รก at the end of mathฤmatikรก means it is plural. The way we use now refer to mathematics isn't really plural so when we shorten it, we should actually drop the s and it should become just "math".
Freshestemo412 ยท 1 points ยท Posted at 19:07:37 on May 25, 2016 ยท (Permalink)
The fact is.. I never understood any of it
naughtywarlock ยท 1 points ยท Posted at 19:08:02 on May 25, 2016 ยท (Permalink)
You can get any number by multiplying primes together. You can use the same prime more than once though.
permalink_save ยท 1 points ยท Posted at 19:08:28 on May 25, 2016 ยท (Permalink)
1 is the same number as 0.999...
Try for yourself, divide 1 by 3 then multiply again by 3.
CapnCrump ยท 1 points ยท Posted at 19:08:34 on May 25, 2016 ยท (Permalink)
I have no proof for it, but if you add up all the digits in a number and that number is divisible by 3 then the entire number is divisible by 3.
Example: 6783245 -> 6+7+8+3+2+4+6 = 36 which is divisible by 3. Therefore, 6783245 is also divisible by 3.
Ja89015 ยท 1 points ยท Posted at 19:09:38 on May 25, 2016 ยท (Permalink)
Not a mathematician here, just something that blows my mind. Pi works for calculating both the circumference and area of a circle. I get it that all circles are proportional and the ratio between the radius and circumference will always be the same no matter the size. And I understand that there's a direct relationship between the radius and area that is constant regardless of the size of the circle too. What blows my mind is Pi works for both and there isn't one constant for circumference and another for calculating the area.
wave_theory ยท 1 points ยท Posted at 19:11:19 on May 25, 2016 ยท (Permalink)
That ei*pi = -1
A transcendental number, when raised to the power of an imaginary transcendental number, equals a simple negative integer.
BillionBirdsworth ยท 1 points ยท Posted at 19:11:32 on May 25, 2016 ยท (Permalink)
1+2+3+4+5 ........ (all the way to infinity) = -(1/12)
It's just so hard to grasp and believe this, but we have proofs and all the math checks out!
SilvosForever ยท 1 points ยท Posted at 19:12:39 on May 25, 2016 ยท (Permalink)
The Youtube channel Numberphile is devoted to lots of interesting Math factoids for anyone interested.
Chaos707 ยท 1 points ยท Posted at 19:12:57 on May 25, 2016 ยท (Permalink)
Super easy one. If you are trying to find a percentage of a number the opposite is true. For example if you are trying to find 2% of 50 it is the same number as 50% of 2. Super basic. I really didn't even think about it until a friend told me the other day.
MrBubles01 ยท 1 points ยท Posted at 19:13:25 on May 25, 2016 ยท (Permalink)
1+1=2
Without this.. well, you know.
[deleted] ยท 1 points ยท Posted at 19:13:29 on May 25, 2016 ยท (Permalink)
[deleted]
dannystoll84 ยท 2 points ยท Posted at 19:15:35 on May 25, 2016 ยท (Permalink)
Well, not exactly.
A more mathematically interesting fact is that 420 is the smallest positive number divisible by 1 through 7.
gbs5009 ยท 1 points ยท Posted at 19:27:32 on May 25, 2016 ยท (Permalink)
419.9999999992132...
New_DudeToo ยท 1 points ยท Posted at 19:14:11 on May 25, 2016 ยท (Permalink)
Dolly Parton gained 69 pounds. She said that was 2-2-2 much. She wanted to lose 51 pounds, so the doctor said take these 8 pills every day and it will leave you... 6922251x8=boobless
Chaosfreak610 ยท 1 points ยท Posted at 19:14:13 on May 25, 2016 ยท (Permalink)
Love it
MathleticDept ยท 1 points ยท Posted at 19:14:40 on May 25, 2016 ยท (Permalink)
A number is evenly divisible by 9 if the sum of all individual digits is evenly divisible by 9
I think about this a lot
Omega_Walrus ยท 1 points ยท Posted at 19:14:50 on May 25, 2016 ยท (Permalink)
Exp (i ฯ)=-1
giantEngineer ยท 1 points ยท Posted at 19:15:01 on May 25, 2016 ยท (Permalink)
That there is something called the Law of the unconscious statistician. https://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician
It's used to find the expected value of functions of a random variable when you don't explicitly know the function but know the distribution of the random variable.
Kolego ยท 1 points ยท Posted at 19:15:21 on May 25, 2016 ยท (Permalink)
I thought this would be the first thing people would mention, but I can't find it, so here it is: 1+2+3+4+5+ . . . = -1/12 Mad, huh! There's a great explanation here: https://www.youtube.com/watch?v=w-I6XTVZXww EDIT: Spelling
Treeflower ยท 1 points ยท Posted at 19:15:55 on May 25, 2016 ยท (Permalink)
1/81 = 0.01234567890123... is pretty cool
monsieur_bonana ยท 1 points ยท Posted at 19:16:10 on May 25, 2016 ยท (Permalink)
That English people call it maths.
[deleted] ยท 1 points ยท Posted at 19:16:19 on May 25, 2016 ยท (Permalink)
This is pretty much nothing special but i always found ' derivative' very interesting.
Ex. How deriv of velocity becomes acceleration.
DevilsShad0w ยท 1 points ยท Posted at 19:16:30 on May 25, 2016 ยท (Permalink)
Has to be Fermats last theorem innit fam?
DrDerpberg ยท 1 points ยท Posted at 19:16:37 on May 25, 2016 ยท (Permalink)
You only need 23 people in the same room to have a 50% chance of 2 of them having the same birthday. It seems really counterintuitive, and it's very tempting to say it should be 365/2... but the key to it is that any 2 can have the same birthday.
I find stats which make extremely rare things near-certain similarly interesting. I listened to a podcast recently where a nurse was accused of poisonings because multiple patients had unexpectedly died of respiratory arrest on his watch in the span of a few months, and under nobody else's. Statisticians determined the odds of it happening were in the 1/100,000 range, but by taking into account the number of ER nurses in England and the number of arbitrary 3-month periods (I.e.: December-February, January-March, etc. For every nurse), there had been plenty more than 100,000 possible time periods during which this could've occurred. The nurse ended up being acquitted on appeal, I believe.
NGC660 ยท 1 points ยท Posted at 19:16:40 on May 25, 2016 ยท (Permalink)
I really like Mandelbrot's set. I like that in the initial set every part is the same but smaller, but the more you zoom in it creates some awesome wild fractals. https://youtu.be/PD2XgQOyCCk
ThirddEye ยท 1 points ยท Posted at 19:16:50 on May 25, 2016 ยท (Permalink)
That 7 divided by 22 equals Pi. And the gematria of the word "seven" equals 22. Hence why 7 is a "holy" number. Within itself is Pi.
gbs5009 ยท 2 points ยท Posted at 19:24:35 on May 25, 2016 ยท (Permalink)
Pi is irrational... 22/7 just happens to be kinda sorta close.
vamediah ยท 1 points ยท Posted at 19:16:52 on May 25, 2016 ยท (Permalink)
Gรถdel's incompleteness theorem
It states that there are rather simple formal systems where some truths cannot be proven, but they still remain true. It actually was discovered while looking for exactly opposite result.
This has far-reaching consequences such as that you can't write a finite virus scanner that would run in finite time or be finite in size (this is better stated as halting problem).
Or that a human can't provably simply grasp some truths unless humans are somehow magic (because no steps lead towards such truth.
Jimp0 ยท 1 points ยท Posted at 19:16:55 on May 25, 2016 ยท (Permalink)
Look Around You
IGoJonHamm_ ยท 1 points ยท Posted at 19:17:28 on May 25, 2016 ยท (Permalink)
You can tell whether someone went to school (or grew up) in the US based whether they say math or maths.
ID-10T-ERROR ยท 1 points ยท Posted at 19:18:17 on May 25, 2016 ยท (Permalink)
Boolean Algebra is always required anywhere in the world today.
karmaniak ยท 1 points ยท Posted at 19:18:38 on May 25, 2016 ยท (Permalink)
If you add, to any number, a multiple of 9, in the resulting number has the same sum of digits.
E.g, 55+18 = 73
The sum of individual digits in both 55 and 73 is the same.
nut_fungi ยท 1 points ยท Posted at 19:19:03 on May 25, 2016 ยท (Permalink)*
When doing mental multiplication, just break the numbers down into simple problems. So 13x741=
10x700 = 7000
3x700 = 2100
10x40 = 400
3x40 = 120
13x1 = 13
Add em all together and u get 9633 which is 13x741. All you have to remember is your current total and the next step to take, so the answer goes 7000, 9100, 9500, 9620, 9633.
smbell ยท 1 points ยท Posted at 19:20:02 on May 25, 2016 ยท (Permalink)
.99999... = 1 Not that .9999... is close to 1 but they are actually equal. This goes along with my other favorite fact, there is no smallest number greater than zero. I'd elaborate but I'm on my phone.
iexpi ยท 1 points ยท Posted at 19:20:19 on May 25, 2016 ยท (Permalink)
ii = e-pi/2, which is approximately .2
[deleted] ยท 1 points ยท Posted at 19:21:21 on May 25, 2016 ยท (Permalink)
if you have a table on an infinite plane an a ball drops at a random place, the probability for it to hit the table is 0, but it still has a chance to happen
TeteDeMerde ยท 1 points ยท Posted at 19:21:34 on May 25, 2016 ยท (Permalink)
.99999... = 1
Blew my mind in 7th grade.
CalEPygous ยท 1 points ยท Posted at 19:21:49 on May 25, 2016 ยท (Permalink)
Late to the party because the number of the bus that I took to visit my sick friend was the smallest number expressible as the sum of two cubes two different ways and I was trying to remember which four cubes.
ArenaFlush ยท 1 points ยท Posted at 19:22:31 on May 25, 2016 ยท (Permalink)
Parallel lines intersect at the point at infinity.
[deleted] ยท 1 points ยท Posted at 19:22:50 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is -1/12 somehow.
RmnsRHtBtPls4ThBbs ยท 1 points ยท Posted at 19:23:30 on May 25, 2016 ยท (Permalink)
A group of n people shake hands n(n-1)/2 times. Now prove it in your head. Enjoy.
paanwala ยท 1 points ยท Posted at 19:24:48 on May 25, 2016 ยท (Permalink)
(Not a fact, but a trick) To multiply any number by 5, add a zero in the end and divide it by two. Quite easy to do it mentally...
RmnsRHtBtPls4ThBbs ยท 1 points ยท Posted at 19:25:40 on May 25, 2016 ยท (Permalink)
The arithmetic mean of the sum of measurements with any distribution converges towards the normal distribution as the number of measurements increases towards infinity.
athenashadows ยท 1 points ยท Posted at 19:25:46 on May 25, 2016 ยท (Permalink)*
Math is the same in every language.
RochesterJosh ยท 1 points ยท Posted at 19:26:05 on May 25, 2016 ยท (Permalink)
That no matter how you draw it, a triangle has a total of 180 degrees of angles every time. 3 sided voodooery if you ask me...
Authorofthiscomment ยท 1 points ยท Posted at 19:26:33 on May 25, 2016 ยท (Permalink)
0.(9) = 1
Urcinza ยท 1 points ยท Posted at 19:26:51 on May 25, 2016 ยท (Permalink)
There are as many numbers between 0 and 1 as between 1 and infinity. Because a pair of "a and 1/a" one is beween 0 and 1 and one is between 1 and infinity.
EVISORAX ยท 1 points ยท Posted at 19:27:00 on May 25, 2016 ยท (Permalink)
2+2=5
Gabby_Johnson444 ยท 1 points ยท Posted at 19:27:01 on May 25, 2016 ยท (Permalink)
The rule of 72 and the number nine multiplication table.
worldsgreatestburger ยท 1 points ยท Posted at 19:28:12 on May 25, 2016 ยท (Permalink)
Moreso physics, but whatever. Any moving object is moving back and forth in a wave-like motion. This is only noticeable on the atomic level, since the more massive an object is the smaller the wavelength is. So for example a car rolling down the street is till moving back and forth even though it appears to be moving straight
MurricanEagle ยท 1 points ยท Posted at 19:28:41 on May 25, 2016 ยท (Permalink)
1+1=2 simple lol
FishDawgX ยท 1 points ยท Posted at 19:29:25 on May 25, 2016 ยท (Permalink)
There is an equation that relates the five most important magic numbers in math (0, 1, pi, e, i):
epi*i+1=0
This is called Euler's identity.
scstraus ยท 1 points ยท Posted at 19:29:59 on May 25, 2016 ยท (Permalink)
Thank you for subscribing to maths facts!
paanwala ยท 1 points ยท Posted at 19:30:58 on May 25, 2016 ยท (Permalink)
Rule of 72 To calculate the time it will take to double your investments, divide 72 by the annual rate of interest. Eg. at 8% pa, your money will double in (72/8=) 9 years
teffflon ยท 1 points ยท Posted at 19:31:12 on May 25, 2016 ยท (Permalink)
The Four-Color Theorem: basically says that any map you draw, of any number of countries1, can always be colored with four colors, so that countries sharing a border2 have different colors.
(countries are assumed not to overlap, consist of multiple pieces, or contain other countries inside of them)
(where the border has length greater than zero, not just meeting at a point)
Proved only after enormous effort over many years, and all known proofs use large computations.
20mcgug ยท 1 points ยท Posted at 19:45:00 on May 25, 2016 ยท (Permalink)
Woah this is cool!
magik_man_ ยท 1 points ยท Posted at 19:31:38 on May 25, 2016 ยท (Permalink)
A mistake plus eleven will get you home by seven!
IAmMohit ยท 1 points ยท Posted at 19:33:29 on May 25, 2016 ยท (Permalink)
When number 9 (or any number with sum of its digits 9) is multiplied by any number, the sum of all the digits in the result always add up to 9.
For ex- 9 x 128 = 1152
Consequently, 1 + 1 + 5 + 2 = 9
For ex - 54 x 43 = 2322
Consequently, 2 + 3 + 2 + 2 = 9
XxStoudemire1xX ยท 1 points ยท Posted at 19:33:29 on May 25, 2016 ยท (Permalink)
0.999.. = 1
electricpimp ยท 1 points ยท Posted at 19:33:34 on May 25, 2016 ยท (Permalink)
If the sum of the digits of any number equals 9, then the number is divisible by 9. Example: 7,092 = 7+0+9+2 = 18 = 1+8 = 9, so 7,092 is divisible by 9. It doesn't even matter what order the numbers are in. 7,029; 9,072; 2,970; etc. are all divisible by 9.
Same works for 3 if the the sum is 3, 6 or 9. But fuck 3's.
colski ยท 1 points ยท Posted at 19:35:07 on May 25, 2016 ยท (Permalink)
ii = -0.208...
aperks ยท 1 points ยท Posted at 19:35:32 on May 25, 2016 ยท (Permalink)
ITT: So many people butthurt over the spelling of math vs maths.
TazStun ยท 1 points ยท Posted at 19:35:40 on May 25, 2016 ยท (Permalink)
The book Principia Mathematica proves 1+1=2. It only takes about several hundred pages.
https://en.wikipedia.org/wiki/Principia_Mathematica
InVulgarVeritas ยท 1 points ยท Posted at 19:35:48 on May 25, 2016 ยท (Permalink)
The Monty Hall problem is my personal favorite (more statistics than math, but still).
FriendlyJoe00 ยท 1 points ยท Posted at 19:35:51 on May 25, 2016 ยท (Permalink)
11112 equals 1234321. 111112 equals 123454321. The more 1's you add the larger the sequence gets.
IAMAwerewolfAMA ยท 1 points ยท Posted at 19:36:08 on May 25, 2016 ยท (Permalink)
I finally passed college algebra this year and will never have to worry about that horrible, stupid class again. That's my favorite math fact.
_BsL_ ยท 1 points ยท Posted at 19:36:11 on May 25, 2016 ยท (Permalink)
There is no wrong or right answer to a certain equation, there is only ONE right answer.
flyingjam ยท 1 points ยท Posted at 19:48:45 on May 25, 2016 ยท (Permalink)
No, you can have multiple solutions to equations. For example, x2 - 4 = 0 has two solutions: 2 and -2. cos(x) = 0 has an infinite number of solutions.
IfIRecallCorrectly ยท 1 points ยท Posted at 19:36:37 on May 25, 2016 ยท (Permalink)
People see the "s" at the end of Mathematics and think it's plural.
"Maths" is the incorrect way to spell/pronounce the shortened version of Mathematics. This is because "Mathematics" isn't plural, so you need to make it agree with a singular verb, not a plural one.
You don't say "Mathematics are amazing.", you say "Mathematics is amazing."
::Edit::
Relevant video: https://www.youtube.com/watch?v=SbZCECvoaTA
FluidDynamicist ยท 1 points ยท Posted at 19:36:53 on May 25, 2016 ยท (Permalink)
If you could fold a piece of paper 42 times it would reach all the way to the moon and if you could fold it 51 times it would reach the sun.
carbikebacon ยท 1 points ยท Posted at 19:37:03 on May 25, 2016 ยท (Permalink)
There are an infinite amount of numbers between 1 and 2 as there are infinite numbers.
FluidDynamicist ยท 1 points ยท Posted at 19:38:13 on May 25, 2016 ยท (Permalink)*
(1 + 2 + 3 +....+n)2 = 13 + 23 + 33 + ... + n3
Help_Me_Im_Diene ยท 1 points ยท Posted at 20:11:03 on May 25, 2016 ยท (Permalink)
Your exponent should be 3, not 4, since the sum of all values from k=1 to n is n(n+1)/2 and the sum of all values k=1 to n of k3 is n2(n+1)2/4
FluidDynamicist ยท 1 points ยท Posted at 12:28:32 on May 26, 2016 ยท (Permalink)
You are darn right.
BlackhawkRogueNinjaX ยท 1 points ยท Posted at 19:38:32 on May 25, 2016 ยท (Permalink)
That numbers up to 999 where the 1st & 3rd number add up to the middle number are always divisible by 11, and not only that give you the answer of by how many
For example
484 = 4+4 = 8
and 11 goes into 484 44 times...
198 = 1+8 = 9
and 11 goes into 198 18 times....
451 = 4+1 = 5
and 11 goes into 451 41 times....
So if I say to you what is 36 times 11, you can show off by being a smart arse and say (3+6 =9, therefore the answers is..) 396
Hope that all makes sense
Voltairian3 ยท 1 points ยท Posted at 19:38:51 on May 25, 2016 ยท (Permalink)*
If you put a grain of rice on a square of a chessboard and doubled the amount you put on each succeeding square, by the end if you laid all the grains of rice you had end to end they would reach Alpha Centauri and back. 25 trillion miles there and 25 trillion back.
noworkrino ยท 1 points ยท Posted at 19:39:14 on May 25, 2016 ยท (Permalink)
To check to see if a number is dividable by 3 (w/o remainder), add all of the digits and if the result number is dividable by 3, then the number itself is dividable by 3.
Ex: 123456789/3? 1+2+3+4+5+6+7+8+9=45, 45/3=15, therefore 123456789 can be divided by 3 without a remainder (the asnwer is 41152263)
TheOriginalAbe ยท 1 points ยท Posted at 19:42:29 on May 25, 2016 ยท (Permalink)
This is also true of the sum of the big number so in your example 1+2+3+4+5+6+7+8+9= 45
45/3? 4+5=9 9 is divisible by 3 without remainder
Dalroc ยท 1 points ยท Posted at 19:39:38 on May 25, 2016 ยท (Permalink)
If we square a string of ones of length n, where 0<n<10, we get a number that goes from one up to n and then back down to one. It's easier to show some examples:
12 = 1
112 = 121
1112 = 12321
111112 = 123454321
11111112 = 1234567654321
1111111112 = 12345678987654321
The Fibonacci sequence, 1,1,2,3,5,8,13... is well known and has been mentioned several times in this thread already. What most people don't know though, is that any string of numbers where you add the last two together to get the next one will approach the golden ratio, phi, 1.618, when you divide a number by the one before it. It is not unique for the Fibonacci sequence.
Even if we start with, oh I don't know, let's say 3 and 761, the first 10 numbers we get are:
3, 761, 764, 1525, 2289, 3814, 6103, 9917, 16020, 25937
25937/16020 = 1.61903...
(25927+16020)/25927 = 1.61765...
[deleted] ยท 1 points ยท Posted at 19:39:56 on May 25, 2016 ยท (Permalink)
a2-b2 = a+b where a and b are consecutive.
villageelliot ยท 1 points ยท Posted at 19:40:09 on May 25, 2016 ยท (Permalink)
Someone will probably call me out for inaccuracies, BUT anyway: If there's a disease that only infects 1 in every 1 million people, and you get a test that is 99% accurate that confirms you have the disease, there's only a .01% chance you actually have the disease. I probably described it a little wrong, but it's the False-Positive Paradox.
sibbo11 ยท 1 points ยท Posted at 19:40:53 on May 25, 2016 ยท (Permalink)
If you take 0.5, halve it, and add it again and repeat, you will never reach 1.
E.g. 0.5 + 0.25 + 0.125 + 0.0625 .... you will never get 1.
forwhateveritsworth4 ยท 1 points ยท Posted at 19:41:40 on May 25, 2016 ยท (Permalink)
The fact that some infinity's are larger than other infinity's.
That shit blew my mind when it was first explained. Cause it sounds like childish nonsense when it's first said in the above way. When it's explained it makes total sense
(for anyone confused: there are an infinite number of decimal point numbers between 1.0 and 2.0, but there is a larger set of infinite decimal point numbers between 1.0 and 3.0)
robopanda95 ยท 1 points ยท Posted at 19:42:08 on May 25, 2016 ยท (Permalink)
1/9 is .11 (repeating) and 1/11 is .09
In other words, ninths are multiples of eleven and elevenths are multiples of 9
Also, the digits of multiples of 9 always add up to 9
Abfab12321 ยท 1 points ยท Posted at 19:43:28 on May 25, 2016 ยท (Permalink)
Complex numbers are also vectors. They're the 'missing link' between geometry and number theory - that's what makes them so useful. As a physicist it took way too long to realise that connection and every physicist I've told since had their minds blown.
random_redditor19 ยท 1 points ยท Posted at 19:43:58 on May 25, 2016 ยท (Permalink)
it has to do with nine. all numbers that are multiplications of nine can be added together to make nine.
81=8+1=9
72=7+2=9
63..... and so on....
[deleted] ยท 1 points ยท Posted at 19:44:07 on May 25, 2016 ยท (Permalink)
0.999(repeating) is actually equal to 1. There is a proof for this.
[deleted] ยท 1 points ยท Posted at 19:44:15 on May 25, 2016 ยท (Permalink)
[deleted]
dannystoll84 ยท 1 points ยท Posted at 20:23:00 on May 25, 2016 ยท (Permalink)
Assuming sufficient randomness properties for the digits of pi, the Prime Number Theorem implies that with probability 1, infinitely many starting substrings of the decimal expansion of ฯ are prime (since the harmonic series diverges). So the existence of a single such string really isn't surprising at all.
Krisoz ยท 1 points ยท Posted at 19:44:35 on May 25, 2016 ยท (Permalink)
Pi = 3.14 to 3s.f.
johntmeche3 ยท 1 points ยท Posted at 19:44:50 on May 25, 2016 ยท (Permalink)
Translation: "What is your favorite math fact?"
pencil-pusher ยท 1 points ยท Posted at 19:44:56 on May 25, 2016 ยท (Permalink)
if you add a series of numbers twice and come up with a different answer (as check figure) and the difference between the answers is divisible by nine you have swapped two digits....
ie 27+16+15+21+19=98
27+16+51+21+19=134
134-98=36....36/9=4
as i recall this works for any number of digits or numbers
as a young pencil-pusher in the olden days i used this at least once.
i dont know why this works, i just put numbers in boxes on forms.
Help_Me_Im_Diene ยท 1 points ยท Posted at 19:53:26 on May 25, 2016 ยท (Permalink)
Well, let's start with a 2 digit case.
If only one number has switched digits (15 and 51 in your example), then the numbers can be represented as 10a+b and 10b+a. Say 10a+b>10b+a, thus a>b. The difference is then (10a+b)-(10b+a)=(10a-a)+(b-10b)=9a-9b, which is divisible by 9 and still greater than 0 because a>b
Voley ยท 1 points ยท Posted at 19:45:26 on May 25, 2016 ยท (Permalink)
that 0.9999.. = 1
firedropx ยท 1 points ยท Posted at 19:45:47 on May 25, 2016 ยท (Permalink)
1 + 1 = 11
5 + 5 = 55
most people suck at math, but I do not.
VonnegutIncarnate ยท 1 points ยท Posted at 19:46:10 on May 25, 2016 ยท (Permalink)
I am suddenly reminded of how bad I am at math
Who-trew-dees-beans ยท 1 points ยท Posted at 19:48:11 on May 25, 2016 ยท (Permalink)
To calculate the diameter of the Universe to within the width of a hydrogen atom only requires 53 digits of pi, amazing.
Shawshankredem ยท 1 points ยท Posted at 19:50:08 on May 25, 2016 ยท (Permalink)
compound interest
daemonflame ยท 1 points ยท Posted at 19:50:19 on May 25, 2016 ยท (Permalink)*
1=0.99....
daemonflame ยท 1 points ยท Posted at 19:52:28 on May 25, 2016 ยท (Permalink)
1/3=1/3 1/3=0.33..... 1/3*3=1 0.33..... *3=0.99....
0.99......=1
Magic
Ashallond ยท 1 points ยท Posted at 20:03:16 on May 25, 2016 ยท (Permalink)
Proof:
Let X =0.99999.....
So 10 X = 9.99999.....
Subtract 10X-X =9.99999...-0.99999...
9X= 9
X= 1
But since X was defined as 0.99999...
0.99999... = 1
Vega3gx ยท 1 points ยท Posted at 19:50:59 on May 25, 2016 ยท (Permalink)
eiฯ+1=0 Don't ask me to prove it, just try it (with your calculator in radians).
loptthetreacherous ยท 1 points ยท Posted at 21:20:41 on May 25, 2016 ยท (Permalink)
It's pretty easy to prove:
First, we need the Maclaurin expansion of three functions:
ex = 1 + x + (x2 )/2! + (x3 )/3! + (x4 )/4! + (x5 )/5! + ...
sin(x) = x - x3 /3! + x5 /5! - x7 /7! + ...
cos(x) = 1 - x2 /2! + x4 /4! - x6 /6! + ...
so
tidy up a bit using i2 = -1
tidy up more by multiplying through with the -1's
bracket together the numbers with i's and without i's together
We get the Maclaurin expansions of cos(x) and sin(x)
Subtistite pi=x
cos(pi)=-1, and sin(pi)=0 so:
or
Vega3gx ยท 1 points ยท Posted at 05:10:56 on May 26, 2016 ยท (Permalink)
I understand the Maclaurin expansion. The issue is that providing that to someone who doesn't already know it is like giving someone the equation to solve a word problem without explaining why. Let's be honest. Taylor & Maclaurin is a Calc II topic, and most Calc II students already know this formula.
butteredcrumpet ยท 1 points ยท Posted at 19:51:40 on May 25, 2016 ยท (Permalink)
1 + 1 = window
horrorshowmalchick ยท 1 points ยท Posted at 19:53:16 on May 25, 2016 ยท (Permalink)
Euler's identity is the tits.
eฯi = -1
diskborste ยท 1 points ยท Posted at 19:54:28 on May 25, 2016 ยท (Permalink)
If you want to know if a three numbered figure is divisible by three, you can add the three numbers individually and see if the result is evenly divisible by three.
Examples:
647 = 6+4+7 = 17 = NO
147 = 1+4+7 = 12 = YES
Help_Me_Im_Diene ยท 2 points ยท Posted at 19:59:39 on May 25, 2016 ยท (Permalink)
This actually works for any number of digits, 2,3,4,etc. 15:1+5=6,17:1+7=8.
1236:1+2+3+6=12, 1236/3=412, etc.
In fact, you can extend this to numbers divisible by 9, where any number divisible by 9 will have a sum of it's digits divisible by 9.
Ike348 ยท 1 points ยท Posted at 19:54:38 on May 25, 2016 ยท (Permalink)
My favorite maths fact is that it's called "math".
Nicekicksbro ยท 1 points ยท Posted at 19:55:02 on May 25, 2016 ยท (Permalink)
This thread was fun.
KirkOBane ยท 1 points ยท Posted at 19:55:33 on May 25, 2016 ยท (Permalink)
So it isn't hard to believe that between every two rational numbers there is an irrational number (in fact infinitely many). And in terms of the cardinality of the sets, there are way more irrational numbers than rational ones.
But, and this is the part that still messes with me, between every two irrational numbers there's a rational number, too! In fact, infinitely many!
r_slash_squid ยท 1 points ยท Posted at 19:55:35 on May 25, 2016 ยท (Permalink)
Late to the thread, but
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
and so on until 1111111112 = 12345678987654321, which at that point I haven't been able to find more to the pattern.
source: bored in math class
Aeleas ยท 1 points ยท Posted at 20:41:14 on May 25, 2016 ยท (Permalink)
I wonder how it compares in other bases. Does
1111111111111112 = 123456789ABCDEFEDCBA987654321?
iwan_w ยท 1 points ยท Posted at 19:55:39 on May 25, 2016 ยท (Permalink)*
0.999~ is exactly equal to 1. Not a "little bit less" as most people assume.
floatilla ยท 1 points ยท Posted at 19:55:49 on May 25, 2016 ยท (Permalink)
a little late but:
6+(9x6)+9=69
Deeps_10 ยท 1 points ยท Posted at 19:55:52 on May 25, 2016 ยท (Permalink)
69
dittbub ยท 1 points ยท Posted at 19:56:06 on May 25, 2016 ยท (Permalink)
0.999... is EXACTLY 1
!!!
easyiris ยท 1 points ยท Posted at 19:56:41 on May 25, 2016 ยท (Permalink)
You can take any number over three digits (such as 56823) and add each digit together (= 24) and if the number you get can be divided by three, so can the original number. So 24 can be divided by 3 and 56823 / 3 is in fact 18941.
NiceSasquatch ยท 2 points ยท Posted at 20:09:47 on May 25, 2016 ยท (Permalink)*
keep going:
5 + 6 + 8 + 2 +3 = 24
2 + 4 = 6.
Thus 24 is divisible by three, and therefore 56823 is divisible by three. (so this way you could do it to a number with a bizzilion digits)
easyiris ยท 1 points ยท Posted at 20:29:13 on May 25, 2016 ยท (Permalink)
Ha I've never even noticed that before! Awesome.
scumbot ยท 1 points ยท Posted at 19:57:21 on May 25, 2016 ยท (Permalink)
The sum of all positive integers equals -1/12
ReturnToOdessa ยท 1 points ยท Posted at 19:57:23 on May 25, 2016 ยท (Permalink)
1.0 = 0.999...
riyadhelalami ยท 1 points ยท Posted at 19:57:34 on May 25, 2016 ยท (Permalink)*
My favourite is are the cubic roots of one that aren't one lets call one of them w, the other will be w2 and w+w2 =-1, and w=1/2+-sqrt(3)/2
it will make your life easier before knowing about eulers identity easier.
Basegitar ยท 1 points ยท Posted at 19:59:02 on May 25, 2016 ยท (Permalink)
.9999... = 1. That always blew my mind, not that it's infinitely close to 1, but it is 1.
Abestar909 ยท 1 points ยท Posted at 19:59:36 on May 25, 2016 ยท (Permalink)
That the word math covers multiple mathematical disciplines so when people say maths, they sound silly.
pita_pocket774 ยท 1 points ยท Posted at 19:59:44 on May 25, 2016 ยท (Permalink)
The fourth, fifth, and sixth derivatives of position are called "snap", "crackle", and "pop"
Aeleas ยท 1 points ยท Posted at 20:17:23 on May 25, 2016 ยท (Permalink)
OK so...
position -> velocity -> acceleration -> jerk -> snap -> crackle -> pop
That's more of a physics fact, though.
pita_pocket774 ยท 1 points ยท Posted at 20:32:37 on May 25, 2016 ยท (Permalink)
Yes it's applied to physics but without calculus we wouldn't be able to take derivatives to find them in the first place so I guess you could say it's a multi-topic fact
canuslupusdogeus ยท 1 points ยท Posted at 19:59:46 on May 25, 2016 ยท (Permalink)
0.9 repeating is the the same as 1
nnitro ยท 1 points ยท Posted at 19:59:47 on May 25, 2016 ยท (Permalink)
Eulers Pentagonal Number theorem
JustAMomentofYerTime ยท 1 points ยท Posted at 20:00:08 on May 25, 2016 ยท (Permalink)
If you were to determine the coefficients for any (x+y)z problem, you can find said coefficients by raising 11 to the zth power.
DoesNotTalkMuch ยท 1 points ยท Posted at 20:00:45 on May 25, 2016 ยท (Permalink)
"Maths" is syntactically correct in both singular and plural.
[deleted] ยท 1 points ยท Posted at 20:01:52 on May 25, 2016 ยท (Permalink)*
[deleted]
ThorStaats ยท 1 points ยท Posted at 20:12:02 on May 25, 2016 ยท (Permalink)
That's true, until 9x11.
[deleted] ยท 1 points ยท Posted at 20:13:41 on May 25, 2016 ยท (Permalink)
[deleted]
ThorStaats ยท 2 points ยท Posted at 10:36:51 on May 26, 2016 ยท (Permalink)
See I thought you just meant easy math, it didn't dawn on me to do that, thanks!
Aeleas ยท 1 points ยท Posted at 20:15:24 on May 25, 2016 ยท (Permalink)
9 * 11 = 99
9 + 9 != 9
What may be the case is that the sum of the digits of 9x is
Lovehat ยท 1 points ยท Posted at 20:02:41 on May 25, 2016 ยท (Permalink)
8
[deleted] ยท 1 points ยท Posted at 20:04:45 on May 25, 2016 ยท (Permalink)
Take any two numbers two apart from each other like 6 and 8 and multiply them, 48. Then take the number in between, 7, and square it, 49. Following this pattern the number in between will always be one more than the two numbers two part multiplied.
indeedihavecats ยท 1 points ยท Posted at 20:07:22 on May 25, 2016 ยท (Permalink)
The fact that I will never have to take another math class in my life.
Archimeat ยท 1 points ยท Posted at 20:07:35 on May 25, 2016 ยท (Permalink)
You can make up any three sides of a triangle with two different numbers for u and v (u being the larger number)
x= (u2)-(v2) y=2uv z= (u2)+(v2)
popsicle_cat ยท 1 points ยท Posted at 20:08:19 on May 25, 2016 ยท (Permalink)
a 240 sided shape is a rhombicosidodecahedron
SamuEL_or_Samuel_L ยท 1 points ยท Posted at 20:08:30 on May 25, 2016 ยท (Permalink)
We use a lot of big numbers in astronomy, and I find that millions/billions just get muddled together as "big number" in a lot of talks. This is the best comparison I've seen to communicate the immense different in scale in a way that people intuitively understand:
1 hundred seconds = just under 2 minutes
1 thousand seconds = just over 15 minutes
1 million seconds = just over 11 days
1 billion seconds = just over 31 years
Saying "it's the difference between 11 days and 31 years" does a better job to communicate the difference in scale than simply "it's a thousand times bigger".
[deleted] ยท 1 points ยท Posted at 20:09:24 on May 25, 2016 ยท (Permalink)
The existence of a function which takes every value on every interval.
In other words for every real number r and every interval (a,b) there is a value c for which f(c) = r with a<c<b.
[deleted] ยท 1 points ยท Posted at 20:10:26 on May 25, 2016 ยท (Permalink)
153 is in love with itself.
153 โ 1ยณ + 5ยณ + 3ยณ โ 1 + 125 + 27 โ 153
ilambiquated ยท 1 points ยท Posted at 20:10:29 on May 25, 2016 ยท (Permalink)
Euler's identity
eฯi + 1 = 0
DearKC ยท 1 points ยท Posted at 20:10:49 on May 25, 2016 ยท (Permalink)
I wrote my senior thesis on the distribution on non-standard dice, as seen here
What I loved about this project was the patterns of average roll. The paper explains how the average of 1d6 is 3.5, 2d6 is 7, 3d6 is 10.5, etc. This also applies to 1d4=2.5, 2d4=5, etc and all of the other regular polyhedral dice. I don't know if I'd go so far as to say favorite, per se but I did greatly enjoy this and got to present it an AMA conference at Willamette University a few years back.
rezdm ยท 1 points ยท Posted at 20:11:48 on May 25, 2016 ยท (Permalink)
This: 1 + ei*Pi = 0
binds 5 important numbers together
mostlyemptyspace ยท 1 points ยท Posted at 20:12:37 on May 25, 2016 ยท (Permalink)
Here is a fun problem.
Say you have a rope tied around the Earth's equator such that it makes a circle touching the ground. How much additional rope would it take for that rope to float 1m off the ground?
You'd think a lot right?
The answer is only 6.3m.
So the circumference of the Earth is C = 2piR. You're adding 1m to the radius, so it becomes:
C' = 2pi(R+1) = 2piR + 2pi = C + 2pi
So given any circle, whether it's a cookie or the Earth, would take roughly 6.3m extra rope to increase the radius by 1m.
rezdm ยท 1 points ยท Posted at 20:12:49 on May 25, 2016 ยท (Permalink)
This: 1 + ei*Pi = 0
binds 5 important numbers together
bruin_bear ยท 1 points ยท Posted at 20:12:49 on May 25, 2016 ยท (Permalink)
A
MenstruatingMuffin ยท 1 points ยท Posted at 20:12:54 on May 25, 2016 ยท (Permalink)
That No Man's Sky, with it's 18 Quintilian planets, is entirely generated based on a maths function
[deleted] ยท 1 points ยท Posted at 20:13:54 on May 25, 2016 ยท (Permalink)
*math
Ditto8353 ยท 1 points ยท Posted at 20:13:57 on May 25, 2016 ยท (Permalink)
8353 is a prime number :D
lahickorynut ยท 1 points ยท Posted at 20:13:58 on May 25, 2016 ยท (Permalink)
That British people say "maths."
xdzgor ยท 1 points ยท Posted at 21:02:17 on May 25, 2016 ยท (Permalink)
And American people say "legos".
OnTheGoTrades ยท 1 points ยท Posted at 20:14:22 on May 25, 2016 ยท (Permalink)
Statistically speaking, the average person has less than 2 feet ๐ค
seminoleoc ยท 1 points ยท Posted at 20:14:47 on May 25, 2016 ยท (Permalink)
7 ate 9
yhsanave ยท 1 points ยท Posted at 20:15:09 on May 25, 2016 ยท (Permalink)
Math is the Illuminati
Crazyhair909 ยท 1 points ยท Posted at 20:15:55 on May 25, 2016 ยท (Permalink)
http://m.youtube.com/watch?v=IRsPheErBj8
snuglyotter ยท 1 points ยท Posted at 20:17:04 on May 25, 2016 ยท (Permalink)
There are as many natural numbers (0, 1, 2, 3, ...) as there are integers (natural numbers and their negatives). There are as many natural numbers as there are rational numbers (a/b where a,b are integers and b != 0). However, there are more real numbers (numbers that can be expressed with decimals) in any interval than there are natural numbers.
1KillerMidget ยท 1 points ยท Posted at 20:19:33 on May 25, 2016 ยท (Permalink)
The Monty Hall problem.
FightClubLeader ยท 1 points ยท Posted at 20:19:43 on May 25, 2016 ยท (Permalink)
You can count past infinity, actually really far past infinity. This video explains it pretty well.
Sir_Martinelli ยท 1 points ยท Posted at 20:20:37 on May 25, 2016 ยท (Permalink)
My favorite is that any percent of a number, equals the "number" percent of the "percent."
10% of 20 = 20% of 10 (2) 38% of 126 = 126% of 38 (47.88)
Its pretty simple when you think about it but I only recently realized it and it has made solving quick math on the job a lot faster! Hope it helps!
jbaggins ยท 1 points ยท Posted at 20:20:54 on May 25, 2016 ยท (Permalink)
the result of 11 times any number is the sum of it's digits:
11 * 51 = 561 <-- 5 (5+ 1) 1
11 * 452 = 4972 <-- 4 (4 + 5) (5+2) 4
Any number times 25-- divide the number by 4, multiple the remainder times 25 and append.
25 * 98 = 2450 <-- 98 / 4 = 24 remainder 2. 2 x 25 = 50 --> 2450
dred1367 ยท 1 points ยท Posted at 20:21:00 on May 25, 2016 ยท (Permalink)
That the plural abbreviated form of mathematics isn't maths... It's math.
DarkAlman ยท 1 points ยท Posted at 20:21:06 on May 25, 2016 ยท (Permalink)
The sum of all positive integers = -1/12
Jisamaniac ยท 1 points ยท Posted at 20:21:13 on May 25, 2016 ยท (Permalink)
123x1=123
bilbo2002 ยท 1 points ยท Posted at 20:21:16 on May 25, 2016 ยท (Permalink)
that half the stuff you learn is only applicable under certain jobs and conditions isnt that fun A* in maths
opinionatedidiot ยท 1 points ยท Posted at 20:21:19 on May 25, 2016 ยท (Permalink)
I'm way late to this party, but, starting at 1, each square of a whole number is the just the previous square added to the next odd number. 1x1=1 (+3) 2x2=4 (+5) 3x3=9 (+7) 4x4=16 (+9) Etc.. Sorry for explaining and formatting what is in my head like an idiot.
[deleted] ยท 1 points ยท Posted at 20:21:29 on May 25, 2016 ยท (Permalink)
there's a simple proof for it on numberphile YouTube channel. If you add all positive integers the sum is actually a negative fraction instead of infinity. It has applications in quantum mechanics.
thequickhungryfox ยท 1 points ยท Posted at 20:22:14 on May 25, 2016 ยท (Permalink)
All unique Pythagorean triples have a difference of an odd number squared between the hypotenuse and the even side. And in fact there are an infinite amount of unique Pythagorean triples for EACH odd square difference.
Poxx ยท 1 points ยท Posted at 20:22:28 on May 25, 2016 ยท (Permalink)
-40f and -40c are the same temperature.
MustGetALife ยท 1 points ยท Posted at 20:25:17 on May 25, 2016 ยท (Permalink)
โ-1=i
FlusteredNZ ยท 1 points ยท Posted at 20:27:14 on May 25, 2016 ยท (Permalink)
By some math (which is entirely valid under the right circumstances), the infinite sequence
1+2+3+4+5+...
is equal to
-1/12
Proof
Joose2001 ยท 1 points ยท Posted at 20:28:36 on May 25, 2016 ยท (Permalink)
A simple one, but the answer of the nine times table always ends up adding to nine!
Ex. 6x9=54, 5+4=9
And before someone says, what about big numbers? Keep adding the resulting number, it'll eventually add back to nine
Ex. 5638x9 = 50742
5+0+7+4+2 = 18
1+8 = 9
10sPlaya ยท 1 points ยท Posted at 20:30:15 on May 25, 2016 ยท (Permalink)
red_hare ยท 1 points ยท Posted at 20:32:33 on May 25, 2016 ยท (Permalink)
Four color theorem.
You can color the individual regions (countries, states, counties, etc...) of any map with only 4 colors and never have two of the same colored regions touch each other.
HaruAnt ยท 1 points ยท Posted at 20:33:43 on May 25, 2016 ยท (Permalink)
epi*i-1=0
BBgunz123 ยท 1 points ยท Posted at 20:33:44 on May 25, 2016 ยท (Permalink)
sinx/cosx = tanx
heystevieray ยท 1 points ยท Posted at 20:34:17 on May 25, 2016 ยท (Permalink)
666/212 is very close to Pi. Number of the beast/boiling pt of water in Fahrenheit = pi
Campana12 ยท 1 points ยท Posted at 20:34:25 on May 25, 2016 ยท (Permalink)
12345679 * 8 = 98765432
everyonesgayexceptme ยท 1 points ยท Posted at 20:34:56 on May 25, 2016 ยท (Permalink)
The amount of numbers between 0 and 1 is equal to the amount of numbers there are at all.
Another way to think about it, is that there are as many odd numbers as there are odd+even numbers.
anklfester ยท 1 points ยท Posted at 20:36:28 on May 25, 2016 ยท (Permalink)
very interesting
Dennis__Reynolds ยท 1 points ยท Posted at 20:37:12 on May 25, 2016 ยท (Permalink)
The sum of all real integers equals -1/12
subTexTseer ยท 1 points ยท Posted at 20:38:32 on May 25, 2016 ยท (Permalink)
The one that lets you have infinite chocolate squares
ubsr1024 ยท 1 points ยท Posted at 20:39:02 on May 25, 2016 ยท (Permalink)
My favorite math fact is that saying "maths" is less defensible than saying "math" from a linguistic standpoint.
The point being that when you make "mathematics" agree with a verb, you make it agree with a singular verb, not a plural verb.
Just because there is an "s" at the end of a noun, it doesn't make it plural.
pissface69 ยท 1 points ยท Posted at 20:40:37 on May 25, 2016 ยท (Permalink)
That we solved Fermat's last theorem yet nobody as far as google knows can provide any actual whole number solution whatsoever, just proofs.
[deleted] ยท 1 points ยท Posted at 20:40:41 on May 25, 2016 ยท (Permalink)
.999 repeating is exactly equal to 1.
ihatedogs2 ยท 1 points ยท Posted at 20:41:16 on May 25, 2016 ยท (Permalink)
epi * i + 1 = 0
xDigster ยท 1 points ยท Posted at 20:41:34 on May 25, 2016 ยท (Permalink)
The sum of all positive integers equals -1/12.
[deleted] ยท 1 points ยท Posted at 20:41:40 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers can be written as -1/12.
workthrowaway2016 ยท 1 points ยท Posted at 20:42:16 on May 25, 2016 ยท (Permalink)
A single domino can fall and knock over a dominoe 50% larger than itself. If you continuously stack dominoes 50% larger than the previous in a line, by the 23rd dominoe the height will be the same as the Eiffel tower, by the 31st mount everest, and by the 57th the moon. And they would all be knocked over by tipping the first original dominoe.
GoingToSimbabwe ยท 2 points ยท Posted at 21:07:13 on May 25, 2016 ยท (Permalink)*
Starting by a normal sized domino?
Edit: nvm, normal sized. was bored and calculated it. Only the moon one doesn't fits completely. 14.000km missing :(
workthrowaway2016 ยท 1 points ยท Posted at 08:35:30 on May 26, 2016 ยท (Permalink)
haha, fair enough. OK, so 57.10113597 dominoes to get to the moon...as long as it is exactly 384,000,000m away. Also, assuming the moon is exactly 3474km in diameter, using 58 dominoes we would overshoot the other side of the moon by 165959.5km.
The coolest park is knowing that tipping the first initial 50.8mm domino would still knock over that huge 58th domino.....theoretically.
GoingToSimbabwe ยท 2 points ยท Posted at 08:41:28 on May 26, 2016 ยท (Permalink)
Yeah, I was just joking around. That fact is indeed quite amusing ;).
workthrowaway2016 ยท 1 points ยท Posted at 08:51:08 on May 26, 2016 ยท (Permalink)
I know I know. But I'm bored at work and wanted to work it out. I actually just took it out of a book I'm reading and didn't check to make sure it was right. At least now I know I'm not spreading a lie haha.
lubbi ยท 1 points ยท Posted at 20:42:55 on May 25, 2016 ยท (Permalink)
2+2=4
downlowiss ยท 1 points ยท Posted at 20:43:33 on May 25, 2016 ยท (Permalink)
55378008 written on a calculator and turned upside down.
majesticjg ยท 1 points ยท Posted at 20:44:34 on May 25, 2016 ยท (Permalink)
a2 + b2 = c2 (Pythagorean Theorem)
but
a3 + b3 = c3 is far more difficult to prove. (Fermat's Last Theorem)
robbiearebest ยท 1 points ยท Posted at 20:44:45 on May 25, 2016 ยท (Permalink)
.9 repeating equals 1
math-yoo ยท 1 points ยท Posted at 20:45:35 on May 25, 2016 ยท (Permalink)
When two halves is gone, there's nothin' left. And you're right, it's a little ole worm, who wasn't there. Two nothin's is nothin'. That's mathematics, son! You can argue with me, but you can't argue with figures! Two half nothin's is a whole nothin'!
leicatgw ยท 1 points ยท Posted at 20:46:45 on May 25, 2016 ยท (Permalink)
A penny doubled every day for 31 days equals out to $10,737,418.23.
Mab75 ยท 1 points ยท Posted at 20:47:44 on May 25, 2016 ยท (Permalink)
Riddle: - Which is the most odd prime number?
Spastic_Squirrel ยท 1 points ยท Posted at 20:48:43 on May 25, 2016 ยท (Permalink)
There is ALWAYS an answer, even when the answer is a range, indefinite number, etc. There is always an answer. Also, you can easily ace most multiple-choice algebra tests by plugging the provided answers into the equation - the answer should be equivalent on both sides of the equation. TMYK...
jezer777 ยท 1 points ยท Posted at 20:48:49 on May 25, 2016 ยท (Permalink)
The one that blows my mind still is this: If you were to assign a letter value (1=a, 2=b... 26=z) to every number in Pi (or any other irrational number), somewhere in that number is ever single word you have ever spoken, in order. It contains every book ever written and that ever will be written.
thePurpleAvenger ยท 1 points ยท Posted at 20:49:14 on May 25, 2016 ยท (Permalink)
That the circumference-to-diameter ratio of a circle on a sphere varies between pi and 2.
stereoroid ยท 1 points ยท Posted at 20:49:27 on May 25, 2016 ยท (Permalink)*
I'm fascinated by how the decimal versions of 7ths (1/7, 2/7 ... 6/7) all consist of the same looping 6-digit sequence of numbers (142857), the only difference being the start point in the loop:
142857 is a cyclic number: 142857 = (106 -1) / 7
[deleted] ยท 1 points ยท Posted at 20:49:36 on May 25, 2016 ยท (Permalink)
Let a = b
a * a = a * b
a2 = ab
a2 - b2 = ab - b2
(a+b)(a-b) = b(a-b)
(a+b)(a-b)/(a-b) = b(a-b)/(a-b)
a + b = b
Since a = b,
b + b = b
2b = b
2b/b = b/b
2 = 1
squire95 ยท 5 points ยท Posted at 20:51:20 on May 25, 2016 ยท (Permalink)
But a - b = 0 so this is invalid
[deleted] ยท 1 points ยท Posted at 20:59:49 on May 25, 2016 ยท (Permalink)
:)
Mstarkey0 ยท 1 points ยท Posted at 20:50:51 on May 25, 2016 ยท (Permalink)
eipi -1= 0
e raised to the imaginary pi minus one equals zero. The five most important numbers all in one equation.
squire95 ยท 1 points ยท Posted at 20:54:28 on May 25, 2016 ยท (Permalink)
Plus one
Mstarkey0 ยท 1 points ยท Posted at 21:08:00 on May 25, 2016 ยท (Permalink)
Yeah. My bad. Been awhile haha
zigfried555 ยท 1 points ยท Posted at 20:53:34 on May 25, 2016 ยท (Permalink)
You can determine if a number is divisible by 3 by adding up all the digits and seeing if that number is divisible by 3.
1876984908723
1+8+7+6+9+8+4+9+0+8+7+2+3=72
7+2=9
9 is divisible by 3 so therefore the number 1876984908723 is divisible by 3.
VelociROBtor ยท 1 points ยท Posted at 20:57:02 on May 25, 2016 ยท (Permalink)
This is also true for numbers divisible by 9.
Maplekiller ยท 1 points ยท Posted at 20:53:57 on May 25, 2016 ยท (Permalink)
The birthday paradox! In a room of 23 people it's 50% chance that two people share the same birthday (day and month, not year unless of course everybody in the room is born the same year, like a school class) With 70 people the probability is 99.9%
I also like the fact that there are more possible ways to shuffle a deck of cards than seconds it has been since the big bang
raptors13jays ยท 1 points ยท Posted at 20:54:42 on May 25, 2016 ยท (Permalink)
1+1=2
Todays_Vagabond ยท 1 points ยท Posted at 20:54:46 on May 25, 2016 ยท (Permalink)
Some infinities are larger than others.
There are an infinite amount numbers between 1 and 2 (1.3, 1.5387, etc) but there are also an infinite amount of numbers between 1 and 5. The difference between one and five is greater, even though both differences are infinite.
[deleted] ยท 1 points ยท Posted at 20:55:01 on May 25, 2016 ยท (Permalink)
1x1=2 Howard method
nmagod ยท 1 points ยท Posted at 20:55:43 on May 25, 2016 ยท (Permalink)
Any fraction (Say 14/37) multiplied by the denominator (37) equals the numerator (14)
I never had a single decent mathematics class in my life and this is the kind of thing I figured out on my own
So please tell me if I'm wrong
thegreatlordlucifer ยท 2 points ยท Posted at 21:01:50 on May 25, 2016 ยท (Permalink)
that's because a fraction is literally just dividing the denominator...
jarohe318 ยท 1 points ยท Posted at 20:56:03 on May 25, 2016 ยท (Permalink)
The derivatives in terms of time in Physics go like this: position->velocity->acceleration->jerk->snap->crackle->pop. I always thought this was a hoot
DigitalImpostor ยท 1 points ยท Posted at 20:56:16 on May 25, 2016 ยท (Permalink)
1 + 1 = 2
I'm easy to please.
SuckMyJagon_ ยท 1 points ยท Posted at 20:56:21 on May 25, 2016 ยท (Permalink)
More of a physical property. But Im endlessly fascinated by the fact that when firing photons one after another from 2 sources, they make the same pattern that should only mathematically happen if they were being sent all at once as a wave. Entanglement has so many weird implications, since the light is entangled beyond time does that mean that light exists out of time? When a photon is released does it instantaneously reach is destination from its perspective?
kdevans2012 ยท 1 points ยท Posted at 20:57:46 on May 25, 2016 ยท (Permalink)
Interesting fact: the number of megabytes of an email message grows with the rank of the perceived importance of the role of its sender, while remaining inversely proportional to the importance of its content.
veni_vedi_veni ยท 1 points ยท Posted at 20:58:27 on May 25, 2016 ยท (Permalink)
0.999... = 1.
If 1/3 = 0.333... then 3/3 can both be 0.999... and 1
DrPorzingis ยท 1 points ยท Posted at 20:59:05 on May 25, 2016 ยท (Permalink)
Oh god, childhood C-average-in-math me is having a fucking nightmare scrolling through this thread.
alio84 ยท 1 points ยท Posted at 20:59:08 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+....r = -1/12
Usted11 ยท 1 points ยท Posted at 20:59:09 on May 25, 2016 ยท (Permalink)
Weird thing I found out being bored in class is if you square a number 22 is 4 you can find the square of 3 by adding the number you squared and the number you are trying to find the answer of to the answer.
[deleted] ยท 1 points ยท Posted at 20:59:11 on May 25, 2016 ยท (Permalink)
(10 * 9 * 8 * 7 * 6)/(5+4+3+2+1) = 2016
halsar ยท 1 points ยท Posted at 20:59:50 on May 25, 2016 ยท (Permalink)
1+1=3
[deleted] ยท 1 points ยท Posted at 21:02:35 on May 25, 2016 ยท (Permalink)
That Europe calls math "maths".
KevoSoft ยท 1 points ยท Posted at 21:02:54 on May 25, 2016 ยท (Permalink)
There exists a function (or more properly, a distribution), called the Fermi-Dirac function, for which the following holds:
f(x) = โ where x=0 (the function value is infinity, in case it doesn't show up) f(x) = 0 where xโ 0
What's more interesting, is when you take the integral over this function from negative infinity to infinity, the result equals 1.
Mathemathically speaking I've yet to come across a use case for it, but it is used quite a lot in physics, especially in Quantum physics and Electricity & Magnetism.
h_west ยท 1 points ยท Posted at 21:03:13 on May 25, 2016 ยท (Permalink)
Using degrees, sin(666) = cos(666)= - phi / 2 where phi =( sqrt(5)-1)/2 is the golden mean. This is exact!
stravant ยท 1 points ยท Posted at 21:03:25 on May 25, 2016 ยท (Permalink)
If a person randomly stumbles around a 2D plane forever there is a 100% chance that they will get back home.
If a bird randomly flies around through the air forever there is only a ~2/3 chance that it will get back home.
JALWiz ยท 1 points ยท Posted at 21:04:33 on May 25, 2016 ยท (Permalink)
If you add all positive whole numbers from 1 to infinity you get -1/12
e.g. 1+2+3+4+5+6...+99999999+...=-1/12
The reason for this is that the Sequence S1, 1-1+1-1+1-1+1-1...= 0 or 1 depending where you stop at
And 2*(S1)=0+1
So S1=1/2
Then the Sequence of S2, (which is 1-2+3-4+5-...) is multiplied by 2 is equal to 1/4
e.g. 1-2+3-4+5-6+7-8+9...
is equal to 1-1+1-1+1-1+1-1+1... =1/2
So 2(S2)=1/4
So let's look at the Sequence of S=1+2+3+4+5+6+7+8+9...
Now subtract S2 from this sequence
S-S2= 1+2+3+4+5+6+7+8+9...
This ends up giving you the Sequence of 0+4+0+8+12+16... which is equivalent to 4+8+12+16... which is 4(1+2+3+4+5+6+7+8+9...)
so S-S2=4S
or -(S2)=3S
or -1/4=3S
so then -1/12=S
So 1+2+3+4+5+6+7+8+9=-1/12
JanEric1 ยท 1 points ยท Posted at 10:18:29 on May 26, 2016 ยท (Permalink)
you can only do these steps if it converges, which it doesnt.
nulloid ยท 1 points ยท Posted at 21:04:37 on May 25, 2016 ยท (Permalink)
If you have an infinite series of 1, 2, 3, .. and you try to add them together, with a few clever math tricks, you get -1/12. This result is actually used in some physic problems. See this wiki page
And a link about what it means in physics
lalaninatl ยท 1 points ยท Posted at 21:04:43 on May 25, 2016 ยท (Permalink)
epi*i=-1
planetbomb ยท 1 points ยท Posted at 21:06:19 on May 25, 2016 ยท (Permalink)
2+2=5
HarrisonChevrolet ยท 1 points ยท Posted at 21:06:28 on May 25, 2016 ยท (Permalink)
1+2+3+4+... continued forever = -1/12.
xPlatinumFox ยท 1 points ยท Posted at 22:15:53 on May 25, 2016 ยท (Permalink)
care to explain?
gwot ยท 1 points ยท Posted at 22:44:19 on May 25, 2016 ยท (Permalink)
Its a bit of a maths card trick with an infinite series see wiki here
But IIRC you basicaly re-express the series as an alternating series: 1-2 + 3 -4 + .... and with a bit of algebra you get to -3x = 1/4, (if x was the original series), so x = -1/12
BaadKitteh ยท 1 points ยท Posted at 21:06:30 on May 25, 2016 ยท (Permalink)
The fact that literally no maths above basic addition, subtraction, multiplication, and division are necessary in the average adult's life from day to day.
xHarryR ยท 1 points ยท Posted at 21:07:29 on May 25, 2016 ยท (Permalink)
Finally someone else who says this! haha
the_0wl ยท 1 points ยท Posted at 21:07:00 on May 25, 2016 ยท (Permalink)
Take arbitrary points A,B,C,D and connect them to form a Quadrilateral. Draw a square on the outside of each side. Connect the middles of the squares on opposing sides. Both line segments you get this way are the same length and perpendicular to each other. Illustration
ScrufffyJoe ยท 1 points ยท Posted at 21:07:25 on May 25, 2016 ยท (Permalink)
It's less a maths fact and more about physics, but the explanation is mathsy. If the well-known theory is correct about their being an infinite number of universes, this does not mean that any possibility you can come up with exists in one, despite what people think, because infinity doesn't necessarily work that way.
Basically it can be explained there being an infinite amount of numbers between 0 and 1, 0.1, 0.01, 0.001, you see where I'm going here.
None of these numbers are 2.
scottg96 ยท 1 points ยท Posted at 21:07:32 on May 25, 2016 ยท (Permalink)
ITT: "If you do the math, this math fact makes perfect sense and isn't that cool"
I didn't come here for things that make sense, I came here to be amazed god damn it!
zaqwsx3 ยท 1 points ยท Posted at 21:09:30 on May 25, 2016 ยท (Permalink)
I like the fact that:
1 x 1=1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111=1234321
[deleted] ยท 1 points ยท Posted at 21:09:35 on May 25, 2016 ยท (Permalink)
The Chinese were the first ones to develop the Pythagorean Theorem. Since western ideas were first to be taken into account; Pythagoras was selected for the name of the equation. The Chinese history is largely fragmented due to the different dynasties and wars. Pascal's triangle is also to have been in place centuries before Pascal.
EVERYONESDATINGBUTME ยท 1 points ยท Posted at 21:09:46 on May 25, 2016 ยท (Permalink)
Assuming that the other person is constantly and randomly roaming around, it's theoretically better to constantly wander around if you wanted to look for them, as compared to standing still in the same spot.
Source: https://www.reddit.com/r/askscience/comments/35uljq
Keapexx ยท 1 points ยท Posted at 21:10:48 on May 25, 2016 ยท (Permalink)
brittany spear's boobs weighed 69 pounds
that was 222 much as she wanted them to be 51 pounds
so she had 8 liposuctions (multiply 6922251 by 8)
then she turned out...
groovesauce ยท 1 points ยท Posted at 21:11:58 on May 25, 2016 ยท (Permalink)
If you want to add a series of numbers together that are in a row you multiply the last number by the next higher number and divide by 2. So 1+2+3+4+5 = (5*6)/2 = 15. Go as high as you dare!
lozzero ยท 1 points ยท Posted at 21:13:03 on May 25, 2016 ยท (Permalink)*
It's trivial, but kids love it, and if it gets them in the mood to start a lesson, who can judge? If you take any large number and repeatedly add the digits until you get a single digit (e.g. 456; 4+5+6=15; 1+5=6), if you end up with 3, 6, or 9, the original number is divisible by 3.
Another fun one is for multiplying by 9. Put your hands out in front of you, palm down. Put down your ring finger on your left hand (the second along from the left). You'll have 1 finger to the left and 8 fingers to the right. 9x2=18. Put down your pointer on your left hand (fourth along) and you have 3 to the left and 6 to the right. 9x4=36. It is also really funny to watch a bunch of kids (or drunk adults) put their hands in front of their face and count their fingers.
maxreverb ยท 1 points ยท Posted at 21:14:01 on May 25, 2016 ยท (Permalink)
Some people apparently pluralize "math."
jvpjr77 ยท 3 points ยท Posted at 21:17:24 on May 25, 2016 ยท (Permalink)
Those people are what we call British. That's standard usage in UK English.
FouriestTransform ยท 1 points ยท Posted at 21:14:03 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is equal to -1/12. Numberphile had a nice video explaining it.
mcarpe21 ยท 1 points ยท Posted at 21:14:11 on May 25, 2016 ยท (Permalink)
That the sum of all the natural numbers (I.e. 1,2,3,4...) is equal to -1/12.
Childflayer ยท 1 points ยท Posted at 21:14:56 on May 25, 2016 ยท (Permalink)
1 / 3 = 0.333 (repeating)
3 * 0.333 (repeating) = 0.999 (repeating)
treelicks ยท 1 points ยท Posted at 21:15:16 on May 25, 2016 ยท (Permalink)
4 8 15 16 23 42
Doveen ยท 1 points ยท Posted at 21:17:34 on May 25, 2016 ยท (Permalink)
The fact that I no longer have to study it.
itsharriet ยท 1 points ยท Posted at 21:18:05 on May 25, 2016 ยท (Permalink)
K l
Buburubu ยท 1 points ยท Posted at 21:19:01 on May 25, 2016 ยท (Permalink)
You can use different kinds of math for different things, such as calculating what kind of bird you're looking at, calculating the best flavor to add to a meal, or even calculating the size of something!
EverythingDies0317 ยท 1 points ยท Posted at 21:19:10 on May 25, 2016 ยท (Permalink)
Not even once
PhattieM ยท 1 points ยท Posted at 21:19:21 on May 25, 2016 ยท (Permalink)
This has either been said or will get buried, but, one of the most useful calculations I frequently do is convert pounds to kilograms. Here's the secret: add 10% and double it (same as multiplying by 2.2).
I also have a really simple estimation for Celsius/Fahrenheit that's close within a 1/10th of a degree if anyone is interested.
dadclothes26 ยท 1 points ยท Posted at 21:20:08 on May 25, 2016 ยท (Permalink)
Late to the party so I don't know if this has been said, but the Everything Formula is a pretty interesting idea.
Pretty much it graphs every possible combination of filled points on a certain plain, including (most famously) the picture of the equation itself
EwanMe ยท 1 points ยท Posted at 21:20:40 on May 25, 2016 ยท (Permalink)
This one I actually discovered myself. It's completely useless and I don't know if there is some cool theory behind it, but:
-1(-2)-3(-4)-5(-6)-7(-8)-9(-0)=100
HyperWindKun ยท 1 points ยท Posted at 21:20:42 on May 25, 2016 ยท (Permalink)
1 is actually just 0.(9) and vice versa.
bradintheusa ยท 1 points ยท Posted at 21:20:49 on May 25, 2016 ยท (Permalink)
The number 82000 in base 10 is equal to 10100000001010000 in base 2, 11011111001 in base 3, 110001100 in base 4, and 10111000 in base 5. It is the smallest integer bigger than 1 whose expressions in bases 2, 3, 4, and 5 all consist entirely of zeros and ones.
JaySavvy ยท 1 points ยท Posted at 21:20:57 on May 25, 2016 ยท (Permalink)
Compared to the rest of these, this one is literally childish, but I found the multiples of 9 to be interesting.
9 x (X) = Two numbers that add up to make nine.
9 x 1 = 9
9 x 2 = 18 (1 + 8 = 9)
9 x 3 = 27 (2 + 7 = 9)
9 x 4 = 36 (3 + 6 = 9)
And so on and so forth until:
9 x 9 = 81 (8 + 1 = 9)
9 x 10 = 90 (9 + 0 = 9)
It helped me learn my multiplication tables as a kid.
LukeRhinehart34 ยท 1 points ยท Posted at 21:23:21 on May 25, 2016 ยท (Permalink)
1+2+3+4+5...=-1/12
MustangTech ยท 1 points ยท Posted at 21:31:04 on May 25, 2016 ยท (Permalink)
how? the left side is larger than the right from the first term on
LukeRhinehart34 ยท 1 points ยท Posted at 21:38:16 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
dodge_thiss ยท 1 points ยท Posted at 21:23:39 on May 25, 2016 ยท (Permalink)
Easy trick for multiplying a number by 11 write the number on the far right add that number to the number directly to its left. Then add that second number to the one to its left and so on until the last number which you simply write down. Any double digits as answers when adding the tens spot gets carried. So it is something like this: 2837702 ร 11=
1) 2
2) 22
3) 722
4) 4722
5) 14722
6) 214722
7) 1214722
8) 31214722
Or: 5216 ร 11=
1) 6
2) 76
3) 376
4) 7376
5) 57376
Obviously you simply write the number form right to left not in individual steps but it makes for easy no work math.
studebaker ยท 1 points ยท Posted at 21:25:08 on May 25, 2016 ยท (Permalink)
That I don't have to take a math class again if I so choose!
Bonedragonwillrise ยท 1 points ยท Posted at 21:25:36 on May 25, 2016 ยท (Permalink)
1=0.999999999999999999999999999999...
This is true because 1/3 = .33333333333...
And 1/3+1/3+1/3 = 1 = .3333333... +.3333333...+.33333333333... = .99999999999999...
The ellipses indicate going into infinity.
[deleted] ยท 1 points ยท Posted at 21:26:19 on May 25, 2016 ยท (Permalink)
Biology is the Lesbian Sister of Maths.
dcmix5 ยท 1 points ยท Posted at 21:26:39 on May 25, 2016 ยท (Permalink)
1+1=3 either accidentally or on purpose
James_099 ยท 1 points ยท Posted at 21:26:46 on May 25, 2016 ยท (Permalink)
5x9 is at least 40
[deleted] ยท 1 points ยท Posted at 21:26:57 on May 25, 2016 ยท (Permalink)
[deleted]
Goooooogler ยท 1 points ยท Posted at 21:33:02 on May 25, 2016 ยท (Permalink)
Well, its "Mathematics", not "Mathematic"
[deleted] ยท 1 points ยท Posted at 21:35:54 on May 25, 2016 ยท (Permalink)
[deleted]
ccricers ยท 1 points ยท Posted at 21:44:15 on May 25, 2016 ยท (Permalink)
And it stands for "Mathematical Anti-Telharsic Harfatum Septomin".
[deleted] ยท 1 points ยท Posted at 21:49:25 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 21:27:30 on May 25, 2016 ยท (Permalink)
rdrr
https://m.youtube.com/watch?v=98unLjZRc_8&rdm=21b1u64be&client=mv-google
fatbunyip ยท 1 points ยท Posted at 21:27:44 on May 25, 2016 ยท (Permalink)
Late to the party,but :
The sum of all integers : 1+2+3....= -1/12
yes, negative one twelfth. There's a cool Numberphile youtube video with a very easy to follow proof/explanation.
Sharp_Espeon ยท 1 points ยท Posted at 21:27:53 on May 25, 2016 ยท (Permalink)
Commenting to come back to this later
GroovingPict ยท 1 points ยท Posted at 21:29:47 on May 25, 2016 ยท (Permalink)
Not exactly a maths fact, more like a... numbers fact. Youtube uses a base 64 number system for their video id's (that string you see at the end of a youtube url, consisting of characters A-Z, a-z, 0-9, -, and _). And with just 11 such characters, which is what youtube uses, it has enough url's for every person on the planet to upload a new video every minute... for 18,000 years.
Relevant Tom Scott
Lvl_100_Lurker ยท 1 points ยท Posted at 21:32:02 on May 25, 2016 ยท (Permalink)
The difference between the squares of two consecutive numbers is the sum of those numbers. For example: 3 squared is 9, and 4 squared is 16. 16-9=7, and 3+4=7
PekingGoose ยท 1 points ยท Posted at 21:32:32 on May 25, 2016 ยท (Permalink)
I learned two from high school, both involving squares.
When squaring numbers ending in a 5, take any digits to the left of it, multiply that number by (that number+1), and tack a "25" on the end of it as two digits. Ex. 852 = (8 * 9=72), and add "25" at the end = 7225. 1252 = (12 * 13=156), and add "25" at the end = 15625.
For squaring numbers consisting of only ones (i.e. 11, 111, 1111, etc...), the answer is a sequential number of digits (starting at 1) equalling the number of ones being squared, and then tacking on digits that descend back to the number 1. 111 has three ones, so the answer is 12321, 11112 is 1234321.
slickricflair ยท 1 points ยท Posted at 21:33:23 on May 25, 2016 ยท (Permalink)*
For all "odd" number magic squares, one solution is just simply placing the middle number of the series and then adding/subtracting the next number in sequence in a diagonal direction (wrap around and end) and move up/down one square when you run out of room.
This method works for all odd squares. There is one for even numbers too but I don't remember what the sequence is.
For a 5x5, it looks like this:
Multiple Edits to get formatting right.
XMackerMcDonald ยท 1 points ยท Posted at 21:33:28 on May 25, 2016 ยท (Permalink)
In a number sequence there is only one known number in existence that sits between the square of a number and the cube of another number; i.e 1,2,3,4,5,6,7... Can you guess what the number is?
[deleted] ยท 1 points ยท Posted at 21:34:31 on May 25, 2016 ยท (Permalink)
The fact that without it we would never have got off planet earth, not would we have any complex technology
masterD77 ยท 1 points ยท Posted at 21:34:35 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 +.... = -1/12
Kellianne ยท 1 points ยท Posted at 21:35:52 on May 25, 2016 ยท (Permalink)
Dyscalculia is the sever difficulty in making arithmetical calculations as a result of a brain disorder.
Source: I've got it (stroke) It sucks.
Blimpflower ยท 1 points ยท Posted at 21:36:13 on May 25, 2016 ยท (Permalink)
I haven't needed to do academic math since high school 5 years ago. That's my favourite math fact.
helloder2012 ยท 1 points ยท Posted at 21:36:21 on May 25, 2016 ยท (Permalink)
I forget what it is exactly, but 1+2+3+4+5+ ... = -1/12 (sum of all natural numbers to infinity)
Numberphile YouTube channel did a sweet video on it.
Nacirema ยท 1 points ยท Posted at 21:36:27 on May 25, 2016 ยท (Permalink)
I'm late to this so I hope no one said this already. 111,111,111 x 111,111,111 = 12345678987654321.
TigerB65 ยท 1 points ยท Posted at 21:36:46 on May 25, 2016 ยท (Permalink)
Topologists cannot tell a coffee cup from a doughnut.
agentphunk ยท 1 points ยท Posted at 21:36:48 on May 25, 2016 ยท (Permalink)
The square root of 69 is 'eight something'
TheBlackWomb ยท 1 points ยท Posted at 21:37:06 on May 25, 2016 ยท (Permalink)
142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
142857 x 7 = 999999
142857 x 8 = 1,142856
And so on...
HyperBaboon ยท 1 points ยท Posted at 21:37:20 on May 25, 2016 ยท (Permalink)
The repeating decimal 0.999... is demonstrably the number 1
BobLeibnitz ยท 1 points ยท Posted at 21:37:29 on May 25, 2016 ยท (Permalink)
If you add 0 + 1 + 2 + 3 + 4 + ..... there is a proof that the sum is -1/12
source: https://www.youtube.com/watch?v=w-I6XTVZXww
chronodestroyr ยท 1 points ยท Posted at 21:37:31 on May 25, 2016 ยท (Permalink)
That I don't have to do it anymore. LOL!
Punaholic ยท 1 points ยท Posted at 21:37:56 on May 25, 2016 ยท (Permalink)
Al got rhythm
Drakeytown ยท 1 points ยท Posted at 21:37:57 on May 25, 2016 ยท (Permalink)
.9 repeating is exactly equal to 1.
t00m0nyfr0ts ยท 1 points ยท Posted at 21:40:29 on May 25, 2016 ยท (Permalink)
Well surely it isn't. But it's so infinitely close that it might as well be?
Drakeytown ยท 1 points ยท Posted at 21:49:27 on May 25, 2016 ยท (Permalink)
Nope. Exactly equal.
https://en.wikipedia.org/wiki/0.999...
t00m0nyfr0ts ยท 1 points ยท Posted at 21:53:11 on May 25, 2016 ยท (Permalink)
I 'find it sufficiently counterintuitive that [I] question or reject it.' lol. I'm an engineering student though so it doesn't really effect me. Great fact either way
suredoood ยท 1 points ยท Posted at 21:38:09 on May 25, 2016 ยท (Permalink)
This one is simple yet crazy!
1 = .99999...
Proof:
.99999... = x
10x = 9.99999...
10x - x = 9
9x = 9
x = 1
nthai ยท 1 points ยท Posted at 21:38:43 on May 25, 2016 ยท (Permalink)
We know that e and pi are irrational. But we don't know if e+pi or e*pi is rational or not. But we do know that if one of them were rational the other would have to be irrational.
cakeisnolie1 ยท 1 points ยท Posted at 21:39:37 on May 25, 2016 ยท (Permalink)
Maths.... why.
Styrak ยท 1 points ยท Posted at 21:41:02 on May 25, 2016 ยท (Permalink)
That some people call it "maths".
peffington ยท 1 points ยท Posted at 21:41:21 on May 25, 2016 ยท (Permalink)
that .999 repeating is actually 1...
southern_stallion ยท 1 points ยท Posted at 21:41:25 on May 25, 2016 ยท (Permalink)
The number of possible combinations of a 52 card deck is larger than atoms in the universe
arunnair87 ยท 1 points ยท Posted at 21:41:48 on May 25, 2016 ยท (Permalink)*
Here's a few: multiply 11 x a 2 digit number very quickly. Note x y in the example below is not x times y but a two digit number where digit 1 is x and digit 2 is y. X and y can be equal here no problem.
11 (x y) = x, (x+y), y as the 3 digits. If x+y is a double digit number, add 1 to x, to keep the 2nd digit of the sum of the two numbers in the middle. It's hard to write out as a formula so I'll give some examples.
11 x 45 = 495 11 x 47 = 517 11 x 74 = 814 11 x 36 = 396
//////////////////////////////////////////////////////////////////////////////
Multiplication is distributive. Therefore X (Y+Z) = (XY) + (XZ)
Also hard to see as a formula sometimes so let's break it down.
99 x 45 is really just (100 - 1) x 45. So you could rewrite this was 45 (100-1) or 45 x 100 - 45 = 4500- 45 = 4455.
TheQuestWatts ยท 1 points ยท Posted at 21:42:21 on May 25, 2016 ยท (Permalink)
That 3 rights make a left... I'll see myself out.
SamPike512 ยท 1 points ยท Posted at 21:42:31 on May 25, 2016 ยท (Permalink)
9.9 recurring equals 10 x = 9.999... 10x = 99.999... 9x = 90 x = 90/9 = 10
Chasarooni ยท 1 points ยท Posted at 21:42:46 on May 25, 2016 ยท (Permalink)
The area of a circle with a circle cut out of the middle is equal to the area of a circle whose diameter is a chord on the outer circle and tangent to the inner circle. Example
Area of black disc is the same as the blue circle.
haigins ยท 1 points ยท Posted at 21:45:50 on May 25, 2016 ยท (Permalink)
Let x be represented as follows: x = x1x2x3x4x5... where xi is the ith digit of x.
Ex. if x = 45 then x1 = 4 and x2 = 5
armyjackson ยท 1 points ยท Posted at 21:46:27 on May 25, 2016 ยท (Permalink)
no matter how long the number, if you add up all of the numbers in it and it is divisible by 3, then the number is divisible by 3. Example 720 7+2+0=9 9 is divisible by 3 which means 720 is divisible by three.
alowester ยท 1 points ยท Posted at 21:47:30 on May 25, 2016 ยท (Permalink)
yeah, I'm not smart enough for this thread
TheWeetodd ยท 1 points ยท Posted at 21:47:31 on May 25, 2016 ยท (Permalink)
The transitive property of equality for sure...
If A=B and B=C then A=C.
It works really well for using maths to prove statements. For instance, if someone says "Knowledge is the key to success"... I'll come back with "and knowledge is power... therefore, power is the key to success... life solved with math"
Another one "time is money, and money is the root of all evil, therefore time is the root of all evil"
I think I am the only one who finds it funny, but I still enjoy it.
NSFWdw ยท 1 points ยท Posted at 21:48:33 on May 25, 2016 ยท (Permalink)
IF you give a topologist a mug of coffee and a donut, they won't know which to drink and which to eat.
Asterix1806 ยท 1 points ยท Posted at 21:49:05 on May 25, 2016 ยท (Permalink)
A number is divisible by 3 if and only if the sum of its digits is also divisible by 3. (This result is best proven by induction.)
The same result holds for the number 9.
Each integer power of 11, ie. 11โฟ for some integer n, has 1 as its last digit.
Somewhat similarly, the last digits of powers of 9 alternate between 9 and 1.
Lastly, if two positive integers end in the same digit, all their powers will end in the same digit too. And unlike all the above results, this result is true for any base number.
BradyV20 ยท 1 points ยท Posted at 21:49:23 on May 25, 2016 ยท (Permalink)
Say, if a hand sanitzer kills 99.99% of bacteria, it kills 100% because no number can fit into 99.99999 ->. Just a fun fact.
dgriffith ยท 1 points ยท Posted at 22:53:23 on May 25, 2016 ยท (Permalink)
I have 100,000,000 bacteria on my hands.
I wash them with sanitiser that kills 99.99%, or 99,990,000 of them.
I now have 1,000 bacteria on my hands.
...... which are resistant to that level of exposure antibacterial agent in the sanitiser and quickly multiply again. A few more rounds of this is how you get bacteria that are strongly resistant to antibiotics.
Wizard_of_Ozzy ยท 1 points ยท Posted at 21:49:31 on May 25, 2016 ยท (Permalink)
Between 0 and 1 there lies an infinite amount of numbers
Bedlington13 ยท 1 points ยท Posted at 21:50:35 on May 25, 2016 ยท (Permalink)
There are about pi x 107 seconds in a year.
QuinQuix ยท 1 points ยท Posted at 21:50:56 on May 25, 2016 ยท (Permalink)
It's extremely easy to prove there are an infinite number of primes, taking note of the fact that the first prime, and only the first, is actually even (2).
Suppose the number of primes was finite. Now multiply all these primes and add 1. Done.
You know this number can't be divided by any of the primes you had before because it was made up of all of them, but now it's larger by 1, which is smaller than any prime and no matter by what prime you divided that's what you'll be left with.
Note that the number you get will likely be much much larger than the largest prime in your finite list. It's not a given that it actually will be prime since between the largest prime on your finite list and the monster you created will be many many numbers that could be prime and might divide your monster.
All the proof shows is that if there ever was a 'last' prime, it's impossible that no primes come after that, because if none of numbers afterwards were prime, your unholy monster would have to be one.
Clementinesm ยท 1 points ยท Posted at 21:52:05 on May 25, 2016 ยท (Permalink)
ij=k jk=i k*i=j i2=j2=k2=-1
You can create numbers of the form a+bi+cj+dk
These types of numbers are called Quaternions. They are related to the simple complex/imaginary numbers you learn about in school and were the predecessors to vectors.
derpyderpderpp ยท 1 points ยท Posted at 21:52:08 on May 25, 2016 ยท (Permalink)
That you can count multiples of 9 with your fingers.
VerifiedMod ยท 1 points ยท Posted at 21:52:51 on May 25, 2016 ยท (Permalink)
while multiplying a number with 10n , just add n zeroes to the number after it
5 * 100 = 500
6*10000 = 60000 etc
buggy65 ยท 1 points ยท Posted at 21:53:02 on May 25, 2016 ยท (Permalink)
For some reason I always loved the Birthday Problem. At a party (or classroom) with 23 people in the room? There's a greater than 50% chance that 2 of them share a birthday.
spookyjf ยท 1 points ยท Posted at 22:08:44 on May 25, 2016 ยท (Permalink)
how?
buggy65 ยท 1 points ยท Posted at 03:36:05 on May 26, 2016 ยท (Permalink)
There's a really good wikipedia article on it. It's NOT the probability of someone matching your birthday, its that somewhere in the room two people will match. Basically it's easier to think about it in reverse, how many people can you stick in a room without someone sharing a birthday? The probability that one person alone in a room doesn't match another person is 365/365 (1 of course), the probability 2 people in a room don't match is 364/365, 3 people not matching is 363/365, ... , the 23rd person not matching is 343/365 ways. So all together in one room is (365 x 364 x 363 x ... x 343)/(36523 ) = 0.49, a 49 percent chance of NOT matching! Another simpler way to think about the problem is how many dice can you roll before ANY two of them match? 6/6 x 5/6 x 4/6 = 0.55 chance not matching with only 3 die, with 4 die we drop to 0.27 chance of two not matching!
ValueOfALife ยท 1 points ยท Posted at 21:53:21 on May 25, 2016 ยท (Permalink)
Euler's Identity: epi*i + 1 = 0
https://en.wikipedia.org/wiki/Euler%27s_identity
colbymg ยท 1 points ยท Posted at 21:53:59 on May 25, 2016 ยท (Permalink)*
The equation:
1/2 < floor( mod( floor(y/17) * 2^ (-17 * floor(x) - mod(floor(y),17)) ,2) )
for 0<=y<=106 and k<=x<=k+17
where k is some giant number with about 600 digits.
depending on the value for k, you can literally have it display anything you want in that 17x106 area as pixel art. A series of smiley faces, your name, etc.
The 'Everything' Formula
cstreak ยท 1 points ยท Posted at 21:54:13 on May 25, 2016 ยท (Permalink)
That 0.9 repeating is equal to 1.
revenger2112 ยท 1 points ยท Posted at 21:54:16 on May 25, 2016 ยท (Permalink)
The derivative of e to the x is e to the x.
lazyl ยท 1 points ยท Posted at 22:59:28 on May 25, 2016 ยท (Permalink)
By definition.
D-Shap ยท 1 points ยท Posted at 21:54:23 on May 25, 2016 ยท (Permalink)
E2(pi)i (e as in 2.718281828... i as in root of -1)= 1 It combines four different realms of math, whole numbers, circles, irrational numbers, imaginary numbers) into one simple beautiful equation.
Javorsky ยท 1 points ยท Posted at 21:55:44 on May 25, 2016 ยท (Permalink)
That 25x25=625
2+1=3 3x2=6 25x25=625
35x35=1225 3*4=12 And so on and so on For 2 digit numbers ending in 5
FoopaTroopa_UNLUCKY ยท 1 points ยท Posted at 21:56:08 on May 25, 2016 ยท (Permalink)
1+1 doesn't equal 11
fam1ne ยท 1 points ยท Posted at 21:56:57 on May 25, 2016 ยท (Permalink)
When multiplying by 9 the product when added equals 9. I had figured out this trick way back when I had learned multiplication to "cheat" and know multiples of 9 when tested. For instance 9x15=135 1+3+5=9. It never really came in handy other than learning multiplication when I was in grade school but always found it odd
MrUnderdawg ยท 1 points ยท Posted at 22:47:08 on May 25, 2016 ยท (Permalink)
when adding 9 to any number thats not a multiple of 10, take the ones place and subtract 1 from it and add 1 to the tens place.
Hickesy ยท 1 points ยท Posted at 21:56:57 on May 25, 2016 ยท (Permalink)
That it can be snorted, smoked, swallowed or injected.
BillinSDCA ยท 1 points ยท Posted at 21:57:29 on May 25, 2016 ยท (Permalink)
I found this site week or so ago and it was indeed fascinating - (May have been posted in this thread, I don't know)
Check it out, you'll love it!!
9 Mathematical facts that will blow your mind [and a delicious bonus]
I was OK until #4 then I was lost - memory at 64 isn't great on this stuff anymore - :)
rm_-rf_virginity ยท 1 points ยท Posted at 21:57:31 on May 25, 2016 ยท (Permalink)
This may be incredibly late to the party, and potentially already mentioned, but my favorite fact in math is that there are just as many numbers between 1 and 2, or any neighboring numbers for that matter, as there are numbers period.
For example, if you were to attempt to list every possible decimal point between 1 and 2, it would go on indefinitely.
Kalistoga ยท 1 points ยท Posted at 22:09:47 on May 25, 2016 ยท (Permalink)
"If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told it's two, and that cannot be."
Dimanovic ยท 1 points ยท Posted at 22:12:18 on May 25, 2016 ยท (Permalink)
epi*i +1 = 0
MrUnderdawg ยท 0 points ยท Posted at 22:42:47 on May 25, 2016 ยท (Permalink)
I guess this is the only math fact reddit knows.
Dimanovic ยท 1 points ยท Posted at 22:49:14 on May 25, 2016 ยท (Permalink)
In a thread with almost 10,000 comments I found one other person mentioning it just now.
MrUnderdawg ยท 1 points ยท Posted at 22:57:52 on May 25, 2016 ยท (Permalink)
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3ix3n4
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3jowkx
https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3jnet9
just a few :p
Dimanovic ยท 1 points ยท Posted at 23:06:02 on May 25, 2016 ยท (Permalink)
Two before mine (one barely) out of 10,000 comments. Is this really where you want to spend your outrage?
TheAwesomePipes ยท 1 points ยท Posted at 22:13:25 on May 25, 2016 ยท (Permalink)
How convenient, I have a maths GCSE tomorrow.
Thank you
undecidedquoter ยท 1 points ยท Posted at 22:13:28 on May 25, 2016 ยท (Permalink)
British people say "maths" and Americans say "math".
Penquinn15 ยท 1 points ยท Posted at 22:15:09 on May 25, 2016 ยท (Permalink)
26 is the only number that is inbetween a cube (33) and a square (52)
JM8289 ยท 1 points ยท Posted at 22:17:06 on May 25, 2016 ยท (Permalink)
Not sure how true this fact is but i heard every time you shuffle a deck of cards, the chance that the order of the cards has even once been replicated is incredibly small.
loptthetreacherous ยท 1 points ยท Posted at 22:42:26 on May 25, 2016 ยท (Permalink)
The number is so small, that it's perfectly safe to say "it's never happened before in the history of humanity and will never happen again" (assuming the deck was shuffled well).
Vsauce does a good video explaining just how big the number is
JohnnyVegas666 ยท 1 points ยท Posted at 22:20:00 on May 25, 2016 ยท (Permalink)
There are 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 different possible combinations for the order of a deck of cards.
northrupthebandgeek ยท 1 points ยท Posted at 22:20:04 on May 25, 2016 ยท (Permalink)
Jenny's phone number (8675309) is prime.
yuoopwe ยท 1 points ยท Posted at 22:22:15 on May 25, 2016 ยท (Permalink)
2+2 DOES NOT = 5
Dazz316 ยท 1 points ยท Posted at 22:22:55 on May 25, 2016 ยท (Permalink)
What's that fact that if you have three cards you have 1/3 of choosing the correct one. But if you choose wrong, take that card away and choose between the remaining two you still have 1/3 chance of choosing the right card or something.
loptthetreacherous ยท 1 points ยท Posted at 22:33:42 on May 25, 2016 ยท (Permalink)
That's the Monty Hall paradox.
Your playing a game with a friend and and they put 3 cards down, 2 black and 1 red and they know the position of each and you have to find the red. You choose one of the cards (not flipping it over) then your friend flips one of the black cards over and give you the option to choose again, the odds of the red being under the one you chose previously is 1/3rd while the odds of it being under the other remaining one is 2/3rds.
Dazz316 ยท 1 points ยท Posted at 22:47:04 on May 25, 2016 ยท (Permalink)
Right this is the thing I don't understand, how does the old decision affect the new one? I Rkinda get it but the new decision involves 2 cards. The previously chosen card has been ejected and is now non exisitant in the new decision.
loptthetreacherous ยท 1 points ยท Posted at 22:54:30 on May 25, 2016 ยท (Permalink)
That's the point, it seems entirely counterintuitive, but the mathematics behind it assures us that that is the case.
Dazz316 ยท 1 points ยท Posted at 23:00:30 on May 25, 2016 ยท (Permalink)
But aren't all the mathematics completely wiped at the point it jumps between 2 decisions?
loptthetreacherous ยท 1 points ยท Posted at 23:06:44 on May 25, 2016 ยท (Permalink)
No. Here is a video of a person doing it 100 times and showing 71% of the time switching won, 29% of the time staying won (which is close to 66% and 33%).
Dazz316 ยท 1 points ยท Posted at 23:28:57 on May 25, 2016 ยท (Permalink)
Well it doesn't actually show us though. But I've looked up others and seems you're right.
It does suggest "chance" doesn't exist.
loptthetreacherous ยท 1 points ยท Posted at 23:31:45 on May 25, 2016 ยท (Permalink)
A good way to prove it is to go in steps:
Say we have 3 cards, 2 black 1 red and you want the red:
First say you choose a card, then look at it then the two other cards. You expect to get the red 1/3rd of the time.
Second, say you choose a card and I flip over a black card and then you look at your card. Nothing has changed from the first time except the order the cards have been flipped over. You still expect to get the red 1/3rd of the time.
Third, say you choose a card, I flip over a black card then hand the other card over to someone else. As before, you're expecting to get the red card 1/3rd of the time, so clearly the other person has to get the red card 2/3rds of the time.
Dazz316 ยท 1 points ยท Posted at 23:46:00 on May 25, 2016 ยท (Permalink)
Yes but that's to say these happens each time. So we have outcoms 1 2 and 3 here.
How does it have to land 1,2&3 1,3&2 etc. Why not 1,1 then 3? or 32 then 1? There's again a 1 inn 3 of any of these happening each time. Chances are higher not getting all three than getting all 3.
ravenQ ยท 1 points ยท Posted at 22:23:33 on May 25, 2016 ยท (Permalink)
e{i \pi} + 1 = 0
I got ton, but this one blows my mind.
Spiv5 ยท 1 points ยท Posted at 22:24:03 on May 25, 2016 ยท (Permalink)
I think that the mobus loop is pretty cool, if thats a maths trick
dalcowboiz ยท 1 points ยท Posted at 22:24:29 on May 25, 2016 ยท (Permalink)
X2 = (x-1)2 + x + (x-1)
Might seem like a boring fact but it means if you know 25 squared is 625, then you know 26 squared is 625+25+26 = 676. Can make for some easy mental math sometimes. I just like it cuz I thought it was like a magical math thing i invented when i was in school.
greyfade ยท 1 points ยท Posted at 22:24:35 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is -1/12
PenNamee ยท 1 points ยท Posted at 22:25:02 on May 25, 2016 ยท (Permalink)
The fact that a negative multiples by a negative is a positive gives me hope for future generations
spartanburt ยท 2 points ยท Posted at 22:51:54 on May 25, 2016 ยท (Permalink)
Bad news... adding negative numbers results in even more negative numbers.
cynoclast ยท 1 points ยท Posted at 22:26:56 on May 25, 2016 ยท (Permalink)
The classic birthday paradox. If you have a room with 50 people in it, two of you have the same birthday.
What helped me grok it is that it's the number of pairs in the room, and pairs aren't consumed on use. So person #1 compared with #2 through #50. Then person #2 compared with #3 through #50. And for every birthday that someone has, no one else can have it or you have two people with the same birthday, so just by having 50 people you have 316 possibilities, and 1,225.
It's a classic, but I didn't see it listed here yet. But it's not even probability, but more of a graph theory problem.
Yanman_be ยท 1 points ยท Posted at 22:27:01 on May 25, 2016 ยท (Permalink)
0.99999999...... equals 11
MrUnderdawg ยท 1 points ยท Posted at 22:39:16 on May 25, 2016 ยท (Permalink)
1*
Yanman_be ยท 1 points ยท Posted at 05:19:35 on May 26, 2016 ยท (Permalink)
Yes sorry.
Pcote_Qc ยท 1 points ยท Posted at 22:28:39 on May 25, 2016 ยท (Permalink)
The guy who proved the existence of irrational numbers was murdered for his discovering.
spartanburt ยท 1 points ยท Posted at 22:29:03 on May 25, 2016 ยท (Permalink)
I dont know how mathy this really is, but the discussion of the Monty Hall problem in this thread reminds me of The Island of the Blue-Eyed People. I have to reeeally stretch my mind to make sense of that one.
Doomacracy ยท 1 points ยท Posted at 22:29:59 on May 25, 2016 ยท (Permalink)
the fact that I never have to take it again.
awakening_life ยท 1 points ยท Posted at 22:32:07 on May 25, 2016 ยท (Permalink)
epi*i = -1
-Cunning-Stunt- ยท 1 points ยท Posted at 22:33:18 on May 25, 2016 ยท (Permalink)
You can construct a line segment of length โ2 units using a ruler, but can never measure it.
JasonOnTheBeach ยท 1 points ยท Posted at 22:33:18 on May 25, 2016 ยท (Permalink)
that 1 nut is one nut. but 2 nuts are DEEZ NUTS!!!!
varisforge ยท 1 points ยท Posted at 22:33:20 on May 25, 2016 ยท (Permalink)
I like that 7 is the first (whole) number that doesn't evenly divide into 360 (the number of degrees in a circle). The second number to do that is 11. They both are non-terminating and repeating values, 0.01944444444~4 and 0.03055555555~5 respectively.
But if you add 7 and 11 together, they equal 18, which is 1/20th of 360, and does divide evenly into it. (0.05)
I secretly suspect that mathemagicians, geometers and numerologists have raved about this fact since the dark ages.
renoscottsdale ยท 1 points ยท Posted at 22:33:55 on May 25, 2016 ยท (Permalink)
There are over 400 numbers.
MrUnderdawg ยท 1 points ยท Posted at 22:38:51 on May 25, 2016 ยท (Permalink)
Woah, I think you might need to check your facts there buddy.
ryanmcstylin ยท 1 points ยท Posted at 22:35:49 on May 25, 2016 ยท (Permalink)
over 99.99% of all numbers contain the number 9.
Gabriel's horn is a theoretical 3d figure that is infinitely long but has a finite volume.
spartanburt ยท 1 points ยท Posted at 22:50:34 on May 25, 2016 ยท (Permalink)
If you could fill the horn with paint (which you should be able to because it's a known finite volume) and the paint could soak through to the other side, you could paint an infinitely long surface with a finite amount of paint.
I know, i know, not really but its still pretty cool.
ryanmcstylin ยท 1 points ยท Posted at 22:59:09 on May 25, 2016 ยท (Permalink)
you actually cannot fill the horn completely with paint because at one point the diameter of paint atoms will be wider than the diameter of the horn creating a block and leaving an infinite length of horn unfilled. A horn is even a bad example because that needs a medium to travel through. A medium which at one point will be too think to enter the narrower parts of the horn.
InverseParadiddle ยท 1 points ยท Posted at 22:38:19 on May 25, 2016 ยท (Permalink)
I love that Math is called Maths in England?
Micheldemontaigne153 ยท 1 points ยท Posted at 22:38:27 on May 25, 2016 ยท (Permalink)
My neighbor has 2 children. One of them is a boy. What is the probability that the other is a girl? 2/3.
My other neighbor has 2 children. The oldest one is a boy. What is the probability that the other is a girl? 1/2.
godel32 ยท 1 points ยท Posted at 22:38:31 on May 25, 2016 ยท (Permalink)
You'll eventually find the digit Pi with Pi if you keep looking long enough... even though it's an irrational number.
thatguywithglasses97 ยท 1 points ยท Posted at 22:39:39 on May 25, 2016 ยท (Permalink)
To me, every single math fact is fucking amazing. Think about it. 1 + 1 = 2 is true here, there, and anywhere in the universe. The value of pi is the same in any place, in any language, in any representation. Using maths, we've effectively created a universal language. If we want to talk to aliens, we can communicate to them by using math facts.
Sine_Wave_ ยท 1 points ยท Posted at 22:44:59 on May 25, 2016 ยท (Permalink)
Some math is poetic, quite literally. Take for instance:
(12 + 144 + 20 + 3(sqrt(4))) / 7 + 3 x 11 = 92 + 0
Do the math and it is a valid equation. But read it out like this and it turns into a limerick:
A dozen, a gross and a score Plus three times the square root of four Divided by seven, plus three times eleven Is nine squared and not a bit more!
Dshinjiakyn ยท 1 points ยท Posted at 22:46:00 on May 25, 2016 ยท (Permalink)
I'm late to the party but maybe someone will see.
You can easily square two digit numbers as long as the last one is a 5. You always take 5ร5 and put it to the end. Then multiply the first digit with itself +1. Then just write them next to each other.
x52 = x ร (x+1) and 25
Example: 652 = 6ร7 and 5ร5 6ร7 = 42 5ร5 = 25 This means: 652 = 4225
SelfProclaimedBadAss ยท 1 points ยท Posted at 22:46:38 on May 25, 2016 ยท (Permalink)
If you multiply 2 negatives it makes a positive...
Somehow I feel lied to in my youth... "2 negatives don't make a positive"- My parents
2D_n_2Deep ยท 1 points ยท Posted at 22:47:28 on May 25, 2016 ยท (Permalink)
I don't have to understand it anymore once I graduate!
Tupilaqadin ยท 1 points ยท Posted at 22:49:02 on May 25, 2016 ยท (Permalink)
"If you smoke it regularly, your reading ability is goin..... oh"
CantTeachIt ยท 1 points ยท Posted at 22:50:43 on May 25, 2016 ยท (Permalink)
11 times table
Add the first and last number and stick that number in the middle.
Eg. 11x27 =297 (2+7) and stick it in the middle!
kthxtyler ยท 1 points ยท Posted at 22:55:46 on May 25, 2016 ยท (Permalink)
I remember my first math tutor told me that the sum of any number, however large, adds up to a number divisible by 3, then so is the entire number. Example, 123,456,789. 1+2+3+4+5+6+7+8+9=45. Because 45 is divisible by 3, so is 123,456,789
onacloverifalive ยท 1 points ยท Posted at 22:56:07 on May 25, 2016 ยท (Permalink)
So here's one that I figured out in the eighth grade in algebra class.
Want to quickly figure out which numbers are squares without having to multiply things repeatedly?
Consecutive squares are the sum of consecutive odd integers. 0. 0. 0 +1 1. 1 +3 4. 2 +5 9. 3 +7 16. 4 +9 25. 5 +11 36. 6 +13 49. 7
Txtoker ยท 1 points ยท Posted at 22:56:20 on May 25, 2016 ยท (Permalink)
.999 repeating is equal to 1
boba-fett-life ยท 1 points ยท Posted at 22:56:32 on May 25, 2016 ยท (Permalink)
Given a number N, if you add all of the digits in N and that number is divisible by three, then N is divisible by three.
thinkforgetfull ยท 1 points ยท Posted at 22:57:22 on May 25, 2016 ยท (Permalink)
that there are no uninteresting numbers, for by not being interesting, it would be interesting.
alexdas77 ยท 1 points ยท Posted at 23:00:08 on May 25, 2016 ยท (Permalink)
if you have 20 books on a bookshelf, the number of ways you could arrange those books is 2,432,902,008,176,640,000. For reference of how big that number is, there are 100,000,000,000 stars in the milky way.
turkishcat ยท 1 points ยท Posted at 23:01:33 on May 25, 2016 ยท (Permalink)
My favorite is that any natural number {1, 2, 3, ...} can be written as the sum of four perfect squares. For example, 15 = 9 + 4 + 1 + 1, 24 = 16 + 4 + 4 + 0, etc.
The proof I'm most familiar with uses properties of convex bodies in 4 dimensional space and their interactions with lattices -- basically studying objects in a different area of math results in this beautiful piece of number theory in a wonderful, unexpected way. Also you need at least 4 squares to write every natural number in this way; for example, there's no way to write 15 as the sum of just three squares.
CongrooElPsy ยท 1 points ยท Posted at 23:01:49 on May 25, 2016 ยท (Permalink)
Eฯi = -1
It's insane that two irrational numbers and an imaginary number end up as such a simple number. It's called Euler's identity if you want to look up videos on why it works.
[deleted] ยท 1 points ยท Posted at 23:02:20 on May 25, 2016 ยท (Permalink)
You can multiply 25 by any number easily. Take the number you're multiplying and divide it by 4. Then add 2 zeros to the number. If you have "1" remainder, then add 25, "2" remainder then 50 and "3" remainder then 75.
Here's an example:
25 x 66 = 66/4 = 16 with a 2 remainder. 1600+50=1650
Bad_in_bed ยท 1 points ยท Posted at 23:02:42 on May 25, 2016 ยท (Permalink)
Probably too late to the party but I like the fact because it it practical. If you have a wobbling table on a static surface (uneven floor without steps) then there is a position of the table within a rotation of 90 degrees such that the table no longer wobbles.
ashwashere ยท 1 points ยท Posted at 23:07:38 on May 25, 2016 ยท (Permalink)
Fibonacci sequence and its occurrence in nature. I barely learned about it this year because the Fibonacci sequence is one of the topics our outreach group attempts to teach kids in elementary schools. Now I constantly find myself picking up pinecones, brussel sprout stalks, and flowers to count the number of spirals; without fail, the number always falls within the sequence. Sure wish I learned about it earlier!
Karmic_Backlash ยท 1 points ยท Posted at 23:09:01 on May 25, 2016 ยท (Permalink)
0 < you see this thing, fuck this thing.
Videoboysayscube ยท 1 points ยท Posted at 23:09:04 on May 25, 2016 ยท (Permalink)
Without tearing or creasing it, you can turn a sphere inside out.
https://www.youtube.com/watch?v=R_w4HYXuo9M
sw1ff2 ยท 1 points ยท Posted at 23:09:32 on May 25, 2016 ยท (Permalink)
any number times 5 is half the original number from a decimal.
pokachyreddit ยท 1 points ยท Posted at 23:10:27 on May 25, 2016 ยท (Permalink)
17*3 = 51
I heard this once on some TV show about the morning announcer team, at some chool that had Warthogs as a mascot. They had a trivia competition one episode, and this fact kind ajust stuck with me.
Lose__Not__Loose ยท 1 points ยท Posted at 23:11:38 on May 25, 2016 ยท (Permalink)
My favorite math fact is that, in America, mathematics is shortened to math, not maths.
Quick_A_Distraction ยท 1 points ยท Posted at 01:20:18 on May 26, 2016 ยท (Permalink)
Do you shorten calculus to calcs
Lose__Not__Loose ยท 1 points ยท Posted at 09:45:29 on May 26, 2016 ยท (Permalink)
No, that would be as dumb as shortening mathematics to maths.
MrBubbles21 ยท 1 points ยท Posted at 23:13:21 on May 25, 2016 ยท (Permalink)
Probably that eฯi=-1, also known as the Euler identity. Or that 1!=1 and 0!=1 (factorials).
iWheatMan ยท 1 points ยท Posted at 23:14:33 on May 25, 2016 ยท (Permalink)
If you multiply any number full of ones (eg. 1111) up to nine ones with another number of ones, you will receive a palindrome with the highest number in the palindrome, being the lowest number of ones you used in one of your numbers.
alfiestoppani ยท 1 points ยท Posted at 23:14:37 on May 25, 2016 ยท (Permalink)
I like how the roots of the polynomial f(x)=x2 +9x +14 are -7 and -2. I like polynomials.
foundanoreo ยท 1 points ยท Posted at 23:15:00 on May 25, 2016 ยท (Permalink)
Fourier law stating that any periodic function under the Dirilicht conditions can be constructed using a sum of sinusoidals of varying frequency, wavelength and amplitude. This means you can take sine waves to sum up to make. Square wave. Furthermore every aperiodic function can also be estimated using these methods. Doing this allows one to observe any waveform as a function of frequency which is very interesting. This idea has some remarkable applications ranging from thermodynamics, image processing, sound, signals, communications, etc.
Kindlegarten ยท 1 points ยท Posted at 23:19:11 on May 25, 2016 ยท (Permalink)
An irrational number raised to an irrational power can yield a rational result. We know that โ2โ2 has to be either rational or irrational. If itโs rational then our task is done. If itโs irrational, then ( โ2โ2 )โ2 = 2 proves the statement.
BACEXXXXXX ยท 1 points ยท Posted at 23:19:48 on May 25, 2016 ยท (Permalink)
If you ever want to multiply a number by 11, simply add the digits, separate them, and drop that new sum in the middle. For example:
11*72
7+2=9
72
792
This works with all numbers, but gets more and more complex as you go.
gwalker4 ยท 1 points ยท Posted at 23:20:42 on May 25, 2016 ยท (Permalink)
my favorite maths fact is that it's possible to determine the curve of someone's ass using derivatives
WillyMacBatman ยท 1 points ยท Posted at 23:20:44 on May 25, 2016 ยท (Permalink)
For any circle imaginable, if you take the circumference and divide it by the diameter, you will always get the same irrational number. Pi.
Jrepicness101 ยท 1 points ยท Posted at 23:20:50 on May 25, 2016 ยท (Permalink)
1111111111x1111111111=12345678987654321 (I think)
pupmaster ยท 1 points ยท Posted at 23:20:56 on May 25, 2016 ยท (Permalink)
I can't into maths
fairysdad ยท 1 points ยท Posted at 23:21:25 on May 25, 2016 ยท (Permalink)
It is possible to talk coherently with full and real words for over a minute without using the letter A. (Although it might not make sense.)
Simply count.
You won't hit an 'A' until you get to 101 (or 1001 if you don't say the 'and' in 'one hundred and one' for some reason).
AequitasKiller ยท 1 points ยท Posted at 23:29:14 on May 25, 2016 ยท (Permalink)
Not really a math fact, but indicial notation is awesome. It allows you to present long and tedious matrix calculations in a very compact and simple form.
[deleted] ยท 1 points ยท Posted at 23:30:02 on May 25, 2016 ยท (Permalink)
The infinite monkey theorem does not state that you are guaranteed to get any string of text. It states you have a probability of 1 of getting any string of text.
You also have a probability of 1 that if you select a real number at random that it's irrational. Claiming the infinite monkey theorem means you're guaranteed the works of Shakespeare is like saying rational numbers don't exist (inside the reals).
bjhufstetler2014 ยท 1 points ยท Posted at 23:31:42 on May 25, 2016 ยท (Permalink)
The integral of sec3 is a mise en abyme
dug99 ยท 1 points ยท Posted at 23:31:52 on May 25, 2016 ยท (Permalink)
Coastline Paradox
bloonail ยท 1 points ยท Posted at 23:34:22 on May 25, 2016 ยท (Permalink)
Constellations, the form of the 7 sisters, IP network reconfiguration protocols and dating algorithms are all tied together with the same basic math in graph theory.
fantumn ยท 1 points ยท Posted at 23:34:43 on May 25, 2016 ยท (Permalink)
The gap between perfect squares increases by 2 each time and is always odd.
estrogenius ยท 1 points ยท Posted at 23:35:30 on May 25, 2016 ยท (Permalink)
I ate and ate and got sick on the floor. 8x8=64
Elementary school teacher here. Math facts mean something completely different in my world.
Shanshan16 ยท 1 points ยท Posted at 00:14:39 on May 26, 2016 ยท (Permalink)
Got any more?
fish_with_sword ยท 1 points ยท Posted at 23:43:58 on May 25, 2016 ยท (Permalink)
Ants are really good at counting. They can work out how far they've walked by counting the steps they've taken, they can work out what job they need to do by counting how many ants are doing each job, and they can work out the size of an area by walking around randomly and counting how many times they're in the same place, which they use to check the quality of potential nest areas.
expateli ยท 1 points ยท Posted at 23:45:01 on May 25, 2016 ยท (Permalink)
You + Me = Us
ProfWhite ยท 2 points ยท Posted at 23:55:22 on May 25, 2016 ยท (Permalink)
Or for those with BPD, you + me = me.
expateli ยท 1 points ยท Posted at 00:20:25 on May 26, 2016 ยท (Permalink)
Well done Professor. Well done.
wallyeb ยท 1 points ยท Posted at 23:47:31 on May 25, 2016 ยท (Permalink)
my favorite, I suppose is that
(e to the (pi time i) power) minus 1 equals 0
(where i is the square root of minus 1)
phatness_everdeen ยท 1 points ยท Posted at 23:50:58 on May 25, 2016 ยท (Permalink)
Lmao yes it was joke
truetalentwasted ยท 1 points ยท Posted at 23:52:03 on May 25, 2016 ยท (Permalink)
1*1=2 Terrence Howard
Gsquared94 ยท 1 points ยท Posted at 23:55:40 on May 25, 2016 ยท (Permalink)
I don't know much about mathematics, but I love the Gaussian integral. I love the fact that the total area under the curve of e-x2 is root(pi). I've taken enough calculus to know what that means philosophically, but I've never tried to actually go about solving it.
thezim ยท 1 points ยท Posted at 00:02:48 on May 26, 2016 ยท (Permalink)
I'll reply in the form of a video:
https://www.youtube.com/watch?v=CAkMUdeB06o
[deleted] ยท 1 points ยท Posted at 00:04:26 on May 26, 2016 ยท (Permalink)
[deleted]
thezim ยท 1 points ยท Posted at 00:06:36 on May 26, 2016 ยท (Permalink)
I don't know what you are saying, but I think that seeing the Pythagorean theorem in a visual form is pretty cool and enlightening.
overconvergent ยท 2 points ยท Posted at 00:07:28 on May 26, 2016 ยท (Permalink)
Haha ignore me, I responded to the wrong post...
NighaMcNugget ยท 1 points ยท Posted at 00:05:11 on May 26, 2016 ยท (Permalink)
Oov
johnnyrottenjr ยท 1 points ยท Posted at 00:06:04 on May 26, 2016 ยท (Permalink)
As time t increases, the probability of this question being asked again approaches 1.
udbluehens ยท 1 points ยท Posted at 00:10:44 on May 26, 2016 ยท (Permalink)
ln(-1)/sqrt(-1) = pi. Im just rewriting eulers theorem, but its funny to me that these weird operations somehow come together to be pi.
FatKidsRHard2Kidnap ยท 1 points ยท Posted at 00:11:03 on May 26, 2016 ยท (Permalink)
"pythagorean triples" 345 triangle. it is most handy for DIY projects if youre not in construction
[deleted] ยท 1 points ยท Posted at 00:14:02 on May 26, 2016 ยท (Permalink)
My favourite math fact is that i got a B+ in my final math exam after maintaining a solid D for the past few years. Riddle me this!
shank2000 ยท 1 points ยท Posted at 00:16:12 on May 26, 2016 ยท (Permalink)
In a room of just 23 people thereโs a 50-50 chance of two people having the same birthday. In a room of 75 thereโs a 99.9% chance of two people matching.
LooseDuece ยท 1 points ยท Posted at 00:22:01 on May 26, 2016 ยท (Permalink)
A little less than 1ft is approximately the distance that light travels in a nanosecond. I think it's the best way that I've found to wrap my head around the scale of 1 billion.
The actual distance is 0.914...ft
[deleted] ยท 1 points ยท Posted at 00:23:40 on May 26, 2016 ยท (Permalink)
Right now, it would have to be the central limit theorem. The sum of n independent and identically distributed random variables becomes normal as n tends toward infinity. This is not only remarkable in and of itself, but also is important for many practical reasons.
[deleted] ยท 1 points ยท Posted at 04:14:32 on May 26, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 04:44:35 on May 26, 2016 ยท (Permalink)
Fair enough. However, this is Ask Reddit, and not my probability final. These details are not so important to statisticians, since all useful random variables have well-defined variance. As for how the sum is normalized, obviously I'm talking about the sample mean. I'm not sure how you could suggest this is only "vaguely" right, but OK.
rboy31 ยท 1 points ยท Posted at 00:25:27 on May 26, 2016 ยท (Permalink)
.9 recurring = 1
[deleted] ยท 1 points ยท Posted at 00:34:51 on May 26, 2016 ยท (Permalink)
A great and fun mathematical fact is this: The "size" (or cardinality) of the set of rational numbers is equal to that of the set of integers. And the cardinality of the power set of the natural numbers (that is, the set of all subsets of the natural numbers) is equal to that of the real numbers. Amazing.
tekkie1618 ยท 1 points ยท Posted at 00:37:34 on May 26, 2016 ยท (Permalink)
If you take every number in the Fibonacci sequence and devide it by the number before it, the higher you go, the closer you will get to Phi.
ElGoorf ยท 1 points ยท Posted at 00:40:36 on May 26, 2016 ยท (Permalink)
ITT: Grammar Nazis but no math[s]
JPfreak ยท 1 points ยท Posted at 00:43:17 on May 26, 2016 ยท (Permalink)
If you multiply 11 by a two digit number, you take the two digits, add them and place the sum in the middle and that's the answer. Eg 11x23 =253 (2+3=5) If the digits add to a two digit number, you just add a 1 to the front of the final sum. Eg 11x29 = 319 because 2+9 is 11, so it will be 2119 if you don't carry the one, but when you do it's 319. It's a bit hard to explain when typing on mobile but I think it's a cool trick worth sharing.
Steinrik ยท 1 points ยท Posted at 00:43:18 on May 26, 2016 ยท (Permalink)
One MILLION seconds is about 11 days.
One BILLION seconds is about 31 years.
virtualdrummer ยท 1 points ยท Posted at 00:46:08 on May 26, 2016 ยท (Permalink)
I miss math class and wish I had of paid more attention. Statistics on college was one of my favorite classes
CreepyStickGuy ยท 1 points ยท Posted at 00:49:55 on May 26, 2016 ยท (Permalink)
Ramanujan's sum.
Also, measuring the perimeter of a ridged object (specifically coastlines) because of (oversimplifying here) fractals. Mandelbrot was a cool dude.
shev_rolet ยท 1 points ยท Posted at 00:50:34 on May 26, 2016 ยท (Permalink)
1st year engineering school, Euler's identity ei*pi + 1 = 0 . The five most significant numbers in mathematics all in one beautiful equation.
[deleted] ยท 1 points ยท Posted at 00:54:17 on May 26, 2016 ยท (Permalink)
Pascal triangle appears everywhere. It's useful for (x +y)p. What I'm not liking is perturbation theory. It feels so wishy washy.
lankylizards ยท 1 points ยท Posted at 00:54:47 on May 26, 2016 ยท (Permalink)
Not exactly a fact, but the popcorn function is a really cool looking function that's defined as: f(x) = 1 if x = 0, 0 if x is irrational, 1/b if x is rational and x=a/b in lowest terms. The graph of the function from x = 0 to 1 looks like popping popcorn!
https://en.wikipedia.org/wiki/Thomae%27s_function#/media/File:Thomae_function_%280,1%29.svg
SumOMG ยท 1 points ยท Posted at 00:57:04 on May 26, 2016 ยท (Permalink)
British people says Maths and Americans say Math
AllPurposeNerd ยท 1 points ยท Posted at 00:58:49 on May 26, 2016 ยท (Permalink)
Graham's number. It's a number that's so impossibly fucking huge, you need a specialized system of notation to describe it.
[deleted] ยท 1 points ยท Posted at 01:01:24 on May 26, 2016 ยท (Permalink)
ITT: people that don't know the entire world doesn't use the same word to refer to mathematics.
JVink ยท 1 points ยท Posted at 01:05:19 on May 26, 2016 ยท (Permalink)
111,111,111 x 111,111,111 = 12,345,678,987,654,321
I can never forget this once I figured it out
RobotJeffersonDavis ยท 1 points ยท Posted at 01:10:43 on May 26, 2016 ยท (Permalink)
1 isn't prime.
decaturbadass ยท 1 points ยท Posted at 01:15:55 on May 26, 2016 ยท (Permalink)
That naught times naught = naught. Thank you Jethro Bodine
Ghenges ยท 1 points ยท Posted at 01:17:48 on May 26, 2016 ยท (Permalink)
In America they say 'math' and in the UK they say 'maths'.
wiegleyj ยท 1 points ยท Posted at 01:20:09 on May 26, 2016 ยท (Permalink)
Every even number is the sum of two primes. (But this isn't proven yet so maybe not a "fact").
spartanburt ยท 1 points ยท Posted at 02:52:33 on May 26, 2016 ยท (Permalink)
Its also not true at all. 10 = 1 + 9, for example.
blairandchuck ยท 1 points ยท Posted at 04:10:00 on May 26, 2016 ยท (Permalink)
10 = 7+3. "Every even number can be expressed as the sum of two primes" is not the same as "every way of expressing an even number as a sum of two numbers implies the two numbers are prime."
spartanburt ยท 1 points ยท Posted at 04:15:47 on May 26, 2016 ยท (Permalink)
Ah ok, that makes sense.
MasteringTheFlames ยท 1 points ยท Posted at 01:24:47 on May 26, 2016 ยท (Permalink)
Stolen from the last time a similar thread came up:
The Collatz Conjecture is an unproven theory which states that with any given number, that number can be reduced to 1 through two steps: if the starting number is even, divide by two. If odd, multiply by 3 and add 1. After repeating these steps enough times, any number will reduce to 1. For example, let's start at 10. 10 is even, so we divide by 2 and get 5. 5 is odd, so we multiply by 3 and add 1 to get 16. 16 divided by 2 is 8, then 4, then 2, and finally, 1. This theorem has been proven for every number up to 1060
[deleted] ยท 1 points ยท Posted at 01:29:09 on May 26, 2016 ยท (Permalink)
I have one, although I am terrible at math and everyone probably knows this one, but multiplying 9 by any of the digits 1-9 will give you a 2 digit number that adds up to make 9.
JohnnyMcG ยท 1 points ยท Posted at 01:31:40 on May 26, 2016 ยท (Permalink)*
Sterling's Approximation (wiki here). It basically says that in the limit as N increases to infinity,
N*ln(N) - N -> ln(N!)
Edit: Formula. Forgot ln(N!) instead of just N!.
It basically makes the field of statistical mechanics possible as the approximation is treated as exact due to N generally being on the order of >6.022x1026.
ScottieScrotumScum ยท 1 points ยท Posted at 01:31:47 on May 26, 2016 ยท (Permalink)
Okay you smarty pants. Please explain the "mother nature" factoid. Like I know that some shells are mathematically correct. What is this and how does this work?
morphicc ยท 1 points ยท Posted at 01:35:02 on May 26, 2016 ยท (Permalink)
2+2=4? I'm not exactly a mathlete
rishellz ยท 1 points ยท Posted at 01:37:12 on May 26, 2016 ยท (Permalink)
Think of all possible numbers between 0 and 1. The number is infinite, yes? Now think of all possible numbers between 1 and 2. This is also infinite, yes? But NONE of the numbers that appeared between 0 and 1 will EVER appear between 1 and 2, despite there being an infinite number of each. MIND BLOWN!
Buburubu ยท 1 points ยท Posted at 01:43:11 on May 26, 2016 ยท (Permalink)
We haven't discovered what the largest number is for sure yet, but mathematicians think it's probably more than 78 billion!
BoogsterSU2 ยท 1 points ยท Posted at 01:46:48 on May 26, 2016 ยท (Permalink)
ฯ(subscript ฯ) is the largest number. Ever.
Fuck, I wish we can format subscript text!
Superdorps ยท 1 points ยท Posted at 06:45:31 on May 26, 2016 ยท (Permalink)
Sorry, nope.
Even when we take something like the ordinals or the surreals, where ฯ is well-defined, it's not the largest member of the class. For that matter, taking ฯฯฯฯฯ... until it reaches a fixed point isn't the largest member of the class, because you still have the successor operator to rely on.
What890 ยท 1 points ยท Posted at 01:48:43 on May 26, 2016 ยท (Permalink)
ii is a real number.
Dropped60 ยท 1 points ยท Posted at 01:49:19 on May 26, 2016 ยท (Permalink)
I can't remember what it's called but when you measure 3' from a corner one way, then 4' in the other direction, and when you measure between the ends of those lines it should equal 5' to assure the corner is square. Sorry I'm a math idiot but I've used this when I've built shit
Bigenoughpieceofcake ยท 1 points ยท Posted at 02:14:39 on May 26, 2016 ยท (Permalink)
http://youtu.be/fO1Vhc88QkM
MettayyaDoBuda ยท 1 points ยท Posted at 01:59:16 on May 26, 2016 ยท (Permalink)
This came at the perfect time. Now I'm ready to math debate.
monetized_account ยท 1 points ยท Posted at 02:02:05 on May 26, 2016 ยท (Permalink)
ei.Pi = -1
Once I understood this, a whole world of math opened up for me.
Go_caps227 ยท 1 points ยท Posted at 02:08:27 on May 26, 2016 ยท (Permalink)*
The equation:
epi * i+1=0, contains the 5 most important numbers in math.
edit:switched the sign
Indivicivet ยท 1 points ยท Posted at 11:33:58 on May 26, 2016 ยท (Permalink)
And unfortunately it's wrong... ei pi - 1 = -2... :)
PolarBearITS ยท 1 points ยท Posted at 02:14:40 on May 26, 2016 ยท (Permalink)
eฯi = -1
blatterbeast ยท 1 points ยท Posted at 02:14:45 on May 26, 2016 ยท (Permalink)
9รท9= .9 repeating and also 1 Therefore .9 repeating=1
[deleted] ยท 1 points ยท Posted at 02:23:34 on May 26, 2016 ยท (Permalink)
This has been really fun to read while stoned
krnichin ยท 1 points ยท Posted at 02:25:34 on May 26, 2016 ยท (Permalink)
-0
faithispoison ยท 1 points ยท Posted at 02:27:24 on May 26, 2016 ยท (Permalink)
In England they call it maths rather than math.
tomparker ยท 1 points ยท Posted at 02:38:37 on May 26, 2016 ยท (Permalink)
10 out of 9 people don't understand fractions.
tomparker ยท 1 points ยท Posted at 02:39:28 on May 26, 2016 ยท (Permalink)
There are nine guys in a pavillion.
jmadd31 ยท 1 points ยท Posted at 02:50:31 on May 26, 2016 ยท (Permalink)
1 = 0.999... https://en.m.wikipedia.org/wiki/0.999...
mochablendedfun ยท 1 points ยท Posted at 03:10:43 on May 26, 2016 ยท (Permalink)
The average wife of Paul McCartney has 1.667 legs.
Japanglish ยท 1 points ยท Posted at 03:12:52 on May 26, 2016 ยท (Permalink)
The square root of 69 is 8 something
BigTwigz ยท 1 points ยท Posted at 03:19:43 on May 26, 2016 ยท (Permalink)
That a googol plex is 1 followed by a googol zeros.
Kransington ยท 1 points ยท Posted at 03:39:16 on May 26, 2016 ยท (Permalink)
1 is the loneliest number.
GokuMoto ยท 1 points ยท Posted at 05:16:19 on May 26, 2016 ยท (Permalink)
i heard 2 could be just as bad
operator10 ยท 1 points ยท Posted at 04:03:47 on May 26, 2016 ยท (Permalink)
One plus none is over.
QuantumFury ยท 1 points ยท Posted at 04:26:53 on May 26, 2016 ยท (Permalink)
You can have infinite surface area but not infinite volume
booyah_27 ยท 1 points ยท Posted at 04:30:13 on May 26, 2016 ยท (Permalink)
2.
2 is Prime (the first, smallest and the only even prime).
2! = 2
2+2 = 2*2 = 22 = 4
..there are dozens of other deeper facts about 2, but the simplest are the most elegant.
nosalad4me ยท 1 points ยท Posted at 15:35:11 on May 26, 2016 ยท (Permalink)
It's the first, 1 isn't
nosalad4me ยท 1 points ยท Posted at 15:35:22 on May 26, 2016 ยท (Permalink)
It's the first, 1 isn't
beccabliss ยท 1 points ยท Posted at 04:32:21 on May 26, 2016 ยท (Permalink)
R+L=J Love it. And I'm a math teacher.
An0therB ยท 1 points ยท Posted at 04:33:26 on May 26, 2016 ยท (Permalink)
Reddit formatting took a big shit all over your asterisks.
Dima_Parachute ยท 1 points ยท Posted at 04:35:30 on May 26, 2016 ยท (Permalink)
I know one thing about math, you can't cook it, make millions and then unbalance the entire crime structure of an entire state.
GokuMoto ยท 1 points ยท Posted at 05:13:40 on May 26, 2016 ยท (Permalink)
math not even once
[deleted] ยท 1 points ยท Posted at 04:41:31 on May 26, 2016 ยท (Permalink)
Dammit!
ssbmhero ยท 1 points ยท Posted at 04:42:11 on May 26, 2016 ยท (Permalink)
Eiฯ+1=0
kabukistar ยท 1 points ยท Posted at 04:57:22 on May 26, 2016 ยท (Permalink)
There are as many numbers between 0 and 1 are there are between -โ and โ
[deleted] ยท 1 points ยท Posted at 04:59:47 on May 26, 2016 ยท (Permalink)
1.999repeating IS 2. Not even the God of your choice can tell the difference.
schoolmonkey ยท 1 points ยท Posted at 06:00:47 on May 26, 2016 ยท (Permalink)
But even I can tell the difference! The first one has a bunch of nines in it!
drunkinnmunky ยท 1 points ยท Posted at 05:22:01 on May 26, 2016 ยท (Permalink)
That an odd number + an odd number always = an even number.
belguim1 ยท 1 points ยท Posted at 05:45:35 on May 26, 2016 ยท (Permalink)
*Correct, the limit of 1 - ((x-1)/x)x as x approaches infinity is 1 - (1/e) If I remember correctly you end up using the "sandwich" method for that proof, and it was a good one.
anvilcrawlers ยท 1 points ยท Posted at 05:54:31 on May 26, 2016 ยท (Permalink)
Fact: British and Australians say Maths, Americans (US) and Canadians say Math, but only Americans (US) spell Favorite, all you others add the "u".
[deleted] ยท 1 points ยท Posted at 06:24:08 on May 26, 2016 ยท (Permalink)
Probably the present value of an annuity certain formula. It's a great way to forecast how much your money will accumulate to of you invest it properly. The formula is accumulated value = (annual payment amount)(((1 + interest rate)number of payments-1)/ interest rate) For example, if you are 24 years old and make a 5000 investment at 8% on your 25th, 26th ... to 65th birthday, you will have $1.4 million dollars at age 65.
cornette ยท 1 points ยท Posted at 06:33:17 on May 26, 2016 ยท (Permalink)
Scott Steiner - The Numbers Don't Lie
SupersonicSpitfire ยท 1 points ยท Posted at 06:33:41 on May 26, 2016 ยท (Permalink)
sin2(t) +ย cos2(t) = 1
MagicAce8 ยท 1 points ยท Posted at 06:46:59 on May 26, 2016 ยท (Permalink)
The imaginary number square root of -1 raised to the power of itself, i.e. sqrt(-1)sqrt(-1), gives a real number 0.20787957635.
dudeusama ยท 1 points ยท Posted at 06:50:23 on May 26, 2016 ยท (Permalink)
"So that's why 60% of the time it works every time."
AndroxxTraxxon ยท 1 points ยท Posted at 07:01:10 on May 26, 2016 ยท (Permalink)
In Pascal's Triangle, on the Nth row, the first row being the 0th row, if N is prime, then all of the numbers on that row (excluding the external 1's) are multiples of said prime number.
dipping_sauce ยท 1 points ยท Posted at 07:03:31 on May 26, 2016 ยท (Permalink)
Anyone remember that unsolvable math card trick? This guy solved it! YAY!
Nide9 ยท 1 points ยท Posted at 07:21:02 on May 26, 2016 ยท (Permalink)
1+1=2 You can't fail With the basic.
GruesomeCola ยท 1 points ยท Posted at 07:27:27 on May 26, 2016 ยท (Permalink)*
Multiply 9 by any number (except 0) and the sum of the digits which make up that number will eventually give you 9. E.g. 9 * 9 = 81, 8 + 1 = 9; 9 * 56 = 504, 5 + 0 + 4 = 9; 9 * 213 = 1917, 1 + 9 + 1 + 7 = 18, 1 + 8 = 9. Ouala!
Excalibur21 ยท 1 points ยท Posted at 07:41:22 on May 26, 2016 ยท (Permalink)
Same with 3 and 6 I think...
Firzen_ ยท 1 points ยท Posted at 08:40:15 on May 29, 2016 ยท (Permalink)
6 already fails at 2*6=12
Excalibur21 ยท 1 points ยท Posted at 07:52:48 on May 31, 2016 ยท (Permalink)
Oh crap for some reason I was thinking of the divisibility test...
Ahtobe_original ยท 1 points ยท Posted at 07:46:54 on May 26, 2016 ยท (Permalink)
If you spin a wobbling table it will eventually not wobble. Numberphile did an episode on it.
madmenyo ยท 1 points ยท Posted at 07:58:08 on May 26, 2016 ยท (Permalink)
That everything around us is math really pretty much like The Matrix. Not just buildings and men made objects but everything really. https://www.sciencenews.org/article/mathematical-lives-plants
xkna21 ยท 1 points ยท Posted at 08:14:51 on May 26, 2016 ยท (Permalink)
Still your top
bnewlin ยท 1 points ยท Posted at 08:18:12 on May 26, 2016 ยท (Permalink)
ei(pi)=-1 of course!
JanEric1 ยท 1 points ยท Posted at 10:22:24 on May 26, 2016 ยท (Permalink)
ei(pi) = -1
bnewlin ยท 1 points ยท Posted at 11:31:34 on May 26, 2016 ยท (Permalink)
Really?
JanEric1 ยท 1 points ยท Posted at 11:34:49 on May 26, 2016 ยท (Permalink)
your formatting was messed up a bit
Maxwelldoggums ยท 1 points ยท Posted at 08:33:28 on May 26, 2016 ยท (Permalink)
Pretty much any of those awesome geometric construction techniques where you build perfect shapes with nothing but string and a straightedge.
reader960 ยท 1 points ยท Posted at 08:36:12 on May 26, 2016 ยท (Permalink)
Ulam spiral is pretty cool, albeit not a fact
gavotron ยท 1 points ยท Posted at 08:56:54 on May 26, 2016 ยท (Permalink)
This is a pretty simple one I worked out at school. Everything multiplied by 9 equals a number that when added together, equals 9 or a multiple of 9. Then add that answer and it will equal 9.
Example 9 x 9=81
8 + 1=9
And a random one
352 x 9= 3168
3 + 1 + 6 + 8= 18
1 + 8= 9
boiled_egg_haircut ยท 1 points ยท Posted at 08:57:56 on May 26, 2016 ยท (Permalink)
there is an infinite amount of numbers between 0 and 1
Hamu93 ยท 1 points ยท Posted at 09:16:54 on May 26, 2016 ยท (Permalink)*
16ยฒ-14ยฒ= 60
16 + 14 = 30
16 - 14 = 2
30*2 = 60
It works with every number.
NerdOverlord ยท 1 points ยท Posted at 10:10:39 on May 26, 2016 ยท (Permalink)
Any number with three digits where the two outer digits add up to the one in the middle is divisible by eleven, like 451.
[deleted] ยท 1 points ยท Posted at 10:15:10 on May 26, 2016 ยท (Permalink)
r=(theta) is a cool looking spiral
PenguinSub ยท 1 points ยท Posted at 10:22:58 on May 26, 2016 ยท (Permalink)
More of a history math fact, but when Pythagoras and his people found out there was such a thing as irrational numbers, they had people keep it a secret because it went against how they explained the cosmos. The first guy who spilled the beans? Yeah, he was sailed out to sea and then thrown overboard. The first martyr of mathematics. From "God created the Integers".
[deleted] ยท 1 points ยท Posted at 12:30:36 on May 26, 2016 ยท (Permalink)
This is more geometrical: The length of one side of a triangle is always smaller than the summation of the lengths of the other two sides. I've used this pretty simple and basic rule countless times on navigation (such as finding shortcuts).
Jeyman2000 ยท 1 points ยท Posted at 12:41:23 on May 26, 2016 ยท (Permalink)
The fact that if you write 3.14 on a piece of paper and hold it in front of a mirror, it spells PIE.
[deleted] ยท 1 points ยท Posted at 12:54:41 on May 26, 2016 ยท (Permalink)
I can graph tits now with quadratics :D
nightwind1 ยท 1 points ยท Posted at 13:07:41 on May 26, 2016 ยท (Permalink)
Apparently, Pythagoras threw a man named Hippapus off his boat after Hippapus baffled him with the 1, 1, root 2 triangle.
slacksauce ยท 1 points ยท Posted at 13:14:52 on May 26, 2016 ยท (Permalink)
If you randomize(shuffle) a regular deck of 52 playing cards, you can be certain that a deck has never been in that exact order before.
ViasiMeansPotato ยท 1 points ยท Posted at 14:22:17 on May 26, 2016 ยท (Permalink)
1/9801 is 0.000102030405060708...979899
newaccount20162 ยท 1 points ยท Posted at 14:56:59 on May 26, 2016 ยท (Permalink)
An expensive private college + a degree in photography = in debt for life, unless you have rich parents who coddle you.
Blade2587 ยท 1 points ยท Posted at 15:45:14 on May 26, 2016 ยท (Permalink)
ITT: things I have no chance of understanding. This is like high school all over again!
Qvar ยท 1 points ยท Posted at 17:23:31 on May 26, 2016 ยท (Permalink)
2 + 2 = 5
froghead123 ยท 1 points ยท Posted at 17:36:32 on May 26, 2016 ยท (Permalink)
Hi
footballclub1 ยท 1 points ยท Posted at 17:39:21 on May 26, 2016 ยท (Permalink)
algebra simplifing is my favourite maths fact
Mamokin ยท 1 points ยท Posted at 17:53:26 on May 26, 2016 ยท (Permalink)
It's all rules. Know the rules and you will be fine.
yolafaml ยท 1 points ยท Posted at 18:34:21 on May 26, 2016 ยท (Permalink)
That the probability of this question being asked is in any day is the same as you seeing a dog...
nupanick ยท 1 points ยท Posted at 18:48:19 on May 26, 2016 ยท (Permalink)
0.(9), the repeating decimal with all 9's to the right of the decimal point (forever), is equal to 1. There are lots and lots of good reasons for this, but to some people it "looks wrong" and it's fun to listen to them try to explain why.
DDekker ยท 1 points ยท Posted at 22:33:58 on May 26, 2016 ยท (Permalink)
Dont know why but I love the fact that square root 2 is irrational
MbreezyFly ยท 1 points ยท Posted at 16:17:10 on May 27, 2016 ยท (Permalink)
.j'm k.k.
zer0key123 ยท 1 points ยท Posted at 03:10:09 on May 29, 2016 ยท (Permalink)
To invert a digit's order of numbers in a multiplication table, you have to subtract 5, multiply by 10 and then add 0.5 to the digit.
Example:
1. 6*4=24
((6-5)*10+0.5)*4=10.5*4=42
2. 7*2=14
((7-5)*10+0.5)*2=20.5*4=41
Jacobak ยท 1 points ยท Posted at 19:04:51 on May 30, 2016 ยท (Permalink)
I'm so late BUT 18 is the only number who's digits add to be half of itself. Like, DAMN 18!
trumpetspieler ยท 1 points ยท Posted at 21:15:34 on May 31, 2016 ยท (Permalink)
There is only one smooth structure (up to diffeomorphism) on Euclidean space when the dimension is anything but 4, but when the dimension is 4 there are uncountable many distinct smooth structures which form a continuum.
Zortmannen ยท 1 points ยท Posted at 20:26:46 on June 22, 2016 ยท (Permalink)
If you add up every single positive number (ie 1+2+3+4+5+6+...) the result will be -1/12.
Video explaining this
๐๏ธ TheLoneWolf156 ยท 1 points ยท Posted at 20:34:45 on June 22, 2016 ยท (Permalink)
Bit late haha
webmistress105 ยท 1 points ยท Posted at 17:42:57 on July 8, 2016 ยท (Permalink)
Every prime greater than three is one away from a multiple of six.
callingallkids ยท 0 points ยท Posted at 14:51:18 on May 25, 2016 ยท (Permalink)
That in England, they say "maths" for some reason.
aperson7697 ยท 2 points ยท Posted at 16:35:26 on May 25, 2016 ยท (Permalink)
There is more than one mathematic ;)
veije ยท 2 points ยท Posted at 18:29:55 on May 25, 2016 ยท (Permalink)
Yeah, but two fricatives in a row is painful.
aperson7697 ยท -1 points ยท Posted at 18:52:51 on May 25, 2016 ยท (Permalink)
By its name I think one is
[deleted] ยท 0 points ยท Posted at 12:32:00 on May 25, 2016 ยท (Permalink)
An axiomatic system can't be completely self contained.
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
lordoftheshadows ยท 2 points ยท Posted at 14:23:53 on May 25, 2016 ยท (Permalink)
Not exactly.
PigSmoke ยท 1 points ยท Posted at 11:31:56 on May 25, 2016 ยท (Permalink)
Man, I just like singing that quadratic formula song we learned in math class. That's like the only thing I can remember because of that song - it is forever stuck in my head.
thasquidkid ยท 1 points ยท Posted at 13:16:23 on May 25, 2016 ยท (Permalink)
1=1
[deleted] ยท 1 points ยท Posted at 14:49:19 on May 25, 2016 ยท (Permalink)
Girls require time and money : Girls = timemoney. time is money: Time = money therefore: Girls = moneymoney = (money)2 Money is the root of all evil: Money = โEvil Therefore: Girls = (โEvil)2
Girls = Evil. QED
[deleted] ยท 1 points ยท Posted at 15:15:01 on May 25, 2016 ยท (Permalink)
[deleted]
hunkmonkey ยท 1 points ยท Posted at 01:34:21 on May 26, 2016 ยท (Permalink)
That in American English, we don't say "maths"; we just say "math" which serves for both singular and plural.
astalavista114 ยท 3 points ยท Posted at 05:07:22 on May 26, 2016 ยท (Permalink)
In English, we don't have singular "math", its just the field of mathematics, or maths for short. :D
CitizenCold ยท 1 points ยท Posted at 11:55:02 on May 25, 2016 ยท (Permalink)
1+1=2
Artillect ยท 1 points ยท Posted at 15:19:45 on May 25, 2016 ยท (Permalink)
The proof of this is incredibly interesting as well.
[deleted] ยท 1 points ยท Posted at 16:25:22 on May 25, 2016 ยท (Permalink)
What was it? 50-ish pages?
Artillect ยท 1 points ยท Posted at 16:39:06 on May 25, 2016 ยท (Permalink)
I think it may have been much longer
therock21 ยท 1 points ยท Posted at 13:05:54 on May 25, 2016 ยท (Permalink)
The fact that .99999999 repeating is the same number as 1. I just think it's cool
littlefoxtrot ยท 2 points ยท Posted at 13:24:48 on May 25, 2016 ยท (Permalink)
You can express the pattern as a geometric series which converges to 1
Xhinope ยท 1 points ยท Posted at 13:53:22 on May 25, 2016 ยท (Permalink)
If you were to take your veins and stretch them end-to-end... you would die!
KKYBoneAEA ยท 1 points ยท Posted at 13:55:47 on May 25, 2016 ยท (Permalink)
https://youtu.be/ELjEM4C2QSQ Disney's MathMagicLand literally blew my mind.
Sorry for formatting, on that toilet Reddit.
Xincmars ยท 1 points ยท Posted at 13:58:55 on May 25, 2016 ยท (Permalink)
12345679*9 = 111111111
TraviTheRabbi ยท 1 points ยท Posted at 14:43:33 on May 25, 2016 ยท (Permalink)
Also, 12345679*8 = 98765432
gamingonion ยท 1 points ยท Posted at 14:02:40 on May 25, 2016 ยท (Permalink)*
3x.33 repeating is equal to 1. Why? .33 repeating is equivalent to 1/3, so 3x1/3 is equal to one. This one drives me crazy.
go2kejdz ยท 1 points ยท Posted at 14:08:23 on May 25, 2016 ยท (Permalink)
0.33 then, or the result is 10
gamingonion ยท 1 points ยท Posted at 14:48:35 on May 25, 2016 ยท (Permalink)
you're right im a dumbass
Vallatus_Hydram ยท 1 points ยท Posted at 14:20:59 on May 25, 2016 ยท (Permalink)
the Fibonacci spiral. it's fucking crazy, a sequence of numbers that make a spiral that is commonly found in nature and shit. it goes like: 0 1 2 3 5 8 13 21 34 55 by adding the previous number to the current one. shits crazy bro
wrenchtosser ยท 1 points ยท Posted at 14:24:36 on May 25, 2016 ยท (Permalink)
2x9=18 1+8=9
3ร9=27 2+7=9
4ร9=36 3+6=9
5ร9=45 4+5=9
6ร9=54 5+4=9
7ร9=63 6+3=9
8ร9=72 7+2=9
9ร9=81 8+1=9
[deleted] ยท 1 points ยท Posted at 14:27:00 on May 25, 2016 ยท (Permalink)
Damn
[deleted] ยท 1 points ยท Posted at 14:28:39 on May 25, 2016 ยท (Permalink)
Nice meme
[deleted] ยท 1 points ยท Posted at 14:37:04 on May 25, 2016 ยท (Permalink)
"Maths" used to be called "math" in the USA up until like 4 years ago
Wassayingboourns ยท 1 points ยท Posted at 14:58:37 on May 25, 2016 ยท (Permalink)
It's not anymore? That bothers the shit out of me.
"Hey let's add another letter to something to waste time saying the exact same thing."
[deleted] ยท 1 points ยท Posted at 14:46:37 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 1 points ยท Posted at 15:33:54 on May 25, 2016 ยท (Permalink)
Not true.
gaggzi ยท 1 points ยท Posted at 14:53:34 on May 25, 2016 ยท (Permalink)
Gabriel's Horn : Spin the function 1/x around the x-axis, and make it infinitely long.
You would be able to fill the horn with a finite volume of paint. But it would require an infinite amount of paint to cover the surface area. Hence, you can fill it, but not paint it.
_Eerie ยท 1 points ยท Posted at 16:24:16 on May 25, 2016 ยท (Permalink)
I can't imagine how does it look like. Well, it is a horn. But how is it infinitely long but has volume?
Cyanide-- ยท 1 points ยท Posted at 14:55:21 on May 25, 2016 ยท (Permalink)
This one is incredibly lame, but it blew my mind when I was about 8 or so. I'm not sure how true it actually is, mind you.
0.99999999... = 1 By the logic that 0.333333... = 1/3, 0.66666666... = 2/3, and thus 3/3 would follow the trend being 0.9999999... however 3/3 reduced is one.
superDuperMP ยท 1 points ยท Posted at 14:58:18 on May 25, 2016 ยท (Permalink)
I'm going to get down-voted to hell for this, but any way you look at it bernie Sanders has lost the election to Clinton. She leads by 3 million more votes, over 250 pledged delegates (excluding supers), has won the majority of states and virtually all large states. Has won the majority of open primaries and has a more geographically diverse win. Even if you account for the caucuses, and give Bernie extra votes becuse of "closed" primaries, she would very likely still be leading at this point.
DaJanzk ยท 1 points ยท Posted at 14:59:31 on May 25, 2016 ยท (Permalink)
.9 repeating to infinity actually does equal 1.
ok so let n = .9 (w/vinculum)
assume 10n = 9.9 (w/vinculum)
subtract n from the 10n side (.9 with vinculum from the 9.9 side)
now you have 9n = 9
divide both by 9.
that gives you n = 1
since n also equals .9 repeating forever, 1=.99999999999999999999...
rysto89 ยท 1 points ยท Posted at 15:08:23 on May 25, 2016 ยท (Permalink)*
You can graph a 3-D cone with a curved profile that has a volume that converges to a real number, but has a surface area that diverges to infinity. In other words, you can fill this cone but never paint it. I think this concept is explained in Cal III EDIT: mixed up SA and volume. Apparently this is called Gabriel's Horn. Thanks to narcolepticasian
narcolepticasian ยท 2 points ยท Posted at 15:15:37 on May 25, 2016 ยท (Permalink)
I could be wrong so don't quote me on it, but didn't you get that backwards? It sounds like you're talking about Gabriel's horn, which has infinite surface area but finite volume. You get it by having 1 over x to a power that is greater than 1 (it might be equal to 1 also but I feel like that's not right) and then rotating that graph over the x axis. It's in Calc 2 and also something that really interested me.
Nicko265 ยท 1 points ยท Posted at 17:16:40 on May 25, 2016 ยท (Permalink)
It's also the same for fractal patterns. They repeat a continuously smaller pattern ad infinitum, this having infinite perimeter but a finite area. In a 3D fractal, this results in a finite volume but infinite surface area. Theoretically it would be impossible to paint, yet could actually be the size of a pine cone in volume.
Obviously, it's a moot point in real world because there is a hard limit of lowest size (atoms building said pattern), and thus there will be a point at which we can say the fractal pattern had ended and can work out the perimeter.
acc7x3 ยท 1 points ยท Posted at 15:09:34 on May 25, 2016 ยท (Permalink)
That using base 12 you can count to 144 using both hands.
Phalanx on hand 1 represents each number, Phalanx on hand 2 represents each 12. Using your thumbs as place holders.
sparklingbuttknuckle ยท 1 points ยท Posted at 15:10:33 on May 25, 2016 ยท (Permalink)
The Monty Hall Problem. It's my favorite because PhDs lost their shit:
HereHaveMyKid ยท 1 points ยท Posted at 15:16:23 on May 25, 2016 ยท (Permalink)
In addition to all of its other neat properties, each row of Pascal's triangle corresponds to a power of 11.
11row # - 1 = value at row #
So: row 1 = 110 = 1, row 2 = 111 = 1 1, and row 3 = 112 = 1 2 1
Obviously once you get to row 6 (1 5 10 10 5 1), this doesn't map directly to the actual number. But if you start from the rightmost digit (treating it as the ones place) and work your way to the left, the property still holds:
1(1) + 10(5) + 100(10) + 1,000(10) + 10,000(5) + 100,000(1) = 161,051 = 115 = 116-1
My discrete math professor sketched the outline of a proof of this property for me a few years back, but I'm embarrassed to say I forget the details.
[deleted] ยท 0 points ยท Posted at 15:19:21 on May 25, 2016 ยท (Permalink)
There is just as much "infinity" between 1 and 2 as there is between 1 and infinity.
[deleted] ยท 0 points ยท Posted at 15:38:32 on May 25, 2016 ยท (Permalink)
no way
WheresMyMoneyDenny ยท 1 points ยท Posted at 15:25:20 on May 25, 2016 ยท (Permalink)
55378008
Googunk ยท 1 points ยท Posted at 15:35:10 on May 25, 2016 ยท (Permalink)
If you perfectly shuffle a deck of cards 8 times, it will be in it's original configuration, as though you had never shuffled at all.
NsRhea ยท 1 points ยท Posted at 15:37:26 on May 25, 2016 ยท (Permalink)
I can't remember the exact numbers so I'm not sure I should even mention it but I think it's something like
If you stand in a room of 18 people there is a 50% chance that two people share a birthday.
[deleted] ยท 1 points ยท Posted at 15:52:46 on May 25, 2016 ยท (Permalink)
This is really counterintuitive untill you realise how many pairs of persons you can make with just 18 people.
aizen6 ยท 1 points ยท Posted at 15:37:27 on May 25, 2016 ยท (Permalink)
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Chickenwingbob ยท 1 points ยท Posted at 15:37:28 on May 25, 2016 ยท (Permalink)
You know they say all men are created equal. But you look at me and you look at Samoa Joe and you can see that statement is not true. See, normally if you go one on one with another wrestler, you got a 50-50 chance of winning. But I'm a genetic freak and I'm not normal. So you got a 25 per cent - at best - to beat me. And then you add Kurt Angle to the mix, your chances of winning drastically go down. You see, the three way at Sacrifice you got a 33 and 1/3 chance of winning. But I, I got a 66 and 2/3 chance of winning cause Kurt Angle knows he can't beat me and he's not even gonna try. So Samoa Joe, you take your 33 and 1/3 chance, minus my 25 per cent chance and you got an 8 and 1/3 chance of winning at Sacrifice. But then you take my 75 per cent chance of winning if it goes one on one and then add the 66 and 2/3 per cent chance, I got a 141 and 2/3 chance of winning at Sacrifice. See Joe, the numbers don't lie and they spell disaster for you at Sacrifice.
dezradeath ยท 1 points ยท Posted at 15:39:00 on May 25, 2016 ยท (Permalink)
You can add zero, subtract zero, and multiply by zero. But if you divide by zero the unholy demons of academia will rip your atoms apart and step in your potato salad and then the universe will implode.
Iammackers ยท 1 points ยท Posted at 16:22:16 on May 25, 2016 ยท (Permalink)
My professor did it and I am still alive
gtswagboy ยท 1 points ยท Posted at 15:55:09 on May 25, 2016 ยท (Permalink)
This thread hurts my Brain.
lunarman55 ยท 1 points ยท Posted at 16:09:36 on May 25, 2016 ยท (Permalink)
The sum of every whole number 1 to infinity = -1/12 Sum(N, N=1, N=Infinity)
I don't really understand why...I don't have a PhD in maths, but the guys in this video do!
https://www.youtube.com/watch?v=w-I6XTVZXww
sumostar ยท 1 points ยท Posted at 16:15:25 on May 25, 2016 ยท (Permalink)
This is my fave fact too! The sum of all positive integers from 1 to infinity equals -1/12.
It's not too hard to understand when it's broken down; it's a play on math theorems. It manipulates a couple different number series to come to the -1/12 conclusion. So interesting doe. Maths, man. Maths.
[deleted] ยท 1 points ยท Posted at 16:16:09 on May 25, 2016 ยท (Permalink)
That 50% of all statistics are made up on the spot. That there are 10 types of people. Those that understand Bianary and those that dont.
za419 ยท 1 points ยท Posted at 16:17:28 on May 25, 2016 ยท (Permalink)
And those who weren't expecting a base 3 joke
[deleted] ยท 2 points ยท Posted at 17:00:20 on May 25, 2016 ยท (Permalink)
Get a single and run for home. that... that was a nerd joke too! ha! BOOM!
[deleted] ยท 1 points ยท Posted at 12:30:22 on May 26, 2016 ยท (Permalink)
Them's are 3rd class citizens...
BakedAnswer ยท 1 points ยท Posted at 16:25:32 on May 25, 2016 ยท (Permalink)*
Nobody has come up with a formula to find more prime numbers yet, and there is a million dollars for you if you manage to put one up.
jjrich13 ยท 1 points ยท Posted at 16:37:50 on May 25, 2016 ยท (Permalink)
The sum of the infinite series: 1 + 2 + 3 + 4 + 5 .... is equal to -1/12. Makes no intuitive sense at all.
Video explaining it: https://www.youtube.com/watch?v=w-I6XTVZXww
More in depth video explaining it (more in depth math): https://www.youtube.com/watch?v=E-d9mgo8FGk
Video explaining it more conceptually and why it is useful: https://www.youtube.com/watch?v=0Oazb7IWzbA
NanchoMan ยท 1 points ยท Posted at 16:41:25 on May 25, 2016 ยท (Permalink)
My favorite is
1 + 12 + 24 + 36 + 48 + 60 + ... = 0
That comes from a manipulation of an already insane math theory.
ledzelda9 ยท 1 points ยท Posted at 16:50:14 on May 25, 2016 ยท (Permalink)
There are different sizes of infinity.
For example, from 0 to infinity is a smaller infinity than from negative infinity to positive infinity. There are other types that are bigger than that too.
Cannon_Drill ยท 1 points ยท Posted at 16:58:48 on May 25, 2016 ยท (Permalink)
0.9999... (.9 repeating) is equal to EXACTLY 1. It's not "almost 1." It doesn't "approach 1." It doesn't approach anything! It IS 1. I wasted hours arguing with an idiot on Facebook about this.
Guitar115 ยท 1 points ยท Posted at 17:01:07 on May 25, 2016 ยท (Permalink)
That in part of the world people call it maths. It sounds so cool to me since people around me say math.
Idiotnextdoor_2 ยท 2 points ยท Posted at 17:28:09 on May 25, 2016 ยท (Permalink)
Read in another comment that mathematics is correctly abbreviated to Math and not Maths.
E.g. we say econ. Instead of Economics.
intensely_human ยท 1 points ยท Posted at 17:07:47 on May 25, 2016 ยท (Permalink)
My favorite maths fact: "Math" is bizarrely called "maths" in some ancient back-woodsy parts of the world that never would have invented jazz if it jumped up and bit them in the ass.
Minotaurius ยท 1 points ยท Posted at 17:14:25 on May 25, 2016 ยท (Permalink)
That 6 was afraid of 7, because 7 ate 9
Blewedup ยท 1 points ยท Posted at 17:15:11 on May 25, 2016 ยท (Permalink)
that it's actually called "math."
milosbelic ยท 1 points ยท Posted at 17:15:17 on May 25, 2016 ยท (Permalink)
If you fold a piece of paper in half 42 times you will reach the Moon.
Iminterested6 ยท 1 points ยท Posted at 17:16:25 on May 25, 2016 ยท (Permalink)
Too British; does not compute
qwicksilver6 ยท 1 points ยท Posted at 17:22:33 on May 25, 2016 ยท (Permalink)
My favorite fact: The plural of Math is Math
subavairpine ยท 1 points ยท Posted at 17:29:10 on May 25, 2016 ยท (Permalink)
The Monty Hall Problem is one of my favorites... but probably only because I got it, while at least half of my Prob & Stat class didn't. It took me a bit to grasp it, to be honest, but once i got it, it was like, duh!
SQLDave ยท 1 points ยท Posted at 17:34:54 on May 25, 2016 ยท (Permalink)
What let me finally "get" it and what I use to explain it to people (mostly successfully) is to change the problem from 3 doors to 100. The key then is that Monty doesn't open ONE door, he opens ALL BUT ONE door (which in a 3-door game is the same thing). Suddenly they realize that the prize almost HAS to be behind the door Monty did not open.
killer3james ยท 1 points ยท Posted at 17:30:53 on May 25, 2016 ยท (Permalink)
1+1=2
Solomanrosenburg ยท 1 points ยท Posted at 17:33:07 on May 25, 2016 ยท (Permalink)
That it is called MATH.
brotoes ยท 1 points ยท Posted at 17:43:34 on May 25, 2016 ยท (Permalink)
Unless you're british
flop_shot ยท 1 points ยท Posted at 17:41:24 on May 25, 2016 ยท (Permalink)
that 1+2+3+4+... = -1/12
xLockeddown ยท 1 points ยท Posted at 17:49:50 on May 25, 2016 ยท (Permalink)
Folding a standard piece of paper 20 times will make it taller then Mt. Everest. Fold it 42 times to get to the moon and 103 times to be as tall as the universe.
RetroDave ยท 1 points ยท Posted at 17:50:11 on May 25, 2016 ยท (Permalink)
The fact that outside of the United States it is called "Maths" in this context instead of "Math".
AZUSO ยท 1 points ยท Posted at 18:03:30 on May 25, 2016 ยท (Permalink)
Ramanujan summation 1+2+3+4+5+6+7+......inf=-1/12
MrFlibble81 ยท 1 points ยท Posted at 18:05:58 on May 25, 2016 ยท (Permalink)
If you were to take all of the veins from your body and lay them end to end, you would die.
analest-analyst ยท 1 points ยท Posted at 18:22:00 on May 25, 2016 ยท (Permalink)
The blue crystals have higher purity and yield.
Oh. "Math".
G3POh ยท 1 points ยท Posted at 18:31:48 on May 25, 2016 ยท (Permalink)
Don't know if this applies but i was amazed when i heard that story about a rich man offering a poor man a job at whatever salary he desired.
So the poor man asked for a penny the first day of work and for the rich man to double that everyday for a month, comes out a millionaire or something like that at the end of the month.
hyker1811 ยท 1 points ยท Posted at 18:45:52 on May 25, 2016 ยท (Permalink)
If you have a pizza with radius "z" and thickness "a" then its volume is pi * z * z * a.
NO831 ยท 1 points ยท Posted at 18:48:19 on May 25, 2016 ยท (Permalink)
0/0 could either be 0, 1, or undefined
Faildice ยท 1 points ยท Posted at 19:29:18 on May 25, 2016 ยท (Permalink)
The fact that there are as many even numbers as whole numbers is really interesting. Because there are both an infinite number of even number and an infinite number of whole number, there are just as many even numbers as whole.
infinity/2 = infinity
[deleted] ยท 1 points ยท Posted at 20:02:49 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is -1/12.
TubaJesus ยท 1 points ยท Posted at 20:06:22 on May 25, 2016 ยท (Permalink)
The fact that it's actually math and not maths
[deleted] ยท 1 points ยท Posted at 20:47:51 on May 25, 2016 ยท (Permalink)
There are an infinite number of infinities.
previsualconsent ยท 1 points ยท Posted at 22:02:09 on May 25, 2016 ยท (Permalink)
If I give you half of mine and you give me half of yours, we have the same amount.
Lord_Rob ยท 1 points ยท Posted at 22:15:26 on May 25, 2016 ยท (Permalink)
That Pi, as an infinite non-repeating number, contains somewhere within it (encoded somewhere in it in ASCII or another format of your choosing), the unbroken narrative of your life.
Everything that happens to you, everyone you meet, everything you achieve or fail to do, is right there.
loptthetreacherous ยท 1 points ยท Posted at 22:47:49 on May 25, 2016 ยท (Permalink)
There's no reason to believe that. Infinite non-repeating numbers don't necessarily contain every possible string of numbers possible.
For example:
0.123456789112233445566778899111222333444555666777888999 etc. is an infinite, non-repeating number that will never have 13 in it, or any string of numbers exept for xx or x(x+1)
Lord_Rob ยท 2 points ยท Posted at 06:51:45 on May 26, 2016 ยท (Permalink)
Huh. Good point.
overconvergent ยท 1 points ยท Posted at 23:01:03 on May 25, 2016 ยท (Permalink)
Pi is finite. The decimal expansion of pi is infinite. And no, this does not mean that the decimal expansion of pi contains every finite string of decimal digits. This is conjectured to be true, but has not been proven.
calichomp ยท 1 points ยท Posted at 22:21:02 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12.
Seriously.
Google it.
lazyl ยท 1 points ยท Posted at 22:36:49 on May 25, 2016 ยท (Permalink)*
https://plus.maths.org/content/infinity-or-just-112
Edit: Actually, that guys math seems a little sketchy to me. I don't think you can just append something on to the end of a divergent set the way he does when trying to disprove 'the trick'.
overconvergent ยท 1 points ยท Posted at 23:00:02 on May 25, 2016 ยท (Permalink)
This is not true.
calichomp ยท 1 points ยท Posted at 23:03:38 on May 25, 2016 ยท (Permalink)
Based on?
overconvergent ยท 1 points ยท Posted at 23:04:33 on May 25, 2016 ยท (Permalink)
Based on math. The series 1+2+3+4+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
brassmonkey4288 ยท 1 points ยท Posted at 22:28:18 on May 25, 2016 ยท (Permalink)
That it's called math.
onequbit ยท 1 points ยท Posted at 22:37:08 on May 25, 2016 ยท (Permalink)
There is more infinity counting between integers than counting the integers themselves.
thundertool ยท 1 points ยท Posted at 22:55:16 on May 25, 2016 ยท (Permalink)
The S is silent.
[deleted] ยท 1 points ยท Posted at 23:36:10 on May 25, 2016 ยท (Permalink)
Integers really don't exist except for counting. Everything else is rounded.
1lb doesn't exist.
1ft doesn't exist.
spartanburt ยท 1 points ยท Posted at 03:14:22 on May 26, 2016 ยท (Permalink)
Ugh, how'd you come up with this nonsense?
[deleted] ยท 1 points ยท Posted at 06:12:43 on May 26, 2016 ยท (Permalink)
logic, you?
spartanburt ยท 1 points ยท Posted at 10:31:54 on May 26, 2016 ยท (Permalink)
Ok, that's what I figured. It's just your made up interpretation of what certain words mean. Neither math, or a fact. Just semantics.
[deleted] ยท 1 points ยท Posted at 14:28:58 on May 26, 2016 ยท (Permalink)
Just stating round-off happens everywhere and there is no way to get exact integers. Or to be 100% confident in them. Not an "interpretation" its a fact. This is why we have a standard for everything, even constant have uncertainty. The semantics are important and not to be glossed over.
cahser11 ยท 1 points ยท Posted at 23:49:07 on May 25, 2016 ยท (Permalink)
The fact that the English spell it maths.
XperiMental21 ยท 1 points ยท Posted at 23:58:00 on May 25, 2016 ยท (Permalink)
That British people call it maths. Why is it plural?
spartanburt ยท 1 points ยท Posted at 03:08:02 on May 26, 2016 ยท (Permalink)
MathematicS
[deleted] ยท 1 points ยท Posted at 00:41:30 on May 26, 2016 ยท (Permalink)
Let's say you have three doors to choose. One of them has a car behind it.
If you choose a door, and then told the car is not behind one of the remaining two doors you should change your answer 66% of the time I think.
So for example left right and middle door. I pick the left door, and then I'm told the car is not behind the middle door, there is a 66% chance I should change my answer to the right door.
Edit: quick google I learned it's called the Monty hall problem, https://en.m.wikipedia.org/wiki/Monty_Hall_problem
Strangely_quarky ยท 1 points ยท Posted at 00:55:37 on May 26, 2016 ยท (Permalink)
TL;DR - every answer from last weeks' thread, reposted.
pleasejumpoffabridge ยท 1 points ยท Posted at 01:11:20 on May 26, 2016 ยท (Permalink)
There must be a diameter of the earth such that the two end points of the diameter have the same temperature.
starwarsfreak314 ยท 1 points ยท Posted at 01:37:41 on May 26, 2016 ยท (Permalink)
. 9999999 repeating equals 1
Proof:
1/3=.3333333
2/3=.6666666
1/3 + 2/3 = 1
.33333+.6666666=.9999999
Superdorps ยท 1 points ยท Posted at 06:46:14 on May 26, 2016 ยท (Permalink)
Last time I checked, .33333 + .6666666 = .9999966. Your move, atheists.
1UPZ_ ยท 1 points ยท Posted at 01:39:19 on May 26, 2016 ยท (Permalink)
There's an infinite amount of numbers between 0 and 1.
lets-get-dangerous ยท 1 points ยท Posted at 01:58:50 on May 26, 2016 ยท (Permalink)
ii is a real number
dadumk ยท 1 points ยท Posted at 03:21:02 on May 26, 2016 ยท (Permalink)*
Fact: "Maths" is impossible to say, and yet the British insist on saying it.
astalavista114 ยท 2 points ยท Posted at 04:39:29 on May 26, 2016 ยท (Permalink)
Which just goes to prove that it isn't impossible to say :D
Australian's do it as well. Only in theirs, they only have one adjective.
EuniceGutierrez ยท 2 points ยท Posted at 11:41:49 on May 26, 2016 ยท (Permalink)
this is to a greater degree a measurements certainty, however in the event that there is a 1 in x possibility of something occurrence, in x endeavors, for substantial numbers more than 50 or thereabouts, the probability of it incident is around 63%
1-(1-1/x)x
For instance, if there's a 1 in 10,000 shot of getting hit by a meteor in the event that you go outside, on the off chance that you go outside 10,000 times, you have a 63% possibility of getting hit with a meteor sooner or later. In the event that there's a 1 in a million shot of winning the lottery and you purchase a million (arbitrary) lottery tickets, you have a 63% possibility of winning.
Alter: for the lottery illustration, the watchword is arbitrary - no doubt in the event that you deliberately purchase each conceivable mix then it's 100%. In the event that you purchase one ticket in a million distinct lotteries, or a million haphazardly produced tickets for any one in a million lottery, then it's 63%.
DumbBullDoor ยท -25 points ยท Posted at 11:45:13 on May 25, 2016 ยท (Permalink)
Fact: in america we just call it math.
[deleted] ยท 15 points ยท Posted at 17:49:41 on May 25, 2016 ยท (Permalink)
whose language are you speaking, burger?
eddie1975 ยท 3 points ยท Posted at 22:11:05 on May 25, 2016 ยท (Permalink)
1 Math + 1 Math = 2 Maths
Decalance ยท 24 points ยท Posted at 14:10:25 on May 25, 2016 ยท (Permalink)
Fact: the rest of the world doesn't care
speedisavirus ยท -26 points ยท Posted at 16:01:31 on May 25, 2016 ยท (Permalink)
Fact the rest of the world needs to learn how to properly pluralize words and not to when there isn't a plural.
Decalance ยท 16 points ยท Posted at 17:03:19 on May 25, 2016 ยท (Permalink)
Tell me, who decided this rule?
speedisavirus ยท -27 points ยท Posted at 17:11:03 on May 25, 2016 ยท (Permalink)
Linguists? It's a mass noun. It can't be counted. Mathematics is a singular. Hence the abbreviation should not end in an S as if it's plural.
Decalance ยท 14 points ยท Posted at 17:25:36 on May 25, 2016 ยท (Permalink)
First of all, your point is wrong, and you're stupid.
Second of all, following your warped logic, well, why isn't it plural? There are different mathematics, algebra, calc, geometry.
speedisavirus ยท -25 points ยท Posted at 18:00:27 on May 25, 2016 ยท (Permalink)
Because it's a mass noun. Mathematics is a singular thing. Linguistics agree that it is a mass noun. There are not multiple mathematics. There is one mathematics and there is one algebra and one geometry and one calculus. There are descriptors of each but each is singular.
Decalance ยท 18 points ยท Posted at 18:17:10 on May 25, 2016 ยท (Permalink)
Alright, so back to the first argument, you're stupid.
I'll explain why : linguists don't dictate how language works, they merely study it. People do. Language is primarily a way of communication, and we strive to optimize it all the time, be it by simplifying it or by organizing it. There are two branches, descriptivists and prescriptivists. The first ones think that if a majority uses a certain word to describe something, then that is the meaning of the word. The second ones believe in choosing a meaning and sticking by it. The only problem is that language evolves all the time, favouring the first branch.
And really dude ? A whole country is wrong and you're right ? You can't be this deluded
speedisavirus ยท -4 points ยท Posted at 18:36:44 on May 25, 2016 ยท (Permalink)
Back to my original argument there is an entire field dedicated to the study and research of language and it's evolution and they are calling you retarded.
NeilZod ยท 18 points ยท Posted at 20:12:38 on May 25, 2016 ยท (Permalink)
Here's the thing: since at least the end of WWII, the US has been sending all sorts of things to the UK to try to get them to speak like Americans; things like movies, TV shows, and even Ruby Wax. During that time, the Brits have responded by continuing to speak like Brits while they retaliated by exporting Piers Morgan. You might even say the Brits are responding as if they invented the language.
So where do the linguists fit in? They'll happily record what the Brits are doing with their English and what the Americans are doing with their English. Those linguists are diligently working to identify the rules that everyone is following, and they're interested in whether we are following different rules.
So how does that help us here? Linguists know that Brits shorten mathematics to maths while Americans shorten it to math. Linguists would likely advise you to write math in American English and maths in British English. You may well ask what advice linguists would give to people writing on the Internet. I suspect that they won't tell you what to do - instead, they will wait to see what all of us decide on and then try to figure out why we did it that way.
But you really should never expect a linguist to deride someone for using their native English.
Decalance ยท 10 points ยท Posted at 18:43:45 on May 25, 2016 ยท (Permalink)
I don't think so, they research it, they don't say it's right or wrong.
the-postminimalist ยท 8 points ยท Posted at 03:27:28 on May 26, 2016 ยท (Permalink)
I'm a linguistics minor.
No linguist ever says one dialect is wrong and the other is right. English majors might, but not linguists.
When I say "English majors", I mean, like, 3% of them. I'm sure the other 97% agrees that other dialects exist and have their own rules.
ProllyJustWantsKarma ยท 6 points ยท Posted at 05:41:03 on May 26, 2016 ยท (Permalink)
Well, you got linked on /r/badlinguistics, so I think it's safe to say you were wrong about whatever you seem to think the field of linguistics is.
Lockjaw7130 ยท 3 points ยท Posted at 19:51:28 on May 25, 2016 ยท (Permalink)
Uuuf, that's almost r/badlinguistics material. Sure, Linguists decided a rule for a language. Man, prescriptivism is alive and well, I guess.
TheNaughtyMonkey ยท -9 points ยท Posted at 17:22:32 on May 25, 2016 ยท (Permalink)
I just bought a mathematic yesterday. Got a real good deal on it.
In England, they spell things strangely, sometimes. For instance, they spell "different" W-r-o-n-g.
onlyjoking ยท 5 points ยท Posted at 21:58:50 on May 25, 2016 ยท (Permalink)
Wait do you guys call it mathematic? Because maths is an abbreviation of mathematics, hence the 's'. Unless I'm misunderstanding your point completely (quite possible).
Lunnes ยท 0 points ยท Posted at 15:28:50 on May 27, 2016 ยท (Permalink)
It's always funny how Americans try to criticize foreigners because of a grammatical mistake, yet most of them can only speak English. Try speaking four languages and see if you don't make small mistakes sometimes.
rrealnigga ยท -11 points ยท Posted at 16:40:08 on May 25, 2016 ยท (Permalink)
English spelling is retarded.
Flyberius ยท 5 points ยท Posted at 09:36:22 on May 26, 2016 ยท (Permalink)
No, English is spelling is English. American spelling is retarded.
rrealnigga ยท -4 points ยท Posted at 10:35:32 on May 26, 2016 ยท (Permalink)
English language spelling is retarded in general.
22fortox ยท 2 points ยท Posted at 17:14:07 on May 26, 2016 ยท (Permalink)
I'm English and I agree with you. It would be nice if words were spelt phonetically.
rrealnigga ยท 2 points ยท Posted at 18:00:15 on May 26, 2016 ยท (Permalink)
Yes, like German and Arabic. It's a fact that English spelling is fucked up despite what proud idiots think.
[deleted] ยท -8 points ยท Posted at 02:06:27 on May 26, 2016 ยท (Permalink)
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Decalance ยท 6 points ยท Posted at 05:03:57 on May 26, 2016 ยท (Permalink)
Like at your world series in a sport only you play ?
[deleted] ยท -10 points ยท Posted at 05:13:23 on May 26, 2016 ยท (Permalink)
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Decalance ยท 7 points ยท Posted at 05:14:26 on May 26, 2016 ยท (Permalink)
Hahahaha
[deleted] ยท -8 points ยท Posted at 05:22:30 on May 26, 2016 ยท (Permalink)
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Decalance ยท 7 points ยท Posted at 05:30:42 on May 26, 2016 ยท (Permalink)
You're even more retarded than i thought. What do you think is the meaning of literally ?
[deleted] ยท -1 points ยท Posted at 05:32:20 on May 26, 2016 ยท (Permalink)
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Decalance ยท 5 points ยท Posted at 08:08:27 on May 26, 2016 ยท (Permalink)
I think if your parents could have seen you right now when you were conceived they would have aborted you.
[deleted] ยท 1 points ยท Posted at 05:27:20 on May 27, 2016 ยท (Permalink)*
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[deleted] ยท -1 points ยท Posted at 19:56:38 on May 27, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 22:47:00 on May 27, 2016 ยท (Permalink)*
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[deleted] ยท 0 points ยท Posted at 23:15:05 on May 27, 2016 ยท (Permalink)
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[deleted] ยท 0 points ยท Posted at 02:16:06 on May 28, 2016 ยท (Permalink)*
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MattyOlyOi ยท -7 points ยท Posted at 22:45:55 on May 25, 2016 ยท (Permalink)
Do Queen's subjects also study "trigonometries?" and "algebras?"
RoadieRich ยท 9 points ยท Posted at 23:22:42 on May 25, 2016 ยท (Permalink)
Yes, we have basic algebra, abstract algebra, and boolean algebra to name a few. Don't you?
MattyOlyOi ยท -6 points ยท Posted at 23:33:03 on May 25, 2016 ยท (Permalink)
Don't you mean basics algebras? and abstracts algebras? and booleans algebras?
treebard127 ยท 6 points ยท Posted at 23:54:29 on May 25, 2016 ยท (Permalink)
Oh no. Honey, I don't think you know how that works. You're digging a hole. Or is that holes?
MattyOlyOi ยท -4 points ยท Posted at 00:06:59 on May 26, 2016 ยท (Permalink)
It's "diggings"
Luvmuchine ยท 1 points ยท Posted at 14:46:03 on May 25, 2016 ยท (Permalink)
Math is made of numbers. And that's a fact. For your health.
YouMayHaveSeenMeOnTV ยท -2 points ยท Posted at 15:06:15 on May 25, 2016 ยท (Permalink)
That you silly British people call it maths instead of the way better math.
(Bracing for impact.)
[deleted] ยท -1 points ยท Posted at 18:13:03 on May 25, 2016 ยท (Permalink)
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overconvergent ยท 4 points ยท Posted at 22:42:36 on May 25, 2016 ยท (Permalink)
This is not true.
jevans102 ยท 1 points ยท Posted at 23:22:16 on May 25, 2016 ยท (Permalink)
Relevant username.
Yeah I don't get it either .
MasterPerry ยท -2 points ยท Posted at 09:56:46 on May 26, 2016 ยท (Permalink)
It is, somehow https://plus.maths.org/content/infinity-or-just-112
overconvergent ยท 1 points ยท Posted at 15:08:47 on May 26, 2016 ยท (Permalink)
No, it is not true. The series 1+2+3+... diverges. There are other ways of associating values to infinite series, and a few of these ways associate the value -1/12 with the series 1+2+3+... But this does not mean that 1+2+3+...=-1/12.
TerriblePrompts ยท -8 points ยท Posted at 13:04:18 on May 25, 2016 ยท (Permalink)
The sum of all all positive integers can be proven to be:
1 + 2 + 3 + 4 + 5 + 6 + 7 +... = -1/12
It only works as long as you treat it as an approximation to an infinite sum, but it is still valid math.
bearsnchairs ยท 9 points ยท Posted at 13:48:47 on May 25, 2016 ยท (Permalink)
You almost qualified it completely, but no the sum of all positive integers is trivially divergent. The Ramanujan sum of those integers has that value.
galacticdick ยท 5 points ยท Posted at 14:14:05 on May 25, 2016 ยท (Permalink)
No, no it's not. The formula used is assuming a geometric progression where the difference between the numbers is strictly less than one. It is not.
antibubbles ยท 1 points ยท Posted at 18:19:15 on May 25, 2016 ยท (Permalink)*
wubalubadubdub What is this?
[deleted] ยท 2 points ยท Posted at 13:49:24 on May 25, 2016 ยท (Permalink)
I remember learning about this but I forget how. Can you give an explanation why?
[deleted] ยท 0 points ยท Posted at 14:11:41 on May 25, 2016 ยท (Permalink)
This is one of the better videos explaining why:
https://www.youtube.com/watch?v=jcKRGpMiVTw
WikiWantsYourPics ยท 0 points ยท Posted at 14:21:05 on May 25, 2016 ยท (Permalink)
Numberphile has some very nice videos on the topic:
https://www.youtube.com/watch?v=w-I6XTVZXww
https://www.youtube.com/watch?v=E-d9mgo8FGk
rrealnigga ยท 4 points ยท Posted at 16:40:57 on May 25, 2016 ยท (Permalink)
That's horseshit
bearsnchairs ยท 3 points ยท Posted at 01:35:47 on May 26, 2016 ยท (Permalink)
It is horse shit,, the sum of all natural numbers is undefined.
The Ramanujam sum, or the value of the Riemann zeta function for this series is -1/12 which can be found through some manipulation.
jywn4679 ยท 3 points ยท Posted at 14:14:11 on May 25, 2016 ยท (Permalink)
Not really, the sum is divergent to infinity. It's fairly easy to prove so. Also it is a (relatively trivial) theorem in analysis that a series of nonnegative terms must (if it converges at all) converge to a nonnegative number.
maghfira ยท -2 points ยท Posted at 13:29:40 on May 25, 2016 ยท (Permalink)
Came here to say this. I love this one.
RonyTheTiger ยท -2 points ยท Posted at 13:01:45 on May 25, 2016 ยท (Permalink)
In the right love triangle, my dick is the hypotenuse.
[deleted] ยท -6 points ยท Posted at 15:38:16 on May 25, 2016 ยท (Permalink)*
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[deleted] ยท 0 points ยท Posted at 17:52:35 on May 25, 2016 ยท (Permalink)
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JanEric1 ยท 1 points ยท Posted at 10:36:17 on May 26, 2016 ยท (Permalink)
the sum is not -1/12, the series diverges
baldspacemarine ยท 0 points ยท Posted at 20:42:40 on May 25, 2016 ยท (Permalink)
It's "math" and I would commit genocide to enforce this fact. "Maths" sounds so stupid
filippo333 ยท 2 points ยท Posted at 20:45:51 on May 25, 2016 ยท (Permalink)*
In the UK nobody, honestly I've never once heard a single person say "Math" ever in my life. Only Americans on the internet.
Interfaced84 ยท 2 points ยท Posted at 21:02:54 on May 25, 2016 ยท (Permalink)
It's not Mathematic, it's mathematicS.
mrcydonia ยท 2 points ยท Posted at 00:32:30 on May 26, 2016 ยท (Permalink)
Why do you say sport instead of sports? Huh? Huh?
Interfaced84 ยท 0 points ยท Posted at 22:20:14 on May 26, 2016 ยท (Permalink)
It's not the same at all, but I'm not here to teach you English.
[deleted] ยท -11 points ยท Posted at 11:41:40 on May 25, 2016 ยท (Permalink)*
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Kvothealar ยท 8 points ยท Posted at 12:28:52 on May 25, 2016 ยท (Permalink)
This is the reason I hate numberphile with a burning passion.
NE_master ยท 8 points ยท Posted at 11:57:13 on May 25, 2016 ยท (Permalink)
It's not. Numberphile tricked you. https://plus.maths.org/content/infinity-or-just-112
TheSemiTallest ยท -1 points ยท Posted at 13:34:35 on May 25, 2016 ยท (Permalink)
This leads to an interesting question: Which maths brain do you trust more, Ramanujan and bunches of other mathematicians, or the author of this article? Personally, I'm inclined to side with Ramanujan et al.
bearsnchairs ยท 3 points ยท Posted at 13:51:40 on May 25, 2016 ยท (Permalink)
Ramanujan is right, but this person is wrong in saying that sum is anything but divergent and even Ramanujan would agree.
You need to specify that the Ramanujan sum has that value.
jywn4679 ยท 3 points ยท Posted at 14:15:49 on May 25, 2016 ยท (Permalink)
No sane mathematician claims that the sum of all natural numbers is -1/12. In some situations it makes sense to assign it that value, but under the normal definition of infinite sum it is obviously not equal to -1/12. It isn't difficult to prove this.
redditsoaddicting ยท -8 points ยท Posted at 12:35:38 on May 25, 2016 ยท (Permalink)
This is what you get when you go outside the "normal" realm of Mathematics and accept something that we deem impossible by regular standards, similarly to how we accepted that i2 = -1 and continued from there to get a whole bunch of useful complex stuff.
ERRORMONSTER ยท -6 points ยท Posted at 12:30:18 on May 25, 2016 ยท (Permalink)
This one blows my mind. The sum of natural numbers is -1/12. What the hell.
Wikipedia
Numberphile
whatIsThisBullCrap ยท 6 points ยท Posted at 13:39:27 on May 25, 2016 ยท (Permalink)
It's not. The sum diverges to infinity, as one would expect. Using zeta functions you can replace the sum with -1/12 but in most contexts it doesn't make any sense
ERRORMONSTER ยท -7 points ยท Posted at 14:19:36 on May 25, 2016 ยท (Permalink)*
The sum is -1/12. You need not use zeta functions. Using basic algebra and substitution you can show that. Watch the video I linked or go through the wiki article.
A simpler proof is that 1 + 2 + 4 + 8 + ... = -1.
Everything in that proof is mathematically legal
Edit: I'm not saying if you add up all positive numbers you'll get -1/12. I'm saying you can prove that the sum is equal to -1/12.
whatIsThisBullCrap ยท 8 points ยท Posted at 14:30:38 on May 25, 2016 ยท (Permalink)
No its not. You can't line up divergent infinite sums like that and start removing terms. It doesn't make sense.
Someone else posted this really simple proof that the sum is not -1/12 in response to another comment: https://www.reddit.com/r/AskReddit/comments/4kz3di/z/d3izyg3
ERRORMONSTER ยท 1 points ยท Posted at 15:59:04 on May 25, 2016 ยท (Permalink)
Where did I remove terms? I'd really like to know because claims that the sum of whole numbers is finite piss me off
lordoftheshadows ยท 4 points ยท Posted at 16:27:25 on May 25, 2016 ยท (Permalink)
You didn't remove numbers you changed the order and scale. When you multiplied by two you screwed it up. But that's not really the point. You can't do addition as you normally would with infinity.
ERRORMONSTER ยท 1 points ยท Posted at 18:04:32 on May 25, 2016 ยท (Permalink)
Wait wait wait. Am I not allowed to multiply series by 2? That changes the scale, after all.
bearsnchairs ยท 1 points ยท Posted at 19:05:30 on May 25, 2016 ยท (Permalink)
You can with a convergent series, you can't expect to multiply a divergent series by 2 and get consistent math.
[deleted] ยท 0 points ยท Posted at 20:26:11 on May 25, 2016 ยท (Permalink)*
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bearsnchairs ยท 2 points ยท Posted at 20:33:27 on May 25, 2016 ยท (Permalink)
You can in a series, just not every series. Convergent series have a finite value. Divergent series tend towards infinity and you can't just multiply infinities. You should go to the askamathematician subreddit for a detailed answer.
[deleted] ยท 0 points ยท Posted at 20:51:38 on May 25, 2016 ยท (Permalink)*
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jywn4679 ยท 3 points ยท Posted at 23:30:14 on May 25, 2016 ยท (Permalink)
There is no inconsistency. Multiplication is defined on real numbers, and in general series are NOT real numbers, they are just series. In the case of convergent series then they can been seen as real numbers, which allows us to multiply and add them. But divergent series cannot been seen as real numbers, so you cannot multiply or add them.
ERRORMONSTER ยท 0 points ยท Posted at 00:11:05 on May 26, 2016 ยท (Permalink)
But all multiplication can be defined as a series.
We do multiplication on numbers that aren't real... That's the only reason you're typing this message to me (AC electricity.) Unless you're telling me you can add real numbers and get a category of non-real numbers. That seems super sketchy as well.
jywn4679 ยท 3 points ยท Posted at 00:15:10 on May 26, 2016 ยท (Permalink)
We do multiplication on things that aren't real numbers. In the case of complex numbers we are lucky that multiplication works out fine. In fact it is nearly identical to how it works on the real numbers.
However in the case of series it is much harder to suitably define multiplication and addition in a consistent way, and to show what rules it follows. Using only addition and multiplication of real numbers, how do you define multiplication and addition of series?
What I'm asking is, given to series A=sum of a_i and B=sum of b_i, what is A+B? If c is some real number, what is cA? You could also ask what AB is, but you never multiplied two series together in your proof so it isn't needed.
ERRORMONSTER ยท 1 points ยท Posted at 00:25:35 on May 26, 2016 ยท (Permalink)
I'm not sure why the sum of two series is unclear. Is it supposed to be something other than the sums of the individual series? Sums are defined as term by term addition, and addition is associative, so you can combine the series term by term, assuming they cross the same space (1 to 10 and 1 to 10 and not 1 to 10 and 2 to 5.)
As for scalar multiplication on a series, that's very well defined by distribution. A * (B + C) = A * B + A * C, (at least in my experience) no matter what space you're in.
jywn4679 ยท 3 points ยท Posted at 00:26:45 on May 26, 2016 ยท (Permalink)
You haven't told me what A+B is. What do you mean by combine them term by term? What series corresponds to A+B?
ERRORMONSTER ยท 1 points ยท Posted at 00:34:09 on May 26, 2016 ยท (Permalink)
Well if A is a series, which I assume you know what a series is, then A is some sum of a1 + a2 + a3 + ... + an. B is similarly defined. Therefore if C = A + B and A and B cross the same space, then C = a1 + a2 + ... + an + b1 + b2 + ... + bn, and since addition is associative, C = a1 + b1 + a2 + b2 + ... + an + bn. If they don't cross the same space then there will be an extra series at the end containing the difference (again, term by term.)
I apologize, but I feel like I'm talking to a middle schooler, having to explain what a series is...
jywn4679 ยท 3 points ยท Posted at 00:37:10 on May 26, 2016 ยท (Permalink)
To be clear, are you saying that C=sum of (a_i+b_i)?
I don't know what you mean by same space.
Remember these are infinite series, not finite ones, so saying C=a1+...+an+b1+...+bn, is not OK, as the an's never end so the bn's cannot even begin.
ERRORMONSTER ยท 1 points ยท Posted at 01:49:53 on May 26, 2016 ยท (Permalink)
You never said infinite series. You just said series.
Likewise, I can still say the same thing. Just add a "+ ..." to the end and everything still makes sense. Call it a proof by induction and the fact that addition is still associative.
jywn4679 ยท 5 points ยท Posted at 01:52:42 on May 26, 2016 ยท (Permalink)
Series is shorthand for infinite series typically. I have never seen finite sums refered to as series.
Are you saying that A+B is the series sum (a_i+b_i)?
You cannot say a1+a2+...+b1+b2+..., that makes no sense under normal notation.
ERRORMONSTER ยท -1 points ยท Posted at 02:00:17 on May 26, 2016 ยท (Permalink)
Let me say this again slowly, because apparently you don't get it.
Can you take it from there? As for the apparent inability to multiply series by a scalar, are you saying that two times the sum of reciprocal squares is not necessarily two times the square of pi divided by 6? Because it is. Because that's how math works. 2(a + b + c + ...) = 2a + 2b + 2c + ... though I'd love to see anyone try to dispute that statement and say it's not allowed for some reason.
jywn4679 ยท 4 points ยท Posted at 02:04:49 on May 26, 2016 ยท (Permalink)
You haven't defined anything there. Saying C=(a1+b)+(A-a1)+(B-b1) relies on knowing what series A-a1 is, and then know what (A-a1)+(B-b1) is. But the latter is summing series. You can't define the sum of 2 series as a different sum of 2 series, it's circular. Can you state clearly what the nth term of the series corresponding to A+B is?
As for scalar multiplication, that happens to be as easy as you have said. Adding series is also easy but I'm wanting you to explain it so I don't put words into your mouth. Normally the sum of two series (sum of an from n=0 to infinity)+(sum of bn from n=0 to infinity) is given by sum of (an+bn) from n=0 to infinity, i.e. you jsut add the corresponding terms together. I have been asking if this is what you mean and you haven't answered.
ERRORMONSTER ยท -1 points ยท Posted at 03:58:56 on May 26, 2016 ยท (Permalink)
If I have to tell you that a is a number and b is a number then I think we're done here. If you can't even make basic connections that the presence of an addition sign between two symbols when we're discussing infinite summation implies strongly enough that you can believe my symbols represent numbers (real, imaginary, purple, whatever you want to call it) then I have no business trying to discuss anything further with you.
jywn4679 ยท 5 points ยท Posted at 12:49:19 on May 26, 2016 ยท (Permalink)
I belive your symbols represent infinite series, which are absolutely NOT real or complex numbers (they aren't even a field).
I get paid to teach this stuff to undergrads, and am published in this field (more specifically functional analysis). DO not patronise me, I know this area far better than you. It is you who has completely failed to explain what you mean. I kept asking you are yes or no question which you refused to answer.
ERRORMONSTER ยท -2 points ยท Posted at 14:39:00 on May 26, 2016 ยท (Permalink)
I feel like I should just give up and stop repeating myself. Do you know the difference between A and an in the examples? A is the series, and an is an element in the series. That's how I came to the definition that A is the sum of terms a1, a2, a3, ..., all the way to an. You're welcome to say the little "a" is a series all its own, which is technically true, as it's a series of one element or an infinite series that sums up to some value an. We know of plenty of series with finite value that you could manipulate (with multiplication, oohh) to be any of the summing terms aboce. Here is one example, and I know I'm being sloppy and not rigorous, but it's about all I can handle after having to teach an undergrad teacher who doesn't even know that he hasn't been asking yes or no questions
Anyway, take the sum of reciprocal squares. We know it adds up to a sixth the square of pi. If you double the sum of the series, you get a third the square of pi, right? That's been proven by smarter people than I. Well what is multiplication? Multiplication by definition is adding something to itself. So what do you get when you add (1 + 1/4 + 1/9 + ...) + (1 + 1/4 + 1/9 + ...)? Looks to me like one third of the square of pi. But wait, I'm not allowed to put ellipses in the middle of an equation because reasons! Even though these are well defined sequences with a given pattern, it isn't allowed because it looks weird. Ok, then rearrange term by term (as I've explained, we can do this because a + b + c + d = a + c + b + d. It's the basis of addition.) So we get 1 + 1 + 1/4 + 1/4 + 1/9 + 1/9 + ... and hey! We only have one ellipse at the end. Even though that ellipse represents twice as many digits, it's still infinite, so we haven't changed anything or truncated anything or obfuscated anything. I just made it look prettier for you. And the sum is still a third the square of pi.
Also, throwing around your professorship only makes it a little sad that I'm having to explain this stuff to you. Don't ever tell someone "believe me because I have a degree in this stuff and teach it to 18-21 year olds for a living." It's logically useless and senseless to do, not to mention a little arrogant.
Unless you're saying that the individual terms a1 to an are each their own infinite series and you're asserting that I can't add them because it's senseless to add infinite series therefore my A, which I defined as literally the most generally defined series imaginable (the sum of some numbers) is undefined or circularly defined. So that'd be pretty funny.
jywn4679 ยท 2 points ยท Posted at 14:54:50 on May 26, 2016 ยท (Permalink)
I have never said that the little a's are series, they have always been the terms in the series. I have used capitals to refer to series in all my posts.
I'll ask again because you seem to be refusing to answer. This is a very simple yes or no question. I think I know your answer but I don't want to put words into your mouth.
Is the series corresponding to A+B the series sum of (an+bn) from n=0 to infinity, where A is the sum of an from n=0 to infinity, and B is the sum of bn from n=0 to infinity? YES OR NO?
ERRORMONSTER ยท 1 points ยท Posted at 17:00:56 on May 26, 2016 ยท (Permalink)
I am not here for your amusement. I came here to learn. Fuck off.
[deleted] ยท 2 points ยท Posted at 18:07:43 on May 26, 2016 ยท (Permalink)
Believe it or not, that is exactly what /u/jywn4679 is trying to do: help you learn by identifying and correcting material you don't understand fully.
ERRORMONSTER ยท 1 points ยท Posted at 20:26:17 on May 26, 2016 ยท (Permalink)
are you sure about that? he had no intention of actually telling me why I was wrong. He was just trolling me so he could post it here later.
[deleted] ยท 3 points ยท Posted at 21:41:35 on May 26, 2016 ยท (Permalink)
No, I don't believe that's what he was doing. He was hoping that you would see what's wrong. Sometimes the best way to teach is to guide someone to understanding that what they thought was correct was not. Now this is not always the best way as it doesn't work with everyone. He could have done a better job, yeah. But this is the Internet, and those kind of discussions often work best in real life, face to face.
jywn4679 ยท 2 points ยท Posted at 22:23:22 on May 26, 2016 ยท (Permalink)
No. I know your math was wrong, so I know somewhere you were going to make a mistake. I think I know where your mistake is as well, you assume that the left shift operator applied to series with initial term 0 is equal to the identity operator, which is proveably false.
rjem ยท 2 points ยท Posted at 23:24:00 on May 25, 2016 ยท (Permalink)
The number systems we usually work with don't include infinite values at all. If you do want to include infinities (which is sometimes very useful) then you have to change the rules slightly to avoid contradictions.
And infinite series aren't actually numbers, they are infinitely long lists of numbers. You have to do some work to make sure that a series is nicely-behaved before you can start manipulating it in the way you were doing. For example, the series
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...
actually does converge to a finite value, but if you simply reorder the terms to, say,
1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + ...
(taking the first two positive terms, then the first negative term, then the next two positive terms, then the next negative term, and so on) then it converges to a completely different finite value. You could try coding it up if you don't believe me.
If 2*infinity=infinity, then surely we can do:
infinity + infinity - infinity = 2*infinity - infinity = infinity - infinity = 0
But hang on, we can also say that:
infinity + infinity - infinity = infinity + (infinity - infinity) = infinity + 0 = infinity
So infinity = 0? Or does infinity break the rule that x - x = 0, for any x? One way or another, we have to change the ordinary rules of arithmetic if we treat infinity as a number.
ERRORMONSTER ยท -1 points ยท Posted at 00:15:07 on May 26, 2016 ยท (Permalink)
I didn't treat infinity as a number. I treated the series as a number. You said the series is infinite. You also can't say the series is equal to infinity, which means your substituting my "S" for your "infinity" doesn't hold as a valid substitution. It's a circular argument. If S is infinite then you can't add or subtract it. Well yeah. You can say the limit is infinite, but I'm not concerned with the limit. And you can say the only way we can look at infinite series is by looking at the limit. And I can ask "why?" and you'd say "because it's been the only way to approximate all of these other series." and I would say "but you know that's not mathematically rigorous."
lordoftheshadows ยท 6 points ยท Posted at 14:25:55 on May 25, 2016 ยท (Permalink)
No. You cannot arbitrarily rearrange a divergent sum. Just nope.
ERRORMONSTER ยท -3 points ยท Posted at 15:44:33 on May 25, 2016 ยท (Permalink)
I didn't rearrange anything. It isn't like I said "well I know that 216 is in there somewhere, so I'll just pull it out."
lordoftheshadows ยท 2 points ยท Posted at 15:47:50 on May 25, 2016 ยท (Permalink)
You are wrong. Period. End of discussion. Let's talk about the mistakes.
Nope. S isn't a number. S is defined as the limit of the partial sums of the series which does not exist.
Nope. You're wrong.
ERRORMONSTER ยท -2 points ยท Posted at 16:02:46 on May 25, 2016 ยท (Permalink)
I didn't define S as a partial sum or a limit. S is the sum. And it looks to me like a number. That number is -1. Show me the step that is not allowed.
You said you would talk about the mistakes then flat out didn't talk about any mistakes lol.
lordoftheshadows ยท 5 points ยท Posted at 16:03:48 on May 25, 2016 ยท (Permalink)
Right. The sum of a series is the limit of the partial sums of the series. That limit does not exist. Go ask on /r/math about this. We'll be sure to tell you exactly why it doesn't work.
ERRORMONSTER ยท -2 points ยท Posted at 16:19:00 on May 25, 2016 ยท (Permalink)
I still don't see where the math falls apart. You're basically saying "hey you can't do that. Why not? Because it's wrong. Well why's it wrong? Because it is. You just can't do that."
I'm not saying that if you add up all non-negative powers of 2 beginning with 20 that you'll get -1. I'm saying that the sum of the series 1 + 2 + 4 + 8 + ... is equal to -1. Similar to how there is no real reason for 0.999... to be equal to 1. It is so because we say it is so. It's useful for us to define it that way, therefore it is. You aren't saying that if you add enough nines you'll get to 1. You're just saying that the existence of an infinite number of 9s means the value is 1.Likewise, adding positive numbers will not get you a negative number, but we aren't explicitly breaking any rules, and it is useful for us to do so, therefore it is.
22fortox ยท 3 points ยท Posted at 17:40:18 on May 26, 2016 ยท (Permalink)
If your method works, then you can replace the first part with S = 1 + 2 + 3 + ... = -1 and it would give you the same result.
Either way, it doesn't work because you just can't sum a divergent series.
ERRORMONSTER ยท 0 points ยท Posted at 17:59:39 on May 26, 2016 ยท (Permalink)
So if my method worked, I could assume my conclusion? If I started out by stating that the sum of natural numbers were -1 then it wouldn't make sense to say that it's anything later in the proof because you already asserted that it's -1.
22fortox ยท 3 points ยท Posted at 18:13:17 on May 26, 2016 ยท (Permalink)*
This is the reason you can't just assign values to divergent series so otherwise you would be able to prove that any divergent series would equal -1 using your proof. Using similar proofs you would be able to say that any divergent series is equal to any number you want, which would be blatantly false (since you would be able to get things like 1 = 2, which is a contradiction).
bearsnchairs ยท 5 points ยท Posted at 16:37:06 on May 25, 2016 ยท (Permalink)
The math falls apart because you assume S is a number, it isn't. That sum is divergent. Ramanujan sums assign finite values to divergent sums but they aren't true sums.
jywn4679 ยท 5 points ยท Posted at 15:22:15 on May 25, 2016 ยท (Permalink)
What is S? It isn't a number, since that sum diverges.
[deleted] ยท 2 points ยท Posted at 16:42:32 on May 25, 2016 ยท (Permalink)
[removed]
[deleted] ยท 2 points ยท Posted at 19:49:47 on May 26, 2016 ยท (Permalink)
Come on.
rrealnigga ยท 1 points ยท Posted at 20:09:32 on May 26, 2016 ยท (Permalink)
?
[deleted] ยท 1 points ยท Posted at 19:48:29 on May 26, 2016 ยท (Permalink)
No. Pretty much the opposite. The series is divergent.
SouRzCSGO ยท -1 points ยท Posted at 11:52:16 on May 25, 2016 ยท (Permalink)
The 3, 4, 5 triangle or whatever it is. It's fucking awesome.
Edit: not 2+3=4 lol
KDirty ยท 2 points ยท Posted at 17:52:38 on May 25, 2016 ยท (Permalink)
Those are called Pythagorean Triples.
xmastreee ยท 1 points ยท Posted at 12:13:41 on May 25, 2016 ยท (Permalink)
There's also 5, 12, 13
OldButStillFat ยท 1 points ยท Posted at 19:25:58 on May 25, 2016 ยท (Permalink)
Awesome at making 90 degree angles.
identiifiication ยท -2 points ยท Posted at 13:49:35 on May 25, 2016 ยท (Permalink)
That everything in the universe is calculated by Maths.
A physicist even found computer code in the equations of String theory
PazDak ยท -7 points ยท Posted at 14:49:05 on May 25, 2016 ยท (Permalink)
That it is Math. I know Math comes form Mathematics, but can you think of a another word where you when shortening it you still carry the s?
It isn't used in a plural sense in our language. Think of this do you say Maths is fun or Maths are fun? Every person I have seen has used the is version which is singular and not plural so the (s) makes even less sense.
I have a British wife and we have fought about this several times and I will defend to the death that it is Math over Maths.
mtiyl ยท 2 points ยท Posted at 22:11:50 on May 25, 2016 ยท (Permalink)
Statistics? As in the academic field, not the plural of "statistic".
I'm struggling to think of similar words that are routinely shorted anyway. I think "economics" is sometimes shortened to "econ" in the US, but I have never heard this in the UK.
Tuviah ยท 3 points ยท Posted at 15:26:35 on May 25, 2016 ยท (Permalink)
But we also say that "mathematics" is fun, rather than mathematics are fun. We do so because "mathematics" is a mass noun which is generally only used in its singular form. There is some evidence that in the early 1800s a contracted version of the word (math's) was used in publications, and this may have diverged between the US and UK later in the century when the UK dropped the apostrophe leaving "maths" and the US abbreviated it to just "math", though I'm not aware of an exact etymology for either variant. There are a number of good response to this question found by googling math vs maths, if you're interested in learning more, but in short both are likely as valid as each other.
foerboerb ยท 3 points ยท Posted at 19:09:25 on May 25, 2016 ยท (Permalink)
Considering that the languages name is english and the english say it's maths, I'm leaning towards maths.
hrtfthmttr ยท -6 points ยท Posted at 15:40:04 on May 25, 2016 ยท (Permalink)
That it makes you sound like a fool when you say "maths", because there is no "s" after the "th" in "mathematics", and anyways the word is an uncountable noun (and so no plural form).
TheBeardyGamer ยท -1 points ยท Posted at 13:08:30 on May 25, 2016 ยท (Permalink)
This
AnalogPen ยท -1 points ยท Posted at 14:03:09 on May 25, 2016 ยท (Permalink)
I only have to take one more math class for my degree.
[deleted] ยท -1 points ยท Posted at 14:49:39 on May 25, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 0 points ยท Posted at 22:51:55 on May 25, 2016 ยท (Permalink)
No it is not, as the introduction of the article you linked clearly states.
ohmyfreakingoodness ยท -1 points ยท Posted at 18:07:28 on May 25, 2016 ยท (Permalink)
Women are time and money; women = time x money
Time is money; time = money
Therefore women are money squared; women = money2
Money is the root of all evil; money = sqrt(evil); money 2 = evil
Women are evil; Women = money2 = evil
Women = evil
black_mamba_08 ยท -1 points ยท Posted at 22:02:27 on May 25, 2016 ยท (Permalink)
59,009=boobs.
roman8888 ยท -1 points ยท Posted at 04:36:26 on May 26, 2016 ยท (Permalink)
2=1+1 2=1+โ1 2=1+โ(-1)(-1) 2=1+โ-1 โขโ-1 2=1+iโขi 2=1+(-1) 2=0
Usagii_YO ยท -1 points ยท Posted at 11:01:24 on May 26, 2016 ยท (Permalink)
2 is greater than 1.
[deleted] ยท -8 points ยท Posted at 11:07:08 on May 25, 2016 ยท (Permalink)
1+1=11
tomholder ยท 9 points ยท Posted at 11:33:25 on May 25, 2016 ยท (Permalink)
Not even true in binary
[deleted] ยท 1 points ยท Posted at 11:42:43 on May 25, 2016 ยท (Permalink)
monary?
Hodor_The_Great ยท 10 points ยท Posted at 11:56:46 on May 25, 2016 ยท (Permalink)
I believe it's called unary
ktkps ยท 2 points ยท Posted at 12:03:44 on May 25, 2016 ยท (Permalink)
sounds interesting...do people moan in monary?
tomholder ยท 2 points ยท Posted at 12:20:50 on May 25, 2016 ยท (Permalink)
To be fair, yes, it would work then. Unary is odd in not having a number zero.
ERRORMONSTER ยท 1 points ยท Posted at 12:30:51 on May 25, 2016 ยท (Permalink)
Unary
[deleted] ยท 1 points ยท Posted at 12:14:39 on May 25, 2016 ยท (Permalink)
Not true anywhere... I was being silly, as per the lack of serious tag.
Artillect ยท 1 points ยท Posted at 15:19:18 on May 25, 2016 ยท (Permalink)
Nope it's true in unary.
ArbainHestia ยท 1 points ยท Posted at 19:24:21 on May 25, 2016 ยท (Permalink)*
It took a while but I almost have my 4 year old convinced this is not correct.
Maymayfish ยท -8 points ยท Posted at 11:26:04 on May 25, 2016 ยท (Permalink)
1+1=window
ktkps ยท 2 points ยท Posted at 12:04:38 on May 25, 2016 ยท (Permalink)
video representation
[deleted] ยท -7 points ยท Posted at 14:40:00 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 4 points ยท Posted at 15:02:30 on May 25, 2016 ยท (Permalink)
.99999999... is the same thing as 1
[deleted] ยท -5 points ยท Posted at 20:12:12 on May 25, 2016 ยท (Permalink)
[deleted]
PM_ME_YOUR_PAULDRONS ยท 2 points ยท Posted at 21:43:08 on May 25, 2016 ยท (Permalink)
That is not correct.
nickbenn ยท 2 points ยท Posted at 17:31:16 on May 26, 2016 ยท (Permalink)
Actually, it is. 0.999โฆ is an infinite series whose sum is exactly 1 (see https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3jj7is); no rounding needed.
TatchM ยท -7 points ยท Posted at 20:03:12 on May 25, 2016 ยท (Permalink)
Only if you round.
PM_ME_YOUR_PAULDRONS ยท 3 points ยท Posted at 21:32:16 on May 25, 2016 ยท (Permalink)
No rounding involved. This is an example of what we call a limit in maths. When we write 0.9999999... this is shorthand for 0.9 + 0.09 + 0.009 + 0.0009 etc so we're actually summing up:
9 * 10-n
For n = 1 to infinity. It is possible to show that this sum is 1.
This is completely rigorous and not at all controversial maths (every mathematics undergraduate student will be taught how to prove this, generally in their first year).
Note that this is actually a general property of the decimal number system. Any number which has a decimal expansion with a finite number of non-zero terms in it actually has two decimal expansions. To get the second one you just subtract 1 from the last digit and then append an infinite series of 9s.
Remember not to get the "map" confused with the "land", here the land is the real number system and the map is the decimal expansions. Some real numbers have multiple decimal expansions, this isn't a fault with the decimal system but its something we should be aware of.
TatchM ยท 2 points ยท Posted at 22:19:11 on May 25, 2016 ยท (Permalink)
As a side note, do you know of any sources dealing with non-natural numbered bases? Or perhaps an explanation on why such cannot exist?
PM_ME_YOUR_PAULDRONS ยท 2 points ยท Posted at 22:36:49 on May 25, 2016 ยท (Permalink)
You certainly can write things out in non natural numbered bases. I don't know of any good sources (my work is very much not in this area) I'm afraid but the wiki page has some interesting stuff.
There is also an extensive page on using the golden ratio as a base since that system has some quite nice properties (largely because ฯ2 = ฯ+1).
TatchM ยท 1 points ยท Posted at 22:43:37 on May 25, 2016 ยท (Permalink)
Thanks for the leads!
TatchM ยท -2 points ยท Posted at 22:15:14 on May 25, 2016 ยท (Permalink)
Not going to lie, your explanation was pretty bad. You probably should have looked up the limit proof before referencing it.
Luckily, the examples provided on Wikipedia are much better.
Well, not the most interesting aspect of math I learned from this thread. Still interesting enough though.
PM_ME_YOUR_PAULDRONS ยท 4 points ยท Posted at 22:30:16 on May 25, 2016 ยท (Permalink)
I didn't go into depth about the proof because either a reader already understands limits, in which case they don't need the proof or they don't know about limits, in which case I can't really explain any of the proof in a reddit comment in a way I'd find satisfactory.
I'd basically have to start from the axioms of the real numbers, define what a limit means from that, have a bunch of explanation about what it and then give the proof using the definitions I'd given. Thats a couple of lectures worth of material in an undergrad course.
I could have given one of the more handwavey explanations, or maybe go into depth using one of the explicit constructions of the reals (Cauchy sequences, Dedekind cuts etc) I guess.
TatchM ยท 2 points ยท Posted at 22:38:34 on May 25, 2016 ยท (Permalink)
That would be nice!
And I understand it can be difficult to explain things briefly. Linking to a proper proof or explanation would have been a good way as well.
Sorry if I came across as salty (as /u/rrussell1 pointed out), I did not mean to be such. It was just that your partial explanation was confusing, and I felt a more in-depth explanation would have been better.
In any case, I found a few good leads on non-natural numbered radix systems. But if you have any good sources related to them, I'm still open to suggestions.
rrussell1 ยท 2 points ยท Posted at 22:28:17 on May 25, 2016 ยท (Permalink)
Don't be salty just because you were called out on your lack of knowledge dude...
nickbenn ยท 1 points ยท Posted at 20:17:40 on May 25, 2016 ยท (Permalink)
It has nothing to do with chaos theory. By definition,
0.999… = 9/10 + 9/100 + 9/1000 + ...
This is a geometric series,
a + ar + ar2 + ar3 + ...
where a = 9/10, r = 1/10.
A geometric series with |r| < 1 converges, with a sum of a/(1 - r). In this case, that is equal to (9/10)/(1 - 1/10) = (9/10)/(9/10) = 1.
ORG5X3-224 ยท -7 points ยท Posted at 14:46:48 on May 25, 2016 ยท (Permalink)
The fact that mathematically Bernie Sanders is out of the race, yet his supporters still believe there is a chance. That one is my favorite.
JanEric1 ยท 3 points ยท Posted at 14:49:13 on May 25, 2016 ยท (Permalink)
he pretty much is out of the race, but if you want to be strict, there is still a mathematical chance for him to win... soooo, your wrong.
for example if he win 100% of the remaining delegates. it wont happen, but the pure math allows it.
CaptZ ยท 0 points ยท Posted at 18:25:56 on May 25, 2016 ยท (Permalink)
Not too mention that when HRC is indicted and drops out of the race, Bernie is in. That is why he staying in the race, Just as HRC did against Obama, stating that he might die while running for POTUS giving her an in to win. What goes around comes around.
xibfeii ยท -2 points ยท Posted at 16:51:19 on May 25, 2016 ยท (Permalink)
The fact that we can do more than just give up when we try to add up infinite numbers, and when we do we get
1+2+3+4+5+... = - 1/12
and that the laws of physics seem to agree!
Gnurreia ยท -1 points ยท Posted at 17:16:01 on May 25, 2016 ยท (Permalink)*
https://youtu.be/w-I6XTVZXww
https://youtu.be/E-d9mgo8FGk
This one is mind blowing and no one seems to care!!
overconvergent ยท 4 points ยท Posted at 22:41:51 on May 25, 2016 ยท (Permalink)
No one cares because it's not true.
Gastricbasilisk ยท -10 points ยท Posted at 11:19:00 on May 25, 2016 ยท (Permalink)
Eย = mcย 2. So basic and simple, yet so fascinating. Thinking of mass and energy as the same thing really opens our eyes and made us better at understanding the universe around us.
[deleted] ยท 13 points ยท Posted at 11:36:32 on May 25, 2016 ยท (Permalink)
[deleted]
Kildragoth ยท 1 points ยท Posted at 11:59:50 on May 25, 2016 ยท (Permalink)
I'm confused... What?
K4ntum ยท 7 points ยท Posted at 12:01:30 on May 25, 2016 ยท (Permalink)
That's physics.
Gastricbasilisk ยท -3 points ยท Posted at 12:16:46 on May 25, 2016 ยท (Permalink)
You do realize the language of physics is mathematics right?
oighen ยท 11 points ยท Posted at 12:52:08 on May 25, 2016 ยท (Permalink)
So? If the question was "What's your favorite fact about the English language?" would every answer count since it's written in English?
FREE-MUSTACHE-RIDES ยท 1 points ยท Posted at 15:47:48 on May 25, 2016 ยท (Permalink)
YES
Gastricbasilisk ยท -8 points ยท Posted at 12:57:13 on May 25, 2016 ยท (Permalink)
It's still math. Whether it's a physics equation is irrelevant. It's still a mathematical equation to calculate something is it not?
oighen ยท 7 points ยท Posted at 13:06:19 on May 25, 2016 ยท (Permalink)
It uses a mathematical language, this doesn't mean it's a math fact any more than the sentence "/u/Gastricbasilisk is a moron" is a grammar fact.
Gastricbasilisk ยท -7 points ยท Posted at 12:18:02 on May 25, 2016 ยท (Permalink)
Not at all. Physics is mathematics. Issac Newton invented calculus in order to solve physics problems. You clearly are just too ignorant to this subject.
[deleted] ยท 3 points ยท Posted at 12:34:11 on May 25, 2016 ยท (Permalink)
[deleted]
Gastricbasilisk ยท 0 points ยท Posted at 12:51:35 on May 25, 2016 ยท (Permalink)
Chill dude. I never said I was superior. All I meant was math and physics literally go hand in hand. And a physics equation is a mathematical equation. No need to get butthurt over someone else's opinion.
Dd_8630 ยท 2 points ยท Posted at 14:04:45 on May 25, 2016 ยท (Permalink)
It's also only a corner case of the more complete and much more interesting equation: Eยฒ = mยฒcโด + pยฒcยฒ.
ktkps ยท 3 points ยท Posted at 11:39:11 on May 25, 2016 ยท (Permalink)
E = MC2
MrSynckt ยท 1 points ยท Posted at 11:52:16 on May 25, 2016 ยท (Permalink)
Unless you're talking about the Mariah Carey album, it's E = mc2
ktkps ยท -2 points ยท Posted at 12:22:31 on May 25, 2016 ยท (Permalink)
Mine is not an Einstein E, it is evolutionary E.
Evolution = Monkey times Creativity2
*trying hard not to look like a stupid
Gastricbasilisk ยท 0 points ยท Posted at 12:18:49 on May 25, 2016 ยท (Permalink)
I'm on my phone and don't know how to add the squared symbol. But you evidently understood what I meant.
KaptainK27 ยท 2 points ยท Posted at 12:39:45 on May 25, 2016 ยท (Permalink)
Jut ad a ^ between the mc and the 2 (with no spaces between) and the 2 becomes superscript
Example
E=mc 2 becomes E=mc2
Gastricbasilisk ยท 2 points ยท Posted at 12:54:13 on May 25, 2016 ยท (Permalink)
E=mc2........ You sir are a wizard! Thank you.
KaptainK27 ยท 1 points ยท Posted at 12:56:38 on May 25, 2016 ยท (Permalink)
Glad to be of service.
FatuousOocephalus ยท -8 points ยท Posted at 11:23:36 on May 25, 2016 ยท (Permalink)
1+1=2. All other math facts derive from that fact.
ktkps ยท 2 points ยท Posted at 12:14:14 on May 25, 2016 ยท (Permalink)
Even 22/7?
Kvothealar ยท 2 points ยท Posted at 12:32:24 on May 25, 2016 ยท (Permalink)
I hate to be that guy but you aren't even close.
What you are looking for are the axioms of the real number system, assuming you want to prove math that exclusively involves the real numbers.
This says nothing about complex numbers. Groups. Rings. Fields. Etc...
ERRORMONSTER ยท 2 points ยท Posted at 12:34:29 on May 25, 2016 ยท (Permalink)
No... no they don't. That statement only defines addition and, by extension, multiplication and exponents. There's no subtraction or division. There's also no trig.
FatuousOocephalus ยท 4 points ยท Posted at 12:51:31 on May 25, 2016 ยท (Permalink)
If the statement 'defines addition and by extension multiplication' then subtraction and division are also covered by extension. If 1+1=2 then 2-1=1. The inverse of multiplication is division. If multiplication is covered by extension then so is division.
Once division is covered then so is the concept of irrational numbers since once you can divide, some asshole will try to divide 5 into 3 parts.
The relationship between sine, cosine and tangent is multiplicative so trig is covered by extension.
The concept of zero isn't covered by 1+1 even by extension.
Dd_8630 ยท 1 points ยท Posted at 14:02:48 on May 25, 2016 ยท (Permalink)
No it's not, you need to define angles, circles, and triangles, before you can then define trig. This all does not come solely from 1+1=2.
FatuousOocephalus ยท 1 points ยท Posted at 16:01:02 on May 25, 2016 ยท (Permalink)
If 1+1โ 2 then 2 one degree angles will not create a 2 degree angle.
If 1+1โ 2 then the angles that make up a triangle will not add up to 180.
Trig requires 1+1=2 to be true.
Dd_8630 ยท 1 points ยท Posted at 16:58:40 on May 25, 2016 ยท (Permalink)
Of course, but trig doesn't come from 1+1=2. We can't say "1+1=2, therefore sinยฒ + cosยฒ = 1". The definitions of sine and cosine need to be made before we can bring trig into the picture, and those definitions aren't derived from arithmetic.
[deleted] ยท 1 points ยท Posted at 16:19:37 on May 25, 2016 ยท (Permalink)
Even 10-Infinity?
whatIsThisBullCrap ยท -1 points ยท Posted at 13:37:59 on May 25, 2016 ยท (Permalink)
Nope. Even simple arithmetic has something like 15 postulates
FatuousOocephalus ยท 0 points ยท Posted at 14:27:25 on May 25, 2016 ยท (Permalink)
So if 1+1โ 2 then some of those postulates are incorrect; the partition postulate comes to mind. Those postulates are dependent on 1 plus 1 equaling 2. The other postulates, the ones that are true regardless any hypothetical sum resulting from adding one and one are independent of the equation and irrelevant to this discussion.
jywn4679 ยท 2 points ยท Posted at 15:28:31 on May 25, 2016 ยท (Permalink)
I have no idea what you are tlaking about but you are totally wrong. None of the standard axioms in mathematics rely on 1+1=2, instead 1+1=2 is a consequence of some of them.
Try proving the axiom of choice from 1+1=2 (hint, it's impossible).
whatIsThisBullCrap ยท 2 points ยท Posted at 15:43:04 on May 25, 2016 ยท (Permalink)*
There's actually a book, Principia Mathematica, that lays out the foundation of mathematics, including formally defining arithmetic, number theory, and several other logical systems. Famously, it take hundreds of pages of postulates, definitions, and theorems until it is finally possible to prove 1+1=2
Burdiac ยท 0 points ยท Posted at 14:15:15 on May 25, 2016 ยท (Permalink)*
1x9 = 09 0+9=9
2x9 = 18 1+8=9
3x9 = 27 2+7=9
4x9 = 36 3+6=9
5x9 = 45 4+5=9
6x9 = 54 5+4=9
7x9 = 63 6+3=9
8x9 = 72 7+2=9
9x9 = 81 8+1=9
10x9=90 9+0=9
fartcomposer ยท 0 points ยท Posted at 14:21:01 on May 25, 2016 ยท (Permalink)
The concept of infinity. Or is that more philosophy?
ZephyrQueso ยท 0 points ยท Posted at 14:28:49 on May 25, 2016 ยท (Permalink)
2+2=fish
CubKits ยท 0 points ยท Posted at 15:00:00 on May 25, 2016 ยท (Permalink)
Mine is: 60 + 30 + 15 + 15 actually just equals 5!
Icko_ ยท 1 points ยท Posted at 15:02:08 on May 25, 2016 ยท (Permalink)
705+3+2+10 = 6!
Saldar1234 ยท 0 points ยท Posted at 15:03:59 on May 25, 2016 ยท (Permalink)
I am fascinated by Zenoโs supertask paradoxes...
Vsauce Link
[deleted] ยท 0 points ยท Posted at 15:05:01 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 1 points ยท Posted at 15:32:10 on May 25, 2016 ยท (Permalink)
Not true.
iTomWright ยท 0 points ยท Posted at 15:05:20 on May 25, 2016 ยท (Permalink)
9+10 = 21
BinsterUK ยท 0 points ยท Posted at 15:21:55 on May 25, 2016 ยท (Permalink)
Pi is exactly 3.
Saytahri ยท 1 points ยท Posted at 19:21:04 on May 25, 2016 ยท (Permalink)
What makes you think that?
BinsterUK ยท 1 points ยท Posted at 20:17:34 on May 25, 2016 ยท (Permalink)
(It's a Simpsons quote...)
willforti ยท 0 points ยท Posted at 15:32:58 on May 25, 2016 ยท (Permalink)
Kind of not what you asked, but it cracks me up how 99% of people refer to circumference as 2 x pi x R instead of Pi x D
aventus-dog ยท 0 points ยท Posted at 16:00:22 on May 25, 2016 ยท (Permalink)
7 ate 9
Mooksayshigh ยท 0 points ยท Posted at 16:06:27 on May 25, 2016 ยท (Permalink)*
1+1= Shut the fuck up.
Edit: For those that never seen this
zagreus9 ยท 0 points ยท Posted at 16:36:25 on May 25, 2016 ยท (Permalink)
Almost every number contains the number 3
Zarobeck ยท 0 points ยท Posted at 16:41:04 on May 25, 2016 ยท (Permalink)
Shifting every letter down 1 in the alphabet in the word Anna makes it become boob
finnchapman ยท -1 points ยท Posted at 17:08:37 on May 25, 2016 ยท (Permalink)
In a similar vein, 'dude' shifted down by 3 is 'arab'. Learnt this programming a Caesar cipher.
FredDerf666 ยท 0 points ยท Posted at 17:07:40 on May 25, 2016 ยท (Permalink)
Math fact:
100% of Canadian hockey players give it 110% every game.
Markual ยท 0 points ยท Posted at 17:10:48 on May 25, 2016 ยท (Permalink)
When u turn an 8 sideways it's an infinity sign.
[deleted] ยท 0 points ยท Posted at 17:28:32 on May 25, 2016 ยท (Permalink)
1 + 1 = 2 ;)
I really like the fact that once something in math is proven, it will remain the same for all the time. The sentence of Pythagoras was true thousand years ago and will be true in thousand years.
wastazoid ยท 0 points ยท Posted at 17:30:25 on May 25, 2016 ยท (Permalink)
The irrationality of infinity hides in the decimals among rational numbers. Chaos and order, tolerating each other. I like that.
[deleted] ยท 0 points ยท Posted at 17:40:48 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 2 points ยท Posted at 17:42:08 on May 25, 2016 ยท (Permalink)
I'm not sure if you're joking but that's how you say/spell math in the UK
rhys2204 ยท 0 points ยท Posted at 17:48:04 on May 25, 2016 ยท (Permalink)
10 + 9 = 21. Always baffled me
[deleted] ยท 0 points ยท Posted at 17:54:35 on May 25, 2016 ยท (Permalink)
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[deleted] ยท 0 points ยท Posted at 18:12:35 on May 25, 2016 ยท (Permalink)
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flyingjam ยท 1 points ยท Posted at 18:13:56 on May 25, 2016 ยท (Permalink)
No, the series is divergent. You can assign it a value with a ramanajun sum or with zeta regularization, but the sum equals nothing.
balrogwarrior ยท 0 points ยท Posted at 18:15:07 on May 25, 2016 ยท (Permalink)
Compound interest.
[deleted] ยท 0 points ยท Posted at 19:59:20 on May 25, 2016 ยท (Permalink)
ei*pi = -1
[deleted] ยท 0 points ยท Posted at 20:24:16 on May 25, 2016 ยท (Permalink)
That English folks call it maths and we call it math in North America.
LieutSerge ยท 0 points ยท Posted at 20:30:36 on May 25, 2016 ยท (Permalink)
the shortest distance between 2 points is a line
TheFecklessRogue ยท 0 points ยท Posted at 20:44:51 on May 25, 2016 ยท (Permalink)
That there are different infinities that have different sizes.
2pages_of_Kennedy ยท 0 points ยท Posted at 21:40:04 on May 25, 2016 ยท (Permalink)
6x9+6+9=69
phatness_everdeen ยท 0 points ยท Posted at 21:43:16 on May 25, 2016 ยท (Permalink)
Pick a number, double it, add 3, subtract 2, subtract 1, multiply by 0.5. You get your initial number, every. single. time.
MrUnderdawg ยท 1 points ยท Posted at 22:52:16 on May 25, 2016 ยท (Permalink)
Unless you're being sarcastic it's because you're just doubling, and then halving a number.
3x2=6
6x.5=3
caterpillarNYC ยท 0 points ยท Posted at 21:53:43 on May 25, 2016 ยท (Permalink)
Math? Knowledge? Be careful reddit, you might offend trump voter's and republicans.
ElGatoBlanco ยท 1 points ยท Posted at 22:42:26 on May 25, 2016 ยท (Permalink)
Good one err... Good .9999999999
Okhlahoma_Beat-Down ยท 0 points ยท Posted at 22:03:38 on May 25, 2016 ยท (Permalink)
111,111,111 x 111,111,111 = 12345678987654321
[deleted] ยท 0 points ยท Posted at 22:09:27 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 0 points ยท Posted at 22:09:27 on May 25, 2016 ยท (Permalink)
A negative boy couldn't decide whether or not he wanted to go to a rad party, but he decided to be square and miss out on four awesome chicks...and it was all over by 2 am.
solve for x, using the reinterpretted...quadratic equation!
chargoggagog ยท 0 points ยท Posted at 22:10:00 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 = 1 * 2 * 3
jaiowners ยท 0 points ยท Posted at 22:14:56 on May 25, 2016 ยท (Permalink)
Laplace functions suck
faithle55 ยท 0 points ยท Posted at 22:33:30 on May 25, 2016 ยท (Permalink)
That there are several tiers of infinity.
LaserBees ยท 0 points ยท Posted at 22:36:40 on May 25, 2016 ยท (Permalink)
What's up with people putting an 'S' on the end of math? Since when did everyone start referring to math as maths?
PM_ME_YOUR_PAULDRONS ยท 2 points ยท Posted at 00:46:00 on May 26, 2016 ยท (Permalink)
People in Britain and America have been using it for at least 180 years. Apparently at some point you guys decided to drop the s. For what its worth we also dropped the apostrophe but in British English maths is absolutely standard (no one here ever says math unless they're trying to do an American accent).
LaserBees ยท 1 points ยท Posted at 01:43:59 on May 26, 2016 ยท (Permalink)
Ah. I've lived throughout the US and never heard maths in person, only on reddit. Seems it's just the Brits using their crazy jibber jabber. Should've known. Thanks for teaching me something today!
Rikon ยท 0 points ยท Posted at 22:39:21 on May 25, 2016 ยท (Permalink)
Every time you divide 1 by 3, you lose 0.1, as 3 times 3 is 9 and not 10
wilts ยท 1 points ยท Posted at 15:20:20 on June 2, 2016 ยท (Permalink)
What?
doubledongbot ยท 0 points ยท Posted at 22:41:59 on May 25, 2016 ยท (Permalink)
If you spent your entire life calculating the digits of pi by hand you would die.
[deleted] ยท 0 points ยท Posted at 22:46:13 on May 25, 2016 ยท (Permalink)
The number of Astronomical Unitsโthe distance between the earth and the sunโin a light year is roughly the same as the number of inches in a mile.
There are 63,072 light years in an AU. There are 63,360 inches in a mile. Close enough, and a neat coincidence.
If I build a model of the solar system where the sun is a speck of sand and the earth is a (much smaller speck of sand) an inch away, then the nearest star would be a couple of grains of sand a few feet apart 4.3 miles away. From there, we can visualize the stars as being anything from sand grains to pebbles to a few boulders, several miles apart. It's a great way to get a sense of perspective on astronomical distances.
Sephrik ยท 2 points ยท Posted at 23:34:10 on May 25, 2016 ยท (Permalink)
You've got it backwards. There are 63240 au in a light year
baconnator12356 ยท 0 points ยท Posted at 22:49:02 on May 25, 2016 ยท (Permalink)
0 times 0 lol
Eating_sweet_ass ยท 0 points ยท Posted at 22:54:14 on May 25, 2016 ยท (Permalink)
That there's no "s" at the end of the word "math"
FlyingScotzman ยท 0 points ยท Posted at 22:54:29 on May 25, 2016 ยท (Permalink)
There are more trees on earth than there are stars in the WHOLE UNIVERSE !!!
Classics_Nerd ยท 0 points ยท Posted at 23:20:52 on May 25, 2016 ยท (Permalink)
Sometimes, the answer is "no solution."
Moos_Mumsy ยท 0 points ยท Posted at 23:32:40 on May 25, 2016 ยท (Permalink)
Nine, nine, nine. Fantastic number nine. Perfectly consistent, it works out every time. Nine, nine, nine, that crazy number nine. Times any number you can find, it all comes back to nine.
2 x 9 = 18. 1 + 8 = 9
3 x 9 = 27. 2 + 7 = 9
4 x 9 = 36. 3 + 6 = 9
5 x 9 = 45. 4 + 5 = 9
6 x 9 = 54. 5 + 4 = 9
7 x 9 = 63. 6 + 3 = 9
8 x 9 = 72. 7 + 2 = 9
9 x 9 = 81. 8 + 1 = 9
9 x 10 is 90. Just drop the zero sign.
9 x 11 is 99. 9 + 9 = 18. 1 + 8 = 9.
Times any number you can find, it all comes back to nine.
Does it work for bigger numbers too? Try:
9 x 3,487 = 31,383
3 + 1 + 3 + 8 + 3 = 18. 1 + 8 = 9.
It always works!
kittykittysnarfsnarf ยท 0 points ยท Posted at 23:59:05 on May 25, 2016 ยท (Permalink)
It's impossible to tune a piano because the harmonic series split into 12 even fractions don't fit into eachother perfectly when dealing with 3rds 4ths and 5ths. You can tune it pretty close though
qpNiTROqp ยท 0 points ยท Posted at 00:11:10 on May 26, 2016 ยท (Permalink)
2 out of every 5 league of legends players have autism
[deleted] ยท 0 points ยท Posted at 00:37:54 on May 26, 2016 ยท (Permalink)
Maths? Math?
Faiyez ยท 0 points ยท Posted at 00:39:45 on May 26, 2016 ยท (Permalink)
This might be dumb, but the fact that integer square roots are infinite, given the limited amount of integer square roots that you'll find in any sequence of integers.
Toover ยท 0 points ยท Posted at 02:34:14 on May 26, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems Godel proved, using Mathematics, that given any theory, it will never be complete, that is to say it will never be able to prove everything. By design, a theory always require axioms, and those axioms tend to lock down a part of the mathematical truth you can consider.
In short: there is no "single truth" whatsoever, and this was proven mathematically.
StudentMathematician ยท 0 points ยท Posted at 02:36:15 on May 26, 2016 ยท (Permalink)
ummm
_Shut_Up_Thats_Why_ ยท 0 points ยท Posted at 03:14:56 on May 26, 2016 ยท (Permalink)
That it is math.
Shifti_Boi ยท 0 points ยท Posted at 03:27:33 on May 26, 2016 ยท (Permalink)
Pi....mmmm pi
[deleted] ยท 0 points ยท Posted at 03:47:32 on May 26, 2016 ยท (Permalink)
Type 55378008 on your calculator.... turn it upside down.
slimeydave ยท 0 points ยท Posted at 03:55:07 on May 26, 2016 ยท (Permalink)
pi
[deleted] ยท 0 points ยท Posted at 03:56:15 on May 26, 2016 ยท (Permalink)
i always liked the old 'cross multiply and divide' trick you can use to solve a variable. not to mention the Pythagorean theorem. made me feel so smart when i was in school lol
GokuMoto ยท 2 points ยท Posted at 05:15:36 on May 26, 2016 ยท (Permalink)
Pythagorean Theorem and the equation for a circle are the same
[deleted] ยท 2 points ยท Posted at 05:17:08 on May 26, 2016 ยท (Permalink)
what equation for a circle? i didnt say anything about circles lol
GokuMoto ยท 2 points ยท Posted at 05:42:08 on May 26, 2016 ยท (Permalink)*
the equation of a circle reads
where a is the x coordinate on a graph and b is the y coordinate. so if we have a circle at the origin or [0,0] then the equation would read
look familiar
monta_redi ยท 0 points ยท Posted at 04:22:18 on May 26, 2016 ยท (Permalink)
its my favorit fact. Say x = 100, so the odds of not winning 100 times in a row are (99/100)100 The compliment of that is simply 1 - (99/100)100 = 0.63397
SonOfaFlynn ยท 0 points ยท Posted at 04:24:51 on May 26, 2016 ยท (Permalink)
Godel's Incompleteness Theorems which prove that a complete system cannot exist. It is more of a metamathematical fact but still some of the most important and misunderstood results in mathematical history.
Redditor2Standingby ยท 0 points ยท Posted at 06:03:39 on May 26, 2016 ยท (Permalink)
A squared plus B squred equals C squared. Also two plus two equals four.
mansguiche ยท 0 points ยท Posted at 06:54:01 on May 26, 2016 ยท (Permalink)
0! = 1
SUN_PRAISIN ยท 0 points ยท Posted at 08:22:17 on May 26, 2016 ยท (Permalink)
999% is the max percentage dmg a player can have on Super Smash Bros
verytypical ยท 0 points ยท Posted at 10:32:18 on May 26, 2016 ยท (Permalink)
1729 = 123 + 13 = 103 + 93
vsully360 ยท 1 points ยท Posted at 17:31:20 on May 31, 2016 ยท (Permalink)
ie the smallest number that is expressible into different ways as a sum of cubes.
made-u-look ยท 0 points ยท Posted at 12:05:35 on May 26, 2016 ยท (Permalink)
A=X
A+A=A+X
2A=A+X
2A-2X=A+X-2X
2(A-X)=A-X
2=1
iSquanch ยท 1 points ยท Posted at 15:26:55 on May 26, 2016 ยท (Permalink)
When you cancel out A-X, you're dividing 0รท0 because A=X. Can't do that - that's where your error is.
made-u-look ยท 1 points ยท Posted at 16:13:01 on May 26, 2016 ยท (Permalink)
ahhh thank you! I've been having trouble with this!
GeoCosmos ยท 0 points ยท Posted at 15:13:51 on May 26, 2016 ยท (Permalink)
That it was not or could not be proven that all even numbers have two prime number components.
glutamic_ ยท 0 points ยท Posted at 23:29:12 on May 26, 2016 ยท (Permalink)
So you have ex = โซ ex right? Rearrange to get ex - โซ ex = 0. Nothing strange there. Now factor out the โซ: (1 - โซ)ex = 0. Huh? Bear with me... Now write ex = 0 * 1 /(1 - โซ). Ok... Expand the geometric series of 1/(1-x): ex = 0 * (1 + โซ + โซโซ + โซโซโซ + ...) Take the 0 inside the integral: ex = 0 + โซ 0 + โซโซ 0 + โซโซโซ 0 + ... Let's ignore integration constants for simplicty, so โซ 0 = 1, โซโซ0 = โซ1 = x, โซโซโซ0 = โซโซ1 = โซx = โซx2/2 and so. This gives ex = 1 + x + x2/2 + x3/3! + ... The regular power series for ex.
[deleted] ยท -7 points ยท Posted at 17:01:14 on May 25, 2016 ยท (Permalink)
[deleted]
Sidco_cat ยท 3 points ยท Posted at 17:10:22 on May 25, 2016 ยท (Permalink)
If you give an inch, they will ram a kilometer down your throat.
Idiotnextdoor_2 ยท 3 points ยท Posted at 17:26:39 on May 25, 2016 ยท (Permalink)
I fucking hate those gallons and miles and pounds and the whole imperial system.
Waiting for downvotes.
ScarletNumbers ยท -4 points ยท Posted at 18:41:02 on May 25, 2016 ยท (Permalink)
math, not maths.
anyway, GCF(a,b)*LCM(a,b)=ab
xxxSnappyxxx ยท 1 points ยท Posted at 18:51:25 on May 25, 2016 ยท (Permalink)
Whoa there fellow American. Not good to assume our way of saying math is the correct way. The term "maths" is the proper British English way to refer to mathematics.
Math sounds singular and maths sounds plural, They both correctly refer to Mathematics.
ScarletNumbers ยท -1 points ยท Posted at 19:31:11 on May 25, 2016 ยท (Permalink)
I know, but this is reddit.com, not reddit.uk
xxxSnappyxxx ยท 2 points ยท Posted at 20:54:27 on May 25, 2016 ยท (Permalink)
True, but in all fairness, when you type in www.reddit.co.uk, it redirects to .com
[deleted] ยท 1 points ยท Posted at 09:22:20 on May 26, 2016 ยท (Permalink)
Well, it's also not reddit.us.
ScarletNumbers ยท 1 points ยท Posted at 15:49:56 on May 26, 2016 ยท (Permalink)
-_-
[.com] was originally administered by the United States Department of Defense, but is today operated by Verisign, and remains under ultimate jurisdiction of U.S. law.
shouldipropose ยท -3 points ยท Posted at 14:36:57 on May 25, 2016 ยท (Permalink)
if you could fold a piece of paper in half 27 times, i would eat a lot more tacos.
CFftVoN ยท -2 points ยท Posted at 15:39:04 on May 25, 2016 ยท (Permalink)*
The sum of all natural numbers (S = 1+2+3+4+5+...) has a finite sum and it happens to be -1/12.
It requires some series manipulation and many people aren't satisfied with one step of the process but it works and has been used in string theory and other strange branches of physics. This only works if you properly go out to infinity. If you stop short, you obviously just get a really large number.
Now take S - S2
JanEric1 ยท 3 points ยท Posted at 15:43:55 on May 25, 2016 ยท (Permalink)
you can only do these steps if your sequence converges, which it doesnt.
you can assign a number to the series and that is used in stringtheory but it is not the normal sum.
CFftVoN ยท -1 points ยท Posted at 15:50:39 on May 25, 2016 ยท (Permalink)
Yeah, that's the step of the process some people don't like. Still my favorite maths fact though so I feel I have adhered to thread requirements even though it's controversial.
[deleted] ยท 2 points ยท Posted at 16:43:33 on May 25, 2016 ยท (Permalink)
it's not even a fact, how can it be your favorite fact.
this is similar to saying my favorite fact is all Americans are overweight gun lovers.
JanEric1 ยท 1 points ยท Posted at 15:56:36 on May 25, 2016 ยท (Permalink)
well the math fact is not that the series converges(it doesnt) but rather that you can sensibly assign a finite value to it(-1/12) which has use in real physics.
what you basically do when you assign -1/12 to the series is that you say that you made a mistake earlier when you wrote 1+2+3... and actually meant zeta(-1) which equals -1/12
calichomp ยท -2 points ยท Posted at 22:38:56 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12. This got deleted earlier by the mods, so I'll post more about it.
It is based on the fact that the limit of the sum 1-1+1-1.... Is 1/2. The proof for this uses Reimann Suns.
From there is doesn't take much of a leap to get to -1/12. The result is used in quantum mechanics and string theory rather ubiquitously.
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_โฏ
Here are some YouTube links: http://m.youtube.com/watch?v=w-I6XTVZXww http://m.youtube.com/watch?v=0Oazb7IWzbA
If this comment gets taken down, I'll know the mods have something against -1/12.
overconvergent ยท 5 points ยท Posted at 22:58:53 on May 25, 2016 ยท (Permalink)
This is not true.
PM_ME_YOUR_PAULDRONS ยท 2 points ยท Posted at 00:35:55 on May 26, 2016 ยท (Permalink)
See my comment here for a proof that if that sum equals any real number x (including -1/12) then 1 = 0. Since 1 does not equal zero we can conclude that that sum does not equal any real number.
todjo929 ยท -2 points ยท Posted at 22:47:41 on May 25, 2016 ยท (Permalink)
sum(1,2,3...) = -1/12.
Source https://m.youtube.com/watch?v=w-I6XTVZXww
overconvergent ยท 3 points ยท Posted at 22:58:17 on May 25, 2016 ยท (Permalink)
This is not true.
PM_ME_YOUR_PAULDRONS ยท 2 points ยท Posted at 00:32:09 on May 26, 2016 ยท (Permalink)
See my answer here. Setting this sum equal to any real number x allows you to derive 1=0 which is a contradiction.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
Sidiabdulassar ยท -1 points ยท Posted at 23:00:15 on May 25, 2016 ยท (Permalink)
Woah. I would never have guessed. Serious brainf*ck.
Zardif ยท -2 points ยท Posted at 04:49:25 on May 26, 2016 ยท (Permalink)
The fact that it's pronounced math.
Iguanatan ยท 2 points ยท Posted at 08:11:21 on May 26, 2016 ยท (Permalink)
Not if you are in Australia.
Zardif ยท -1 points ยท Posted at 09:39:57 on May 26, 2016 ยท (Permalink)
Math was first.
https://youtu.be/SbZCECvoaTA
Iguanatan ยท 1 points ยท Posted at 10:17:00 on May 26, 2016 ยท (Permalink)
That wasn't my point. The fact is that we call it maths in Australia. I also think throughout Asia it is the same. Whatever came first is of zero relevance to my post, if you say math where I am people will look at you like you are an eejit. :)
[deleted] ยท -7 points ยท Posted at 14:34:26 on May 25, 2016 ยท (Permalink)
[deleted]
Umbrall ยท 5 points ยท Posted at 15:00:16 on May 25, 2016 ยท (Permalink)
They have the same number of numbers. We can map each number in (0,1) and (0,2) by simply doubling or halving, so every element pairs up.
Also for what it's worth the vast majority have decimal expansions that don't terminate or repeat, ala pi sqrt(2) etc
[deleted] ยท -3 points ยท Posted at 14:09:24 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 4 points ยท Posted at 15:33:03 on May 25, 2016 ยท (Permalink)
Not true.
[deleted] ยท 1 points ยท Posted at 17:02:00 on May 25, 2016 ยท (Permalink)
[deleted]
jywn4679 ยท 3 points ยท Posted at 17:09:33 on May 25, 2016 ยท (Permalink)
I can prove it.
Suppose 1+2+...=-1/12. Then, by the definition of a limit, with epsilon=1/12, there exists a natural number N such that whenever n is larger than N we have
1+2+...+n<1/12
however this last equality is false for n>0, a contradiction, so it does not converge to -1/12.
AlmightyNeckbeardo ยท -7 points ยท Posted at 14:43:26 on May 25, 2016 ยท (Permalink)
It's spelt math not maths you goddamn Limeys!
Go start a colony in Africa or something.
partofthevoid ยท -7 points ยท Posted at 14:52:47 on May 25, 2016 ยท (Permalink)
It's spelled math. Most of the rest of the (English speaking)world says it wrong.
[deleted] ยท -2 points ยท Posted at 16:07:34 on May 25, 2016 ยท (Permalink)*
[removed]
overconvergent ยท 3 points ยท Posted at 22:44:12 on May 25, 2016 ยท (Permalink)
This is not true. He proved that under some methods of assigning values to divergent infinite series, the divergent series 1+2+3+4+... is assigned the value -1/12. This is not the same thing as saying that the sum of the positive integers is -1/12. The series 1+2+3+4+... obviously diverges.
bmullan ยท 1 points ยท Posted at 16:14:29 on May 25, 2016 ยท (Permalink)
I think its also very cool that he was so poor he worked out all of his spectacular theorems using a piece of slate rock & chalk because he couldn't afford paper. At his death he left behind only 6 notebooks with mathematical theorems so complex that they are still trying to figure some of them out today 100 yrs later.
He has been called the equal of Albert Einstein in pure mathematics but had no real formal education.
eIImcxc ยท -5 points ยท Posted at 17:38:42 on May 25, 2016 ยท (Permalink)
1+2+3+4+...= - 0.5
This have been proven in a physic experiment too which only worked when this mathematic fact has been applied. This formula proves the limit of our imagination for me.
[deleted] ยท -4 points ยท Posted at 19:53:03 on May 25, 2016 ยท (Permalink)
[deleted]
flyingjam ยท 3 points ยท Posted at 19:55:16 on May 25, 2016 ยท (Permalink)
No, that series is divergent and the sum does not exists. You can assign it a value with certain summation methods (Ramanujan and Zeta regularization puts it at -1/12). But that doesn't change the fact that it's divergent.
[deleted] ยท -4 points ยท Posted at 22:05:05 on May 25, 2016 ยท (Permalink)
This was literally posted two days ago. Also learn to spell
loptthetreacherous ยท 3 points ยท Posted at 22:52:36 on May 25, 2016 ยท (Permalink)
I don't see any spelling errors.
[deleted] ยท -2 points ยท Posted at 22:53:41 on May 25, 2016 ยท (Permalink)
*maths
loptthetreacherous ยท 2 points ยท Posted at 23:00:22 on May 25, 2016 ยท (Permalink)
Which is how it's abbreviated in Britain. Not a spelling mistake, a cultural difference.
Iron_Man_977 ยท -4 points ยท Posted at 22:48:35 on May 25, 2016 ยท (Permalink)*
The sum of all natural numbers, i.e. 1+2+3+4+5+6+7+8...... etc. is equal to -1/12. How does that work? Nobody really knows, it just does.
Edit: mixed up real numbers and natural numbers. My bad.
overconvergent ยท 3 points ยท Posted at 22:58:01 on May 25, 2016 ยท (Permalink)
First of all, you mean the natural numbers, not the real numbers. Second, the sum of that series is not -1/12. The series obviously diverges.
Iron_Man_977 ยท -4 points ยท Posted at 23:01:46 on May 25, 2016 ยท (Permalink)
You're right about that first part, sorry, I always get those mixed up. You're only half right about the second part. Yes, the series does diverge, but it is also equal to -1/12
overconvergent ยท 4 points ยท Posted at 23:02:37 on May 25, 2016 ยท (Permalink)
Those statements directly contradict each other.
There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
PM_ME_YOUR_PAULDRONS ยท 3 points ยท Posted at 00:33:23 on May 26, 2016 ยท (Permalink)
See my answer here. Setting that sum equal to any real number gives a contradiction. If that sum converges to a real number (including -1/12) then 1 = 0.
gregIsBae ยท -4 points ยท Posted at 00:27:41 on May 26, 2016 ยท (Permalink)
The sum of all numbers is -1/12
overconvergent ยท 5 points ยท Posted at 01:07:56 on May 26, 2016 ยท (Permalink)
No, it isn't.
magichobo3 ยท -4 points ยท Posted at 03:42:52 on May 26, 2016 ยท (Permalink)
It's spelled math not maths
iSquanch ยท 3 points ยท Posted at 03:53:43 on May 26, 2016 ยท (Permalink)
In Asia the subject is called maths, not math. The more you know.
astalavista114 ยท 3 points ยท Posted at 04:24:17 on May 26, 2016 ยท (Permalink)
FTFY
atc ยท 3 points ยท Posted at 05:32:41 on May 26, 2016 ยท (Permalink)
This therefore means the majority of the English speaking world says "maths" and not math.
AlekRivard ยท -1 points ยท Posted at 12:43:38 on May 25, 2016 ยท (Permalink)*
.99 repeating equals 1
Let n = .99 so 10n = 9.99
Subtracting the first equation from the second yields: 9n = 9
Since the repeating decimals subtract out which gives us n = 1, but we know that n = .99 so .99 = 1
oighen ยท 0 points ยท Posted at 12:59:17 on May 25, 2016 ยท (Permalink)
If you type four spaces before your line reddit interprets it as code, just write 0.99... to represent repeating decimals.
[deleted] ยท -1 points ยท Posted at 12:44:47 on May 25, 2016 ยท (Permalink)
[deleted]
Marconator ยท 1 points ยท Posted at 14:16:19 on May 25, 2016 ยท (Permalink)
Awww
Dd_8630 ยท -1 points ยท Posted at 14:07:44 on May 25, 2016 ยท (Permalink)
0.999... = 1
I also find Dedekind cuts to be brain melting.
wasnt_a_fluke ยท -1 points ยท Posted at 14:30:47 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
ben1996123 ยท 1 points ยท Posted at 18:33:27 on May 25, 2016 ยท (Permalink)
false
ze_ben ยท -1 points ยท Posted at 14:33:57 on May 25, 2016 ยท (Permalink)
That in America it's just math.
Purple_Satyr ยท 1 points ยท Posted at 14:39:43 on May 25, 2016 ยท (Permalink)
We're so weird. I mean it's normal for us but we do so many things our own way that the rest of the world does uniformly. It's not even like what we do is better it's just different.
[deleted] ยท -1 points ยท Posted at 14:39:31 on May 25, 2016 ยท (Permalink)
Capitalism can be expressed with one differential equation: d$/dt = k$ (change in money is directly proportional to the amount of money you have)
JonnyNashEquilibria ยท -1 points ยท Posted at 14:45:08 on May 25, 2016 ยท (Permalink)
If you travelled enough distance away from earth and then returned, you would feel the same except you would actually be a mirror-image of yourself.
Was an example used in topolgy when looking at Mobius strips and non-orientable surfaces.
EnterprisingAss ยท -1 points ยท Posted at 14:46:14 on May 25, 2016 ยท (Permalink)
400,000 rupees is worth about $6000 US.
MathDotSqrt ยท -1 points ยท Posted at 14:46:59 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + . . . = -1/12
This one still boggles my mind, but there is a number file vid on it.
ben1996123 ยท 2 points ยท Posted at 18:35:04 on May 25, 2016 ยท (Permalink)
false.
CAKEGamingHub ยท -1 points ยท Posted at 14:49:33 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers (1+2+3+...) is -1/12
ben1996123 ยท 2 points ยท Posted at 18:36:01 on May 25, 2016 ยท (Permalink)
no it isnt
CAKEGamingHub ยท 0 points ยท Posted at 19:39:56 on May 25, 2016 ยท (Permalink)
https://youtu.be/w-I6XTVZXww
Explaination of the proof.
ben1996123 ยท 2 points ยท Posted at 20:08:56 on May 25, 2016 ยท (Permalink)
i am well aware of this completely incorrect video.
CAKEGamingHub ยท 0 points ยท Posted at 20:46:15 on May 25, 2016 ยท (Permalink)
So why is it incorrect then, when Riemann Zeta function proofs exist?
ben1996123 ยท 2 points ยท Posted at 20:55:13 on May 25, 2016 ยท (Permalink)
zeta(-1) = -1/12, but zeta(s) is only defined as 1 + 1/2s + 1/3s + ... when re(s) > 1. -1 is not greater than 1 so this definition does not apply
JanEric1 ยท 2 points ยท Posted at 10:24:54 on May 26, 2016 ยท (Permalink)
fighting the good fight
[deleted] ยท -1 points ยท Posted at 14:51:26 on May 25, 2016 ยท (Permalink)*
[deleted]
ben1996123 ยท 3 points ยท Posted at 18:36:19 on May 25, 2016 ยท (Permalink)
no it is not
brandonmcgritle ยท -1 points ยท Posted at 14:54:19 on May 25, 2016 ยท (Permalink)
69 = sex
only-the-lonely ยท -1 points ยท Posted at 14:54:53 on May 25, 2016 ยท (Permalink)
Toast + 3 = Green
ArkonOridan ยท -1 points ยท Posted at 14:55:03 on May 25, 2016 ยท (Permalink)
2 + 2 = Fish.
[deleted] ยท 1 points ยท Posted at 17:28:34 on May 25, 2016 ยท (Permalink)
https://qph.is.quoracdn.net/main-qimg-d9e2a77943a9fbd347683cc05f9e330e?convert_to_webp=true
ArkonOridan ยท 1 points ยท Posted at 17:35:19 on May 25, 2016 ยท (Permalink)
So it was foretold!
[deleted] ยท -1 points ยท Posted at 14:56:42 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 2 points ยท Posted at 14:58:17 on May 25, 2016 ยท (Permalink)*
[removed]
MoXY_Jellyfish ยท -1 points ยท Posted at 14:58:15 on May 25, 2016 ยท (Permalink)
111,111,111*111,111,111=123,456,789,987,654,321
Gawd_Awful ยท -1 points ยท Posted at 14:59:08 on May 25, 2016 ยท (Permalink)
Multiplying things by 9 and if you keep adding the digits in the product, you eventually get back to 9.
louden255 ยท -1 points ยท Posted at 15:01:17 on May 25, 2016 ยท (Permalink)
1+1=4
[deleted] ยท -1 points ยท Posted at 15:02:39 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 22:05:54 on May 25, 2016 ยท (Permalink)
You're being somewhat unfairly downvoted, as there are ways to manipulate the sequence in order to argue that it sums to -1/12. These are called summation methods. There are lots of them, so it's misleading to say that any one answer is the "right" answer. You may get a different answer from a given infinite divergent series sum depending on the method you go with.
ben1996123 ยท 1 points ยท Posted at 18:38:05 on May 25, 2016 ยท (Permalink)
the sum of all natural numbers is not -1/12.
[deleted] ยท 0 points ยท Posted at 18:56:26 on May 25, 2016 ยท (Permalink)
[deleted]
ben1996123 ยท 2 points ยท Posted at 18:58:27 on May 25, 2016 ยท (Permalink)
the sum of all natural numbers is infinite.
[deleted] ยท 0 points ยท Posted at 18:57:52 on May 25, 2016 ยท (Permalink)
[deleted]
ben1996123 ยท 2 points ยท Posted at 18:58:37 on May 25, 2016 ยท (Permalink)
no you can not.
overconvergent ยท 1 points ยท Posted at 22:54:41 on May 25, 2016 ยท (Permalink)
You cannot prove that the sum of that series is -1/12 because that series diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 0 points ยท Posted at 03:24:40 on May 26, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 1 points ยท Posted at 03:30:04 on May 26, 2016 ยท (Permalink)
It is correct to say that zeta(-1)=-1/12. It is correct to say that the Ramanujan summation of the function f(x)=x on the positive integers is -1/12. It is not correct to say that the sum of the natural numbers is -1/12. The series 1+2+3+... diverges and does not have a value in the usual sense.
GaiusAurus ยท -1 points ยท Posted at 15:06:55 on May 25, 2016 ยท (Permalink)
The proof of 1+1=2 can be very long (300 pages long), depending on how many things you consider axiomatic, or too trivial to need to prove.
ASLOBEAR ยท -1 points ยท Posted at 15:07:17 on May 25, 2016 ยท (Permalink)
The unit circle can be memorized using your left hand https://youtu.be/LE6dmczMc68
MercenaryOfTroy ยท -1 points ยท Posted at 15:10:40 on May 25, 2016 ยท (Permalink)
1+2+3+4+... = -1/12
ben1996123 ยท 3 points ยท Posted at 18:38:56 on May 25, 2016 ยท (Permalink)
incorrect
MercenaryOfTroy ยท 0 points ยท Posted at 19:08:46 on May 25, 2016 ยท (Permalink)
look it up. it is correct
ben1996123 ยท 3 points ยท Posted at 19:10:34 on May 25, 2016 ยท (Permalink)
no it is not.
MercenaryOfTroy ยท 0 points ยท Posted at 19:12:04 on May 25, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
ben1996123 ยท 2 points ยท Posted at 19:16:27 on May 25, 2016 ยท (Permalink)
i am well aware of the existence of this article. 1+2+3+... does not equal -1/12.
MercenaryOfTroy ยท 0 points ยท Posted at 19:25:05 on May 25, 2016 ยท (Permalink)
here is a video explaining it
https://www.youtube.com/watch?v=w-I6XTVZXww
ben1996123 ยท 3 points ยท Posted at 19:25:51 on May 25, 2016 ยท (Permalink)
i am well aware of the existence of this (completely incorrect) video.
buffalosubcon ยท -1 points ยท Posted at 15:18:49 on May 25, 2016 ยท (Permalink)*
The sum of all natural numbers (positive numbers etc.) is - 1/12.
You've added all these numbers and you get a negative number!
Edit: explained natural numbers
overconvergent ยท 2 points ยท Posted at 22:36:11 on May 25, 2016 ยท (Permalink)
This is not true.
buffalosubcon ยท 0 points ยท Posted at 01:16:07 on May 26, 2016 ยท (Permalink)
This is absolutely true. There's a great proof of it here: https://youtu.be/w-I6XTVZXww
The key is remembering that we're starting from one and adding natural numbers. There aren't any negatives. And we don't ever stop adding these numbers. It's an infinite sum. You couldn't prove this on a calculator because as soon as you pressed the equals key, it wouldnt be infinite.
It's crazy but it's true. I promise.
overconvergent ยท 2 points ยท Posted at 01:20:11 on May 26, 2016 ยท (Permalink)
This video is extremely misleading, and the math it uses is completely incorrect. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
kof_zpt ยท -1 points ยท Posted at 15:40:01 on May 25, 2016 ยท (Permalink)
infinity=1
CrazyKirby97 ยท -1 points ยท Posted at 15:40:09 on May 25, 2016 ยท (Permalink)
Technically, if 1/0=infinity, 1/infinity=0. Infinity is a number so big that it fits into any other number exactly 0 times.
[deleted] ยท 1 points ยท Posted at 16:42:12 on May 25, 2016 ยท (Permalink)
infinity isn't a number.
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 22:02:05 on May 25, 2016 ยท (Permalink)
Infinity isn't a real number. There exist (perfectly sane, well studied, well behaved and understood) number systems in which you can treat infinity. For example infinity is certainly a projective real number. It is also an affine real number, a projective complex number and a whole bunch of others.
cubonelvl69 ยท -1 points ยท Posted at 15:42:08 on May 25, 2016 ยท (Permalink)*
1+2+3+4...... all the way to infinity is equal to -1/12.
Also, in order to prove this, you also prove that 1-2+3-4+5...is equal to 1/4
https://www.youtube.com/watch?v=w-I6XTVZXww
overconvergent ยท 2 points ยท Posted at 22:36:29 on May 25, 2016 ยท (Permalink)
This is not true.
seanrm92 ยท -1 points ยท Posted at 15:42:57 on May 25, 2016 ยท (Permalink)
1+2+3+4+5.....= -1/12
JanEric1 ยท 2 points ยท Posted at 10:26:00 on May 26, 2016 ยท (Permalink)
no!
Quikheat ยท -1 points ยท Posted at 15:44:07 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is equal to -1/12.
1 + 2 + 3 + 4 + 5 +....... = -1/12.
JanEric1 ยท 2 points ยท Posted at 10:26:06 on May 26, 2016 ยท (Permalink)
no!
rets_law ยท -1 points ยท Posted at 15:57:43 on May 25, 2016 ยท (Permalink)
That people who call it maths are idiots.
_marther_ ยท 1 points ยท Posted at 18:50:57 on May 25, 2016 ยท (Permalink)
Or people from anywhere other than the US.
Banzai51 ยท -1 points ยท Posted at 15:58:40 on May 25, 2016 ยท (Permalink)
That we told a king to go get bent so we could call it math.
;-)
zombiebandit ยท -1 points ยท Posted at 16:06:10 on May 25, 2016 ยท (Permalink)
My favorite is the fact that I don't have to do math anymore. #graduated
[deleted] ยท -1 points ยท Posted at 16:19:14 on May 25, 2016 ยท (Permalink)
[deleted]
elspazzo ยท 3 points ยท Posted at 16:46:27 on May 25, 2016 ยท (Permalink)
Yeah, but 22/7 is close to pi than 3.14 is.
Plus, it's not supposed to be pi, just an easy approximation using smallish integers.
Almostatimelord ยท -1 points ยท Posted at 16:42:03 on May 25, 2016 ยท (Permalink)
My favorite fact is that it's called "math"
hamsterbars ยท -1 points ยท Posted at 16:43:18 on May 25, 2016 ยท (Permalink)
The sum of all the integers from 1 up to infinity is equal to -1/12
benkbenkbenk ยท -1 points ยท Posted at 16:43:50 on May 25, 2016 ยท (Permalink)
If you line up all the people in the world stood up toe to toe around the equator, you'll be late for work.
Troll_Random ยท -1 points ยท Posted at 16:49:49 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + 6 + 7 + .... = -1/12
redditisadamndrug ยท 2 points ยท Posted at 16:51:42 on May 25, 2016 ยท (Permalink)
If you add up every number from 1 to infinity, AN answer is -1/12.
Another answer is that it is divergent and does not sum to a finite number. It all depends on your definition of "infinite sum".
sebwiers ยท -1 points ยท Posted at 16:50:13 on May 25, 2016 ยท (Permalink)
The sum of the infinite series containing all the positive integers is -1/12
JanEric1 ยท 1 points ยท Posted at 10:26:21 on May 26, 2016 ยท (Permalink)
stooooop
crugerdk ยท -1 points ยท Posted at 16:56:08 on May 25, 2016 ยท (Permalink)
That the infinite sum of all natural numbers equals -1/12
It doesnt make any sense, but its true.
redditisadamndrug ยท 1 points ยท Posted at 16:58:53 on May 25, 2016 ยท (Permalink)
An infinite sum of all natural numbers can equal -1/12. You can also validly say that they don't sum to a finite number.
It depends on your definitions of infinite sums.
kharnel917 ยท -1 points ยท Posted at 17:05:01 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+..... = -1/12
[deleted] ยท -1 points ยท Posted at 17:23:06 on May 25, 2016 ยท (Permalink)
E=McVagina, vagina. I wanna have sex with your vagina...
cpierr03 ยท -1 points ยท Posted at 17:32:40 on May 25, 2016 ยท (Permalink)
FACT:
Every person that has or will major in mathematics will die, or has died.
Let that sink in for a moment.
Squiddleh ยท -1 points ยท Posted at 17:37:38 on May 25, 2016 ยท (Permalink)
Used to be ei*pi - 1 = 0 , but now its: The sum of all natural numbers = -1/12 https://m.youtube.com/watch?v=w-I6XTVZXww
Warbl_Garbl ยท -1 points ยท Posted at 17:39:24 on May 25, 2016 ยท (Permalink)
Favourite? Maths? You're from the UK.
darichtt ยท -1 points ยท Posted at 17:41:58 on May 25, 2016 ยท (Permalink)
Sum of all natural numbers is -1/12.
JanEric1 ยท 2 points ยท Posted at 10:34:22 on May 26, 2016 ยท (Permalink)
nope
[deleted] ยท -1 points ยท Posted at 17:43:13 on May 25, 2016 ยท (Permalink)
1+1=1
DeerOnTheRocks ยท -1 points ยท Posted at 17:49:39 on May 25, 2016 ยท (Permalink)
The sum from 1 to infinity is 1/12
JanEric1 ยท 2 points ยท Posted at 10:34:34 on May 26, 2016 ยท (Permalink)
nope
DeerOnTheRocks ยท 1 points ยท Posted at 15:10:27 on May 26, 2016 ยท (Permalink)
Opps I meant -1/12. http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.8029
JanEric1 ยท 2 points ยท Posted at 15:58:13 on May 26, 2016 ยท (Permalink)
neither
DeerOnTheRocks ยท 1 points ยท Posted at 15:59:31 on May 26, 2016 ยท (Permalink)
What do you mean? It is true. Pretty much everyone learns this in college calculus
JanEric1 ยท 2 points ยท Posted at 16:08:41 on May 26, 2016 ยท (Permalink)
well it is wrong, just do the cauchy-test. you see that it obviously diverges
DeerOnTheRocks ยท 1 points ยท Posted at 16:12:53 on May 26, 2016 ยท (Permalink)
Technically yes but it still can go to -1/12. Let's be honest you and me both don't understand this proof enough to fully debate it, so just drop it.
JanEric1 ยท 2 points ยท Posted at 16:14:51 on May 26, 2016 ยท (Permalink)
...the series is divergent. even a 5th grader can check that.
DeerOnTheRocks ยท 1 points ยท Posted at 16:18:43 on May 26, 2016 ยท (Permalink)
THATS NOT THE POINT OF THE PROOF
JanEric1 ยท 2 points ยท Posted at 16:22:43 on May 26, 2016 ยท (Permalink)
the sum is not -1/12 as the series diverges, aka it has no sum...
DeerOnTheRocks ยท 1 points ยท Posted at 16:26:22 on May 26, 2016 ยท (Permalink)
But you have to manipulate the sum
JanEric1 ยท 2 points ยท Posted at 16:28:25 on May 26, 2016 ยท (Permalink)
but you cant because it doesnt converge
DeerOnTheRocks ยท 1 points ยท Posted at 16:29:55 on May 26, 2016 ยท (Permalink)
Who says you can't! It's not a simple converge/diverge test
JanEric1 ยท 2 points ยท Posted at 16:45:13 on May 26, 2016 ยท (Permalink)
you have to first show that a series converges to then be allowed to manipulate it like this.
simply because these operations are only defined on the real numbers. and it turns out that if the series converges and you do these operations the end result converges again to the expected result if you do it with the normal limits. thats why you can do it for convergent ones.
DeerOnTheRocks ยท 1 points ยท Posted at 16:00:49 on May 26, 2016 ยท (Permalink)
The proof is not false
JanEric1 ยท 2 points ยท Posted at 16:09:30 on May 26, 2016 ยท (Permalink)
the one where you take the series and multiply it and move it around? that one is.
Potemkin78 ยท -1 points ยท Posted at 17:50:10 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is probably -1/12.
https://www.youtube.com/watch?v=w-I6XTVZXww
flyingjam ยท 3 points ยท Posted at 17:50:36 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
mariejo06 ยท -1 points ยท Posted at 17:51:40 on May 25, 2016 ยท (Permalink)
That it's hard and makes life complicated hahaha
naty-molas ยท -1 points ยท Posted at 17:51:56 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+... = -1/12. I can't begin to explain it but I've read the explanation and it checks out.
flyingjam ยท 5 points ยท Posted at 17:53:22 on May 25, 2016 ยท (Permalink)
No, the ramanujan or zeta sum of the series of all natural numbers is -1/12. The series is quite obviously divergent.
You probably watched the numberphile video. You cannot do the manipulations they did with a divergent sum.
naty-molas ยท 0 points ยท Posted at 18:05:02 on May 25, 2016 ยท (Permalink)
Would you mind citing sources disproving it? I don't claim to know enough to back up my claim, but I did see the numberphile video and read the wiki and a few other articles and it seemed to check out everytime.
flyingjam ยท 3 points ยท Posted at 18:06:52 on May 25, 2016 ยท (Permalink)
Here's the wikipedia page. https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
The very first line is
Numberphile actually has a followup video in which they clear some of the misconceptions that they had in the original video.
Piss_on ยท -1 points ยท Posted at 17:52:04 on May 25, 2016 ยท (Permalink)
LoL Nerd Alert!
backspace8908 ยท -1 points ยท Posted at 17:52:35 on May 25, 2016 ยท (Permalink)
The sum of all whole numbers is - 1/12
Fusion2k ยท -1 points ยท Posted at 17:53:26 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+ ... = -1/12 Blew my mind...
JanEric1 ยท 1 points ยท Posted at 10:35:44 on May 26, 2016 ยท (Permalink)
because it is wrong
Fusion2k ยท 1 points ยท Posted at 20:00:18 on May 28, 2016 ยท (Permalink)
not really https://www.youtube.com/watch?v=w-I6XTVZXww
JanEric1 ยท 1 points ยท Posted at 20:07:13 on May 28, 2016 ยท (Permalink)
that video is wrong, or rather misleading.
Fusion2k ยท 1 points ยท Posted at 13:57:23 on May 29, 2016 ยท (Permalink)
Why is that?
JanEric1 ยท 1 points ยท Posted at 13:58:46 on May 29, 2016 ยท (Permalink)
because you cant manipulate non-convergent serieses like that
guntygoo ยท -1 points ยท Posted at 17:54:54 on May 25, 2016 ยท (Permalink)
all the numbers is infinity.
Negro_Jihad ยท -1 points ยท Posted at 17:55:48 on May 25, 2016 ยท (Permalink)
mathematics is gay?
tisom ยท -1 points ยท Posted at 17:56:04 on May 25, 2016 ยท (Permalink)
1+2+3+4+...=-1/12
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_โฏ
flyingjam ยท 2 points ยท Posted at 17:58:20 on May 25, 2016 ยท (Permalink)
The very first line is
The series is very obviously divergent and goes towards infinity. You can assign it a value (-1/12) with the zeta function.
tisom ยท 0 points ยท Posted at 03:04:46 on May 26, 2016 ยท (Permalink)
It is a divergent series, and it does appear to be heading towards infinity, but then the question comes up of what we mean by infinity. Of course, infinity is not really a number that is well defined, so we have to use the Riemann Zeta function to make sense of it. You seem to not like the idea of "assigning" it a value, but it actually comes from the idea of analytic continuation, which is a of critical importance to dealing with functions that have singularities. The fact that we can sum all these numbers and put a bounded answer on it is really important for things like calculating the Casimir force in physics (basically the idea is that electromagnetic fields are quantized or discreet, and each "mode" carries energy and can exert radiation pressure. If we run an experiment where we put two metal plates very close together, we actually restrict what modes can exist between them. We find that due to the lack of these modes, we also forbids vacuum fluctuations from occurring at these frequencies, and this causes the radiation pressure between the plates to be slightly less than on the outer edges, giving the places a small attractive force). The fact that electromagnetic fields can exist at frequencies that seem to diverge means that to understand them we have to be able to sum their contributions without just getting infinity, as you suggest by writing off my comment.
JanEric1 ยท 1 points ยท Posted at 10:38:37 on May 26, 2016 ยท (Permalink)
1+2+3+4.. does not equal -1/12. but as you said you can assign that value to it which does have physical meaning. but what you do when you assign that value to the series is kinda like saying that you made a mistake when you wrote 1+2+3... and should have wrote zeta(-1) which equals -1/12
tisom ยท 1 points ยท Posted at 12:40:02 on May 26, 2016 ยท (Permalink)*
What do you mean by a mistake? Isn't zeta(-1) = 1+ 2 + 3 + ... ?
Edit: ok I found an article which seems to support what you and u/flyingjam seem to be on the brigade about, that this result is "wrong:"
https://plus.maths.org/content/infinity-or-just-112
But at the same time, it explains how the Riemann Zeta function is just what you get when you use analytic continuation on the Euler Zeta function, extending the values you can plug in from x>1 to include x<=-1 as well as complex numbers. And when you do that, you get the -1/12. So are the author and you arguing that analytic continuation is wrong, even though it's a pretty important principle in complex analysis? At what stage do things go awry? Also, if the result of us assigning a value to the series is incorrect, but actually corresponds to experimentally verified results (for s=-3 because they are looking at 3D Casimir forces rather than 1D), then doesn't that validate the theory which you are claiming is wrong?
I'm not a mathematician, so please forgive me if I am missing some subtlety here, but I ask because I'm genuinely curious and want to learn.
JanEric1 ยท 1 points ยท Posted at 13:27:16 on May 26, 2016 ยท (Permalink)
zeta function is only defined by that series for s>1, which -1 isnt.
and -1/12 is what you get from the analytic continuation and plugging in -1. which is why you can assign the value -1/12 to is and why this appears in physics. what you do when you replace 1+2+3.. with -1/12 is that you say that you made a mistake when you wrote 1+2+3 and actually meant zeta(-1)(which isnt 1+2+3..) which is -1/12.
so there are ways to assign -1/12 to this series, but it is not the normal sum, as the series obviously diverges.
[deleted] ยท -1 points ยท Posted at 17:58:28 on May 25, 2016 ยท (Permalink)*
deleted What is this?
[deleted] ยท -1 points ยท Posted at 17:58:31 on May 25, 2016 ยท (Permalink)
[deleted]
JanEric1 ยท 1 points ยท Posted at 10:39:08 on May 26, 2016 ยท (Permalink)
if you have a proof go and collect your million dollars
mrkisch ยท -1 points ยท Posted at 17:59:00 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
Just blow my mind everytime !
https://www.youtube.com/watch?v=w-I6XTVZXww
eyal0 ยท -1 points ยท Posted at 18:02:03 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7... = 1/12
antibubbles ยท -1 points ยท Posted at 18:02:12 on May 25, 2016 ยท (Permalink)*
wubalubadubdub What is this?
mattysimp27 ยท -1 points ยท Posted at 18:03:15 on May 25, 2016 ยท (Permalink)
If you add all the natural numbers, so 1+2+3+4+5+..., All the way up to infinity it equals -1/12.
Also 0.99999..., so 0.9 recurring, is exactly equal to 1.
phat_asian_kid ยท -1 points ยท Posted at 18:04:16 on May 25, 2016 ยท (Permalink)
The sum of all positive integers equals -1/12. video
nirad ยท -1 points ยท Posted at 18:04:21 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers = -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
POINTEEEE ยท -1 points ยท Posted at 18:04:34 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers equals -1/12
1 + 2 + 3 + 4 + 5 + ... = -1/12
Not only is this completely counterintuitive but it actually shows up in physics and is a useful theorem.
Physex4Phun ยท -1 points ยท Posted at 18:08:42 on May 25, 2016 ยท (Permalink)
The sum of positive integers from 1 to infinity is equal to -1/12 https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
flyingjam ยท 3 points ยท Posted at 18:10:21 on May 25, 2016 ยท (Permalink)
The very first line from the wikipedia page:
The series is divergent and doesn't not equal anything. But you can assign values to it with certain summation methods.
Physex4Phun ยท 1 points ยท Posted at 22:51:35 on May 25, 2016 ยท (Permalink)
What is the difference between assigning a value to it and saying it's equal? I'm not a mathematician, and I'm genuinely curious. I like these videos that explaining better than I can: https://www.youtube.com/watch?v=w-I6XTVZXww https://www.youtube.com/watch?v=jcKRGpMiVTw It's also related to the Riemann-Zeta function, which is used in explaining physical phenomenon (a lot in QED).
flyingjam ยท 1 points ยท Posted at 22:54:20 on May 25, 2016 ยท (Permalink)
It's kinda like saying "This series diverges, BUT what if it didn't? What would happen if we used these summation methods which work for converging series and applied it to this divergent series?". The value you get is not the sum of the series, but it can still be useful. Really, the reason why this one is so famous is that it has applications in string theory regarding the number of dimensions needed to do what they want.
BringATwenty ยท -1 points ยท Posted at 18:18:27 on May 25, 2016 ยท (Permalink)
That on average one person dies on earth every 2 seconds..
So if you believe in Jesus you only have two seconds for that long, leisurely "walk and talk" with him like in "Footprints in the Sand" until the next person shows up for their long walk and talk lol.
Internutt ยท -1 points ยท Posted at 18:20:02 on May 25, 2016 ยท (Permalink)
8008135
InertBaller ยท -1 points ยท Posted at 18:20:40 on May 25, 2016 ยท (Permalink)*
My favorite maths fact is, "There's no way we're using this trigonometry shit after high school."
*Oh, for god's sake, nerds, it was a joke. You do all the calculus you like, I'll stick to the math with a dollar sign in front of it.
s0lv3 ยท 2 points ยท Posted at 18:49:36 on May 25, 2016 ยท (Permalink)
Decides to study physics/math
JanEric1 ยท 2 points ยท Posted at 10:40:35 on May 26, 2016 ยท (Permalink)
im using that stuff, ALOT
Caasi67 ยท -1 points ยท Posted at 18:30:25 on May 25, 2016 ยท (Permalink)
1/3 is the same as .3..., but 1/3 + 1/3 + 1/3 = a nice even 1, whereas .3... equals .9...
The arithmetic doesn't really add up, but we pretend it does and it's super useful to solve real world problems... but it doesn't really add up!
flyingjam ยท 2 points ยท Posted at 18:33:30 on May 25, 2016 ยท (Permalink)
.999... is equal to 1. ... is defined by an infinite series, and for .999..., it's the infinite series (9/10)n, which is equal to 1.
Caasi67 ยท 0 points ยท Posted at 18:48:09 on May 25, 2016 ยท (Permalink)
Those are the rules we define, and it works to solve problems, but isn't also technically correct to say .9... is infinitely close to 1 but not actually 1?
flyingjam ยท 2 points ยท Posted at 19:05:24 on May 25, 2016 ยท (Permalink)
No, it is exactly equal to 1. Math is what we define; and we have defined to be the sum of that infinite series, which is equally 1.
Caasi67 ยท 1 points ยท Posted at 19:27:12 on May 25, 2016 ยท (Permalink)
I agree and maybe your point is that since math has defined it that way it doesn't count as a math fact?
Out of curiosity, what would you define as the closest possible number to 1 that is not also 1?
flyingjam ยท 2 points ยท Posted at 19:30:14 on May 25, 2016 ยท (Permalink)
There is no such number in the reals. You can have infinitesimals in other number systems, like the hyperreals, but let's just not go there.
s0lv3 ยท 1 points ยท Posted at 18:44:51 on May 25, 2016 ยท (Permalink)
1/3 does not equal .3 though.
Caasi67 ยท 1 points ยท Posted at 18:47:16 on May 25, 2016 ยท (Permalink)
the ... was meant to indicate that the number repeats forever, or is that not what you meant?
NowISeeBeesIWon ยท -1 points ยท Posted at 18:30:34 on May 25, 2016 ยท (Permalink)
The sum of all whole numbers: 1+2+3+4+5...forever is -1/12. The sum of the cubes of all whole numbers: 13 + 23 + 33 + 43 + 53 + 63 + ... is +1/120. True story!
s0lv3 ยท 1 points ยท Posted at 18:44:19 on May 25, 2016 ยท (Permalink)
Okay if you are a mathematician or something PLEASE explain to me the first one and how that can be true. I've had it proved for me mathematically, and I get the math. But how is it that when you add positive integers, you get a negative number that is not an integer.
overconvergent ยท 1 points ยท Posted at 22:48:49 on May 25, 2016 ยท (Permalink)
Neither of these statements is true. There are ways of assigning values to divergent infinite series, and under some (but not all) of these methods, the value -1/12 is assigned to the series 1+2+3+4+... But as you would correctly assume, if you are using the standard definitions, the series 1+2+3+4+... obviously diverges (grows larger without bound as you add more terms).
NowISeeBeesIWon ยท 1 points ยท Posted at 04:39:35 on May 26, 2016 ยท (Permalink)
Nobody really knows "why" but these values emerge in the real world (eg, The Cassimir Effect uses 1/120 as a substitute for the sum of cubes, and it's proven as accurate). Some say that, really, it's -1/12 + infinity, or 1/120 + infinity, and that in solving these maths creatively the infinities cancel out. That's all I got!
s0lv3 ยท 1 points ยท Posted at 07:22:27 on May 26, 2016 ยท (Permalink)
So interesting I can't wait to learn these things.
oscars2010 ยท -1 points ยท Posted at 18:43:11 on May 25, 2016 ยท (Permalink)
please excuse my dear aunt sally- parenthesis exponents multiplication division addition subtraction
Douchebro86 ยท -1 points ยท Posted at 18:43:56 on May 25, 2016 ยท (Permalink)
3+3*2=12 on a normal calculator, but 9 on a scientific calculator
amrasmin ยท -1 points ยท Posted at 18:44:15 on May 25, 2016 ยท (Permalink)
Math stinks, thats a fact!
JX3D97 ยท -1 points ยท Posted at 18:56:59 on May 25, 2016 ยท (Permalink)
That in Britain other subjects are Historys, Sciences, Englishs...
KingstonHurtsville ยท -1 points ยท Posted at 18:58:47 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12. Mind boggling
Matech ยท 1 points ยท Posted at 19:11:33 on May 25, 2016 ยท (Permalink)
Yup , my hatred for math grows. Even as Eli5 i still dont understand or agree, he even sayd its rounded.. The fuck? U cant just do that, thats a lie, you cant continually add whole numbers and get a fraction zero fucking sense you would just get a larger and larger whole number, ass hat math making something that isnt there.
JanEric1 ยท 1 points ยท Posted at 10:42:39 on May 26, 2016 ยท (Permalink)
your hatred for doing math wrong should grow. the sum of all natural numbers goes to infinity.
LukeWiLDz ยท -1 points ยท Posted at 19:01:53 on May 25, 2016 ยท (Permalink)
missed spelled favorite
[deleted] ยท -1 points ยท Posted at 19:02:40 on May 25, 2016 ยท (Permalink)
If time is infinite, the probability of something happening becomes 1
falcon_from_bombay ยท -1 points ยท Posted at 19:06:40 on May 25, 2016 ยท (Permalink)
Any whole number itself -(Sum of digits in a number)= divisible by 9.
Eg. In case of 47,
47-(4+7)= 36= 9*3
Myid0810 ยท -1 points ยท Posted at 19:10:00 on May 25, 2016 ยท (Permalink)
as a child i was heavily into mental maths and crunching numbers...i had come up with a formula on my own back then...just pure dumb luck and lots of time at hand helped... true story and my own fav math fact...
monitorape ยท -1 points ยท Posted at 19:10:19 on May 25, 2016 ยท (Permalink)
That infinity > infinity
WesleyPosvar ยท -1 points ยท Posted at 19:13:10 on May 25, 2016 ยท (Permalink)
This always works for anyone any age:
take your age
add 7
subtract 5
subtract 2
and you will have your age!
gbs5009 ยท 1 points ยท Posted at 19:27:47 on May 25, 2016 ยท (Permalink)
y'don't say!
20mcgug ยท 1 points ยท Posted at 19:49:03 on May 25, 2016 ยท (Permalink)
Didn't work for me
[deleted] ยท -1 points ยท Posted at 19:18:06 on May 25, 2016 ยท (Permalink)
[deleted]
The_Lars_Takarin ยท 1 points ยท Posted at 19:31:59 on May 25, 2016 ยท (Permalink)
At 3:10, why do they shift the second set of number to the right one place? That part right there seems like the "mathematical Hocus Pocus" they mention later.
cdleech ยท 2 points ยท Posted at 21:13:59 on May 25, 2016 ยท (Permalink)
That's just moving terms around on the paper, by lining them up you can see how they simplify. It's not changing any terms, like shifting decimal places.
I'd say the "hocus pocus" is assigning a value of 1/2 to S1, which is a divergent series. It's a valid way to assign a value to S1, which leads to the equally valid value of -1/12, but it's not the only summation method or a true limit value.
[deleted] ยท -1 points ยท Posted at 19:27:04 on May 25, 2016 ยท (Permalink)*
[deleted]
gnarledrose ยท 1 points ยท Posted at 19:30:40 on May 25, 2016 ยท (Permalink)
8
emblemfire ยท -1 points ยท Posted at 19:30:48 on May 25, 2016 ยท (Permalink)
That it's called math, and not maths.
maz-o ยท 1 points ยท Posted at 19:31:49 on May 25, 2016 ยท (Permalink)
north america is the only place that calls it math, everywhere else it's maths.
emblemfire ยท 0 points ยท Posted at 20:00:02 on May 25, 2016 ยท (Permalink)
Do you guys also learn how to Reads and Writes? Or do you only arbitrarily add an s to math?
maz-o ยท 1 points ยท Posted at 20:11:38 on May 25, 2016 ยท (Permalink)
It's called Mathematics
emblemfire ยท 0 points ยท Posted at 20:40:04 on May 25, 2016 ยท (Permalink)
So when you shorten words do you normally take the first few letters and then add on the last letter?
Do you research things in your labY to find out infoN about the world? Or do you simply have a poor vocabY?
Oh wait, that sounds ridiculous, just like maths.
happycamperjack ยท -1 points ยท Posted at 19:50:27 on May 25, 2016 ยท (Permalink)
1+2+3+4+..... (infinity) = -1/12
https://www.youtube.com/watch?v=w-I6XTVZXww
mini_fast_car ยท -1 points ยท Posted at 19:54:47 on May 25, 2016 ยท (Permalink)
The sum of all natural number is -1/12.
(or : 1+2+3+4+5+... = -1/12)
[deleted] ยท -1 points ยท Posted at 20:09:03 on May 25, 2016 ยท (Permalink)
If you ignore it math goes away.
sharingan10 ยท -1 points ยท Posted at 20:18:13 on May 25, 2016 ยท (Permalink)
The sum of 1+2+3...... forever is -1/12
The reason this is the case is because the Riemann zeta function is defined at negative 1
If you don't believe me, check it out here
It's the most counter intuitive, bizarre thing I've ever heard of. But it's true!
overconvergent ยท 2 points ยท Posted at 22:37:30 on May 25, 2016 ยท (Permalink)
No it isn't.
dannystoll84 ยท 1 points ยท Posted at 20:34:11 on May 25, 2016 ยท (Permalink)
That site says "The general form of the Riemann zeta function for the argument "s" is: <sum of n^(-s) from 1 to infinity>"
This is completely and blatantly wrong. That is a representation of the Riemann zeta function only for Re(s)>1. The general formula is obtained through analytic continuation and is much more complicated.
[deleted] ยท -1 points ยท Posted at 20:32:43 on May 25, 2016 ยท (Permalink)
[removed]
Jacob_Blackford ยท 1 points ยท Posted at 20:35:30 on May 25, 2016 ยท (Permalink)
Nobody wants to play your shitty scratch game, so don't fucking spam the link everywhere, because nobody fucking cares.
syndus ยท -1 points ยท Posted at 21:58:49 on May 25, 2016 ยท (Permalink)
2+3=chair
Nevermynde ยท -1 points ยท Posted at 22:08:15 on May 25, 2016 ยท (Permalink)
Exp(i * tau) = 1
loptthetreacherous ยท 1 points ยท Posted at 22:51:51 on May 25, 2016 ยท (Permalink)
Damn tauists! Get off my lawn!
Nevermynde ยท 1 points ยท Posted at 11:07:26 on May 27, 2016 ยท (Permalink)
You're safe. I've been downmodded into oblivion.
letmebehealthy ยท -1 points ยท Posted at 22:28:25 on May 25, 2016 ยท (Permalink)
I believe it's this series, correct me if I'm wrong but...
1/2 + 1/4 + 1/8+1/16 converges to -1/12
overconvergent ยท 1 points ยท Posted at 22:59:31 on May 25, 2016 ยท (Permalink)
1/2 + 1/4 + 1/8 + 1/16 + ... = 1
letmebehealthy ยท 1 points ยท Posted at 23:02:44 on May 25, 2016 ยท (Permalink)
Oops. Which one is -1/12 then?
overconvergent ยท 3 points ยท Posted at 23:04:05 on May 25, 2016 ยท (Permalink)
You are probably thinking of the commonly-repeated "fact" that 1+2+3+...=-1/12. However, this statement is not true.
letmebehealthy ยท 1 points ยท Posted at 00:20:20 on May 26, 2016 ยท (Permalink)
Oh I heard it from my calc 2 teacher in class. Why is it wrong? Genuinely curious!
overconvergent ยท 1 points ยท Posted at 00:23:35 on May 26, 2016 ยท (Permalink)
The series 1+2+3+4+... diverges, as you probably learned in Calc 2. There are other ways of assigning values to divergent series, and some (but not all) of these methods assign the value -1/12 to this series. But this does not mean that 1+2+3+4+...=-1/12.
letmebehealthy ยท 1 points ยท Posted at 00:27:00 on May 26, 2016 ยท (Permalink)
Huh thanks for the brief, elucidating explication:)
cubonelvl69 ยท 1 points ยท Posted at 00:41:50 on May 26, 2016 ยท (Permalink)
not really sure what he's talking about. its true..
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
cubonelvl69 ยท -1 points ยท Posted at 00:38:25 on May 26, 2016 ยท (Permalink)
nope, its true. https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
overconvergent ยท 1 points ยท Posted at 00:40:10 on May 26, 2016 ยท (Permalink)
From your own link:
It is true that there is an interesting mathematical way of associating the number -1/12 with the sequence 1,2,3,4,5,... but it is most definitely not true that 1+2+3+4+...=-1/12. The article you linked to explains this in detail.
cubonelvl69 ยท -1 points ยท Posted at 00:48:52 on May 26, 2016 ยท (Permalink)
The article explains in detail how to calculate -1/12 using the sequence of 1+2+3...., and it is a fact that is used in physics. Watch numberphiles video on it. Its true
overconvergent ยท 3 points ยท Posted at 00:56:18 on May 26, 2016 ยท (Permalink)
I have a PhD in math, and am a professional research mathematician. 1+2+3+... does not equal -1/12. Numberphile's (first) video is complete garbage.
Like I said, there are ways of associating the number -1/12 with that series. That does NOT mean that the SUM of the series is -1/12. It means that there is some other interesting mathematical relation between the sequence 1,2,3,4,... and the number -1/12.
kakaooo987 ยท -1 points ยท Posted at 22:39:03 on May 25, 2016 ยท (Permalink)
I'm probably late for the party, but if you add up all the natural numbers, so 1+2+3+4+... and this goes forever the sum will be -1/12. This is proven, and is used today in different scientifical fields.
Ieatcookiesyummy ยท -1 points ยท Posted at 22:41:33 on May 25, 2016 ยท (Permalink)
My brain hurts when I try to understand divergent series...
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 ... = 1/4
overconvergent ยท 3 points ยท Posted at 22:58:35 on May 25, 2016 ยท (Permalink)
This is not true.
BigMuskieTom ยท -1 points ยท Posted at 22:41:55 on May 25, 2016 ยท (Permalink)
The sum of all positive integers is -1/12 https://www.youtube.com/watch?v=w-I6XTVZXww&feature=youtu.be
overconvergent ยท 1 points ยท Posted at 23:44:28 on May 25, 2016 ยท (Permalink)
This is not true.
ramesesknibs ยท -1 points ยท Posted at 22:44:05 on May 25, 2016 ยท (Permalink)
That if you add 1+2+3+4+5...etc, the answer is -1/12
overconvergent ยท 2 points ยท Posted at 22:58:28 on May 25, 2016 ยท (Permalink)
This is not true.
ramesesknibs ยท 1 points ยท Posted at 23:03:19 on May 25, 2016 ยท (Permalink)
Did I not understand the Ramanujan Summation correctly?
overconvergent ยท 4 points ยท Posted at 23:05:46 on May 25, 2016 ยท (Permalink)
It is true that the Ramanujan summation of the function f(x)=x evaluated at the positive integers is -1/12. It is not true that 1+2+3+4+...=-1/12. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. Ramanujan summation is one example of these methods. But that does not mean that 1+2+3+...=-1/12.
ramesesknibs ยท 2 points ยท Posted at 23:08:49 on May 25, 2016 ยท (Permalink)
Thanks :)
Hayes77519 ยท 1 points ยท Posted at 23:20:17 on May 25, 2016 ยท (Permalink)
What is an example of a method that yields a different result?
overconvergent ยท 3 points ยท Posted at 23:26:07 on May 25, 2016 ยท (Permalink)
Under most methods of assigning values to divergent series, this series is not assigned any value. No stable linear summation method can assign this series a value (see the wiki article if you want to know what those words mean). Even Ramanujan summation can assign this series different values. Ramanujan summation depends on the interpolating function you use. if you use the function f(x)=x, you get the value -1/12. If you use a different function such that f(n)=n for the positive integers, you'll get a different value. For example, you could take f(x)=x+sin(pi*x) or even f(x)=x+g(x)*sin(pi*x) for any function g.
Hayes77519 ยท -1 points ยท Posted at 23:14:33 on May 25, 2016 ยท (Permalink)
That the sum of all the positive natural numbers is a negative number, -1/12 I believe. I'm serious, look:
https://www.youtube.com/watch?v=w-I6XTVZXww
Edit: I'm sorry, all positive natural numbers.
overconvergent ยท 3 points ยท Posted at 23:14:59 on May 25, 2016 ยท (Permalink)
This is not true.
Hayes77519 ยท 1 points ยท Posted at 23:18:13 on May 25, 2016 ยท (Permalink)
Though I see you have other comments on this, I'll check those out as well.
Hayes77519 ยท 0 points ยท Posted at 23:16:44 on May 25, 2016 ยท (Permalink)
it's natural numbers, sorry. Thanks.
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 00:13:00 on May 26, 2016 ยท (Permalink)*
Still not true. The sum 1+2+3+4+... is not equal to any real number (or any complex number for that matter). We can come up with some ways of assigning labels to such divergent sequences, which are sometimes useful. Some (but not all) of these methods happen to assign the label -1/12 to the sequence 1+2+3+4+5+... but that certainly does not mean that -1/12 is the sum of the sequence.
In fact as divergent sequences go 1+2+3+4+5 is quite a bad one. Most of the usual methods we have for labelling it simply do not work.
Here is an example of the sort of bad stuff which happens if you assume that the sequence has a finite sum:
Since x is just a finite number we can add 0 to it and not change anything:
Subtracting the first and last line above gives:
Then we can play the "add zero" trick again:
Subtracting the last two lines again gives:
So you can only "sum" this series in a number system in which 1=0. Certainly this is not true in the integers, rationals, reals, complex numbers or any extensions of such. Given the other axioms of the reals its actually possible to show that if 1=0 then every number equals zero. In other words asking for this series to have a sum leads to our number system becoming trivial.
[deleted] ยท -1 points ยท Posted at 23:18:14 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7+8... = -1/12
MIND BLOWN!
overconvergent ยท 3 points ยท Posted at 23:27:18 on May 25, 2016 ยท (Permalink)
This is not true.
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 00:25:32 on May 26, 2016 ยท (Permalink)
See my answer here. Setting this sum equal to any real number x allows you to derive 1 = 0 which contradicts with the axioms of the real numbers. Therefore this sum can't be equal to any real number (including x=-1/12). This fits with our intuition that this sum gets larger and larger and doesn't converge.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
[deleted] ยท -1 points ยท Posted at 23:26:04 on May 25, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 3 points ยท Posted at 23:26:53 on May 25, 2016 ยท (Permalink)
This is not true.
[deleted] ยท 0 points ยท Posted at 23:44:36 on May 25, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 3 points ยท Posted at 23:47:05 on May 25, 2016 ยท (Permalink)
This series diverges, so you cannot set S1 equal to that series. Same problem with basically every line of your "proof." There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 1 points ยท Posted at 00:11:41 on May 26, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 1 points ยท Posted at 00:16:21 on May 26, 2016 ยท (Permalink)
While you can interpret S1 as a Cesaro sum, 1+2+3+4+... is not Cesaro summable.
Maybe "associate a value" is a better term. There are many ways of associating a value to an infinite series. For example I could pick out the first term of the series, so 1+2+3+4+... gets the value 1, and 5+10+15+20+... gets the value 5, etc. Under a few methods of assigning values to infinite series (Dirichlet series continuation, zeta summation, Ramanujan summation applied to the function f(x)=x, etc.), the series 1+2+3+4+... gets the value -1/12. But none of the methods used to associate the value -1/12 to the series 1+2+3+... behave anything like summation. For example, no linear stable method can assign a value to this series.
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 00:18:12 on May 26, 2016 ยท (Permalink)
See my answer here. Setting this sum equal to any real number x allows one to derive 1=0 which contradicts with the axioms of the real numbers.
Note that every line in my proof is rigorous if you assume that 1 + 2 + 3 + 4 + 5 +.... = x, for some value x has meaning. Thats the only assumption I made except for the standard axioms.
[deleted] ยท 1 points ยท Posted at 00:43:35 on May 26, 2016 ยท (Permalink)
[deleted]
PM_ME_YOUR_PAULDRONS ยท 1 points ยท Posted at 00:55:07 on May 26, 2016 ยท (Permalink)
The rule that you break is that you can only add a finite number of real numbers. The reals are closed under finite sums but an infinite sum is utterly meaningless. Some sequences have an additional property called convergence and it is convenient to talk about adding infinite sums which are convergent but that is only shorthand for mathematically rigorous operations including limits. We never (ever, ever, ever) actually add infinitely many terms.
Incidentally this is wrong:
Subtracting 1/4 from -1/8 triples its size.
[deleted] ยท -1 points ยท Posted at 23:28:24 on May 25, 2016 ยท (Permalink)
This is probably already said somewhere in these 10k comments, but if you take the sum of all the integers (infinitely): 1+2+3+4+5+... and so on, that sum will equal -1/12.
overconvergent ยท 3 points ยท Posted at 23:30:16 on May 25, 2016 ยท (Permalink)
Yes, this has been said hundreds of times, and no, it is not true.
[deleted] ยท 1 points ยท Posted at 23:40:58 on May 25, 2016 ยท (Permalink)
What do you mean by not true?
overconvergent ยท 3 points ยท Posted at 23:45:47 on May 25, 2016 ยท (Permalink)
I mean that the series 1+2+3+4+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท 1 points ยท Posted at 23:50:05 on May 25, 2016 ยท (Permalink)
So by your words, some of those methods come to that conclusion, and some do not. Having a degree in physics myself, I am more inclined to agree with the physics theory side of the problem. But it feels like this is coming to opinion more than anything.
overconvergent ยท 1 points ยท Posted at 23:54:42 on May 25, 2016 ยท (Permalink)
No. None of these methods come to the conclusion that 1+2+3+...=-1/12. As I said, there are other ways of assigning a value to the series 1+2+3+..., and some of these methods assign the value -1/12 to this series. This does not mean that the sum of the series is -1/12. It just means that the number -1/12 has some other mathematical relation to the sequence of numbers 1,2,3,4,...
[deleted] ยท 2 points ยท Posted at 23:56:40 on May 25, 2016 ยท (Permalink)
Oh, I see what you mean by that. Also, that would make more sense as well with what Numberphile said in their video about this result being used in String Theory and other areas of theoretical physics. Thanks for the clarification.
seedpod02 ยท 1 points ยท Posted at 05:48:16 on May 26, 2016 ยท (Permalink)
Just asking.. what would the answer actually be?
overconvergent ยท 1 points ยท Posted at 06:00:36 on May 26, 2016 ยท (Permalink)
The series 1+2+3+4+... diverges, so it does not have a value. As you add more terms, the sum grows larger without bound.
There are other ways of associating a number with an infinite series like this, and a few of these associate the number -1/12 to the series 1+2+3+4+..., but none of these claim that the sum of this series is -1/12.
_retromario_ ยท -1 points ยท Posted at 23:32:29 on May 25, 2016 ยท (Permalink)
The sum of all positive natural numbers = - 1 / 12. That's right negative 1 / 12
overconvergent ยท 2 points ยท Posted at 23:32:59 on May 25, 2016 ยท (Permalink)
This is not true, as the wiki article you linked to explicitly states.
_retromario_ ยท 1 points ยท Posted at 07:18:53 on May 27, 2016 ยท (Permalink)
Where exactly?
overconvergent ยท 2 points ยท Posted at 16:05:56 on May 27, 2016 ยท (Permalink)
_retromario_ ยท 1 points ยท Posted at 10:54:48 on May 28, 2016 ยท (Permalink)
Fair enough. I shared it because it's a fascinating formula and a bit of a mind fuck, but I should have worded it differently.
holden_maaaayse ยท -1 points ยท Posted at 23:52:16 on May 25, 2016 ยท (Permalink)
Omega comes after infinity.
Bkwordguy ยท -1 points ยท Posted at 00:22:24 on May 26, 2016 ยท (Permalink)
The fact that "math" is singular and not plural.
danieloneill ยท -1 points ยท Posted at 00:46:32 on May 26, 2016 ยท (Permalink)
What's your favourite meth fact?
Emerald_Triangle ยท -1 points ยท Posted at 00:48:19 on May 26, 2016 ยท (Permalink)
That the proper way to abbreviate mathematics is math, not maths.
semiauto227 ยท -1 points ยท Posted at 01:03:06 on May 26, 2016 ยท (Permalink)
Favorite math fact? Let me think about it
[deleted] ยท -1 points ยท Posted at 02:56:24 on May 26, 2016 ยท (Permalink)
https://youtu.be/uDWpb5b1qVc
overconvergent ยท 2 points ยท Posted at 03:00:05 on May 26, 2016 ยท (Permalink)
Unfortunately the "fact" about pi in this video has not been proven. We do not yet know if the decimal expansion of pi contains every finite decimal string. This is conjectured to be true, but has not been proven.
[deleted] ยท -2 points ยท Posted at 03:06:01 on May 26, 2016 ยท (Permalink)
It's been proven. It was proven in 2010 at the University of Gundenberg Germany by a team of Mathematicians lead by Dr. Lichbaulz. He won the Nobel Prize for Computer Science that year. If you're interested in reading about it, the study is linked here: wwlichmybaulz.com
Commander-A-Shepard ยท -1 points ยท Posted at 04:05:26 on May 26, 2016 ยท (Permalink)
Pi never ends....always blew my mind
samomezzz ยท -1 points ยท Posted at 04:19:53 on May 26, 2016 ยท (Permalink)*
The largest number is less than 5 but it could also be almost any other number. Think of non terminating decimals like .1111111
JanEric1 ยท 1 points ยท Posted at 10:50:34 on May 26, 2016 ยท (Permalink)
wat
rockon4life45 ยท -1 points ยท Posted at 06:53:07 on May 26, 2016 ยท (Permalink)*
Math is a more accurate shortening of mathematics than maths is.
https://www.youtube.com/watch?v=SbZCECvoaTA
Mazux2 ยท -1 points ยท Posted at 07:47:44 on May 26, 2016 ยท (Permalink)
My favourite math fact is that I dislike math.
[deleted] ยท -1 points ยท Posted at 11:28:47 on May 26, 2016 ยท (Permalink)
12x12=144 is the first thing I remember learning.
bahzad_jee4u ยท -1 points ยท Posted at 11:44:33 on May 26, 2016 ยท (Permalink)
For me Math & Girls are same Both never understandable
TryHuard ยท 0 points ยท Posted at 19:14:32 on May 26, 2016 ยท (Permalink)
My personal favourite is that 6+9 = 69. This got me laid so many times, u have no idea.
[deleted] ยท -5 points ยท Posted at 16:53:13 on May 25, 2016 ยท (Permalink)*
[deleted]
overconvergent ยท 2 points ยท Posted at 22:44:46 on May 25, 2016 ยท (Permalink)
This is not true.
[deleted] ยท -2 points ยท Posted at 13:41:15 on May 25, 2016 ยท (Permalink)
that the function is objectively and correctly called "math", not "maths".
[deleted] ยท 0 points ยท Posted at 14:13:37 on May 25, 2016 ยท (Permalink)
nothing is objective in the English Language
Scrappy_Larue ยท -2 points ยท Posted at 13:45:33 on May 25, 2016 ยท (Permalink)
A US dollar can be broken into small change 293 different ways.
[deleted] ยท -2 points ยท Posted at 13:56:35 on May 25, 2016 ยท (Permalink)
Fun Fact: In America the abbreviation for mathematics is "math." In the UK it's "maths."
schwermetaller ยท -2 points ยท Posted at 14:18:45 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12.
saybhausd ยท 1 points ยท Posted at 14:49:09 on May 25, 2016 ยท (Permalink)
This got me curious. Why is this true?
jywn4679 ยท 2 points ยท Posted at 15:33:36 on May 25, 2016 ยท (Permalink)
It isn't.
[deleted] ยท -2 points ยท Posted at 14:23:43 on May 25, 2016 ยท (Permalink)*
[deleted]
jywn4679 ยท 3 points ยท Posted at 15:29:26 on May 25, 2016 ยท (Permalink)
Not true.
giants4210 ยท -2 points ยท Posted at 14:28:20 on May 25, 2016 ยท (Permalink)
The sum of the natural numbers, i.e. 1+2+3+4+5... = -1/12
jywn4679 ยท 1 points ยท Posted at 15:29:31 on May 25, 2016 ยท (Permalink)
Not true.
[deleted] ยท -2 points ยท Posted at 14:36:13 on May 25, 2016 ยท (Permalink)
[deleted]
lsrwLuke ยท 2 points ยท Posted at 14:52:03 on May 25, 2016 ยท (Permalink)
Yeah, because of the other fact that 0.999... == 1
keeper420 ยท 1 points ยท Posted at 14:57:39 on May 25, 2016 ยท (Permalink)
Infinity exists in math. You eventually have to round that last 9 up. But with infinity, there it's no last 9, it kees going. That's why limits approach a number, but don't hit it.
lsrwLuke ยท 1 points ยท Posted at 15:15:46 on May 25, 2016 ยท (Permalink)
1/9 == 0.11...
2/9 == 0.22...
3/9 == 0.33... ...
8/9 == 0.88... 9/9 == 0.99... 9/9 == 1
Therefore:
0.99... == 1
jywn4679 ยท 1 points ยท Posted at 15:30:34 on May 25, 2016 ยท (Permalink)
0.99... is really exactly equal to 1. The wikipedia article on it gives a load of proofs. 0.99... is not a process, it is a fixed and unchainging number.
Saytahri ยท 1 points ยท Posted at 19:23:04 on May 25, 2016 ยท (Permalink)
Limits don't approach. Series approach limits.
The limit of the infinite sum denoted by 0.999... is exactly 1. No rounding required.
If it were smaller, there would be a number between it and 1, which there isn't.
JanEric1 ยท 1 points ยท Posted at 14:51:44 on May 25, 2016 ยท (Permalink)
ahhhmmm 1/3+2/3=3/3=1...
[deleted] ยท -2 points ยท Posted at 14:36:54 on May 25, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12.
overconvergent ยท 1 points ยท Posted at 22:50:46 on May 25, 2016 ยท (Permalink)
No it is not.
JanEric1 ยท 1 points ยท Posted at 14:53:38 on May 25, 2016 ยท (Permalink)
the series over the natural number diverges
catcalliope ยท -2 points ยท Posted at 14:38:08 on May 25, 2016 ยท (Permalink)
That somehow, if you start adding numbers 1 + 2 + 3 + 4 + 5 +... to infinity, you wind up with... -1/12. I guess it's not so much a fact as it is a proof, but... but.... wow.
Smart people explain this here.
ben1996123 ยท 1 points ยท Posted at 18:34:20 on May 25, 2016 ยท (Permalink)
no you do not
[deleted] ยท -2 points ยท Posted at 14:38:22 on May 25, 2016 ยท (Permalink)
that maths sucks :D
[deleted] ยท -2 points ยท Posted at 14:47:18 on May 25, 2016 ยท (Permalink)
Godels Ontological Proof.
Proof of God in a way science can understand.
perpetual_motion ยท 1 points ยท Posted at 15:09:55 on May 25, 2016 ยท (Permalink)
Not science, just logic. There's no experiment or data or hypotheses etc.
[deleted] ยท 1 points ยท Posted at 16:37:06 on May 25, 2016 ยท (Permalink)
There is a mathematical formula inside the link.
perpetual_motion ยท 1 points ยท Posted at 17:02:36 on May 25, 2016 ยท (Permalink)
It's a purely logical argument, just like plenty of others that have been made for God going back centuries.
[deleted] ยท -2 points ยท Posted at 15:03:33 on May 25, 2016 ยท (Permalink)
Math*
nickbhe ยท -2 points ยท Posted at 15:07:02 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 + 4 + 5 + ... = -1/12
Don't believe me? https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
perpetual_motion ยท 3 points ยท Posted at 15:13:43 on May 25, 2016 ยท (Permalink)
You need to put the equals sign in quotes or something. The series diverges...
overconvergent ยท 1 points ยท Posted at 22:53:13 on May 25, 2016 ยท (Permalink)
The wikipedia article you linked to explicitly says that the sum of that series is not -1/12.
Junius_Bonney ยท -2 points ยท Posted at 15:17:19 on May 25, 2016 ยท (Permalink)
The sum of every positive integer (1+2+3+4... ad infinitum) is negative 1/12.
overconvergent ยท 1 points ยท Posted at 22:55:02 on May 25, 2016 ยท (Permalink)
No it is not.
Junius_Bonney ยท 1 points ยท Posted at 01:39:47 on May 26, 2016 ยท (Permalink)
Watch this: https://www.youtube.com/watch?v=w-I6XTVZXww
overconvergent ยท 1 points ยท Posted at 01:43:58 on May 26, 2016 ยท (Permalink)
This video is extremely misleading, and the math it uses is completely incorrect. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
Junius_Bonney ยท 1 points ยท Posted at 01:45:57 on May 26, 2016 ยท (Permalink)
Well yes, it's a divergent series, but this way of looking at it is a fun little party trick, and I'd say it counts as my favorite math "fact". Or math trivia, if you will
R0kss ยท -2 points ยท Posted at 15:17:42 on May 25, 2016 ยท (Permalink)
Sum of all natural numbers is -1/12 ... I find that mindblowing
overconvergent ยท 1 points ยท Posted at 22:54:57 on May 25, 2016 ยท (Permalink)
That's not true.
[deleted] ยท -2 points ยท Posted at 15:18:02 on May 25, 2016 ยท (Permalink)
The sum of all positive integers from 1 to infinity is -1/12.
overconvergent ยท 1 points ยท Posted at 22:55:09 on May 25, 2016 ยท (Permalink)
No it is not.
[deleted] ยท -2 points ยท Posted at 15:19:02 on May 25, 2016 ยท (Permalink)
The sum of all positive integers (1+2+3+4+5...) is -1/12
jywn4679 ยท 2 points ยท Posted at 15:32:25 on May 25, 2016 ยท (Permalink)
Not true.
[deleted] ยท 0 points ยท Posted at 15:37:22 on May 25, 2016 ยท (Permalink)*
It is 100% true. You can look up the proof if you'd like, but here's a simplified version. And it's used in physics!
jywn4679 ยท 2 points ยท Posted at 15:40:25 on May 25, 2016 ยท (Permalink)
You cannot manipulate divergent series like that, or you get nonsense like this. A very simple proof to the contrary is to go to the definition of a limit, set epsilon to be 1/12. Then you would need there to be a natural number N>0 such that |(1+2+3+4+...+N)|<1/12, however this is clearly false for every N, as 1>1/12.
Eldorado1234 ยท -2 points ยท Posted at 15:20:43 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+7+8...(forever) = -1/12
overconvergent ยท 1 points ยท Posted at 22:55:30 on May 25, 2016 ยท (Permalink)
This is not true.
EricT59 ยท -2 points ยท Posted at 15:39:06 on May 25, 2016 ยท (Permalink)
That "Math" is not plural
goodshout ยท 2 points ยท Posted at 15:55:31 on May 25, 2016 ยท (Permalink)
Not a Plural... a collective noun.
EricT59 ยท 1 points ยท Posted at 16:57:35 on May 25, 2016 ยท (Permalink)
Well to my freedom ears it sounds wrong :)
Woodsy21 ยท -2 points ยท Posted at 15:41:00 on May 25, 2016 ยท (Permalink)
Fact: math sucks.
God-of-Thunder ยท -2 points ยท Posted at 17:40:08 on May 25, 2016 ยท (Permalink)
The sum of all integers (1+2+3+4...) is equal to -1/12
JanEric1 ยท 1 points ยท Posted at 10:34:02 on May 26, 2016 ยท (Permalink)
the series diverges...
God-of-Thunder ยท 1 points ยท Posted at 13:48:19 on May 26, 2016 ยท (Permalink)
That's what you'd think. But it's an infinite series, and shit gets weird when you deal with infinities. Check out this video from numberphile where they give several proofs that it equals -1/12
https://youtu.be/w-I6XTVZXww
JanEric1 ยท 1 points ยท Posted at 13:50:10 on May 26, 2016 ยท (Permalink)
it does not equal -1/12, the proof is false
God-of-Thunder ยท 1 points ยท Posted at 15:17:21 on May 26, 2016 ยท (Permalink)
Really? If you would be so kind as to elaborate it would be much appreciated
JanEric1 ยท 1 points ยท Posted at 15:57:57 on May 26, 2016 ยท (Permalink)
you cant manipulate a series like that if it doesnt converge.
God-of-Thunder ยท 1 points ยท Posted at 16:01:39 on May 26, 2016 ยท (Permalink)
But how do you know that it doesn't converge?
JanEric1 ยท 1 points ยท Posted at 16:07:55 on May 26, 2016 ยท (Permalink)
do the cauchy-test
missdopamine ยท -2 points ยท Posted at 17:41:48 on May 25, 2016 ยท (Permalink)*
If you add every positive integer together (1+2+3+4 etc.) the solution is -1/12.
Edit: proof - https://youtu.be/w-I6XTVZXww
JanEric1 ยท 2 points ยท Posted at 10:34:13 on May 26, 2016 ยท (Permalink)
no it does not
missdopamine ยท -1 points ยท Posted at 13:05:38 on May 26, 2016 ยท (Permalink)
Actually, yes, it does: https://youtu.be/w-I6XTVZXww
JanEric1 ยท 2 points ยท Posted at 13:23:40 on May 26, 2016 ยท (Permalink)
i am aware if this video, which is very misleading and wrong...
missdopamine ยท 1 points ยท Posted at 18:22:45 on May 26, 2016 ยท (Permalink)
Can you explain why? Genuinely curious
JanEric1 ยท 2 points ยท Posted at 18:37:22 on May 26, 2016 ยท (Permalink)
you simply cant manipulate infinite sums like that. you cant even always add a 0 for example:
c=1+2+3... lets add a 0
0+1+2+3...=c+0=c
now lets do:
1+2+3+4... -
0+1+2+3...
=1+1+1+1+1...=c-c=0
now lets add another 0
0+1+1+1+1....=0+0=0
and substract again
1+1+1+1... -
0+1+1+1...
=1=0
Predmid ยท -2 points ยท Posted at 17:57:57 on May 25, 2016 ยท (Permalink)*
The sum of all natural numbers from 1 to infinity is -1/12.
EDIT: For people downvoting for not believing this fact. proof
And Numberphile video.
JanEric1 ยท 3 points ยท Posted at 10:38:48 on May 26, 2016 ยท (Permalink)
nope
Predmid ยท 1 points ยท Posted at 13:45:48 on May 26, 2016 ยท (Permalink)
Um....
What do you mean "nope".
It's true.
JanEric1 ยท 3 points ยท Posted at 13:49:46 on May 26, 2016 ยท (Permalink)
not it is not, quite obviously diverges
Predmid ยท 1 points ยท Posted at 14:46:38 on May 26, 2016 ยท (Permalink)
apologize for the terrible handwriting, but here's the proof
JanEric1 ยท 3 points ยท Posted at 14:56:19 on May 26, 2016 ยท (Permalink)
i know the proof, i have seen it.
the problems are that S1 doesnt converge(just do the cauchy test) and neither does S2, you thus cannot simply multiply,add or substract these serieses.
Predmid ยท 1 points ยท Posted at 15:04:51 on May 26, 2016 ยท (Permalink)*
Abel and Cesร ro sums....
JanEric1 ยท 3 points ยท Posted at 16:42:26 on May 26, 2016 ยท (Permalink)*
first: then you dont have the sum but an abel or cesaro sum.
second: 1+2+3.. is not cesaro or abel summable.
third: the step where you go from 0+4+0+8... to 4(1+2+3...) is not justified. you cant simply add 0s to infinite sums.
for example:
c=1+2+3... lets add a 0
0+1+2+3...=c+0=c
now lets do:
1+2+3+4... -
0+1+2+3...
=1+1+1+1+1...=c-c=0
now lets add another 0
0+1+1+1+1....=0+0=0
and substract again
1+1+1+1... -
0+1+1+1...
=1=0
Predmid ยท 1 points ยท Posted at 19:00:50 on May 26, 2016 ยท (Permalink)
I understand what you're saying, but this is beyond my level of maths and I'm just going off what I've learned through numberphile.
JanEric1 ยท 1 points ยท Posted at 19:08:37 on May 26, 2016 ยท (Permalink)
you should probably go off of this:
https://www.reddit.com/r/askscience/wiki/maths/sum_natural_numbers
s0lv3 ยท -2 points ยท Posted at 18:50:26 on May 25, 2016 ยท (Permalink)
Algebra. Not calculus because calculus is simply an estimation that is never 100% correct.
oblio3 ยท -2 points ยท Posted at 01:41:56 on May 26, 2016 ยท (Permalink)
Can someone explain when math became maths? Is deer going to become deers next?
astalavista114 ยท 2 points ยท Posted at 05:06:06 on May 26, 2016 ยท (Permalink)
Its what is used in places like the UK, and Australia (and, as far as I can tell, most other English speaking countries apart from the US). It comes from maths being short for mathematics (which is always plural).
xkcdFan1011011101111 ยท -2 points ยท Posted at 02:02:03 on May 26, 2016 ยท (Permalink)*
Irrational numbers contain all information.
Irrational numbers are numbers that can't be expressed as a ratio of integers (those would be rational numbers, which I think of as ratio-able numbers). Irrational numbers, when written in decimal form, have infinitely many digits on the right side of the decimal point that never repeat. Some famous examples are pi, sqrt(2), and e, but there are infinitely many irrational numbers. Actually, there are more irrational numbers than rational numbers.
If you were to decide on an encoding between digits and letters (like, for example, ASCII, which encodes the letter "A" as 65, and so on) then you could convert the digits in an irrational number to letters and punctuation.
Most of the converted digits would be gibberish (in fact, infinitely man of the converted digits would be gibberish); however, any sentence you can think of would also be in the converted sequence. As would all the works of Shakespeare, the bible, every novel, every textbook, and every publication that has ever been written. Also included are all future publications that haven't been written yet!
Instead of converting digits to ASCII symbols, we could instead use the digits in an irrational number to specify the amount of red, green, and blue in each pixel in a digital image. Inside your irrational number, you'll find that this choice of encoding will mostly be gibberish, but will also contain every digital image ever taken (as well as every image that ever will be taken).
edit: as pointed out by u/overconvergent, this doesn't hold for some irrational numbers such as 0.10100100010000100000...
edit 2: not sure why I'm being downvoted.... wtf? if you don't like this math fact, just move along?
overconvergent ยท 4 points ยท Posted at 02:10:18 on May 26, 2016 ยท (Permalink)
Irrational numbers are numbers that can't be expressed as a ratio of integers
This is not true. For example, the number 0.101001000100001000001..... is irrational, but its decimal expansion never contains the digit 2.
xkcdFan1011011101111 ยท 0 points ยท Posted at 13:30:05 on May 26, 2016 ยท (Permalink)
Fair point that some irrationals contain patterns that preclude random information encoding. The issue of never containing digit 2 (or others) is less of a concern as the choice of encoding could instead be binary.
overconvergent ยท 1 points ยท Posted at 15:09:41 on May 26, 2016 ยท (Permalink)
Even if the encoding is binary, the expansion of this number never contains two 1s in a row.
xkcdFan1011011101111 ยท 1 points ยท Posted at 15:56:14 on May 26, 2016 ยท (Permalink)
I agree, and hence I said:
and I edited the original post to point out your correction
BuzzBadpants ยท -2 points ยท Posted at 03:27:24 on May 26, 2016 ยท (Permalink)
If you add up every single positive integer through infinity, you end up with a sum of -1/12
https://youtu.be/w-I6XTVZXww
overconvergent ยท 5 points ยท Posted at 03:31:10 on May 26, 2016 ยท (Permalink)
No you don't. This video is extremely misleading, and the math it uses is completely incorrect. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
GokuMoto ยท 2 points ยท Posted at 05:16:55 on May 26, 2016 ยท (Permalink)
the longer 21 minute video makes more sense
jletha ยท -2 points ยท Posted at 03:33:12 on May 26, 2016 ยท (Permalink)
1+2+3+4+... = -(1/12)
overconvergent ยท 4 points ยท Posted at 03:35:02 on May 26, 2016 ยท (Permalink)
This is not true. The series 1+2+3+... diverges. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท -9 points ยท Posted at 11:42:20 on May 25, 2016 ยท (Permalink)*
[deleted]
Desertman123 ยท 4 points ยท Posted at 12:59:37 on May 25, 2016 ยท (Permalink)*
With the Riemann zeta function, yes. But taking your statement more literally not so much.
My super basic proof: http://m.imgur.com/usnLiJ4
n represents all naturals
acejohn ยท 1 points ยท Posted at 13:57:31 on May 25, 2016 ยท (Permalink)
Did you just do that on snapchat?
Desertman123 ยท 1 points ยท Posted at 13:58:34 on May 25, 2016 ยท (Permalink)
you bet, i was on mobile in bed lol
acejohn ยท 1 points ยท Posted at 14:01:14 on May 25, 2016 ยท (Permalink)
awesome
JanEric1 ยท 3 points ยท Posted at 12:07:19 on May 25, 2016 ยท (Permalink)
that sum does not converge in the traditional sense
redditsoaddicting ยท 3 points ยท Posted at 12:48:10 on May 25, 2016 ยท (Permalink)
It's -1/12, and there are certain assumptions that come with it.
TheSemiTallest ยท 1 points ยท Posted at 13:35:33 on May 25, 2016 ยท (Permalink)
*negative 1/12
eatmorchicken ยท -3 points ยท Posted at 13:38:03 on May 25, 2016 ยท (Permalink)
Holy shift! Check out the asymptote on that mother function.
twiggymac ยท -3 points ยท Posted at 14:19:17 on May 25, 2016 ยท (Permalink)
That mathematics is not a plural word and therefore the shorthand "maths" is incorrect
repost_worker ยท -3 points ยท Posted at 14:33:53 on May 25, 2016 ยท (Permalink)*
Summing the infinite series 1+2+3+4+5+... does not add up to infinity and actually adds up to -1/12. Infinity is very interesting.
Here is a video explaining this: http://m.youtube.com/watch?v=w-I6XTVZXww
Edit: Reworded because only the infinite series of 1+2+3+4+5+... adds to -1/12, not any infinite series
JanEric1 ยท 2 points ยท Posted at 14:36:17 on May 25, 2016 ยท (Permalink)
the sequence 1,3,6... does not have a limit.(in the traditional sense)
https://en.wikipedia.org/wiki/Limit_of_a_sequence
perpetual_motion ยท 2 points ยท Posted at 15:15:10 on May 25, 2016 ยท (Permalink)
No, it is infinite. The -1/12 number refers to something other than traditional summing.
repost_worker ยท 1 points ยท Posted at 01:57:44 on May 26, 2016 ยท (Permalink)
What type of summing does it refer to? I'd like to learn about it if I'm misunderstanding the topic.Any resources would be appreciated. thanks!
mohammed_abdalla ยท -2 points ยท Posted at 14:48:13 on May 25, 2016 ยท (Permalink)
That most of the stuff you learn in school is completely pointless
SmaugtheStupendous ยท -3 points ยท Posted at 17:48:59 on May 25, 2016 ยท (Permalink)
1 + 2 + 3 ... = -(1/12)
JanEric1 ยท 1 points ยท Posted at 10:34:27 on May 26, 2016 ยท (Permalink)
nope
SmaugtheStupendous ยท -1 points ยท Posted at 10:46:15 on May 26, 2016 ยท (Permalink)
proof?
JanEric1 ยท 3 points ยท Posted at 11:06:35 on May 26, 2016 ยท (Permalink)
https://en.wikipedia.org/wiki/Cauchy's_convergence_test
you will see that the series does not converge
Matech ยท -3 points ยท Posted at 19:13:04 on May 25, 2016 ยท (Permalink)
Fuck this thread. Fuck op. I hate you all. Buncha nerds making shit up.
20mcgug ยท 1 points ยท Posted at 19:49:18 on May 25, 2016 ยท (Permalink)
Hey, fuck you buddy
TheErriott ยท -3 points ยท Posted at 23:50:01 on May 25, 2016 ยท (Permalink)
The sum of all positive integers from one to infinity is - 1/12
overconvergent ยท 4 points ยท Posted at 23:51:14 on May 25, 2016 ยท (Permalink)
No it isn't.
TheErriott ยท -1 points ยท Posted at 00:00:05 on May 26, 2016 ยท (Permalink)
https://youtu.be/w-I6XTVZXww
overconvergent ยท 2 points ยท Posted at 00:02:32 on May 26, 2016 ยท (Permalink)
This video is extremely misleading, and the math it uses is completely incorrect. There are methods of assigning values to divergent series, and under some (but not all) of those methods, the series 1+2+3+... is assigned the value -1/12. But that does not mean that 1+2+3+...=-1/12.
[deleted] ยท -3 points ยท Posted at 00:18:15 on May 26, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 5 points ยท Posted at 00:18:59 on May 26, 2016 ยท (Permalink)
No you won't.
[deleted] ยท -3 points ยท Posted at 00:25:42 on May 26, 2016 ยท (Permalink)
1 + 2 + 3 + 4..... up to infinity can be substituted with negative one twelfth.
aiya_au ยท -4 points ยท Posted at 07:07:02 on May 26, 2016 ยท (Permalink)
The sum of all positive integers 1 + 2 + 3 + 4 + 5 + ... = -1/12
explained in this numberphile video: https://www.youtube.com/watch?v=w-I6XTVZXww
JanEric1 ยท 6 points ยท Posted at 10:50:47 on May 26, 2016 ยท (Permalink)
no
aiya_au ยท 1 points ยท Posted at 04:38:45 on May 27, 2016 ยท (Permalink)*
no?
Dirk_Gently-42 ยท -2 points ยท Posted at 07:10:35 on May 26, 2016 ยท (Permalink)*
The sum of all natural numbers (positive integers) 1+2+3 to infinity = -1/12 ... Google it
overconvergent ยท 3 points ยท Posted at 15:38:44 on May 26, 2016 ยท (Permalink)
This is not true.
robot_lurker ยท -4 points ยท Posted at 14:55:51 on May 26, 2016 ยท (Permalink)
The sum of all natural numbers is -1/12. Meaning 1+2+3+4+5... =-1/12
Source: https://youtu.be/w-I6XTVZXww
overconvergent ยท 3 points ยท Posted at 15:37:34 on May 26, 2016 ยท (Permalink)
This is not true, and that video is not correct.
[deleted] ยท -31 points ยท Posted at 11:06:19 on May 25, 2016 ยท (Permalink)
That you don't need it outside of school.
[deleted] ยท 9 points ยท Posted at 11:07:07 on May 25, 2016 ยท (Permalink)
Well, that depends on your choice of work. I make my living on applied math.
MinerAlum ยท 1 points ยท Posted at 21:28:30 on May 25, 2016 ยท (Permalink)
I have been thinking of an applied math degree. What do you do?
Greatgrowler ยท 4 points ยท Posted at 14:26:54 on May 25, 2016 ยท (Permalink)
That's not true. You just don't realise that you are using it every time you buy something, measure something, weigh out ingredients or budget your pay. It was drummed into you so much as a child that you use it without even knowing so.
Bengalman753 ยท 3 points ยท Posted at 15:03:22 on May 25, 2016 ยท (Permalink)
I work in a smoke shop and have tons of customers that cant even estimate what a 15% off coupon will get them. We need math, at least to some level, even normal people.
๐๏ธ TheLoneWolf156 ยท 2 points ยท Posted at 11:07:20 on May 25, 2016 ยท (Permalink)
Not everyone
PM_PIC_4_COMPLIMENTS ยท 2 points ยท Posted at 11:22:46 on May 25, 2016 ยท (Permalink)
Architecture and animation come to mind
L-ot-O-MO ยท 1 points ยท Posted at 17:40:44 on May 25, 2016 ยท (Permalink)
And construction in general ("that door needs framed, use these one-bys. Opening is 38", need to keep it 36"."), operating a gas station ("If there are 20 inches of fuel left in the tank, how many gallons is that?"), baking ("The recipe calls for 1.5 tsp of baking powder but I'm tripling it, so I'll need..."), and so many other day-to-day things. Everything is math.
L-ot-O-MO ยท 1 points ยท Posted at 17:30:54 on May 25, 2016 ยท (Permalink)
Are you my 14-year old son? We just had this conversation after I was working on a woodworking project and showed him how I had to use algebra and geometry to come up with some measurements. He insisted for way too long there was a way to do it without math, but he was sorely wrong.
That's actually one of my big gripes with people saying, "I don't ever use any of that math stuff I learned in school." Just because you're not using it exactly as the textbook showed you does not mean you're not using it. You are. But in real life, math is not a simple equation; it's a word problem where you have to separate the wheat from the chaff and use the numbers available to do something. That's also why you had to do all those word problems that were 'so stupid and not realistic at all.'
You might not need to be able to figure out how far apart two trains are after they left a town traveling in opposite directions at 60 miles an hour, but I can assure you there are multiple times in your life you will do a very similar problem in your head without realizing it. "Hmm... If I take the interstate, I can make $Town in 2 hours 45 minutes, but it'll be an extra 20 miles. If I go state roads, I save 20 miles, but it takes an extra 10 minutes. Which should I do?" You are now doing math and a cost-benefit analysis to see if the extra time or extra gas/wear and tear on the car are worth it.
Disengaging dad-mode.
JobberTrev ยท 1 points ยท Posted at 18:14:20 on May 25, 2016 ยท (Permalink)
I got into fantasy football. I actually went and learned more statistics than what I was taught in college.
I also want to get into marketing. Same thing.
Megazor ยท -4 points ยท Posted at 14:14:55 on May 25, 2016 ยท (Permalink)*
This
An infinite sum of natural numbers S=1+2+3+...+n converges to -1/12
It's bonkers when you think about it, but there is some physics experiments like the Casimir effect that supports the result.
https://plus.maths.org/content/infinity-or-just-112
perpetual_motion ยท 2 points ยท Posted at 15:14:18 on May 25, 2016 ยท (Permalink)
The sum does not converge. Read the article you posted.
Megazor ยท 1 points ยท Posted at 21:26:37 on May 25, 2016 ยท (Permalink)
True, but the point still stands
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results, some of which have applications in other fields such as complex analysis, quantum field theory, and string theory. Many summation methods are used in mathematics to assign numerical values even to a divergent series. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of โ1/12, which is expressed by a famous formula:[2]
jywn4679 ยท 1 points ยท Posted at 15:33:26 on May 25, 2016 ยท (Permalink)
This is easy to prove false.
Megazor ยท 1 points ยท Posted at 21:25:14 on May 25, 2016 ยท (Permalink)
You are missing the point. Read the article and about the Casimir effect
https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
jywn4679 ยท 1 points ยท Posted at 22:04:08 on May 25, 2016 ยท (Permalink)
Under the standard meaning of converge, that sum does not converge.
bmorgy ยท -4 points ยท Posted at 14:43:50 on May 25, 2016 ยท (Permalink)
1+2+3+4+5+6+...+โ = -1/12
jywn4679 ยท 2 points ยท Posted at 15:30:48 on May 25, 2016 ยท (Permalink)
It doesn't.
bmorgy ยท 0 points ยท Posted at 16:23:47 on May 25, 2016 ยท (Permalink)
Oh but it does!
Lets start with the series: 1-1+1-1+1...that goes on for infinity. For simplicity's sake, I'll call this series "A". Now, Depending on where you stop (which is never if you go on for infinity), the answer to this series is either 1 or 0. With that logic, you can say that A = 1/2, which is the average of 1 and 0.
From there I'll direct you to the next series: 1-2+3-4+5...and so on, which we will call series "B". Using a bit of trickery, we can do the following (Its hard to format in reddit, but what is happening is that I am adding B to itself, but shifting the 2nd row over by one, which is allowed since this series goes on for infinity):
1-2+3-4+5-6
+1-2+3-4+5-6
1-1+1-1+1...
As you (hopefully) see above, I have just shown that B+B = A, or 2B = A. Since we already know that A = 1/2, that means that 2B = 1/4.
Finally, we are going to subtract B from the initial series, which we are going to call "C". That gives us:
. 1+2+3+4+5+6
-[1-2+3-4+5-6]
0+4+0+8+12...
By simplifying that answer, we get, 4+8+12+16... which can be reduced to 4(1+2+3+4...). So, what we have shown is:
C-B = 4C. We know B = 1/4, so solving for C we get: -B = 3C, so -1/4 = 3C, which gives us: C = -1/12!
ย
TL;DR - Watch this video.
jywn4679 ยท 3 points ยท Posted at 16:29:32 on May 25, 2016 ยท (Permalink)
Right there is the first error. The series does not converge, so it has no value under the usual meanings of converge.
[deleted] ยท -4 points ยท Posted at 20:02:19 on May 25, 2016 ยท (Permalink)
Math is gay. Suck my dick.
TribalScissors ยท 1 points ยท Posted at 20:13:47 on May 25, 2016 ยท (Permalink)
Wash that thing first
[deleted] ยท -4 points ยท Posted at 00:12:35 on May 26, 2016 ยท (Permalink)
[deleted]
overconvergent ยท 4 points ยท Posted at 00:17:10 on May 26, 2016 ยท (Permalink)
This is not true.
fckyouverymuchreddit ยท -4 points ยท Posted at 07:30:23 on May 26, 2016 ยท (Permalink)
1 = 1+0+0+0+0+.... = 1 + 0 * infinite
1 = 1 + 0*infinite
0 = 0*infinite
0/0 = infinite
jbutens ยท -5 points ยท Posted at 11:17:39 on May 26, 2016 ยท (Permalink)
1+2+3+4+5+6...= -1/12
Sp0k3 ยท -17 points ยท Posted at 11:09:42 on May 25, 2016 ยท (Permalink)
"It's boring"
neoforce ยท -8 points ยท Posted at 12:34:07 on May 25, 2016 ยท (Permalink)
Pi is Wrong and should not be used as the circle constant.
http://tauday.com/tau-manifesto
https://youtu.be/jG7vhMMXagQ
[deleted] ยท 3 points ยท Posted at 12:50:22 on May 25, 2016 ยท (Permalink)
[deleted]
neoforce ยท -2 points ยท Posted at 13:21:37 on May 25, 2016 ยท (Permalink)
It's a lot easier to teach and more elegant. Take a look at the links for discussion about it.
[deleted] ยท -2 points ยท Posted at 13:25:50 on May 25, 2016 ยท (Permalink)
Because that way a circle is just Tau. Half circle is Tau/2, Quarter circle is Tau/4.
More intuitive for teaching, though the same for every mathematics profession..
whatIsThisBullCrap ยท 4 points ยท Posted at 13:33:22 on May 25, 2016 ยท (Permalink)
But then you would have a bunch of tau/2s everywhere
oighen ยท 4 points ยท Posted at 12:57:58 on May 25, 2016 ยท (Permalink)
Numbers can't be wrong, and literally nobody cares about pi/tau when doing actual math.
InShortSight ยท 1 points ยท Posted at 21:55:32 on May 25, 2016 ยท (Permalink)
Well the rational mathematicians certainly dont.
oighen ยท 1 points ยท Posted at 22:18:30 on May 25, 2016 ยท (Permalink)
It all boils down to the fact that there's no actual reason to change, writing 2ฯ or ฯ is the same thing, it's convention. Just use the symbol most people would recognize.
jywn4679 ยท 1 points ยท Posted at 14:19:53 on May 25, 2016 ยท (Permalink)
It isn't wrong, it still works it just leaves a few factors of 2 lying around. Nobody really cares enough to change it.
[deleted] ยท -8 points ยท Posted at 13:34:22 on May 25, 2016 ยท (Permalink)
It's "math."
Murica
[deleted] ยท -16 points ยท Posted at 11:34:15 on May 25, 2016 ยท (Permalink)
[deleted]
[deleted] ยท 1 points ยท Posted at 16:21:07 on May 25, 2016 ยท (Permalink)
Only if you're to stupid to use it.
derrrfes ยท 1 points ยท Posted at 17:12:25 on May 25, 2016 ยท (Permalink)
too stupid not to stupid .
[deleted] ยท 2 points ยท Posted at 17:14:29 on May 25, 2016 ยท (Permalink)
I'm a math nerd. Not an English one.
derrrfes ยท 2 points ยท Posted at 17:34:38 on May 25, 2016 ยท (Permalink)
I'm not an English nerd for trying to ensure proper spelling of words . I am simply trying to help someone not look stupid.
[deleted] ยท 1 points ยท Posted at 17:40:12 on May 25, 2016 ยท (Permalink)
English is weird. Nobody can deny that. Thank you and sorry.
derrrfes ยท 1 points ยท Posted at 17:50:48 on May 25, 2016 ยท (Permalink)
There should probably be a song called everything is weird , heck even weird is weird.
tangoshukudai ยท -24 points ยท Posted at 13:32:10 on May 25, 2016 ยท (Permalink)
Math*
Dd_8630 ยท 12 points ยท Posted at 14:05:28 on May 25, 2016 ยท (Permalink)
It's 'math' in the US, 'maths' everywhere else.
tangoshukudai ยท -24 points ยท Posted at 14:27:35 on May 25, 2016 ยท (Permalink)
Yep, but the US is the only one that matters.